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diff --git a/19AzT4oBgHgl3EQfRvso/content/tmp_files/2301.01219v1.pdf.txt b/19AzT4oBgHgl3EQfRvso/content/tmp_files/2301.01219v1.pdf.txt
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+Task-Guided IRL in POMDPs that Scales
+Franck Djeumou∗, Christian Ellis∗∗, Murat Cubuktepe∗, Craig Lennon, Ufuk Topcu∗
+Abstract
+In inverse reinforcement learning (IRL), a learning agent infers a reward function en-
+coding the underlying task using demonstrations from experts. However, many ex-
+isting IRL techniques make the often unrealistic assumption that the agent has access
+to full information about the environment. We remove this assumption by developing
+an algorithm for IRL in partially observable Markov decision processes (POMDPs).
+We address two limitations of existing IRL techniques. First, they require an exces-
+sive amount of data due to the information asymmetry between the expert and the
+learner. Second, most of these IRL techniques require solving the computationally in-
+tractable forward problem—computing an optimal policy given a reward function—in
+POMDPs. The developed algorithm reduces the information asymmetry while increas-
+ing the data efficiency by incorporating task specifications expressed in temporal logic
+into IRL. Such specifications may be interpreted as side information available to the
+learner a priori in addition to the demonstrations. Further, the algorithm avoids a com-
+mon source of algorithmic complexity by building on causal entropy as the measure of
+the likelihood of the demonstrations as opposed to entropy. Nevertheless, the resulting
+problem is nonconvex due to the so-called forward problem. We solve the intrinsic
+nonconvexity of the forward problem in a scalable manner through a sequential linear
+programming scheme that guarantees to converge to a locally optimal policy. In a series
+of examples, including experiments in a high-fidelity Unity simulator, we demonstrate
+that even with a limited amount of data and POMDPs with tens of thousands of states,
+our algorithm learns reward functions and policies that satisfy the task while inducing
+similar behavior to the expert by leveraging the provided side information.
+1. Introduction
+A robot can satisfy certain human-specified tasks by describing desired behavior
+through a reward function. However, the design of such a reward function is a non-
+trivial task. Inverse reinforcement learning (IRL) is an established technique that in-
+fers a reward function encoding the underlying task using expert demonstrations. IRL
+∗The University of Texas at Austin
+∗∗The University of Massachusetts: Dartmouth
+United States Army Research Laboratory
+Email addresses: fdjeumou@utexas.edu (Franck Djeumou), cellis3@umassd.edu
+(Christian Ellis), mcubuktepe@utexas.edu (Murat Cubuktepe),
+craig.t.lennon.civ@army.mil (Craig Lennon), utopcu@utexas.edu (Ufuk Topcu)
+Preprint submitted to Elsevier
+January 4, 2023
+arXiv:2301.01219v1  [cs.LG]  30 Dec 2022
+
+techniques have found a wide range of applications in various domains such as ac-
+robatic helicopter flight [1], inferring future actions of people [2], human-autonomy
+interaction [3, 4], robotic surgery [5, 6], and robotic manipulation tasks [7]. Most
+existing work [1, 8, 9, 10, 3, 7] has focused on Markov decision processes (MDPs),
+assuming that the learner can fully observe the state of the environment and expert
+demonstrations. However, the learner will not have access to full state observations in
+many applications. For example, a robot will never know everything about its envi-
+ronment [11, 12, 13] and may not observe the internal states of a human with whom it
+works [14, 15]. Such information limitations violate the intrinsic assumptions made in
+most existing IRL techniques.
+We investigate IRL in partially observable Markov decision processes (POMDPs),
+a widely used model for decision-making under imperfect information. Partial observ-
+ability brings two key challenges in IRL. The first challenge is due to the so-called
+information asymmetry between the expert and the learner. The expert typically has
+either full or partial information about the environment, while the learner has only a
+partial view of the state and the expert’s demonstrations. Even in the hypothetical
+case in which the underlying reward function is known to the learner, its optimal pol-
+icy under limited information may not yield the same behavior as an expert with full
+information due to such information asymmetry.
+The second challenge is due to the computational complexity of policy synthesis in
+POMDPs. Indeed, many standard IRL techniques rely on a subroutine that solves the
+so-called forward problem, i.e., computing an optimal policy for a given reward. Solv-
+ing the forward problem for POMDPs is significantly more challenging than MDPs,
+both theoretically and practically [16]. Optimal policies for POMDPs may require infi-
+nite memory of observations [17], whereas memoryless policies are enough for MDPs.
+An additional limitation in existing IRL techniques is due to the limited expressiv-
+ity and often impracticability of state-based reward functions in representing complex
+tasks [18]. For example, it will be tremendously difficult to define a merely state-based
+reward function to describe requirements such as “do not steer off the road while reach-
+ing the target location and coming back to home” or “monitor multiple locations with
+a certain order”. However, such requirements can be concisely and precisely speci-
+fied in temporal logic [19, 20]. Therefore, recent work has demonstrated the utility of
+incorporating temporal logic specifications into IRL in MDPs [21, 22].
+In this work, we address these challenges and limitations in state-of-the-art IRL
+techniques by investigating the following problem.
+Task-Guided IRL in POMDPs: Given a POMDP, a set of expert demonstrations,
+and, if available, a task specification expressed in temporal logic, learn a policy
+along with the underlying reward function that maximizes the causal entropy of
+the induced stochastic process, induces a behavior similar to the expert’s, and
+ensures the satisfaction of the specification.
+We highlight two parts of the problem statement. Using causal entropy as an opti-
+mization criterion instead of traditional entropy results in a least-committal policy that
+induces a behavior obtaining the same accumulated reward as the expert’s demonstra-
+tions while making no additional assumptions about the demonstrations. Task specifi-
+2
+
+cations given as task requirements guide the learning process by describing the feasible
+behaviors and allow the learner to learn performant policies with respect to the task re-
+quirements. Such specifications can be interpreted as side information available to
+the learner a priori in addition to the demonstrations aimed at partially alleviating the
+information asymmetry between the expert and the learner.
+Specifically, we tackle the IRL on POMDPs problem by a reformulation into a
+maximum causal entropy (MCE) problem. Then, we develop a new solver for the
+MCE problem that improves computational tractability over existing approaches. The
+developed solver can enforce prior task knowledge expressed as temporal logic specifi-
+cations, which guides the learning, improves the data efficiency, and partially alleviates
+the information asymmetry problem.
+Most existing work on IRL relies on entropy as a measure of the likelihood of the
+demonstrations, yet, when applied to stochastic MDPs, has to deal with nonconvex
+optimization problems [8, 10]. On the other hand, IRL techniques that adopt causal
+entropy as the measure of likelihood enjoy formulations based on convex optimiza-
+tion [9, 10, 23]. We show similar algorithmic benefits in maximum-causal-entropy
+IRL carry over from MDPs to POMDPs.
+A major difference between MDPs and POMDPs in maximum-causal-entropy IRL
+is, though, due to the intrinsic nonconvexity of policy synthesis in POMDPs, which
+yields a formulation of the task-guided IRL problem as a nonconvex optimization
+problem. It is known that this nonconvexity severely limits the scalability for syn-
+thesis in POMDPs [16]. We develop an iterative algorithm that solves the resulting
+nonconvex problem in a scalable manner by adapting sequential convex programming
+(SCP) [24, 25].
+In each iteration, it linearizes the underlying nonconvex problem
+around the solution from the previous iteration. The algorithm introduces several ex-
+tensions to alleviate the errors resulting from the linearization. One of these extensions
+is a verification step not present in existing SCP schemes. We show that the proposed
+algorithm computes a sound and locally optimal solution to the task-guided problem.
+Additionally, we empirically demonstrate that the algorithm scales to POMDPs
+with tens of thousands of states as opposed to tens of states in most existing work.
+In POMDPs, finite-memory policies that are functions of the history of the observa-
+tions outperform memoryless policies [26]. Besides, computing a finite-memory pol-
+icy for a POMDP is equivalent to computing a memoryless policy on a larger product
+POMDP [27]. Thus, we leverage the scalability of our algorithm to compute more per-
+formant policies that incorporate memory using finite-state controllers [28, 29]. On the
+other hand, the existing IRL techniques on POMDPs aforementioned cannot effectively
+utilize memory, as they do not scale to large POMDPs.
+We demonstrate the applicability of the approach through several examples, in-
+cluding a simulated wheeled ground robot operating in a high-fidelity, continuous, 3-
+D Unity simulation. We show that, without task specifications, the developed algo-
+rithm can compute more performant policies than a straight adaptation of the original
+GAIL [30] to POMDPs. Then, we demonstrate that by incorporating task specifications
+into the IRL procedure, the learned reward function and policy accurately describe
+the behavior of the expert while outperforming the policy obtained without the task
+specifications. We observe that with more limited data, the performance gap becomes
+more prominent between the learned policies with and without using task specifica-
+3
+
+tions. Most importantly, we empirically demonstrate the scalability of our approach
+for solving the forward problem through extensive comparisons with several state-of-
+the-art POMDP solvers and show that on larger POMDPs, the algorithm can compute
+more performant policies in significantly less time.
+2. Preliminaries
+The following section provides a review of prerequisite understanding for POMDPs,
+their accompanying policies and how a POMDP’s belief over states is updated using
+Bayesian techniques.
+Notation. We denote the set of nonnegative real numbers by R+, the set of all proba-
+bility distributions over a finite or countably infinite set X by Distr(X), the set of all
+(infinite or empty) sequences x0, x1, . . . , x∞ with xi ∈ X by (X)∗ for some set X,
+and the expectation of a function g of jointly distributed random variables X and Y by
+EX,Y [g(X, Y )].
+2.1. Partially Observable Markov Decision Process
+A partially observable Markov decision process (POMDP) is a framework for mod-
+eling sequential interaction between an agent and a partially observable environment,
+where the agent cannot perceive its underlying state but must infer it based on the given
+noisy observation.
+POMDPs. We define a POMDP by a tuple M = (S, A, P, Z, O, R, µ0, γ), where S,
+A, and Z are finite sets of states, actions, and observations, respectively. The function
+µ0 : S �→ R+ provides the initial distribution of the agent’s state and γ ∈ [0, 1) is
+a discount factor over a possibly infinite planning horizon. At each decision time, an
+agent selects an action α ∈ A and the transition function P : S × A �→ Distr(S)
+defines the probability P(s′|s, α) of reaching state s′ ∈ S given the current state s ∈ S
+and action α. After the state transition, the agent receives an observation z′ ∈ Z
+according to the function O : S �→ Distr(Z), which defines the probability O(z′|s′)
+of perceiving z′ at state s′. The agent also receives a reward function R(s, α) from the
+function R : S × A �→ R encoding the task specification. In the following, without
+loss of generality, we consider infinite-horizon problems.
+Policies. An observation-based policy σ : (Z × A)∗ × Z �→ Distr(A) for a POMDP
+M maps a sequence of observations and actions to a distribution over actions. A M-
+finite-state controller (M-FSC) is a tuple C = (Q, qI, η, δ), where Q = {q1, q2, . . . , qM}
+is a finite set of memory states, qI is the initial memory state, η : Q×Z �→ Distr(A) is
+a decision function, and δ : Q × Z × A �→ Distr(Q) is a memory transition function.
+The action mapping η(n, z) takes a FSC memory state n and an observation z ∈ Z,
+and returns a distribution over the POMDP actions. The memory update δ(n, z, α) re-
+turns a distribution over memory states and is a function of the action α selected by η.
+An FSC induces an observation-based policy by following a joint execution of these
+two functions upon a trace of the POMDP. An FSC is memoryless if there is a single
+4
+
+memory state. Memoryless FSCs, denoted by σ: Z → Distr(A), are observation-
+based policies, where σ(α|z) = σz,α is the probability of taking the action α given
+solely observation z.
+Remark 1 (REDUCTION TO MEMORYLESS POLICIES). In the remainder of the pa-
+per, for ease of notation, we synthesize optimal M-FSCs for POMDPs (so-called for-
+ward problem) by computing memoryless policies σ on theoretically-justified larger
+POMDPs obtained from the so-called product of the memory update δ and the original
+POMDPs. Indeed, the authors of [27] provide product POMDPs, whose sizes grow
+polynomially only with the size of the domain of δ.
+Belief Update. Given a history on the POMDP M as the perceived observation and
+executed action sequence τ = {(z0, α0), (z1, α1), . . . , (zT , αT )}, where zi ∈ Z, αi ∈
+A, i ∈ {0, . . . , T} and T is the length of the trajectory, the belief state specifies the
+probability of being in each state of the POMDP given an initial belief b0 = µ0. Such
+a belief state can be updated at each time step using the following Bayes rule
+bt+1(s′) =
+O(zt|s′) �
+s∈S P(s′|s, αt)bt(s)
+�
+s′′∈S O(zt|s′′) �
+s∈S P(s′′|s, αt)bt(s).
+(1)
+2.2. Causal Entropy in POMDPs.
+For a POMDP M, a policy σ induces the stochastic processes Sσ
+0:∞ := (Sσ
+0 , . . . , Sσ
+∞),
+Aσ
+0:∞ := (Aσ
+0, . . . , Aσ
+∞), and Zσ
+0:∞ := (Zσ
+0 , . . . , Zσ
+∞). At each time index t, the ran-
+dom variables Sσ
+t , Aσ
+t , and Zσ
+t take values st ∈ S, αt ∈ A, and zt ∈ Z, respec-
+tively. The probability P(A0:T ||S0:T ) of A0:T causally-conditioned on S0:T , given
+by [10, 31, 32] P(A0:T ||S0:T ) := �T
+t=0 P(At|S0:t, A0:t−1), defines a correlation be-
+tween the stochastic processes, where each variable At is conditionally influenced by
+only the earlier predicted variables S0:t, A0:t−1, and not the future variables St+1:T .
+Let H(A|S) ≜ EA,S[− log P(A|S)] be the conditional entropy of a random variable
+A given a random variable S. In the finite-horizon setting, the causal entropy Hσ in-
+duced by a given policy σ is defined as Hσ := EAσ
+0:T ,Sσ
+0:T [− log P(Aσ
+0:T ||Sσ
+0:T )] =
+�T
+t=0 H(Aσ
+t |Sσ
+0:t, Aσ
+0:t−1). Then, the causal entropy in the infinite-horizon setting,
+namely the discounted causal entropy [9, 33], is defined as
+Hγ
+σ :=
+�∞
+t=0 γtH(Aσ
+t |Sσ
+0:t, Aσ
+0:t−1) =
+�∞
+t=0 γtEAσ
+t ,Sσ
+t [− log P(Aσ
+t |Sσ
+t )],
+(2)
+where the second equality is due to the Markov property.
+Remark 2. The entropy of POMDPs (or MDPs) involves the future policy decisions [8],
+i.e., Sσ
+t+1:T , at a time index t, as opposed to the causal entropy in POMDPs (or MDPs).
+Thus, the authors of [8] show that the problem of computing a policy that maximizes
+the entropy is nonconvex, even in MDPs. Inverse reinforcement learning techniques
+that maximize the entropy of the policy rely on approximations or assume that the tran-
+sition function of the MDP is deterministic. On the other hand, computing a policy that
+maximizes the causal entropy can be formulated as a convex optimization problem in
+MDPs [10, 9].
+5
+
+2.3. LTL Specifications.
+We use general linear temporal logic (LTL) to express complex task specifications
+on the POMDP M. Given a set AP of atomic propositions, i.e., Boolean variables
+with truth values for a given state s or observation z, LTL formulae are constructed
+inductively as following:
+ϕ := true | a | ¬ϕ | ϕ1 ∧ ϕ2 | Xϕ | ϕ1Uϕ2,
+where a ∈ AP, ϕ, ϕ1, and ϕ2 are LTL formulae, ¬ and ∧ are the logic negation and
+conjunction, and X and U are the next and until temporal operators. Besides, temporal
+operators such as always (G) and eventually (F) are derived as Fϕ := trueUϕ and
+Gϕ := ¬F¬ϕ. We denote by Prσ
+M(ϕ) the probability of satisfying the LTL formula ϕ
+when following the policy σ on the POMDP M. A detailed description of the syntax
+and semantics of LTL is beyond the scope of this paper and can be found in [20, 19].
+3. Problem Formulation
+In this section, we formulate the problem of task-guided inverse reinforcement
+learning (IRL) in POMDPs. Given a POMDP M with an unknown reward function
+R, we seek to learn a reward function R along with an underlying policy σ that in-
+duces a behavior similar to the expert demonstrations.
+We define an expert trajectory on the POMDP M as the perceived observation and
+executed action sequence τ = {(z0, α0), (z1, α1), . . . , (zT , αT )}, where zi ∈ Z and
+αi ∈ A for all i ∈ {0, . . . , T}, and T denotes the length of the trajectory. Similarly to
+[34], we assume given or we can construct from τ (via Bayesian belief updates (1)) the
+belief trajectory bτ = {b0 := µ0, . . . , bT }, where bi(s) is the estimated probability of
+being at state s at time index i. In the following, we assume that we are given a set of
+belief trajectories D = {bτ1, . . . , bτN } from trajectories τ1, . . . , τN, where N denotes
+the total number of underlying trajectories.
+We parameterize the unknown reward function R by a differentiable function (with
+respect to the parameter) Rθ : S × A �→ Rd, where θ ∈ RF is a parameter that defines
+uniquely the reward function. Such an encoding includes traditional representations of
+the reward such as Rθ(s, α) = gθ(φ(s, α)), where φ : S × A �→ Rd is a known vector
+of basis functions with components referred to as feature functions, d is the number
+of features, and gθ can be any function approximator such as neural networks. For
+example, in the traditional linear encoding, we have gθ(z) = θTz.
+Specifically, we seek for a parameter θ defining Rθ and a policy σ such that its
+discounted return expectation Rθ
+σ matches an empirical discounted return expectation
+¯Rθ of the expert demonstration D. That is, we have that Rθ
+σ = ¯Rθ, where
+Rθ
+σ :=
+∞
+�
+t=0
+γtESσ
+t ,Aσ
+t [Rθ(Sσ
+t , Aσ
+t )|σ] and ¯Rθ = 1
+N
+�
+bτ ∈D
+�
+bi∈bτ
+γi �
+s∈S
+bi(s)Rθ(s, αi).
+In the case of linear encoding of the reward, the above condition is called feature match-
+ing expectation, and it can be simplified by replacing Rθ with the feature function φ.
+6
+
+Nevertheless, the problem is ill-posed and there may be infinitely many reward
+functions and policies that can satisfy the above matching condition. To resolve the
+ambiguities, we seek for a policy σ that also maximizes the discounted causal entropy
+Hγ
+σ. We now define the problem of interest.
+Problem 1. Given a reward-free POMDP M, a demonstration set D, and a feature φ,
+compute a policy σ and weight θ such that (a) The matching condition holds; (b) The
+causal entropy Hγ
+σ given by (2) is maximized by σ.
+Furthermore, we seek to incorporate, if available, a priori high-level side informa-
+tion on the task demonstrated by the expert in the design of the reward and policy.
+Problem 2. Given a linear temporal logic formula ϕ, compute a policy σ and weight
+θ such that the constraints (a) and (b) in Problem 1 are satisfied, and Prσ
+M(ϕ) ≥ λ for
+a given parameter λ ≥ 0.
+Although the parameter λ that specifies the threshold for satisfaction of ϕ is as-
+sumed to be given, the approach can easily be adapted to compute the optimal λ.
+4. Nonconvex Formulation for IRL in POMDPs
+In this section, we formulate Problem 1 and Problem 2 as finding saddle points of
+a nonconvex functions. Then, we propose an algorithm based on solving a nonconvex
+optimization problem to compute such saddle points. We emphasize (see Remark 1)
+that we compute M-FSC for POMDPs by computing memoryless policies σ on larger
+product POMDPs. Indeed, in the remainder of the paper, we reason directly on the
+product POMDP, which is the product of a POMDP and an FSC, and it yields a POMDP
+with state memory pairs [27].
+Substituting Visitation Counts. We eliminate the (infinite) time dependency in Hγ
+σ
+and the matching condition by a substitution of variables involving the policy-induced
+discounted state visitation count µγ
+σ : S �→ R+ and state-action visitation count νγ
+σ :
+S×A �→ R+. For a policy σ, state s, and action α, the discounted state and state-action
+visitation counts are defined by
+µγ
+σ(s) := ESt[
+∞
+�
+t=1
+γt1{St=s}|σ] and νγ
+σ(s, α) := EAt,St[
+∞
+�
+t=1
+γt1{St=s,At=α}|σ],
+where 1{·} is the indicator function. From these definitions, it is straightforward to
+deduce that νγ
+σ(s, α) = πs,αµγ
+σ(s), where πs,α = P[At = a|St = s]. It is also
+straightforward to check that for all s ∈ S and α ∈ A, µγ
+σ(s) ≥ 0, νγ
+σ(s, α) ≥ 0, and
+µγ
+σ(s) = �
+α∈A νγ
+σ(s, α).
+We first provide a concave expression for the discounted causal entropy Hγ
+σ as a
+7
+
+function of the visitation counts µγ
+σ and νγ
+σ:
+Hγ
+σ :=
+�∞
+t=0 γtESσ
+t ,Aσ
+t [− log(πst,αt)]
+=
+�∞
+t=0
+�
+(s,α)∈S×A −(log πs,α)πs,αγtP[Sσ
+t = s]
+=
+�
+(s,α)∈S×A −(log πs,α)πs,αµγ
+σ(s)
+=
+�
+(s,α)∈S×A − log νγ
+σ(s, α)
+µγ
+σ(s) νγ
+σ(s, α),
+(3)
+where the first equality is due to the definition of the discounted causal entropy Hγ
+σ,
+the second equality is obtained by expanding the expectation. The third and fourth
+equalities follow by the definition of the state visitation count µγ
+σ, and the state-action
+visitation count νγ
+σ. We prove in the appendix that the above expression is indeed
+concave in the visitation counts. Next, we obtain a linear expression in νγ
+σ for the
+discounted return expectation Rθ
+σ as:
+Rθ
+σ =
+∞
+�
+t=0
+�
+(s,α)∈S×A
+Rθ(s, α)γtP[Sσ
+t = s, Aσ
+t = α]
+=
+�
+(s,α)∈S×A
+Rθ(s, α)νγ
+σ(s, α),
+(4)
+where the second equality is obtained by the definition of the visitation count νγ
+σ. The
+following nonconvex constraint in µγ
+σ(s) and σz,α ensures observation-based policies:
+νγ
+σ(s, α) = µγ
+σ(s)
+�
+z∈Z O(z|s)σz,α.
+(5)
+Finally, the variables for the discounted visitation counts must satisfy the so-called
+Bellman flow constraint [9] to ensure that the policy is well-defined. For each state
+s ∈ S,
+µγ
+σ(s) = µ0(s) + γ
+�
+s′∈S
+�
+α∈A
+P(s|s′, α)νγ
+σ(s′, α).
+(6)
+Saddle Point Formulation. Computing a policy σ that satisfies the return matching
+constraint Rθ
+σ = ¯Rθ might be infeasible due to ¯Rθ being an empirical estimate from
+the finite set of demonstrations D. Additionally, the feature matching constraint might
+also be infeasible due to the information asymmetry between the expert and the learner,
+e.g., the expert has full observation.
+We build on a saddle point computation problem to incorporate the return matching
+constraints into the objective of the forward problem, similar to other IRL algorithms
+in the literature. Specifically, the desired weight vector θ and policy σ of Problem 1
+and Problem 2 are the solutions of minθ f(θ) := maxσ Hγ
+σ +(Rθ
+σ − ¯Rθ). The function
+f corresponds to the inner optimization problem when the reward parameter is fixed.
+That is, f(θ) computes a policy σ that maximizes the sum Hγ
+σ + Rθ
+σ of the causal
+8
+
+Algorithm 1 Compute the weight vector θ and policy σ solution of the Lagrangian
+relaxation of the IRL problem.
+Input: Feature expectation ¯Rφ from D, initial weight θ0, step size η : N �→ R+, and
+(if available) a priori side information ϕ and λ ∈ [0, 1] imposing Prσ
+M(ϕ) ≥ λ .
+1: σ0 ← uniform policy
+▷ Initialize uniform policy
+2: for k = 0, 1, . . . , do
+▷ Compute θ via gradient descent
+3:
+σk+1 ← SCPForward(θk, σk, ϕ, λ)
+▷ Solve the forward problem (7)–(9)
+with optional ϕ and λ
+4:
+θk+1 ← θk − η(k)∇θf(θk; σk+1)
+▷ Gradient step
+5: end for
+6: return σk, θk
+entropy and the current estimate of the reward function. In other words, f(θ) returns
+the solution to the forward problem, i.e., finding optimal policy on the POMDP when
+the entropy term is removed.
+Algorithm 1 updates the reward weights by using gradient descent. Initially, the
+policy σ0 is a random uniform variable and the weight θ0 is a nonzero vector. At
+iteration k ≥ 0, the policy σk+1 = arg maxσ Hγ
+σ + (Rθk
+σ − ¯Rθk) is the optimal policy
+on the POMDP under the current reward estimate Rθk given by θk. That is, σk+1 is the
+solution to the forward problem. Then, to update the weight θ, Algorithm 1 computes
+the gradient ∇θf with respect to θ as follows:
+∇θf(θ; σ) =
+�
+s,α∈S×A
+νγ
+σ(s, α)∇θRθ(s, α) − 1
+N
+�
+bτ ∈D
+�
+bi∈bτ
+γi �
+s∈S
+bi(s)∇θRθ(s, αi).
+We develop the algorithm SCPForward, presented in next section, to solve the
+forward problem, i.e., computing σk+1 given θk, in an efficient and scalable manner
+while incorporating high-level task specifications to guide the learning.
+Nonconvex Formulation of the Forward Problem. Given a weight vector θk, we take
+advantage of the obtained substitution by the expected visitation counts to formulate
+the forward problem associated to Problem 1 as the nonconvex optimization problem:
+maximize
+µγ
+σ,νγ
+σ,σ
+�
+(s,α)∈S×A
+− log νγ
+σ(s, α)
+µγ
+σ(s) νγ
+σ(s, α) +
+�
+(s,α)∈S×A
+Rθk(s, α)νγ
+σ(s, α)
+(7)
+subject to
+(5) − (6),
+∀(s, α) ∈ S × A, µγ
+σ(s) ≥ 0, νγ
+σ(s, α) ≥ 0,
+(8)
+∀(s, α) ∈ S × A, µγ
+σ(s) =
+�
+α∈A νγ
+σ(s, α),
+(9)
+where the source of nonconvexity is from (5), and we remove the constant − ¯Rθk from
+the cost function of the above optimization problem.
+9
+
+5. Sequential Linear Programming Formulation
+We develop an algorithm, SCPForward, adapting a sequential convex program-
+ming (SCP) scheme to efficiently solve the nonconvex forward problem (7)–(9). In-
+deed, SCPForward involves a verification step to compute sound policies and visi-
+tation counts, which is not present in the existing SCP schemes. Additionally, we de-
+scribe in the next section how to take advantage of high-level task specification (Prob-
+lem 2) through slight modifications of the obtained optimization problem solved by
+SCPForward.
+5.1. Linearizing Nonconvex Optimization Problem
+SCPForward iteratively linearizes the nonconvex constraints in (5) around a pre-
+vious solution. However, the linearization may result in an infeasible or unbounded
+linear subproblem [25]. We first add slack variables to the linearized constraints to
+ensure feasibility. The linearized problem may not accurately approximate the non-
+convex problem if the solutions to this problem deviate significantly from the previous
+solution. Thus, we utilize trust region constraints [25] to ensure that the linearization is
+accurate to the nonconvex problem. At each iteration, we introduce a verification step
+to ensure that the computed policy and visitation counts are not just approximations but
+actually satisfy the nonconvex policy constraint (5), improves the realized cost function
+over past iterations, and satisfy the temporal logic specifications, if available.
+Linearizing Nonconvex Constraints and Adding Slack Variables. We linearize the
+nonconvex constraint (5), which is quadratic in µγ
+σ(s) and σz,α, around the previously
+computed solution denoted by ˆσ, µγ
+ˆσ, and νγ
+ˆσ. However, the linearized constraints may
+be infeasible. We alleviate this drawback by adding slack variables ks,α ∈ R for
+(s, α) ∈ S × A, which results in the affine constraint:
+νγ
+σ(s, α) + ks,α = µγ
+ˆσ(s)
+�
+z∈Z O(z|s)σz,α +
+(10)
+�
+µγ
+σ(s) − µγ
+ˆσ(s)
+� �
+z∈Z O(z|s)ˆσz,α.
+Trust Region Constraints. The linearization may be inaccurate if the solution deviates
+significantly from the previous solution. We add following trust region constraints to
+alleviate this drawback:
+∀(z, α) ∈ Z × A,
+ˆσz,α/ρ ≤ σz,α ≤ ˆσz,αρ,
+(11)
+where ρ is the size of the trust region to restrict the set of allowed policies in the lin-
+earized problem. We augment the cost function in (7) with the term −β �
+(s,α)∈S×A ks,α
+to ensure that we minimize the violation of the linearized constraints, where β is a large
+positive constant.
+10
+
+Linearized Problem. Finally, by differentiating x �→ x log x and y �→ x log(x/y),
+we obtain the coefficients required to linearize the convex causal entropy cost function
+in (7). Thus, we obtain the following linear program (LP):
+maximize
+µγ
+σ,νγ
+σ,σ
+�
+(s,α)∈S×A −
+�
+βks,α −
+�νγ
+ˆσ(s, α)
+µγ
+ˆσ(s)
+�
+µγ
+σ(s)
++
+�
+log νγ
+ˆσ(s, α)
+µγ
+ˆσ(s)
++ 1
+�
+νγ
+σ(s, α)
+�
++
+�
+(s,α)∈S×A
+Rθk(s, α)νγ
+σ(s, α) (12)
+subject to
+(6), (8) − (11).
+Verification Step. After each iteration, the linearization might be inaccurate, i.e, the
+resulting policy ˜σ and potentially inaccurate visitation counts ˜νγ
+˜σ, ˜µγ
+˜σ might not be fea-
+sible to the nonconvex policy constraint (5). As a consequence of the potential infea-
+sibility, the currently attained (linearized) optimal cost might significantly differ from
+the realized cost by the feasible visiation counts for the ˜σ. Additionally, existing SCP
+schemes linearizes the nonconvex problem around the previously inaccurate solutions
+for ˜νγ
+˜σ, and ˜µγ
+˜σ, further propagating the inaccuracy. The proposed verification step
+solves these issues. Given the computed policy ˜σ, SCPForward computes the unique
+and sound solution for the visitation count µγ
+˜σ by solving the corresponding Bellman
+flow constraints:
+µγ
+˜σ(s) =µ0(s) + γ
+�
+s′∈S
+�
+α∈A
+P(s|s′, α)µγ
+˜σ(s′)
+�
+z∈Z
+O(z|s)˜σz,α,
+(13)
+for all s ∈ S, and where µγ
+˜σ ≥ 0 is the only variable of the linear program. Then,
+SCPForward computes νγ
+˜σ(s, α) = µγ
+˜σ(s′) �
+z∈Z O(z|s)˜σz,α and the realized cost
+at the current iteration is defined by
+C(˜σ, θk) =
+�
+(s,α)∈S×A
+− log νγ
+˜σ(s, α)
+µγ
+˜σ
+νγ
+˜σ(s, α) +
+�
+(s,α)∈S×A
+Rθk(s, α)νγ
+˜σ(s, α),
+(14)
+where we assume 0 log 0 = 0. Finally, if the realized cost C(˜σ, θk) does not improve
+over the previous cost C(ˆσ, θk), the verification step rejects the obtained policy ˜σ, con-
+tracts the trust region, and SCPForward iterates with the previous solutions ˆσ, µγ
+ˆσ,
+and νγ
+ˆσ . Otherwise, the linearization is sufficiently accurate, the trust region is ex-
+panded, and SCPForward iterates with ˜σ, µγ
+˜σ and νγ
+˜σ. By incorporating this verifica-
+tion step, we ensure that SCPForward always linearizes the nonconvex optimization
+problem around a solution that satisfies the nonconvex constraint (5).
+5.2. Incorporating High-Level Task Specifications
+Given high-level side information on the agent tasks as the LTL formula ϕ, we first
+compute the product of the POMDP and the ω-automaton representing ϕ to find the
+set T ⊆ S of states, called target or reach states, satisfying ϕ with probability 1 by
+11
+
+using standard graph-based algorithms as a part of preprocessing step. We refer the
+reader to [19] for a detailed introduction on how LTL specifications can be reduced to
+reachability specifications given by T .
+As a consequence, the probability of satisfying ϕ is the sum of the probability of
+reaching the target states s ∈ T , which are given by the undiscounted state visitation
+count µsp
+σ . That is, Prσ
+M(ϕ) = �
+s∈T µsp
+σ (s). Unless γ = 1, µsp
+σ
+̸= µγ
+σ. Thus,
+we introduce new variables µsp
+σ , νsp
+σ , and the adequate constraints in the linearized
+problem (12).
+Incorporating Undiscounted Visitation Variables to Linearized Problem. We append
+new constraints, similar to (8), (9), and (10), into the linearized problem (12), where
+the variables µγ
+σ, νγ
+σ, ks,α, µγ
+ˆσ, νγ
+ˆσ are replaced by µsp
+σ , νsp
+σ , ksp
+s,α, µsp
+ˆσ , νsp
+ˆσ , respectively.
+Further, we add the constraint
+µsp
+σ (s) = µ0(s) +
+�
+s′∈S\T
+�
+α∈A
+P(s|s′, α)νsp
+σ (s′, α),
+(15)
+which is a modification of the Bellman flow constraints such that µsp
+σ (s) for all s ∈ T
+only counts transitions from non-target states. Finally, we penalize the introduced slack
+variables for feasibility of the linearization by augmenting the cost function with the
+term −β �
+(s,α)∈S×A ksp
+s,α.
+Relaxing Specification Constraints. To incorporate the probability of satisfying the
+specifications, We add the following constraint to the linearized problem:
+(spec) :=
+�
+s∈T
+µsp
+σ (s) + Γsp ≥ λ,
+(16)
+where we introduce Γsp ≥ 0 as a slack variable ensuring that the linearized problem
+is always feasible. Further, we augment the cost function with −βspΓsp to penalize
+violating ϕ, where βsp is a positive hyperparameter.
+Updating Verification Step. We modify the previously-introduced realized cost C(˜σ, θk)
+to penalize when the obtained policy does not satisfy the specification ϕ. This cost also
+accounts for the linearization inaccuracy of the new policy constraint due to σ, µsp
+σ ,
+and νsp
+σ . At each iteration, SCPForward computes the accurate µsp
+˜σ of current pol-
+icy ˜σ through solving a feasibility LP with constraints given by the modified Bellman
+flow constraints (15). Then, it augments Csp
+˜σ = min{0, (�
+s∈T µsp
+˜σ (s) − λ)βsp} to the
+realized cost to take the specification constraints into account.
+Convergence to Local Optimum Solution. The convergence guarantees of the pro-
+posed sequential convex scheme with trust regions follow straightforwardly from the
+general convergence of sequential convex programming (SCP) schemes as proved in
+Theorem 3.14 and Theorem 4.7 of [25]. Specifically, weak convergence is ensured as
+the SCP algorithm generates a set of convergent subsequences, all of which satisfy the
+first-order conditions [25]. This is not convergence in its strict sense due to potential
+oscillation between several limit points. Still, surprisingly most of the convergence
+12
+
+Algorithm 2 SCPForward: Linear programming-based algorithm to solve the for-
+ward problem (7)–(9), i.e., compute a policy σk+1 that maximizes the causal entropy,
+considers the matching constraint, and satisfies the specifications, if available.
+Input: Current weight estimate θk, current best policy ˆσ = σk, side information ϕ
+and λ, trust region ρ > 1, penalization coefficients β, βsp ≥ 0, constant ρ0 to
+expand or contract trust region, and a threshold ρlim for trust region contraction.
+1: Find µγ
+ˆσ via linear constraint (13) and νγ
+ˆσ = µγ
+ˆσ(s′) �
+z∈Z O(z|s)ˆσz,α, given ˆσ ▷
+Realized visitation counts
+2: Find µsp
+ˆσ via linear constraint (15) with νsp
+ˆσ = µsp
+ˆσ (s′) �
+z∈Z O(z|s)ˆσz,α, given ˆσ
+▷ If ϕ is available
+3: Compute the realized cost C(ˆσ, θk) ← (14) + Csp
+ˆσ , given ˆσ ▷ Add specifications’
+violation
+4: while ρ > ρlim do
+▷ Trust region threshold
+5:
+Find optimal ˜σ to the augmented LP (12) via ˆσ, µγ
+ˆσ, νγ
+ˆσ, µsp
+ˆσ , νsp
+ˆσ
+▷ We
+augment the LP with constraints (8), (9), (10), (15), and (16) induced by µsp
+σ , νsp
+σ ,
+and by adding −β �
+(s,α)∈S×A ksp
+s,α − βspΓsp to the cost (12).
+6:
+Compute the realized µγ
+˜σ, νγ
+˜σ,µsp
+˜σ , νsp
+˜σ , and C(˜σ, θk) via ˜σ as in lines 1–3
+7:
+{ˆσ ← ˜σ; ρ ← ρρ0} if C(˜σ, θk) ≥ C(ˆσ, θk) else {ρ ← ρ/ρ0}
+▷ Verification
+step
+8: end while
+9: return σk+1 := ˆσ
+claims of nonlinear optimization schemes fall into this category. Furthermore, under
+the right regularity assumptions on the cost function, the authors of [25] proved that
+SCP schemes with trust regions can converge to a local optimum solution with a super-
+linear convergence rate.
+6. Numerical Experiments
+We evaluate the proposed IRL algorithm on several POMDP instances from [35],
+and a simulated wheeled ground robot operating in a high-fidelity, continuous, and 3-D
+Unity simulation. We first compare our IRL algorithm with a straightforward variant
+of GAIL [30] adapted for POMDPs. Then, we provide results on the data-efficiency
+of the proposed approach when taking advantage of side information. Finally, we
+demonstrate the scalability of the routine SCPForward for solving the forward prob-
+lem through comparisons with state-of-the-art solvers such as SolvePOMDP [36],
+SARSOP [37], PRISM-POMDP [38]. We provide the code for reproducibility of the
+results in this paper at https://github.com/wuwushrek/MCE IRL POMDPS.
+6.1. Simulation on Hand-Crafted POMDP Instances
+We first evaluate the proposed IRL algorithm on several POMDP instances ex-
+tracted from the work [35].
+13
+
+1
+2
+3
+4
+5
+6
+9
+12
+7
+10
+13
+8
+11
+14
+Figure 1: Some examples from the benchmark set provided in [35]. From left to right, we have the Maze,
+Avoid, and Evade environments, respectively.
+Benchmark Set. The POMDP instances are as follows. Evade is a turn-based game
+where the agent must reach a destination without being intercepted by a faster player.
+In Avoid, the agent must avoid being detected by two other moving players following
+certain preset, yet unknown routes. In Intercept, the agent must intercept another player
+who is trying to exit a gridworld. In Rocks, the agents must sample at least one good
+rock over the several rocks without any failures. In Obstacle, an agent must find an exit
+in a gridworld without colliding with any static obstacles. In these instances, the agent
+only observes a fixed radius around its current position, see Figure 1. Finally, in Maze,
+the agent must exit a maze as fast as possible while observing only the walls around it
+and should not get stuck in any of the trap states.
+Variants of Learned Policies and Experts. We refer to four types of policies. The
+type of policy depends on whether it uses side information from a temporal specifi-
+cation ϕ or not, and whether it uses a memory size M = 1 or M = 10. We also
+consider two types of experts. The first expert has full information about the envi-
+ronment and computes an optimal policy in the underlying MDP. The second expert
+has partial observation and computes a locally optimal policy in the POMDP with a
+memory size of M = 15. Recall that the agent always has partial information. There-
+fore, the first type of expert corresponds to having information asymmetry between the
+learning agent and expert. Besides, we consider as a baseline a variant of GAIL where
+we learn the policy on the MDP without side information, and extend it to POMDPs
+via an offline computation of the belief in the states. Specifically, we find the optimal
+policy on the MDP by solving the convex optimization problem corresponding to the
+forward problem on MDPs. The resulting policy is a state-based policy that needs to
+be transformed in order to act on a POMDP. The transformation is done by exploiting
+the expert demonstrations to construct a belief state. That is, the trajectories τ of the
+expert are used in a Bayesian belief updates (1) to estimate the probability of being in
+each state of the POMDP. Thus, by combining the computed belief and the state-based
+policy, we obtain an observation-based policy for the POMDP. Doing so could provide
+a significant advantage to the GAIL variant since the state-based policy is the optimal
+policy on the MDP. However, despite the high performance in practice, the policy on
+the POMDP is generally suboptimal, even if the MDP policy were optimal.
+We discuss the effect of side information and memory in the corresponding policies.
+While we detail only on the Maze example, where the agent must exit a maze as fast as
+possible, we observe similar patterns for other examples. Detailed results for the other
+examples are provided in the appendix.
+14
+
+A low state-space Avoid instance
+0
+1
+2
+3
+4
+5
+x=0,y=0
+0
+X=2,y=2,d=E
+X=0,y=4,d=E
+1
+west
+east
+2
+north
+south
+3 
+adv
+placement
+5
+XA low state-space Evade instance
+0
+1
+2
+3
+4
+5
+x=1,y=0
+0
+x=2,y=3
+1
+scan
+adv
+2
+north
+east
+3
+placement
+west
+south
+4 
+5
+XNo information asymmetry
+Under information asymmetry
+GAIL
+0
+25
+50
+75
+100
+−20
+0
+20
+40
+60
+Finite-memory policy
+Without side
+information
+Rθ
+σ
+0
+25
+50
+75
+100
+Memoryless policy
+0
+25
+50
+75
+100
+−20
+0
+20
+40
+60
+Time Steps
+With side
+information
+Rθ
+σ
+0
+25
+50
+75
+100
+Time Steps
+Figure 2: Representative results on the Maze example; each sub-figure represents the average accumulated
+reward under the true reward function (Rθ
+σ) over 1000 runs as a function of time. Compare the two rows:
+The policies in the top row that do not utilize side information suffer a performance drop under information
+asymmetry. On the other hand, in the bottom row, the performance of policies incorporating side information
+into learning does not decrease under information asymmetry. Compare the two columns: The performance
+of the finite-memory policies in the left column is significantly better than memoryless policies. Except for
+the memoryless policies without side information, our algorithm outperforms GAIL. The expert reward on
+the MDP is in average 48.22, while we obtain the value 47.83 for an expert acting on the POMDP.
+6.1.1. Maze Example
+The POMDP M is specified by S = {s1, . . . , s14} corresponding to the cell labels
+in Figure 1. An agent in the maze only observes whether or not there is a wall (in blue)
+in a neighboring cell. That is, the set of observations is O = {o1, . . . , o6, o7}. For
+example, o1 corresponds to observing west and north walls (s1), o2 to north and south
+walls (s2, s4), and o5 to east and west walls (s6, s7, s8, s9, s10, s11). The observations
+o6 and o7 denote the target state (s13) and bad states(s12, s14). The transition model is
+stochastic with a probability of slipping p = 0.1. Further, the states s13 and s14 lead to
+the end of the simulation (trapping states).
+In the IRL experiments, we consider three feature functions. We penalize taking
+more steps with φtime(s, α) = −1 for all s, α. We provide a positive reward when
+reaching s13 with φtarget(s, α) = 1 if s = s13 and φtarget(s, α) = 0 otherwise. We
+penalize bad states s12 and s14 with φbad(s, α) = −1 if s = s12 or s = s14, and
+φbad(s, α) = 0 otherwise. Finally, we have the LTL formula ϕ = G ¬ bad as the
+task specification, where bad is an atomic proposition that is true if the current state
+s = s12 or s = s14. We constrain the learned policy to satisfy Prσ
+M(G ¬ bad) ≥ 0.9.
+Side Information Alleviates the Information Asymmetry. Figure 2 shows that if there
+is an information asymmetry between the learning agent and the expert, the policies
+that do not utilize side information suffer a significant performance drop. The policies
+15
+
+With side information
+Without side information
+GAIL
+0
+75
+150
+225
+300
+−20
+0
+20
+40
+Time Steps
+Total Reward
+Figure 3: Representative results on the Avoid example showing the reward of the policies under the true
+reward function (Rθ
+σ) versus the time steps.
+that do not incorporate side information into learning obtain a lower performance by
+57% under information asymmetry, as shown in the top row of Figure 2. On the other
+hand, as seen in the bottom row of Figure 2, the performance of the policies that use
+side information is almost unaffected by the information asymmetry.
+Memory Leads to More Performant Policies. The results in Figure 2 demonstrate that
+incorporating memory into the policies improves the performance, i.e., the attained
+reward, in all examples, both in solving the forward problem and learning policies
+from expert demonstrations. Incorporating memory partially alleviates the effects of
+information asymmetry, as the performance of the finite-memory policy decreases by
+18% under information asymmetry as opposed to 57% for the memoryless policy.
+We see that in Table 1, incorporating memory into policy on the Maze and Rocks
+benchmarks, allows SCPForward to compute policies that are almost optimal, evi-
+denced by obtaining almost the same reward as the solver SARSOP.
+Side Information Improves Data Efficiency. Figure 4 shows that even on a low data
+regime, learning with task specifications achieves significantly better performance than
+without the task specifications.
+5
+10
+15
+20
+30
+40
+Number of trajectories
+Total reward
+Without LTL
+With LTL
+Opt. Rew. POMDP
+5
+10
+15
+40
+42
+44
+46
+Number of trajectories
+Figure 4: We show the data efficiency of the proposed approach through the total reward obtained by the
+learned policies as a function of the number of expert demonstrations (No information asymmetry). The
+figure on the left shows the performance of learning memoryless policies, while the figure on the right shows
+the performance of a 5-FSC.
+16
+
+SCPForward
+SARSOP
+SolvePOMDP
+Problem
+|S|
+|S × O|
+|O|
+Rθ
+σ
+Time (s)
+Rθ
+σ
+Time (s)
+Rθ
+σ
+Time (s)
+Maze
+17
+162
+11
+39.24
+0.1
+47.83
+0.24
+47.83
+0.33
+Maze (3-FSC)
+49
+777
+31
+44.98
+0.6
+NA
+NA
+NA
+NA
+Maze (10-FSC)
+161
+2891
+101
+46.32
+2.04
+NA
+NA
+NA
+NA
+Obstacle[10]
+102
+1126
+5
+19.71
+8.79
+19.8
+0.02
+5.05
+3600
+Obstacle[10](5-FSC)
+679
+7545
+31
+19.77
+38
+NA
+NA
+NA
+NA
+Obstacle[25]
+627
+7306
+5
+19.59
+14.22
+19.8
+0.1
+5.05
+3600
+Rock
+550
+4643
+67
+19.68
+12.2
+19.83
+0.05
+−
+−
+Rock (3-FSC)
+1648
+23203
+199
+19.8
+15.25
+NA
+NA
+−
+−
+Rock (5-FSC)
+2746
+41759
+331
+19.82
+97.84
+NA
+NA
+−
+−
+Intercept[5, 2, 0]
+1321
+5021
+1025
+19.83
+10.28
+19.83
+13.71
+−
+−
+Intercept[5, 2, 0.1]
+1321
+7041
+1025
+19.81
+13.18
+19.81
+81.19
+−
+−
+Evade[5, 2, 0]
+2081
+13561
+1089
+97.3
+26.25
+97.3
+3600
+−
+−
+Evade[5, 2, 0.1]
+2081
+16761
+1089
+96.79
+26.25
+95.28
+3600
+−
+−
+Evade[10, 2, 0]
+36361
+341121
+18383
+94.97
+3600
+−
+−
+−
+−
+Avoid[4, 2, 0]
+2241
+5697
+1956
+9.86
+34.74
+9.86
+9.19
+−
+−
+Avoid[4, 2, 0.1]
+2241
+8833
+1956
+9.86
+14.63
+9.86
+210.47
+−
+−
+Avoid[7, 2, 0]
+19797
+62133
+3164
+9.72
+3503
+−
+−
+−
+−
+Table 1: Results for the benchmark sets for solving the forward problem. On larger benchmarks (e.g., Evade
+and Avoid), SCPForward can compute locally optimal policies, while the other solvers fail to provide
+solutions in the given time limit. In the environments Obstacle[n], Intercept[n, r, slip], Evade[n, r, slip],
+and Avoid[n, r, slip], the parameters n, r, and slip are the size of the gridworld, the view radius of the agent,
+and the probability of slippery, respectively. We set the time-out to 3600 seconds. An empty cell (denoted by
+−) represents the solver failed to compute any policy before the time-out, while NA refers to not applicable
+due to the approach being based on belief updates.
+Side Information Improves Performance. Besides, in a more complicated environ-
+ment such as Avoid, Figure 3 shows that task specifications are crucial to hope even
+to learn the task. Specifically, Avoid[n, r, slip] is a turn-based game, where the agent
+must reach an exit point while avoiding being detected by two other moving players
+following certain predefined yet unknown routes. The agent can only observe the play-
+ers if they are within a fixed radius from the agent’s current position when the action
+scan is performed. Besides, with the players’ speed being uncertain, their position in
+the routes can not be inferred by the agent. The parameters n, r, and slip specify the
+dimension of the grid, the view radius, and the slippery probability, respectively.
+We consider four feature functions to parameterize the unknown reward. The first
+feature provides a positive reward to the agent upon reaching the exit point. The second
+feature penalizes the agent if it collides with a player. The third feature penalizes the
+agent if it is detected by a player. The fourth feature imposes a penalty cost for each
+action taken. We encode the side information as the temporal logic task specification
+avoid being detected until reaching the exit point with probability greater than 0.98.
+Figure 3 shows that the algorithm is unable to learn without side information while
+side information induces a learned policy that is optimal. Specifically, the learned
+policy without side information seems to only focus on avoiding being detected and
+collision as the corresponding learned features were close to zero.
+17
+
+Figure 5: Left: A simulated Clearpath Warthog operating in a Unity simulation. Right: A demonstration
+provided by an expert.
+6.1.2. SCPForward Yields Better Scalability
+We highlight three observations regarding the scalability of SCPForward. First,
+the results in Table 1 show that only SARSOP is competitive with SCPForward on
+larger POMDPs. SolvePOMDP runs out of time in all but the smallest benchmarks,
+and PrismPOMDP runs out of memory in all benchmarks. Most of these approaches
+are based on updating a belief over the states, which for a large state space can become
+extremely computationally expensive.
+Second, in the benchmarks with smaller state spaces, e.g., Maze and Rock, SARSOP
+can compute policies that yield better performance in less time. This is due to the effi-
+ciency of belief-based approaches on small-size problems. On the other hand, SARSOP
+does not scale to larger POMDPs with a larger number of states and observations. For
+example, by increasing the number of transitions in Intercept benchmark from 5021 to
+7041, the computation time for SARSOP increases by 516%. On the other hand, the
+increase of the computation time of SCPForward is only 28%.
+Third, on the largest benchmarks, including tens of thousands of states and obser-
+vations, SARSOP fails to compute any policy before time-out, while SCPForward
+found a solution. Finally, we also note that SCPForward can also compute a policy
+that maximizes the causal entropy and satisfies an LTL specification, unlike SARSOP.
+6.2. Simulation on a Ground Robot
+We demonstrate an application of the proposed algorithm in a continuous 3-D Unity
+environment containing a ClearPath warthog operating in a semi-structured village. A
+screen shot of the robot operating in this environment and its corresponding trajectory
+can be seen in Figure 5. This environment contains a variety of obstacles including
+buildings, trees, and vehicles as well as three terrain types describing our features, φ,
+grass, gravel, and road. The simulated environment operates in a state space consisting
+of 3350 states, 33254 transitions and 944 total observations. This simulation is used to
+18
+
+0
+5
+10
+15
+20
+25
+30
+0
+10
+20
+30
+grass
+gravel
+road
+unknown
+Figure 6: Gridworld representation of the environment. The figure shows the area of the unity environment
+where we applied the developed algorithm.
+gather data for training, and test an agent’s ability to follow a policy from the learned
+reward function in two experimental scenarios. In this experiment, we demonstrate
+the agent’s ability to learn a reward function from demonstrations that are sub-optimal
+with respect to a known, true reward function. We also show how the learned policies
+perform compared to the optimal policies with full and partial observations obtained
+by solving the MDP or POMDP problem with the true reward function.
+The ground vehicle contains an autonomy stack consisting of three main subsys-
+tems—mapping, perception, and planning. The mapping subsystem based on Omni-
+Mapper[? ] performs simultaneous localization and mapping (SLAM) using LiDAR
+and IMU sensors, providing a map used during planning. The perception subsystem
+provides pixel level semantic segmentation for each image in a video stream from a
+RGB camera to an ontology of terrain and object classes. Each semantic image is
+passed to a terrain projection algorithm which builds N binary occupancy feature maps
+of the known environment used for reward learning where N is the number of features.
+The planning subsystem uses the maps produced from previous subsystems and the
+trajectory from a learned policy to autonomously navigate to a waypoint.
+Expert Demonstrations and Reward Feature Encoding. We collected 10 demonstra-
+tions of an expert teleoperating a robot to a predetermined waypoint (see Figure 6).
+The expert has an implicit preference to traverse the road followed by grass, and lastly
+gravel. Consequently, we encode the unknown reward function as a linear combination
+of known features: Rθ = θ1φroad + θ2φgravel + θ3φgrass + θ4φtime + θ5φgoal, where
+φi returns a value of 0 when the feature of the corresponding state is not feature i, or
+1 otherwise. In order to incentivize the shortest path, the feature time penalizes the
+number of actions taken in the environment before reaching the waypoint. Further-
+19
+
+(a) The trajectories resulting from executing each policy
+with and without task specifications. The learner exploit-
+ing task specifications (orange) is able to reach one of the
+target states, while avoiding the gravel along the path. In
+contrast, the learner without side information (purple) fails
+to avoid the gravel.
+0
+100
+200
+300
+−20
+0
+20
+Expert MDP
+Expert POMDP
+With LTL
+Without LTL
+(b) Evolution of the cumulative reward obtained by the
+learner as a function of the number of environment inter-
+actions.
+Expert MDP and Expert POMDP are the opti-
+mal policies on the MDP and POMDP, respectively for the
+ground truth reward function.
+Figure 7: Impact of incorporating task specifications into reward learning.
+more, goal provides a positive reward upon reaching the waypoint. For comparisons
+of the learned policy, we use the values θ = [0.2, −30, −2, −0.5, 50] as the ground
+truth reward weight vector. We emphasize that the demonstrations are sub-optimal
+with respect to the above ground truth reward as the vehicle often traverses gravel,
+corresponding to a high penalty reward.
+Modeling Robot Dynamics as POMDPs. From a ground truth map of the environment
+in the simulation, we obtain a high-level MDP abstraction of the learner’s behavior on
+the entire state space. Then, we impose a partial observability of the robot as follows:
+The robot does not see the entire map of the world but only see a fixed radius r = 4
+(in terms of the number of grid cells) around its current position. Furthermore, we also
+incorporate uncertainty on the sensor classification of terrain features such that with
+probability p = 0.9 the prediction is correct.
+Task Specifications. In addition to the expert demonstrations, we constrain the learned
+policy to satisfy Prσ
+M(¬ gravel U goal) ≥ 0.9, where gravel is an atomic proposition
+that is true for states having gravel as its feature, and goal is an atomic proposition that
+is true at each target state. Note that this side information does not necessarily enforce
+that the learner should reach the set of target states. Instead, if the learner reaches the
+target state, it should not drive on gravel with probability at least
+Results. Figure 7a shows how the learner with side information avoids the gravel com-
+pared to the learner without side information. Figure 7b further illustrates this result by
+empirically demonstrating that the proposed approach can efficiently take advantage
+of side information to compute policies that matches the expert’s desired behavior.
+Specifically, Figure 7b shows that the gain in the total reward of a learner without side
+20
+
+information increases by 294% with respect to a learner with side information. Ad-
+ditionally, it is important to note in Figure 6 how the initial state distribution of the
+demonstrator trajectories is different from the initial state distribution during the eval-
+uation of the learned policies (Figure 7a). Nevertheless, despite these distinctions, the
+learned policies can effectively navigate toward points present in the expert demonstra-
+tions and then maximally mimic these trajectories.
+7. Related work.
+The closest work to ours is by [34], where they extend classical maximum-margin-
+based IRL techniques for MDPs to POMDPs. However, even on MDPs, maximum-
+margin-based approaches cannot resolve the ambiguity caused by suboptimal demon-
+strations, and they work well when there is a single reward function that is clearly better
+than alternatives [39]. In contrast, we adopt causal entropy that has been shown [39, 10]
+to alleviate these limitations on MDPs. Besides, [34] rely on efficient off-the-shelf
+solvers to the forward problem. Instead, this paper also develops an algorithm that
+outperforms off-the-shelf solvers and can scale to POMDPs that are orders of magni-
+tude larger compared to the examples in [34]. Further, [34] do not incorporate task
+specifications in their formulations.
+One of the basic challenges in IRL, is that finding a reward function and a policy
+that induces a similar behavior to the expert is an ill-defined problem. Prior work has
+addressed this challenge using maximum margin formulations [40, 41, 42], as well as
+probabilistic models to compute a likelihood of the expert demonstrations [43, 8, 10].
+We build on the latter approach and build on the maximum-causal-entropy IRL [9,
+10, 23], which brings algorithmic benefits to IRL in POMDPs as mentioned in the
+introduction. We note that these maximum-causal-entropy IRL techniques assume that
+both the expert and the agent can fully observe the environment, and these approaches
+only apply for MDPs as opposed to POMDPs.
+IRL under partial information has been studied in prior work [2, 44, 45, 46, 47].
+Reference [44] considers the setting where the features of the reward function are par-
+tially specified as opposed to having partial information over the state of the environ-
+ment. The work in [2] considers a special case of POMDPs. It only infers a distribution
+over the future trajectories of the expert given demonstrations as opposed to computing
+a policy that induces a similar behavior to the expert. The works in [45, 46, 47] assume
+that the states of the environment are either fully observable, or fully hidden to the
+learning agent. Therefore, these approaches also consider a special case of POMDPs,
+like in [2]. We also note that none of these methods incorporate side information into
+IRL and do not provide guarantees on the performance of the policy with respect to a
+task specification.
+The idea of using side information expressed in temporal logic to guide and aug-
+ment IRL has been explored in some previous work. In [48, 22], the authors incor-
+porate side information as in temporal logic specification to learn policies that induce
+a behavior similar to the expert demonstrations and satisfies the specification. Refer-
+ence [21] iteratively infers an underlying task specification that is consistent with the
+expert demonstrations and learns a policy and a reward function that satisfies the task
+21
+
+specification. However, these methods also assume full information for both the expert
+and the agent.
+8. Conclusion
+We develop an algorithm for inverse reinforcement learning under partial obser-
+vation. We empirically demonstrate that by incorporating task specifications into the
+learning process, we can alleviate the information asymmetry between the expert and
+the learner while increasing the data efficiency of the learning scheme. Further, we
+empirically demonstrate that our main routine SCPForward, used inside the IRL al-
+gorithm, solves the forward problem in a scalable manner and outperforms state-of-
+the-art POMDP solvers on instances with a large number of states, observations, and
+transitions.
+Work Limitations. This work assumes that the transition and observation functions of
+the POMDP are known to the algorithm. Future work will investigate removing this
+assumption and developing model-free-based approaches. We will also integrate the
+framework with more expressive neural-network-based reward functions.
+Acknowledgements.. Research was sponsored by the Army Research Laboratory and
+Office of Naval Research accomplished under cooperative agreement number(s) ARL
+W911NF-20-2-0132, ARL W911NF-19-2-0285 and ONR N00014-22-1-2254. The
+views and conclusions contained in this document are those of the authors and should
+not be interpreted as representing the official policies; either expressed or implied,
+of the Army Research Laboratory, Office of Naval Research, or the U.S. Government.
+The U.S. Government is authorized to reproduce and distribute reprints for Government
+purposed notwithstanding any copyright notation herein.
+References
+[1] P. Abbeel, A. Coates, A. Y. Ng, Autonomous Helicopter Aerobatics Through
+Apprenticeship Learning, The International Journal of Robotics Research 29 (13)
+(2010) 1608–1639.
+[2] K. M. Kitani, B. D. Ziebart, J. A. Bagnell, M. Hebert, Activity Forecasting, in:
+European Conference on Computer Vision, Springer, 2012, pp. 201–214.
+[3] D. Hadfield-Menell, S. J. Russell, P. Abbeel, A. D. Dragan, Cooperative Inverse
+Reinforcement Learning, in: NIPS, 2016.
+[4] A. D. Dragan, S. S. Srinivasa, A Policy-Blending Formalism for Shared Control,
+The International Journal of Robotics Research 32 (7) (2013) 790–805.
+[5] T. Osa, N. Sugita, M. Mitsuishi, Online Trajectory Planning in Dynamic Envi-
+ronments for Surgical Task Automation., in: Robotics: Science and Systems,
+Citeseer, 2014, pp. 1–9.
+22
+
+[6] T. Osa, N. Sugita, M. Mitsuishi, Online Trajectory Planning and Force Control
+for Automation of Surgical Tasks, IEEE Transactions on Automation Science and
+Engineering 15 (2) (2017) 675–691.
+[7] C. Finn, S. Levine, P. Abbeel, Guided Cost Learning: Deep Inverse Optimal Con-
+trol via Policy Optimization, in: International conference on machine learning,
+PMLR, 2016, pp. 49–58.
+[8] B. D. Ziebart, A. L. Maas, J. A. Bagnell, A. K. Dey, Maximum Entropy Inverse
+Reinforcement Learning, in: AAAI, Vol. 8, 2008, pp. 1433–1438.
+[9] Z. Zhou, M. Bloem, N. Bambos, Infinite Time Horizon Maximum Causal Entropy
+Inverse Reinforcement Learning, IEEE Transactions on Automatic Control 63 (9)
+(2017) 2787–2802.
+[10] B. D. Ziebart, J. A. Bagnell, A. K. Dey, Modeling Interaction via the Principle of
+Maximum Causal Entropy.
+[11] S. C. Ong, S. W. Png, D. Hsu, W. S. Lee, Pomdps for robotic tasks with mixed
+observability, in: Robotics: Science and Systems, Vol. 5, 2009, p. 4.
+[12] H. Bai, D. Hsu, W. S. Lee, Integrated Perception and Planning in the Continuous
+Space: A POMDP Approach, The International Journal of Robotics Research
+33 (9) (2014) 1288–1302.
+[13] S. Zhang, J. Sinapov, S. Wei, P. Stone, Robot Behavioral Exploration and Mul-
+timodal Perception using POMDPs, in: AAAI Spring Symposium on Interactive
+Multisensory Object Perception for Embodied Agents, 2017.
+[14] K. Akash, K. Polson, T. Reid, N. Jain, Improving Human-Machine Collabora-
+tion Through Transparency-based Feedback–Part I: Human Trust and Workload
+Model, IFAC-PapersOnLine 51 (34) (2019) 315–321.
+[15] X. Liu, A. Datta, Modeling Context Aware Dynamic Trust Using Hidden Markov
+Model, in: Proceedings of the AAAI Conference on Artificial Intelligence,
+Vol. 26, 2012.
+[16] N. Vlassis, M. L. Littman, D. Barber, On the computational complexity of
+stochastic controller optimization in pomdps, ACM Trans. Comput. Theory 4 (4).
+[17] O. Madani, S. Hanks, A. Condon, On the Undecidability of Probabilistic Planning
+and Infinite-Horizon Partially Observable Markov Decision Problems, in: AAAI,
+AAAI Press, 1999, pp. 541–548.
+[18] M. L. Littman, U. Topcu, J. Fu, C. Isbell, M. Wen, J. MacGlashan, Environment-
+Independent Task Specifications via GLTL, arXiv preprint arXiv:1704.04341.
+[19] C. Baier, J.-P. Katoen, Principles of Model Checking, The MIT Press, 2008.
+23
+
+[20] A. Pnueli, The Temporal Logic of Programs, in: Proc. 18th Annu. Symp. Found.
+Computer Sci., Washington, D.C., USA, 1977, pp. 46–57.
+doi:10.1109/
+SFCS.1977.32.
+[21] F. Memarian, Z. Xu, B. Wu, M. Wen, U. Topcu, Active Task-Inference-Guided
+Deep Inverse Reinforcement Learning, in: 2020 59th IEEE Conference on Deci-
+sion and Control (CDC), IEEE, 2020, pp. 1932–1938.
+[22] M. Wen, I. Papusha, U. Topcu, Learning from Demonstrations with High-Level
+Side Information, in: Proceedings of the Twenty-Sixth International Joint Con-
+ference on Artificial Intelligence, 2017.
+[23] B. D. Ziebart, J. A. Bagnell, A. K. Dey, The Principle of Maximum Causal En-
+tropy for Estimating Interacting Processes, IEEE Transactions on Information
+Theory 59 (4) (2013) 1966–1980.
+[24] Y.-x. Yuan, Recent Advances in Trust Region Algorithms, Mathematical Pro-
+gramming 151 (1) (2015) 249–281.
+[25] Y. Mao, M. Szmuk, X. Xu, B. Ac¸ikmese, Successive convexification: A super-
+linearly convergent algorithm for non-convex optimal control problems, arXiv
+preprint arXiv:1804.06539.
+[26] H. Yu, D. P. Bertsekas, On Near Optimality of the Set of Finite-State Controllers
+for Average Cost POMDP, Mathematics of Operations Research 33 (1) (2008)
+1–11.
+[27] S. Junges, N. Jansen, R. Wimmer, T. Quatmann, L. Winterer, J.-P. Katoen,
+B. Becker, Finite-State Controllers of POMDPs using Parameter Synthesis, in:
+Proceedings of UAI, 2018, pp. 519–529.
+[28] N. Meuleau, K.-E. Kim, L. P. Kaelbling, A. R. Cassandra, Solving POMDPs by
+searching the space of finite policies, in: UAI, 1999, pp. 417–426.
+[29] C. Amato, D. S. Bernstein, S. Zilberstein, Optimizing Fixed-Size Stochastic Con-
+trollers for POMDPs and Decentralized POMDPs, AAMAS 21 (3) (2010) 293–
+320.
+[30] J. Ho, S. Ermon, Generative adversarial imitation learning, Advances in neural
+information processing systems 29 (2016) 4565–4573.
+[31] J. Massey, Causality, feedback and directed information, in: Proc. Int. Symp. Inf.
+Theory Applic.(ISITA-90), Citeseer, 1990, pp. 303–305.
+[32] G. Kramer, Directed Information for Channels with Feedback, Citeseer, 1998.
+[33] L. P. Hansen, T. J. Sargent, G. Turmuhambetova, N. Williams, Robust Control
+and Model Misspecification, Journal of Economic Theory 128 (1) (2006) 45–90.
+[34] J. Choi, K.-E. Kim, Inverse Reinforcement Learning in Partially Observable En-
+vironments, Journal of Machine Learning Research 12 (2011) 691–730.
+24
+
+[35] S. Junges, N. Jansen, S. A. Seshia, Enforcing almost-sure reachability in pomdps,
+in: International Conference on Computer Aided Verification, 2020.
+[36] E. Walraven, M. Spaan, Accelerated Vector Pruning for Optimal POMDP Solvers,
+in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 31, 2017.
+[37] H. Kurniawati, D. Hsu, W. S. Lee, Sarsop: Efficient point-based pomdp planning
+by approximating optimally reachable belief spaces., in: Robotics: Science and
+systems, Vol. 2008, Citeseer, 2008.
+[38] G. Norman, D. Parker, X. Zou, Verification and control of partially observable
+probabilistic systems, Real-Time Systems 53 (3) (2017) 354–402.
+[39] T. Osa, J. Pajarinen, G. Neumann, J. Bagnell, P. Abbeel, J. Peters, An Algorithmic
+Perspective on Imitation Learning, Foundations and Trends in Robotics 7 (1-2)
+(2018) 1–179.
+[40] N. D. Ratliff, J. A. Bagnell, M. A. Zinkevich, Maximum Margin Planning, in:
+Proceedings of the 23rd International Conference on Machine Learning, 2006,
+pp. 729–736.
+[41] P. Abbeel, A. Y. Ng, Apprenticeship Learning via Inverse Reinforcement Learn-
+ing, in: Proceedings of the 21st International Conference on Machine Learning,
+2004, p. 1.
+[42] A. Y. Ng, S. J. Russell, et al., Algorithms for Inverse Reinforcement Learning., in:
+Proceedings of the 17th International Conference on Machine Learning, Vol. 1,
+2000, p. 2.
+[43] D. Ramachandran, E. Amir, Bayesian Inverse Reinforcement Learning., in: IJ-
+CAI, Vol. 7, 2007, pp. 2586–2591.
+[44] A. Boularias, O. Kr¨omer, J. Peters, Structured Apprenticeship Learning, in:
+Joint European Conference on Machine Learning and Knowledge Discovery in
+Databases, Springer, 2012, pp. 227–242.
+[45] K. Bogert, P. Doshi, Multi-Robot Inverse Reinforcement Learning under Occlu-
+sion with Interactions, in: Proceedings of the 2014 International Conference on
+Autonomous Agents and Multi-Agent Systems, Citeseer, 2014, pp. 173–180.
+[46] K. Bogert, P. Doshi, Toward Estimating Others’ Transition Models under Occlu-
+sion for Multi-Robot IRL, in: Twenty-Fourth International Joint Conference on
+Artificial Intelligence, 2015.
+[47] K. Bogert, J. F.-S. Lin, P. Doshi, D. Kulic, Expectation-Maximization for Inverse
+Reinforcement Learning with Hidden Data, in: Proceedings of the 2016 Inter-
+national Conference on Autonomous Agents & Multiagent Systems, 2016, pp.
+1034–1042.
+25
+
+[48] I. Papusha, M. Wen, U. Topcu, Inverse Optimal Control with Regular Language
+Specifications, in: 2018 Annual American Control Conference (ACC), IEEE,
+2018, pp. 770–777.
+Appendices
+In this appendix, we provide supplementary derivations for the results in the paper and
+more details on the numerical experiments.
+A. Concavity of Causal Entropy and Derivations of the Bellman Constraints
+In this section, we first recall the obtained expression of the causal entropy Hγ
+σ as a
+function of the visitation counts µγ
+σ and νγ
+σ. We then prove the concavity of the causal
+entropy, which enables convex-optimization-based formulation of the task-guided in-
+verse reinforcement learning (IRL) problem. Then, we provide additional details on
+the derivation of the affine constraint implied by the Bellman flow constraint.
+Concave Causal Entropy. We first recall the definitions of the state and state-action
+visitation counts. For a policy σ, state s, and action α, the discounted state visitation
+counts are defined by µγ
+σ(s) ≜ ESt[�∞
+t=1 γt1{St=s}] and the discounted state-action
+visitation counts are defined by νγ
+σ(s, α) ≜ EAt,St[�∞
+t=1 γt1{St=s,At=α}], where 1{·}
+is the indicator function and t is the time step. From the definitions of the state and
+state-action visitation counts µγ
+σ and νγ
+σ, it is straightforward to deduce that νγ
+σ(s, α) =
+σs,αµγ
+σ(s), where σs,α = P[At = a|St = s]. We use the visitation counts to prove in
+Section 4 that
+Hγ
+σ =
+�
+(s,α)∈S×A
+−(log πs,α)πs,αµγ
+σ(s) =
+�
+(s,α)∈S×A
+− log νγ
+σ(s, α)
+µγ
+σ(s) νγ
+σ(s, α),
+where the last inequality is obtained by using that πs,α = νγ
+σ(s, α)/µγ
+σ(s). We claim
+that Hγ
+σ is a concave fucntion of the visitation counts. Thus, we want to show that
+the function f(νγ
+σ, µγ
+σ) = �
+(s,α)∈S×A − log νγ
+σ(s,α)
+µγ
+σ(s) νγ
+σ(s, α) is concave. To this end,
+consider any λ ∈ (0, 1) and the two sets of variables νγ
+σ, µγ
+σ and ¯νγ
+σ, ¯µγ
+σ. Then, we have
+26
+
+the following result:
+f(λνγ
+σ + (1 − λ)¯νγ
+σ, λ¯µγ
+σ + (1 − λ)¯µγ
+σ)
+=
+�
+(s,α)∈S×A
+− log λνγ
+σ(s, α) + (1 − λ)¯νγ
+σ(s, α)
+λµγ
+σ(s) + (1 − λ)¯µγ
+σ(s, α) (λνγ
+σ(s, α) + (1 − λ)¯νγ
+σ(s, α))
+≥
+�
+(s,α)∈S×A
+−λνγ
+σ(s, α) log λνγ
+σ(s, α)
+λµγ
+σ(s, α) − (1 − λ)¯νγ
+σ(s, α) log (1 − λ)¯νγ
+σ(s, α)
+(1 − λ)¯µγ
+σ(s, α)
+=
+�
+(s,α)∈S×A
+−λνγ
+σ(s, α) log νγ
+σ(s, α)
+µγ
+σ(s, α) − (1 − λ)¯νγ
+σ(s, α) log ¯νγ
+σ(s, α)
+¯µγ
+σ(s, α)
+= λf(νγ
+σ, µγ
+σ) + (1 − λ)f(¯νγ
+σ, ¯µγ
+σ),
+where the first inequality is obtained by applying to the well-known log-sum inequality,
+i.e.,
+x1 log x1
+y1
++ x2 log x2
+y2
+≥ (x1 + x2) log x1 + x2
+y1 + y2
+,
+for nonnegative numbers x1, x2, y1, y2. Specifically, we apply the substitution x1 =
+λνγ
+σ, y1 = λµγ
+σ, x2 = (1 − λ)¯νγ
+σ, and y2 = (1 − λ)¯µγ
+σ. Note that the inequality
+f(λνγ
+σ + (1 − λ)¯νγ
+σ, λ¯µγ
+σ + (1 − λ)¯µγ
+σ) ≥ λf(νγ
+σ, µγ
+σ) + (1 − λ)f(¯νγ
+σ, ¯µγ
+σ)
+implies that f(νγ
+σ, µγ
+σ) is concave in νγ
+σ, and µγ
+σ.
+Bellman Flow Constraint. For the visitation count variables to correspond to a valid
+policy generating actions in the POMDP M , νγ
+σ and µγ
+σ must satisfy the bellman flow
+constraint given by
+µγ
+σ(s) = ESσ
+t
+� ∞
+�
+t=0
+γt1{Sσ
+t =s}
+�
+= µ0(s) + γESσ
+t
+� ∞
+�
+t=0
+γt1{Sσ
+t+1=s}
+�
+= µ0(s) + γ
+∞
+�
+t=0
+�
+s′∈S
+�
+α∈A
+γtP(s|s′, α)P[Sσ
+t = s′, Aσ
+t = α]
+= µ0(s) + γ
+�
+s′∈S
+�
+α∈A
+P(s|s′, α)νγ
+σ(s′, α).
+B. Experimental Tasks
+In this section, we first provide a detailed description of the POMDP models used
+in the benchmark. The simulations on the benchmark examples empirically demon-
+strate that side information alleviates the information asymmetry, and more memory
+leads to more performant policies. Then, we provide additional numerical simulations
+supporting the claim that SCPForward is sound and yields better scalability than
+off-the-shelf solvers for the forward problem, i.e., computing an optimal policy on a
+POMDP for a given reward function.
+27
+
+B.1. Computation Resources and External Assets
+All the experiments of this paper were performed on a computer with an Intel Core
+i9-9900 CPU 3.1GHz ×16 processors and 31.2 Gb of RAM. All the implementations
+are written and tested in Python 3.8, and we attach the code with the supplementary
+material.
+Required Tools. . Our implementation requires Stormpy of Storm [? ] and Gurobipy
+of Gurobi 9.1 [? ]. On one hand, we use Storm, a tool for model checking, to parse
+POMDP file specifications, to compute the product POMDP with the finite state con-
+troller in order to reduce the synthesis problem to the synthesis of memoryless policies,
+and to compute the set T of target states satisfying a specification ϕ via graph prepro-
+cessing. On the other hand, we use Gurobi to solve both the linearized problem in (7)
+and the feasible solution of the Bellman flow constraint needed for the verification step.
+Off-The-Shelf Solvers for Forward Problem.
+. In order to show the scalability of
+the developed algorithm SCPForward, we compare it to state-of-the-art POMDP
+solvers SolvePOMDP [36], SARSOP [37], and PRISM-POMDP [38].
+The solver
+SolvePOMDP implements both exact and approximate value iterations via incremen-
+tal pruning [? ] combined with state-of-the-art vector pruning methods [36]. Finally,
+PrismPOMDP discretizes the belief state and adopts a finite memory strategy to find
+an approximate solution of the forward problem. For all the solvers above, we use the
+default settings except from the timeout enforced to be 3600 seconds. These solvers
+are not provided with our implementation. However, we provide the POMDP models
+that each of the solvers can straightforwardly use. Further details are provided in the
+readme files of our implementation.
+B.2. Benchmark Set
+We evaluate the proposed learning algorithm on several POMDP instances adapted
+from [35]. We attached the modified instances in our code with the automatically
+generated models for each off-the-shelf solver that the reader can straightforwardly
+use to reproduce Table 1. The reader can refer to Table 1 for the number of states,
+observations, and transitions of each environment of the benchmark set. In all the
+examples, we gather 10 trajectories from an expert that can fully observe its current
+state in the environment and an expert having partial observation of the environment.
+Our algorithm learns reward functions from these trajectories under different memory
+policies and high-level side information.
+28
+
+Rocks Instance. In the environment Rocks, an agent navigates in a gridworld to sam-
+ple at least one valuable rock (if a valuable rock is in the grid) over the two possibly
+dangerous rocks, without any failures. When at least one valuable rock has been col-
+lected, or the agent realizes that all the rocks are dangerous, it needs to get to an exit
+point to terminate the mission. The partial observability is due to the agent can only
+observe if its current location is an exit point or a dangerous rock. Furthermore, the
+agent has noisy sensors enabling sampling neighbor cells.
+We consider three feature functions. The first feature provides a positive reward
+when reaching the exit point with at least one valuable rock or no rocks when all of
+them are dangerous. The second feature provides a negative reward when the agent
+is at the location of a dangerous rock. Finally, the third feature penalizes each action
+taken with a negative reward to promote reaching the exit point as soon as possible.
+No information asymmetry
+Under information asymmetry
+GAIL
+0
+75
+150
+225
+300
+0
+50
+100
+Finite-memory policy
+Without side
+information
+Rφ
+σ
+0
+75
+150
+225
+300
+0
+50
+100
+Memoryless policy
+Rφ
+σ
+0
+75
+150
+225
+300
+0
+50
+100
+Time Steps
+With side
+information
+Rφ
+σ
+0
+75
+150
+225
+300
+0
+50
+100
+Time Steps
+Rφ
+σ
+Figure 8: Representative results on the Rock example showing the reward of the policies under the true
+reward function (Rφ
+σ) versus the time steps.
+We compare scenarios with no side information and the a priori knowledge on the
+task such as the agent eventually reaches an exit point with a probability greater than
+0.995. Figure 8 supports our claim that side information indeed alleviates the informa-
+tion asymmetry between the expert and the agent. Additionally, we also observe that
+incorporating memory leads to more performant policies in terms of the mean accumu-
+lated reward.
+29
+
+Obstacle Instance. . In the environment Obstacle[n], an agent must find an exit in a
+gridworld without colliding with any of the five static obstacles in the grid. The agent
+only observes whether the current position is an obstacle or an exit state. The parameter
+n specifies the dimension of the grid.
+Similar to the Rocks example, the agent receives a positive reward if it successfully
+exits the gridworld and a negative reward for every taken action or colliding with an
+obstacle.
+As for the side information, we specify in temporal logic that while learning the
+reward, the agent should not collide any obstacles until it reaches an exit point with a
+probability greater than 0.9.
+No information asymmetry
+Under information asymmetry
+0
+25
+50
+75
+100
+−200
+0
+200
+400
+Finite-memory policy
+Without side
+information
+Rφ
+σ
+0
+25
+50
+75
+100
+−200
+0
+200
+400
+Memoryless policy
+Rφ
+σ
+0
+25
+50
+75
+100
+−200
+0
+200
+400
+Time Steps
+With side
+information
+Rφ
+σ
+0
+25
+50
+75
+100
+−200
+0
+200
+400
+Time Steps
+Rφ
+σ
+Figure 9: Representative results on the Obstacle example showing the reward of the policies under the true
+reward function (Rφ
+σ) versus the time steps.
+Similar to the Maze and Rock examples, Figure 9 supports our claim that side in-
+formation alleviates the information asymmetry and memory leads to more performant
+policies.
+30
+
+Evade Instance. Evade[n, r, slip] is a turn-based game where the agent must reach a
+destination without being intercepted by a faster player. The player cannot access the
+top row of the grid. Further, the agent can only observe the player if it is within a fixed
+radius from its current location and upon calling the action scan. The parameters n, r,
+and slip specify the dimension of the grid, the view radius, and the slippery probability,
+respectively.
+The feature functions are defined such that the agent receives a positive reward if
+at the destination, a high negative reward if it is intercepted by the player, and a small
+negative reward for each action taken, including the scan action.
+With side information
+Without side information
+GAIL
+0
+25
+50
+75
+100
+−10
+0
+10
+20
+Time Steps
+Mean accumulated reward
+Figure 10: Representative results on the Evade example showing the reward of the policies under the true
+reward function (Rφ
+σ) versus the time steps.
+As for the side information, we specify in temporal logic that while learning the
+reward, the agent must reach an exit point with probability greater than 0.98.
+Figure 10 shows that learning with side information provides higher reward than
+without side information. Besides, there is less randomness in the policy with side
+information compared to the policy without side information. Specifically, the standard
+deviation of the policy with side information is significantly smaller than the policy
+without side information.
+We did not discuss the impact of different memory size policies in this example
+since the performance of the memoryless policy is already near-optimal, as the policy
+obtains the same reward as SARSOP (see Table 1 for a reference. Specifically, we
+observe that the optimal policy on the underlying MDP yields comparable policies to
+the optimal memoryless policy on the POMDP. As a consequence, we observe that the
+information asymmetry between the expert and the agent does not hold here either, and
+the learned policies obtain a similar performance.
+31
+
+Intercept Instance. Intercept[n, r, slip] is a variant of Evade where the agent must
+intercept another player who is trying to exit the gridworld. The agent can move in 8
+directions and can only observe the player if it is within a fixed radius from the agent’s
+current position when the action scan is performed. Besides, the agent has a camera
+that enables it to observe all cells from west to east from the center of the gridworld. In
+contrast, the player can only move in 4 directions. The parameters n, r, and slip specify
+the dimension of the grid, the view radius, and the slippery probability, respectively.
+We consider three feature functions to parameterize the unknown reward. The first
+feature provides a positive reward to the agent upon intercepting the player. The second
+feature penalizes the agent if the player exits the gridworld. The third feature imposes
+a penalty cost for each action taken.
+With side information
+Without side information
+GAIL
+0
+25
+50
+75
+100
+−10
+0
+10
+20
+Time Steps
+Mean accumulated reward
+Figure 11: Representative results on the Intercept example showing the reward of the policies under the
+true reward function (Rφ
+σ) versus the time steps.
+We encode the high-level side information as the temporal logic task specification
+Eventually intercept the player with probability greater than 0.98, i.e., the agent should
+eventually reach an observation where its location coincides with the player’s location.
+Figure 11 demonstrates that side information does not improve the performance
+of the policy. This result is because memoryless policies are optimal in this example,
+and a combination of the given reward features can perfectly encode the temporal logic
+specifications, similar to the Evade example.
+B.3. Effects of Side Information
+In this section, we provide additional experiments on how the side information
+speeds up the learning process in terms of computation time and convergence to the
+optimal policy and reward parameters. Then, we quantify the effects of the side infor-
+mation by solving the POMDPs using only the task specifications and no demonstra-
+tions. All these experiments are performed on the Maze example, which is a relatively
+low-size POMDP example.
+32
+
+Convergence of the Learning With and Without Side Information. In the Maze ex-
+periments, we empirically observe that side information enables the learning algorithm
+to converge with eight times less number of iterations compared to learning without
+side information. The number of iterations here denotes both the number of lineariza-
+tions in the sequential convex scheme and the number of gradient steps during reward
+updates. However, the gain in computation time is not as prominent as the gain in
+the number of iterations. In fact, learning with side information is only approximately
+three times faster than learning without side information due to how side information
+almost doubles the number of variables in the convex optimization problem.
+Effects of Side Information Without Any Demonstrations.
+• Experiment 1.
+We consider the exact setting of the Maze example with no
+demonstrations and the LTL specification Prσ
+M(G ¬ bad) ≥ 0.9. Essentially,
+we seek policies that avoid the trapping states with high probability. Without any
+additional reward, the optimal policy is exactly what we expect: High probabil-
+ity for action enforcing no movements and low probability for the others. With
+respect to the true reward, this is clearly suboptimal as the reward will keep de-
+creasing due to no minimization of the amount of time spent in the environment.
+Now, we optimize the problem for a policy that satisfies the LTL specifications
+while penalizing spending time in the environment according to the ground truth
+reward for taking more steps in the environment. The obtained policy has the op-
+timal reward of 47.83, which corresponds to optimizing the ground truth reward
+in the POMDP. Indeed, the fastest way to clear the Maze is to exit through a goal
+state while not getting trapped.
+• Experiment 2.
+We consider the exact setting of the Maze example with no
+demonstrations and the LTL specification Prσ
+M(E target) ≥ 0.95. Essentially,
+we seek policies that eventually reach the target state (exit of the Maze) with
+high probability. Without any additional reward, the optimal policy is subopti-
+mal with respect to the optimal policy on the POMDP, given the ground truth
+reward. Indeed, the policy can reach the target with an optimal reward of 28.63
+due to the amount of time spent to reach the goal. By adding the reward on time
+spent in the environment to the LTL specifications, we can obtain the optimal
+reward on the POMDP again.
+B.4. Summary of the Results
+Side Information Alleviates the Information Asymmetry . As mentioned in the sub-
+mitted manuscript, side information can indeed alleviate the information asymmetry.
+Specifically, we observe that if there is an information asymmetry in the forward prob-
+lem, i.e., the obtained reward from an optimal policy on the underlying POMDP is
+lower than from an optimal policy on the underlying fully observable MDP, incor-
+porating side information in temporal logic specifications alleviates the information
+asymmetry between the expert and the agent. For example, we can see the effects of
+such information asymmetry in the Maze, Rocks, Obstacle, and Avoid examples. In
+33
+
+these examples, having partial observability reduces the obtained reward in the for-
+ward problem. The policies that do not incorporate side information into the learning
+procedure also obtain a lower reward under information asymmetry.
+Memory Leads to More Performance Policies. Similarly to the side information, we
+also observe that if incorporating memory improves the performance of the learned
+policies, if it also improves the obtained reward in the forward problem, as seen in the
+Maze, Rocks, and Obstacle instances. In Table 1, we can also see that incorporating
+memory helps to compute a better optimal policy in these examples, unlike computing
+a memoryless policy.
+34
+
diff --git a/19AzT4oBgHgl3EQfRvso/content/tmp_files/load_file.txt b/19AzT4oBgHgl3EQfRvso/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f9c2f0fee96c06ab5ceac1f8b9158f3c9264ee7b
--- /dev/null
+++ b/19AzT4oBgHgl3EQfRvso/content/tmp_files/load_file.txt
@@ -0,0 +1,1164 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf,len=1163
+page_content='Task-Guided IRL in POMDPs that Scales  Franck Djeumou∗, Christian Ellis∗∗, Murat Cubuktepe∗, Craig Lennon, Ufuk Topcu∗  Abstract  In inverse reinforcement learning (IRL), a learning agent infers a reward function en-  coding the underlying task using demonstrations from experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, many ex-  isting IRL techniques make the often unrealistic assumption that the agent has access  to full information about the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We remove this assumption by developing  an algorithm for IRL in partially observable Markov decision processes (POMDPs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We address two limitations of existing IRL techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' First, they require an exces-  sive amount of data due to the information asymmetry between the expert and the  learner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Second, most of these IRL techniques require solving the computationally in-  tractable forward problem—computing an optimal policy given a reward function—in  POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The developed algorithm reduces the information asymmetry while increas-  ing the data efficiency by incorporating task specifications expressed in temporal logic  into IRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Such specifications may be interpreted as side information available to the  learner a priori in addition to the demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Further, the algorithm avoids a com-  mon source of algorithmic complexity by building on causal entropy as the measure of  the likelihood of the demonstrations as opposed to entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Nevertheless, the resulting  problem is nonconvex due to the so-called forward problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We solve the intrinsic  nonconvexity of the forward problem in a scalable manner through a sequential linear  programming scheme that guarantees to converge to a locally optimal policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In a series  of examples, including experiments in a high-fidelity Unity simulator, we demonstrate  that even with a limited amount of data and POMDPs with tens of thousands of states,  our algorithm learns reward functions and policies that satisfy the task while inducing  similar behavior to the expert by leveraging the provided side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Introduction  A robot can satisfy certain human-specified tasks by describing desired behavior  through a reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, the design of such a reward function is a non-  trivial task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Inverse reinforcement learning (IRL) is an established technique that in-  fers a reward function encoding the underlying task using expert demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' IRL  ∗The University of Texas at Austin  ∗∗The University of Massachusetts: Dartmouth  United States Army Research Laboratory  Email addresses: fdjeumou@utexas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='edu (Franck Djeumou), cellis3@umassd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='edu  (Christian Ellis), mcubuktepe@utexas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='edu (Murat Cubuktepe),  craig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='lennon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='civ@army.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='mil (Craig Lennon), utopcu@utexas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='edu (Ufuk Topcu)  Preprint submitted to Elsevier  January 4, 2023  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='01219v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='LG]  30 Dec 2022  techniques have found a wide range of applications in various domains such as ac-  robatic helicopter flight [1], inferring future actions of people [2], human-autonomy  interaction [3, 4], robotic surgery [5, 6], and robotic manipulation tasks [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Most  existing work [1, 8, 9, 10, 3, 7] has focused on Markov decision processes (MDPs),  assuming that the learner can fully observe the state of the environment and expert  demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, the learner will not have access to full state observations in  many applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For example, a robot will never know everything about its envi-  ronment [11, 12, 13] and may not observe the internal states of a human with whom it  works [14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Such information limitations violate the intrinsic assumptions made in  most existing IRL techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We investigate IRL in partially observable Markov decision processes (POMDPs),  a widely used model for decision-making under imperfect information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Partial observ-  ability brings two key challenges in IRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The first challenge is due to the so-called  information asymmetry between the expert and the learner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The expert typically has  either full or partial information about the environment, while the learner has only a  partial view of the state and the expert’s demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Even in the hypothetical  case in which the underlying reward function is known to the learner, its optimal pol-  icy under limited information may not yield the same behavior as an expert with full  information due to such information asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The second challenge is due to the computational complexity of policy synthesis in  POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Indeed, many standard IRL techniques rely on a subroutine that solves the  so-called forward problem, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', computing an optimal policy for a given reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Solv-  ing the forward problem for POMDPs is significantly more challenging than MDPs,  both theoretically and practically [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Optimal policies for POMDPs may require infi-  nite memory of observations [17], whereas memoryless policies are enough for MDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  An additional limitation in existing IRL techniques is due to the limited expressiv-  ity and often impracticability of state-based reward functions in representing complex  tasks [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For example, it will be tremendously difficult to define a merely state-based  reward function to describe requirements such as “do not steer off the road while reach-  ing the target location and coming back to home” or “monitor multiple locations with  a certain order”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, such requirements can be concisely and precisely speci-  fied in temporal logic [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Therefore, recent work has demonstrated the utility of  incorporating temporal logic specifications into IRL in MDPs [21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  In this work, we address these challenges and limitations in state-of-the-art IRL  techniques by investigating the following problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Task-Guided IRL in POMDPs: Given a POMDP, a set of expert demonstrations,  and, if available, a task specification expressed in temporal logic, learn a policy  along with the underlying reward function that maximizes the causal entropy of  the induced stochastic process, induces a behavior similar to the expert’s, and  ensures the satisfaction of the specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We highlight two parts of the problem statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Using causal entropy as an opti-  mization criterion instead of traditional entropy results in a least-committal policy that  induces a behavior obtaining the same accumulated reward as the expert’s demonstra-  tions while making no additional assumptions about the demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Task specifi-  2  cations given as task requirements guide the learning process by describing the feasible  behaviors and allow the learner to learn performant policies with respect to the task re-  quirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Such specifications can be interpreted as side information available to  the learner a priori in addition to the demonstrations aimed at partially alleviating the  information asymmetry between the expert and the learner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Specifically, we tackle the IRL on POMDPs problem by a reformulation into a  maximum causal entropy (MCE) problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, we develop a new solver for the  MCE problem that improves computational tractability over existing approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The  developed solver can enforce prior task knowledge expressed as temporal logic specifi-  cations, which guides the learning, improves the data efficiency, and partially alleviates  the information asymmetry problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Most existing work on IRL relies on entropy as a measure of the likelihood of the  demonstrations, yet, when applied to stochastic MDPs, has to deal with nonconvex  optimization problems [8, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On the other hand, IRL techniques that adopt causal  entropy as the measure of likelihood enjoy formulations based on convex optimiza-  tion [9, 10, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We show similar algorithmic benefits in maximum-causal-entropy  IRL carry over from MDPs to POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  A major difference between MDPs and POMDPs in maximum-causal-entropy IRL  is, though, due to the intrinsic nonconvexity of policy synthesis in POMDPs, which  yields a formulation of the task-guided IRL problem as a nonconvex optimization  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' It is known that this nonconvexity severely limits the scalability for syn-  thesis in POMDPs [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We develop an iterative algorithm that solves the resulting  nonconvex problem in a scalable manner by adapting sequential convex programming  (SCP) [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  In each iteration, it linearizes the underlying nonconvex problem  around the solution from the previous iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The algorithm introduces several ex-  tensions to alleviate the errors resulting from the linearization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' One of these extensions  is a verification step not present in existing SCP schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We show that the proposed  algorithm computes a sound and locally optimal solution to the task-guided problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Additionally, we empirically demonstrate that the algorithm scales to POMDPs  with tens of thousands of states as opposed to tens of states in most existing work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  In POMDPs, finite-memory policies that are functions of the history of the observa-  tions outperform memoryless policies [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Besides, computing a finite-memory pol-  icy for a POMDP is equivalent to computing a memoryless policy on a larger product  POMDP [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Thus, we leverage the scalability of our algorithm to compute more per-  formant policies that incorporate memory using finite-state controllers [28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On the  other hand, the existing IRL techniques on POMDPs aforementioned cannot effectively  utilize memory, as they do not scale to large POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We demonstrate the applicability of the approach through several examples, in-  cluding a simulated wheeled ground robot operating in a high-fidelity, continuous, 3-  D Unity simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We show that, without task specifications, the developed algo-  rithm can compute more performant policies than a straight adaptation of the original  GAIL [30] to POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, we demonstrate that by incorporating task specifications  into the IRL procedure, the learned reward function and policy accurately describe  the behavior of the expert while outperforming the policy obtained without the task  specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We observe that with more limited data, the performance gap becomes  more prominent between the learned policies with and without using task specifica-  3  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Most importantly, we empirically demonstrate the scalability of our approach  for solving the forward problem through extensive comparisons with several state-of-  the-art POMDP solvers and show that on larger POMDPs, the algorithm can compute  more performant policies in significantly less time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Preliminaries  The following section provides a review of prerequisite understanding for POMDPs,  their accompanying policies and how a POMDP’s belief over states is updated using  Bayesian techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We denote the set of nonnegative real numbers by R+, the set of all proba-  bility distributions over a finite or countably infinite set X by Distr(X), the set of all  (infinite or empty) sequences x0, x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , x∞ with xi ∈ X by (X)∗ for some set X,  and the expectation of a function g of jointly distributed random variables X and Y by  EX,Y [g(X, Y )].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Partially Observable Markov Decision Process  A partially observable Markov decision process (POMDP) is a framework for mod-  eling sequential interaction between an agent and a partially observable environment,  where the agent cannot perceive its underlying state but must infer it based on the given  noisy observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We define a POMDP by a tuple M = (S, A, P, Z, O, R, µ0, γ), where S,  A, and Z are finite sets of states, actions, and observations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The function  µ0 : S �→ R+ provides the initial distribution of the agent’s state and γ ∈ [0, 1) is  a discount factor over a possibly infinite planning horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' At each decision time, an  agent selects an action α ∈ A and the transition function P : S × A �→ Distr(S)  defines the probability P(s′|s, α) of reaching state s′ ∈ S given the current state s ∈ S  and action α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' After the state transition, the agent receives an observation z′ ∈ Z  according to the function O : S �→ Distr(Z), which defines the probability O(z′|s′)  of perceiving z′ at state s′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The agent also receives a reward function R(s, α) from the  function R : S × A �→ R encoding the task specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In the following, without  loss of generality, we consider infinite-horizon problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' An observation-based policy σ : (Z × A)∗ × Z �→ Distr(A) for a POMDP  M maps a sequence of observations and actions to a distribution over actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A M-  finite-state controller (M-FSC) is a tuple C = (Q, qI, η, δ), where Q = {q1, q2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , qM}  is a finite set of memory states, qI is the initial memory state, η : Q×Z �→ Distr(A) is  a decision function, and δ : Q × Z × A �→ Distr(Q) is a memory transition function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The action mapping η(n, z) takes a FSC memory state n and an observation z ∈ Z,  and returns a distribution over the POMDP actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The memory update δ(n, z, α) re-  turns a distribution over memory states and is a function of the action α selected by η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  An FSC induces an observation-based policy by following a joint execution of these  two functions upon a trace of the POMDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' An FSC is memoryless if there is a single  4  memory state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Memoryless FSCs, denoted by σ: Z → Distr(A), are observation-  based policies, where σ(α|z) = σz,α is the probability of taking the action α given  solely observation z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Remark 1 (REDUCTION TO MEMORYLESS POLICIES).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In the remainder of the pa-  per, for ease of notation, we synthesize optimal M-FSCs for POMDPs (so-called for-  ward problem) by computing memoryless policies σ on theoretically-justified larger  POMDPs obtained from the so-called product of the memory update δ and the original  POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Indeed, the authors of [27] provide product POMDPs, whose sizes grow  polynomially only with the size of the domain of δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Belief Update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Given a history on the POMDP M as the perceived observation and  executed action sequence τ = {(z0, α0), (z1, α1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , (zT , αT )}, where zi ∈ Z, αi ∈  A, i ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , T} and T is the length of the trajectory, the belief state specifies the  probability of being in each state of the POMDP given an initial belief b0 = µ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Such  a belief state can be updated at each time step using the following Bayes rule  bt+1(s′) =  O(zt|s′) �  s∈S P(s′|s, αt)bt(s)  �  s′′∈S O(zt|s′′) �  s∈S P(s′′|s, αt)bt(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  (1)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Causal Entropy in POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  For a POMDP M, a policy σ induces the stochastic processes Sσ  0:∞ := (Sσ  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , Sσ  ∞),  Aσ  0:∞ := (Aσ  0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , Aσ  ∞), and Zσ  0:∞ := (Zσ  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , Zσ  ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' At each time index t, the ran-  dom variables Sσ  t , Aσ  t , and Zσ  t take values st ∈ S, αt ∈ A, and zt ∈ Z, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The probability P(A0:T ||S0:T ) of A0:T causally-conditioned on S0:T , given  by [10, 31, 32] P(A0:T ||S0:T ) := �T  t=0 P(At|S0:t, A0:t−1), defines a correlation be-  tween the stochastic processes, where each variable At is conditionally influenced by  only the earlier predicted variables S0:t, A0:t−1, and not the future variables St+1:T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Let H(A|S) ≜ EA,S[− log P(A|S)] be the conditional entropy of a random variable  A given a random variable S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In the finite-horizon setting, the causal entropy Hσ in-  duced by a given policy σ is defined as Hσ := EAσ  0:T ,Sσ  0:T [− log P(Aσ  0:T ||Sσ  0:T )] =  �T  t=0 H(Aσ  t |Sσ  0:t, Aσ  0:t−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, the causal entropy in the infinite-horizon setting,  namely the discounted causal entropy [9, 33], is defined as  Hγ  σ :=  �∞  t=0 γtH(Aσ  t |Sσ  0:t, Aσ  0:t−1) =  �∞  t=0 γtEAσ  t ,Sσ  t [− log P(Aσ  t |Sσ  t )],  (2)  where the second equality is due to the Markov property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The entropy of POMDPs (or MDPs) involves the future policy decisions [8],  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', Sσ  t+1:T , at a time index t, as opposed to the causal entropy in POMDPs (or MDPs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Thus, the authors of [8] show that the problem of computing a policy that maximizes  the entropy is nonconvex, even in MDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Inverse reinforcement learning techniques  that maximize the entropy of the policy rely on approximations or assume that the tran-  sition function of the MDP is deterministic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On the other hand, computing a policy that  maximizes the causal entropy can be formulated as a convex optimization problem in  MDPs [10, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' LTL Specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We use general linear temporal logic (LTL) to express complex task specifications  on the POMDP M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Given a set AP of atomic propositions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', Boolean variables  with truth values for a given state s or observation z, LTL formulae are constructed  inductively as following:  ϕ := true | a | ¬ϕ | ϕ1 ∧ ϕ2 | Xϕ | ϕ1Uϕ2,  where a ∈ AP, ϕ, ϕ1, and ϕ2 are LTL formulae, ¬ and ∧ are the logic negation and  conjunction, and X and U are the next and until temporal operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Besides, temporal  operators such as always (G) and eventually (F) are derived as Fϕ := trueUϕ and  Gϕ := ¬F¬ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We denote by Prσ  M(ϕ) the probability of satisfying the LTL formula ϕ  when following the policy σ on the POMDP M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A detailed description of the syntax  and semantics of LTL is beyond the scope of this paper and can be found in [20, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Problem Formulation  In this section, we formulate the problem of task-guided inverse reinforcement  learning (IRL) in POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Given a POMDP M with an unknown reward function  R, we seek to learn a reward function R along with an underlying policy σ that in-  duces a behavior similar to the expert demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We define an expert trajectory on the POMDP M as the perceived observation and  executed action sequence τ = {(z0, α0), (z1, α1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , (zT , αT )}, where zi ∈ Z and  αi ∈ A for all i ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , T}, and T denotes the length of the trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Similarly to  [34], we assume given or we can construct from τ (via Bayesian belief updates (1)) the  belief trajectory bτ = {b0 := µ0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , bT }, where bi(s) is the estimated probability of  being at state s at time index i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In the following, we assume that we are given a set of  belief trajectories D = {bτ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , bτN } from trajectories τ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , τN, where N denotes  the total number of underlying trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We parameterize the unknown reward function R by a differentiable function (with  respect to the parameter) Rθ : S × A �→ Rd, where θ ∈ RF is a parameter that defines  uniquely the reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Such an encoding includes traditional representations of  the reward such as Rθ(s, α) = gθ(φ(s, α)), where φ : S × A �→ Rd is a known vector  of basis functions with components referred to as feature functions, d is the number  of features, and gθ can be any function approximator such as neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For  example, in the traditional linear encoding, we have gθ(z) = θTz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Specifically, we seek for a parameter θ defining Rθ and a policy σ such that its  discounted return expectation Rθ  σ matches an empirical discounted return expectation  ¯Rθ of the expert demonstration D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' That is, we have that Rθ  σ = ¯Rθ, where  Rθ  σ :=  ∞  �  t=0  γtESσ  t ,Aσ  t [Rθ(Sσ  t , Aσ  t )|σ] and ¯Rθ = 1  N  �  bτ ∈D  �  bi∈bτ  γi �  s∈S  bi(s)Rθ(s, αi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  In the case of linear encoding of the reward, the above condition is called feature match-  ing expectation, and it can be simplified by replacing Rθ with the feature function φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  6  Nevertheless, the problem is ill-posed and there may be infinitely many reward  functions and policies that can satisfy the above matching condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' To resolve the  ambiguities, we seek for a policy σ that also maximizes the discounted causal entropy  Hγ  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We now define the problem of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Problem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Given a reward-free POMDP M, a demonstration set D, and a feature φ,  compute a policy σ and weight θ such that (a) The matching condition holds;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' (b) The  causal entropy Hγ  σ given by (2) is maximized by σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Furthermore, we seek to incorporate, if available, a priori high-level side informa-  tion on the task demonstrated by the expert in the design of the reward and policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Problem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Given a linear temporal logic formula ϕ, compute a policy σ and weight  θ such that the constraints (a) and (b) in Problem 1 are satisfied, and Prσ  M(ϕ) ≥ λ for  a given parameter λ ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Although the parameter λ that specifies the threshold for satisfaction of ϕ is as-  sumed to be given, the approach can easily be adapted to compute the optimal λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Nonconvex Formulation for IRL in POMDPs  In this section, we formulate Problem 1 and Problem 2 as finding saddle points of  a nonconvex functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, we propose an algorithm based on solving a nonconvex  optimization problem to compute such saddle points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We emphasize (see Remark 1)  that we compute M-FSC for POMDPs by computing memoryless policies σ on larger  product POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Indeed, in the remainder of the paper, we reason directly on the  product POMDP, which is the product of a POMDP and an FSC, and it yields a POMDP  with state memory pairs [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Substituting Visitation Counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We eliminate the (infinite) time dependency in Hγ  σ  and the matching condition by a substitution of variables involving the policy-induced  discounted state visitation count µγ  σ : S �→ R+ and state-action visitation count νγ  σ :  S×A �→ R+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For a policy σ, state s, and action α, the discounted state and state-action  visitation counts are defined by  µγ  σ(s) := ESt[  ∞  �  t=1  γt1{St=s}|σ] and νγ  σ(s, α) := EAt,St[  ∞  �  t=1  γt1{St=s,At=α}|σ],  where 1{·} is the indicator function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' From these definitions, it is straightforward to  deduce that νγ  σ(s, α) = πs,αµγ  σ(s), where πs,α = P[At = a|St = s].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' It is also  straightforward to check that for all s ∈ S and α ∈ A, µγ  σ(s) ≥ 0, νγ  σ(s, α) ≥ 0, and  µγ  σ(s) = �  α∈A νγ  σ(s, α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We first provide a concave expression for the discounted causal entropy Hγ  σ as a  7  function of the visitation counts µγ  σ and νγ  σ:  Hγ  σ :=  �∞  t=0 γtESσ  t ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Aσ  t [− log(πst,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='αt)]  =  �∞  t=0  �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A −(log πs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)πs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='αγtP[Sσ  t = s]  =  �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A −(log πs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)πs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='αµγ  σ(s)  =  �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A − log νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  µγ  σ(s) νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  (3)  where the first equality is due to the definition of the discounted causal entropy Hγ  σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  the second equality is obtained by expanding the expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The third and fourth  equalities follow by the definition of the state visitation count µγ  σ, and the state-action  visitation count νγ  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We prove in the appendix that the above expression is indeed  concave in the visitation counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Next, we obtain a linear expression in νγ  σ for the  discounted return expectation Rθ  σ as:  Rθ  σ =  ∞  �  t=0  �  (s,α)∈S×A  Rθ(s, α)γtP[Sσ  t = s, Aσ  t = α]  =  �  (s,α)∈S×A  Rθ(s, α)νγ  σ(s, α),  (4)  where the second equality is obtained by the definition of the visitation count νγ  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The  following nonconvex constraint in µγ  σ(s) and σz,α ensures observation-based policies:  νγ  σ(s, α) = µγ  σ(s)  �  z∈Z O(z|s)σz,α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  (5)  Finally, the variables for the discounted visitation counts must satisfy the so-called  Bellman flow constraint [9] to ensure that the policy is well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For each state  s ∈ S,  µγ  σ(s) = µ0(s) + γ  �  s′∈S  �  α∈A  P(s|s′, α)νγ  σ(s′, α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  (6)  Saddle Point Formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Computing a policy σ that satisfies the return matching  constraint Rθ  σ = ¯Rθ might be infeasible due to ¯Rθ being an empirical estimate from  the finite set of demonstrations D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Additionally, the feature matching constraint might  also be infeasible due to the information asymmetry between the expert and the learner,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', the expert has full observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We build on a saddle point computation problem to incorporate the return matching  constraints into the objective of the forward problem, similar to other IRL algorithms  in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Specifically, the desired weight vector θ and policy σ of Problem 1  and Problem 2 are the solutions of minθ f(θ) := maxσ Hγ  σ +(Rθ  σ − ¯Rθ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The function  f corresponds to the inner optimization problem when the reward parameter is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  That is, f(θ) computes a policy σ that maximizes the sum Hγ  σ + Rθ  σ of the causal  8  Algorithm 1 Compute the weight vector θ and policy σ solution of the Lagrangian  relaxation of the IRL problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Input: Feature expectation ¯Rφ from D, initial weight θ0, step size η : N �→ R+, and  (if available) a priori side information ϕ and λ ∈ [0, 1] imposing Prσ  M(ϕ) ≥ λ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  1: σ0 ← uniform policy  ▷ Initialize uniform policy  2: for k = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , do  ▷ Compute θ via gradient descent  3:  σk+1 ← SCPForward(θk, σk, ϕ, λ)  ▷ Solve the forward problem (7)–(9)  with optional ϕ and λ  4:  θk+1 ← θk − η(k)∇θf(θk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' σk+1)  ▷ Gradient step  5: end for  6: return σk, θk  entropy and the current estimate of the reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In other words, f(θ) returns  the solution to the forward problem, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', finding optimal policy on the POMDP when  the entropy term is removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Algorithm 1 updates the reward weights by using gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Initially, the  policy σ0 is a random uniform variable and the weight θ0 is a nonzero vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' At  iteration k ≥ 0, the policy σk+1 = arg maxσ Hγ  σ + (Rθk  σ − ¯Rθk) is the optimal policy  on the POMDP under the current reward estimate Rθk given by θk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' That is, σk+1 is the  solution to the forward problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, to update the weight θ, Algorithm 1 computes  the gradient ∇θf with respect to θ as follows:  ∇θf(θ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' σ) =  �  s,α∈S×A  νγ  σ(s, α)∇θRθ(s, α) − 1  N  �  bτ ∈D  �  bi∈bτ  γi �  s∈S  bi(s)∇θRθ(s, αi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We develop the algorithm SCPForward, presented in next section, to solve the  forward problem, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', computing σk+1 given θk, in an efficient and scalable manner  while incorporating high-level task specifications to guide the learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Nonconvex Formulation of the Forward Problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Given a weight vector θk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' we take  advantage of the obtained substitution by the expected visitation counts to formulate  the forward problem associated to Problem 1 as the nonconvex optimization problem:  maximize  µγ  σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='νγ  σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='σ  �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A  − log νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  µγ  σ(s) νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) +  �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A  Rθk(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  (7)  subject to  (5) − (6),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  ∀(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) ∈ S × A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' µγ  σ(s) ≥ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) ≥ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  (8)  ∀(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) ∈ S × A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' µγ  σ(s) =  �  α∈A νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  (9)  where the source of nonconvexity is from (5),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' and we remove the constant − ¯Rθk from  the cost function of the above optimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  9  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Sequential Linear Programming Formulation  We develop an algorithm, SCPForward, adapting a sequential convex program-  ming (SCP) scheme to efficiently solve the nonconvex forward problem (7)–(9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In-  deed, SCPForward involves a verification step to compute sound policies and visi-  tation counts, which is not present in the existing SCP schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Additionally, we de-  scribe in the next section how to take advantage of high-level task specification (Prob-  lem 2) through slight modifications of the obtained optimization problem solved by  SCPForward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Linearizing Nonconvex Optimization Problem  SCPForward iteratively linearizes the nonconvex constraints in (5) around a pre-  vious solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, the linearization may result in an infeasible or unbounded  linear subproblem [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We first add slack variables to the linearized constraints to  ensure feasibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The linearized problem may not accurately approximate the non-  convex problem if the solutions to this problem deviate significantly from the previous  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Thus, we utilize trust region constraints [25] to ensure that the linearization is  accurate to the nonconvex problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' At each iteration, we introduce a verification step  to ensure that the computed policy and visitation counts are not just approximations but  actually satisfy the nonconvex policy constraint (5), improves the realized cost function  over past iterations, and satisfy the temporal logic specifications, if available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Linearizing Nonconvex Constraints and Adding Slack Variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We linearize the  nonconvex constraint (5), which is quadratic in µγ  σ(s) and σz,α, around the previously  computed solution denoted by ˆσ, µγ  ˆσ, and νγ  ˆσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, the linearized constraints may  be infeasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We alleviate this drawback by adding slack variables ks,α ∈ R for  (s, α) ∈ S × A, which results in the affine constraint:  νγ  σ(s, α) + ks,α = µγ  ˆσ(s)  �  z∈Z O(z|s)σz,α +  (10)  �  µγ  σ(s) − µγ  ˆσ(s)  � �  z∈Z O(z|s)ˆσz,α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Trust Region Constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The linearization may be inaccurate if the solution deviates  significantly from the previous solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We add following trust region constraints to  alleviate this drawback:  ∀(z, α) ∈ Z × A,  ˆσz,α/ρ ≤ σz,α ≤ ˆσz,αρ,  (11)  where ρ is the size of the trust region to restrict the set of allowed policies in the lin-  earized problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We augment the cost function in (7) with the term −β �  (s,α)∈S×A ks,α  to ensure that we minimize the violation of the linearized constraints, where β is a large  positive constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  10  Linearized Problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally, by differentiating x �→ x log x and y �→ x log(x/y),  we obtain the coefficients required to linearize the convex causal entropy cost function  in (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Thus, we obtain the following linear program (LP):  maximize  µγ  σ,νγ  σ,σ  �  (s,α)∈S×A −  �  βks,α −  �νγ  ˆσ(s, α)  µγ  ˆσ(s)  �  µγ  σ(s)  +  �  log νγ  ˆσ(s, α)  µγ  ˆσ(s)  + 1  �  νγ  σ(s, α)  �  +  �  (s,α)∈S×A  Rθk(s, α)νγ  σ(s, α) (12)  subject to  (6), (8) − (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Verification Step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' After each iteration, the linearization might be inaccurate, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e, the  resulting policy ˜σ and potentially inaccurate visitation counts ˜νγ  ˜σ, ˜µγ  ˜σ might not be fea-  sible to the nonconvex policy constraint (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' As a consequence of the potential infea-  sibility, the currently attained (linearized) optimal cost might significantly differ from  the realized cost by the feasible visiation counts for the ˜σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Additionally, existing SCP  schemes linearizes the nonconvex problem around the previously inaccurate solutions  for ˜νγ  ˜σ, and ˜µγ  ˜σ, further propagating the inaccuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The proposed verification step  solves these issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Given the computed policy ˜σ, SCPForward computes the unique  and sound solution for the visitation count µγ  ˜σ by solving the corresponding Bellman  flow constraints:  µγ  ˜σ(s) =µ0(s) + γ  �  s′∈S  �  α∈A  P(s|s′, α)µγ  ˜σ(s′)  �  z∈Z  O(z|s)˜σz,α,  (13)  for all s ∈ S, and where µγ  ˜σ ≥ 0 is the only variable of the linear program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then,  SCPForward computes νγ  ˜σ(s, α) = µγ  ˜σ(s′) �  z∈Z O(z|s)˜σz,α and the realized cost  at the current iteration is defined by  C(˜σ, θk) =  �  (s,α)∈S×A  − log νγ  ˜σ(s, α)  µγ  ˜σ  νγ  ˜σ(s, α) +  �  (s,α)∈S×A  Rθk(s, α)νγ  ˜σ(s, α),  (14)  where we assume 0 log 0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally, if the realized cost C(˜σ, θk) does not improve  over the previous cost C(ˆσ, θk), the verification step rejects the obtained policy ˜σ, con-  tracts the trust region, and SCPForward iterates with the previous solutions ˆσ, µγ  ˆσ,  and νγ  ˆσ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Otherwise, the linearization is sufficiently accurate, the trust region is ex-  panded, and SCPForward iterates with ˜σ, µγ  ˜σ and νγ  ˜σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' By incorporating this verifica-  tion step, we ensure that SCPForward always linearizes the nonconvex optimization  problem around a solution that satisfies the nonconvex constraint (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Incorporating High-Level Task Specifications  Given high-level side information on the agent tasks as the LTL formula ϕ, we first  compute the product of the POMDP and the ω-automaton representing ϕ to find the  set T ⊆ S of states, called target or reach states, satisfying ϕ with probability 1 by  11  using standard graph-based algorithms as a part of preprocessing step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We refer the  reader to [19] for a detailed introduction on how LTL specifications can be reduced to  reachability specifications given by T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  As a consequence, the probability of satisfying ϕ is the sum of the probability of  reaching the target states s ∈ T , which are given by the undiscounted state visitation  count µsp  σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' That is, Prσ  M(ϕ) = �  s∈T µsp  σ (s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Unless γ = 1, µsp  σ  ̸= µγ  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Thus,  we introduce new variables µsp  σ , νsp  σ , and the adequate constraints in the linearized  problem (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Incorporating Undiscounted Visitation Variables to Linearized Problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We append  new constraints, similar to (8), (9), and (10), into the linearized problem (12), where  the variables µγ  σ, νγ  σ, ks,α, µγ  ˆσ, νγ  ˆσ are replaced by µsp  σ , νsp  σ , ksp  s,α, µsp  ˆσ , νsp  ˆσ , respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Further, we add the constraint  µsp  σ (s) = µ0(s) +  �  s′∈S\\T  �  α∈A  P(s|s′, α)νsp  σ (s′, α),  (15)  which is a modification of the Bellman flow constraints such that µsp  σ (s) for all s ∈ T  only counts transitions from non-target states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally, we penalize the introduced slack  variables for feasibility of the linearization by augmenting the cost function with the  term −β �  (s,α)∈S×A ksp  s,α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Relaxing Specification Constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' To incorporate the probability of satisfying the  specifications, We add the following constraint to the linearized problem:  (spec) :=  �  s∈T  µsp  σ (s) + Γsp ≥ λ,  (16)  where we introduce Γsp ≥ 0 as a slack variable ensuring that the linearized problem  is always feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Further, we augment the cost function with −βspΓsp to penalize  violating ϕ, where βsp is a positive hyperparameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Updating Verification Step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We modify the previously-introduced realized cost C(˜σ, θk)  to penalize when the obtained policy does not satisfy the specification ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' This cost also  accounts for the linearization inaccuracy of the new policy constraint due to σ, µsp  σ ,  and νsp  σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' At each iteration, SCPForward computes the accurate µsp  ˜σ of current pol-  icy ˜σ through solving a feasibility LP with constraints given by the modified Bellman  flow constraints (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, it augments Csp  ˜σ = min{0, (�  s∈T µsp  ˜σ (s) − λ)βsp} to the  realized cost to take the specification constraints into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Convergence to Local Optimum Solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The convergence guarantees of the pro-  posed sequential convex scheme with trust regions follow straightforwardly from the  general convergence of sequential convex programming (SCP) schemes as proved in  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='14 and Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='7 of [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Specifically, weak convergence is ensured as  the SCP algorithm generates a set of convergent subsequences, all of which satisfy the  first-order conditions [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' This is not convergence in its strict sense due to potential  oscillation between several limit points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Still, surprisingly most of the convergence  12  Algorithm 2 SCPForward: Linear programming-based algorithm to solve the for-  ward problem (7)–(9), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', compute a policy σk+1 that maximizes the causal entropy,  considers the matching constraint, and satisfies the specifications, if available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Input: Current weight estimate θk, current best policy ˆσ = σk, side information ϕ  and λ, trust region ρ > 1, penalization coefficients β, βsp ≥ 0, constant ρ0 to  expand or contract trust region, and a threshold ρlim for trust region contraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  1: Find µγ  ˆσ via linear constraint (13) and νγ  ˆσ = µγ  ˆσ(s′) �  z∈Z O(z|s)ˆσz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' given ˆσ ▷  Realized visitation counts  2: Find µsp  ˆσ via linear constraint (15) with νsp  ˆσ = µsp  ˆσ (s′) �  z∈Z O(z|s)ˆσz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' given ˆσ  ▷ If ϕ is available  3: Compute the realized cost C(ˆσ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' θk) ← (14) + Csp  ˆσ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' given ˆσ ▷ Add specifications’  violation  4: while ρ > ρlim do  ▷ Trust region threshold  5:  Find optimal ˜σ to the augmented LP (12) via ˆσ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' µγ  ˆσ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' νγ  ˆσ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' µsp  ˆσ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' νsp  ˆσ  ▷ We  augment the LP with constraints (8),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' (9),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' (10),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' (15),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' and (16) induced by µsp  σ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' νsp  σ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  and by adding −β �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A ksp  s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α − βspΓsp to the cost (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  6:  Compute the realized µγ  ˜σ, νγ  ˜σ,µsp  ˜σ , νsp  ˜σ , and C(˜σ, θk) via ˜σ as in lines 1–3  7:  {ˆσ ← ˜σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' ρ ← ρρ0} if C(˜σ, θk) ≥ C(ˆσ, θk) else {ρ ← ρ/ρ0}  ▷ Verification  step  8: end while  9: return σk+1 := ˆσ  claims of nonlinear optimization schemes fall into this category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Furthermore, under  the right regularity assumptions on the cost function, the authors of [25] proved that  SCP schemes with trust regions can converge to a local optimum solution with a super-  linear convergence rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Numerical Experiments  We evaluate the proposed IRL algorithm on several POMDP instances from [35],  and a simulated wheeled ground robot operating in a high-fidelity, continuous, and 3-D  Unity simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We first compare our IRL algorithm with a straightforward variant  of GAIL [30] adapted for POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, we provide results on the data-efficiency  of the proposed approach when taking advantage of side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally, we  demonstrate the scalability of the routine SCPForward for solving the forward prob-  lem through comparisons with state-of-the-art solvers such as SolvePOMDP [36],  SARSOP [37], PRISM-POMDP [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We provide the code for reproducibility of the  results in this paper at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='com/wuwushrek/MCE IRL POMDPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Simulation on Hand-Crafted POMDP Instances  We first evaluate the proposed IRL algorithm on several POMDP instances ex-  tracted from the work [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  13  1  2  3  4  5  6  9  12  7  10  13  8  11  14  Figure 1: Some examples from the benchmark set provided in [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' From left to right, we have the Maze,  Avoid, and Evade environments, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Benchmark Set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The POMDP instances are as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Evade is a turn-based game  where the agent must reach a destination without being intercepted by a faster player.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  In Avoid, the agent must avoid being detected by two other moving players following  certain preset, yet unknown routes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In Intercept, the agent must intercept another player  who is trying to exit a gridworld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In Rocks, the agents must sample at least one good  rock over the several rocks without any failures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In Obstacle, an agent must find an exit  in a gridworld without colliding with any static obstacles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In these instances, the agent  only observes a fixed radius around its current position, see Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally, in Maze,  the agent must exit a maze as fast as possible while observing only the walls around it  and should not get stuck in any of the trap states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Variants of Learned Policies and Experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We refer to four types of policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The  type of policy depends on whether it uses side information from a temporal specifi-  cation ϕ or not, and whether it uses a memory size M = 1 or M = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We also  consider two types of experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The first expert has full information about the envi-  ronment and computes an optimal policy in the underlying MDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The second expert  has partial observation and computes a locally optimal policy in the POMDP with a  memory size of M = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Recall that the agent always has partial information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' There-  fore, the first type of expert corresponds to having information asymmetry between the  learning agent and expert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Besides, we consider as a baseline a variant of GAIL where  we learn the policy on the MDP without side information, and extend it to POMDPs  via an offline computation of the belief in the states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Specifically, we find the optimal  policy on the MDP by solving the convex optimization problem corresponding to the  forward problem on MDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The resulting policy is a state-based policy that needs to  be transformed in order to act on a POMDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The transformation is done by exploiting  the expert demonstrations to construct a belief state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' That is, the trajectories τ of the  expert are used in a Bayesian belief updates (1) to estimate the probability of being in  each state of the POMDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Thus, by combining the computed belief and the state-based  policy, we obtain an observation-based policy for the POMDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Doing so could provide  a significant advantage to the GAIL variant since the state-based policy is the optimal  policy on the MDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, despite the high performance in practice, the policy on  the POMDP is generally suboptimal, even if the MDP policy were optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We discuss the effect of side information and memory in the corresponding policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  While we detail only on the Maze example, where the agent must exit a maze as fast as  possible, we observe similar patterns for other examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Detailed results for the other  examples are provided in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  14  A low state-space Avoid instance  0  1  2  3  4  5  x=0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='y=0  0  X=2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='y=2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='d=E  X=0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='y=4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='d=E  1  west  east  2  north  south  3  adv  placement  5  XA low state-space Evade instance  0  1  2  3  4  5  x=1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='y=0  0  x=2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='y=3  1  scan  adv  2  north  east  3  placement  west  south  4  5  XNo information asymmetry  Under information asymmetry  GAIL  0  25  50  75  100  −20  0  20  40  60  Finite-memory policy  Without side  information  Rθ  σ  0  25  50  75  100  Memoryless policy  0  25  50  75  100  −20  0  20  40  60  Time Steps  With side  information  Rθ  σ  0  25  50  75  100  Time Steps  Figure 2: Representative results on the Maze example;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' each sub-figure represents the average accumulated  reward under the true reward function (Rθ  σ) over 1000 runs as a function of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Compare the two rows:  The policies in the top row that do not utilize side information suffer a performance drop under information  asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On the other hand, in the bottom row, the performance of policies incorporating side information  into learning does not decrease under information asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Compare the two columns: The performance  of the finite-memory policies in the left column is significantly better than memoryless policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Except for  the memoryless policies without side information, our algorithm outperforms GAIL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The expert reward on  the MDP is in average 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='22, while we obtain the value 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='83 for an expert acting on the POMDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Maze Example  The POMDP M is specified by S = {s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , s14} corresponding to the cell labels  in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' An agent in the maze only observes whether or not there is a wall (in blue)  in a neighboring cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' That is, the set of observations is O = {o1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' , o6, o7}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For  example, o1 corresponds to observing west and north walls (s1), o2 to north and south  walls (s2, s4), and o5 to east and west walls (s6, s7, s8, s9, s10, s11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The observations  o6 and o7 denote the target state (s13) and bad states(s12, s14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The transition model is  stochastic with a probability of slipping p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Further, the states s13 and s14 lead to  the end of the simulation (trapping states).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  In the IRL experiments, we consider three feature functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We penalize taking  more steps with φtime(s, α) = −1 for all s, α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We provide a positive reward when  reaching s13 with φtarget(s, α) = 1 if s = s13 and φtarget(s, α) = 0 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We  penalize bad states s12 and s14 with φbad(s, α) = −1 if s = s12 or s = s14, and  φbad(s, α) = 0 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally, we have the LTL formula ϕ = G ¬ bad as the  task specification, where bad is an atomic proposition that is true if the current state  s = s12 or s = s14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We constrain the learned policy to satisfy Prσ  M(G ¬ bad) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Side Information Alleviates the Information Asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Figure 2 shows that if there  is an information asymmetry between the learning agent and the expert, the policies  that do not utilize side information suffer a significant performance drop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The policies  15  With side information  Without side information  GAIL  0  75  150  225  300  −20  0  20  40  Time Steps  Total Reward  Figure 3: Representative results on the Avoid example showing the reward of the policies under the true  reward function (Rθ  σ) versus the time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  that do not incorporate side information into learning obtain a lower performance by  57% under information asymmetry, as shown in the top row of Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On the other  hand, as seen in the bottom row of Figure 2, the performance of the policies that use  side information is almost unaffected by the information asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Memory Leads to More Performant Policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The results in Figure 2 demonstrate that  incorporating memory into the policies improves the performance, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', the attained  reward, in all examples, both in solving the forward problem and learning policies  from expert demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Incorporating memory partially alleviates the effects of  information asymmetry, as the performance of the finite-memory policy decreases by  18% under information asymmetry as opposed to 57% for the memoryless policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We see that in Table 1, incorporating memory into policy on the Maze and Rocks  benchmarks, allows SCPForward to compute policies that are almost optimal, evi-  denced by obtaining almost the same reward as the solver SARSOP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Side Information Improves Data Efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Figure 4 shows that even on a low data  regime, learning with task specifications achieves significantly better performance than  without the task specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  5  10  15  20  30  40  Number of trajectories  Total reward  Without LTL  With LTL  Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Rew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' POMDP  5  10  15  40  42  44  46  Number of trajectories  Figure 4: We show the data efficiency of the proposed approach through the total reward obtained by the  learned policies as a function of the number of expert demonstrations (No information asymmetry).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The  figure on the left shows the performance of learning memoryless policies, while the figure on the right shows  the performance of a 5-FSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  16  SCPForward  SARSOP  SolvePOMDP  Problem  |S|  |S × O|  |O|  Rθ  σ  Time (s)  Rθ  σ  Time (s)  Rθ  σ  Time (s)  Maze  17  162  11  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='83  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='24  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='83  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='33  Maze (3-FSC)  49  777  31  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='6  NA  NA  NA  NA  Maze (10-FSC)  161  2891  101  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='32  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='04  NA  NA  NA  NA  Obstacle[10]  102  1126  5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='71  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='79  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='02  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='05  3600  Obstacle[10](5-FSC)  679  7545  31  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='77  38  NA  NA  NA  NA  Obstacle[25]  627  7306  5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='59  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='22  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='05  3600  Rock  550  4643  67  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='68  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='2  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='83  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='05  −  −  Rock (3-FSC)  1648  23203  199  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='8  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='25  NA  NA  −  −  Rock (5-FSC)  2746  41759  331  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='82  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='84  NA  NA  −  −  Intercept[5, 2, 0]  1321  5021  1025  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='83  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='28  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='83  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='71  −  −  Intercept[5, 2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1]  1321  7041  1025  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='81  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='18  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='81  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='19  −  −  Evade[5, 2, 0]  2081  13561  1089  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='3  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='25  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='3  3600  −  −  Evade[5, 2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1]  2081  16761  1089  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='79  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='25  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='28  3600  −  −  Evade[10, 2, 0]  36361  341121  18383  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='97  3600  −  −  −  −  Avoid[4, 2, 0]  2241  5697  1956  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='86  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='74  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='86  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='19  −  −  Avoid[4, 2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1]  2241  8833  1956  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='86  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='63  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='86  210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='47  −  −  Avoid[7, 2, 0]  19797  62133  3164  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='72  3503  −  −  −  −  Table 1: Results for the benchmark sets for solving the forward problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On larger benchmarks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', Evade  and Avoid), SCPForward can compute locally optimal policies, while the other solvers fail to provide  solutions in the given time limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In the environments Obstacle[n], Intercept[n, r, slip], Evade[n, r, slip],  and Avoid[n, r, slip], the parameters n, r, and slip are the size of the gridworld, the view radius of the agent,  and the probability of slippery, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We set the time-out to 3600 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' An empty cell (denoted by  −) represents the solver failed to compute any policy before the time-out, while NA refers to not applicable  due to the approach being based on belief updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Side Information Improves Performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Besides, in a more complicated environ-  ment such as Avoid, Figure 3 shows that task specifications are crucial to hope even  to learn the task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Specifically, Avoid[n, r, slip] is a turn-based game, where the agent  must reach an exit point while avoiding being detected by two other moving players  following certain predefined yet unknown routes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The agent can only observe the play-  ers if they are within a fixed radius from the agent’s current position when the action  scan is performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Besides, with the players’ speed being uncertain, their position in  the routes can not be inferred by the agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The parameters n, r, and slip specify the  dimension of the grid, the view radius, and the slippery probability, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We consider four feature functions to parameterize the unknown reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The first  feature provides a positive reward to the agent upon reaching the exit point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The second  feature penalizes the agent if it collides with a player.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The third feature penalizes the  agent if it is detected by a player.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The fourth feature imposes a penalty cost for each  action taken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We encode the side information as the temporal logic task specification  avoid being detected until reaching the exit point with probability greater than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Figure 3 shows that the algorithm is unable to learn without side information while  side information induces a learned policy that is optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Specifically, the learned  policy without side information seems to only focus on avoiding being detected and  collision as the corresponding learned features were close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  17  Figure 5: Left: A simulated Clearpath Warthog operating in a Unity simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Right: A demonstration  provided by an expert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' SCPForward Yields Better Scalability  We highlight three observations regarding the scalability of SCPForward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' First,  the results in Table 1 show that only SARSOP is competitive with SCPForward on  larger POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' SolvePOMDP runs out of time in all but the smallest benchmarks,  and PrismPOMDP runs out of memory in all benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Most of these approaches  are based on updating a belief over the states, which for a large state space can become  extremely computationally expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Second, in the benchmarks with smaller state spaces, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', Maze and Rock, SARSOP  can compute policies that yield better performance in less time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' This is due to the effi-  ciency of belief-based approaches on small-size problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On the other hand, SARSOP  does not scale to larger POMDPs with a larger number of states and observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For  example, by increasing the number of transitions in Intercept benchmark from 5021 to  7041, the computation time for SARSOP increases by 516%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On the other hand, the  increase of the computation time of SCPForward is only 28%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Third, on the largest benchmarks, including tens of thousands of states and obser-  vations, SARSOP fails to compute any policy before time-out, while SCPForward  found a solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally, we also note that SCPForward can also compute a policy  that maximizes the causal entropy and satisfies an LTL specification, unlike SARSOP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Simulation on a Ground Robot  We demonstrate an application of the proposed algorithm in a continuous 3-D Unity  environment containing a ClearPath warthog operating in a semi-structured village.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A  screen shot of the robot operating in this environment and its corresponding trajectory  can be seen in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' This environment contains a variety of obstacles including  buildings, trees, and vehicles as well as three terrain types describing our features, φ,  grass, gravel, and road.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The simulated environment operates in a state space consisting  of 3350 states, 33254 transitions and 944 total observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' This simulation is used to  18  0  5  10  15  20  25  30  0  10  20  30  grass  gravel  road  unknown  Figure 6: Gridworld representation of the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The figure shows the area of the unity environment  where we applied the developed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  gather data for training, and test an agent’s ability to follow a policy from the learned  reward function in two experimental scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In this experiment, we demonstrate  the agent’s ability to learn a reward function from demonstrations that are sub-optimal  with respect to a known, true reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We also show how the learned policies  perform compared to the optimal policies with full and partial observations obtained  by solving the MDP or POMDP problem with the true reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The ground vehicle contains an autonomy stack consisting of three main subsys-  tems—mapping, perception, and planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The mapping subsystem based on Omni-  Mapper[?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' ] performs simultaneous localization and mapping (SLAM) using LiDAR  and IMU sensors, providing a map used during planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The perception subsystem  provides pixel level semantic segmentation for each image in a video stream from a  RGB camera to an ontology of terrain and object classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Each semantic image is  passed to a terrain projection algorithm which builds N binary occupancy feature maps  of the known environment used for reward learning where N is the number of features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The planning subsystem uses the maps produced from previous subsystems and the  trajectory from a learned policy to autonomously navigate to a waypoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Expert Demonstrations and Reward Feature Encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We collected 10 demonstra-  tions of an expert teleoperating a robot to a predetermined waypoint (see Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The expert has an implicit preference to traverse the road followed by grass, and lastly  gravel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Consequently, we encode the unknown reward function as a linear combination  of known features: Rθ = θ1φroad + θ2φgravel + θ3φgrass + θ4φtime + θ5φgoal, where  φi returns a value of 0 when the feature of the corresponding state is not feature i, or  1 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In order to incentivize the shortest path, the feature time penalizes the  number of actions taken in the environment before reaching the waypoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Further-  19  (a) The trajectories resulting from executing each policy  with and without task specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The learner exploit-  ing task specifications (orange) is able to reach one of the  target states, while avoiding the gravel along the path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In  contrast, the learner without side information (purple) fails  to avoid the gravel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  0  100  200  300  −20  0  20  Expert MDP  Expert POMDP  With LTL  Without LTL  (b) Evolution of the cumulative reward obtained by the  learner as a function of the number of environment inter-  actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Expert MDP and Expert POMDP are the opti-  mal policies on the MDP and POMDP, respectively for the  ground truth reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Figure 7: Impact of incorporating task specifications into reward learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  more, goal provides a positive reward upon reaching the waypoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For comparisons  of the learned policy, we use the values θ = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='2, −30, −2, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='5, 50] as the ground  truth reward weight vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We emphasize that the demonstrations are sub-optimal  with respect to the above ground truth reward as the vehicle often traverses gravel,  corresponding to a high penalty reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Modeling Robot Dynamics as POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' From a ground truth map of the environment  in the simulation, we obtain a high-level MDP abstraction of the learner’s behavior on  the entire state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, we impose a partial observability of the robot as follows:  The robot does not see the entire map of the world but only see a fixed radius r = 4  (in terms of the number of grid cells) around its current position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Furthermore, we also  incorporate uncertainty on the sensor classification of terrain features such that with  probability p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='9 the prediction is correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Task Specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In addition to the expert demonstrations, we constrain the learned  policy to satisfy Prσ  M(¬ gravel U goal) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='9, where gravel is an atomic proposition  that is true for states having gravel as its feature, and goal is an atomic proposition that  is true at each target state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Note that this side information does not necessarily enforce  that the learner should reach the set of target states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Instead, if the learner reaches the  target state, it should not drive on gravel with probability at least  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Figure 7a shows how the learner with side information avoids the gravel com-  pared to the learner without side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Figure 7b further illustrates this result by  empirically demonstrating that the proposed approach can efficiently take advantage  of side information to compute policies that matches the expert’s desired behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Specifically, Figure 7b shows that the gain in the total reward of a learner without side  20  information increases by 294% with respect to a learner with side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ad-  ditionally, it is important to note in Figure 6 how the initial state distribution of the  demonstrator trajectories is different from the initial state distribution during the eval-  uation of the learned policies (Figure 7a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Nevertheless, despite these distinctions, the  learned policies can effectively navigate toward points present in the expert demonstra-  tions and then maximally mimic these trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Related work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The closest work to ours is by [34], where they extend classical maximum-margin-  based IRL techniques for MDPs to POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, even on MDPs, maximum-  margin-based approaches cannot resolve the ambiguity caused by suboptimal demon-  strations, and they work well when there is a single reward function that is clearly better  than alternatives [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In contrast, we adopt causal entropy that has been shown [39, 10]  to alleviate these limitations on MDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Besides, [34] rely on efficient off-the-shelf  solvers to the forward problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Instead, this paper also develops an algorithm that  outperforms off-the-shelf solvers and can scale to POMDPs that are orders of magni-  tude larger compared to the examples in [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Further, [34] do not incorporate task  specifications in their formulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  One of the basic challenges in IRL, is that finding a reward function and a policy  that induces a similar behavior to the expert is an ill-defined problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Prior work has  addressed this challenge using maximum margin formulations [40, 41, 42], as well as  probabilistic models to compute a likelihood of the expert demonstrations [43, 8, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We build on the latter approach and build on the maximum-causal-entropy IRL [9,  10, 23], which brings algorithmic benefits to IRL in POMDPs as mentioned in the  introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We note that these maximum-causal-entropy IRL techniques assume that  both the expert and the agent can fully observe the environment, and these approaches  only apply for MDPs as opposed to POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  IRL under partial information has been studied in prior work [2, 44, 45, 46, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Reference [44] considers the setting where the features of the reward function are par-  tially specified as opposed to having partial information over the state of the environ-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The work in [2] considers a special case of POMDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' It only infers a distribution  over the future trajectories of the expert given demonstrations as opposed to computing  a policy that induces a similar behavior to the expert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The works in [45, 46, 47] assume  that the states of the environment are either fully observable, or fully hidden to the  learning agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Therefore, these approaches also consider a special case of POMDPs,  like in [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We also note that none of these methods incorporate side information into  IRL and do not provide guarantees on the performance of the policy with respect to a  task specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The idea of using side information expressed in temporal logic to guide and aug-  ment IRL has been explored in some previous work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In [48, 22], the authors incor-  porate side information as in temporal logic specification to learn policies that induce  a behavior similar to the expert demonstrations and satisfies the specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Refer-  ence [21] iteratively infers an underlying task specification that is consistent with the  expert demonstrations and learns a policy and a reward function that satisfies the task  21  specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, these methods also assume full information for both the expert  and the agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Conclusion  We develop an algorithm for inverse reinforcement learning under partial obser-  vation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We empirically demonstrate that by incorporating task specifications into the  learning process, we can alleviate the information asymmetry between the expert and  the learner while increasing the data efficiency of the learning scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Further, we  empirically demonstrate that our main routine SCPForward, used inside the IRL al-  gorithm, solves the forward problem in a scalable manner and outperforms state-of-  the-art POMDP solvers on instances with a large number of states, observations, and  transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Work Limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' This work assumes that the transition and observation functions of  the POMDP are known to the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Future work will investigate removing this  assumption and developing model-free-based approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We will also integrate the  framework with more expressive neural-network-based reward functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='. Research was sponsored by the Army Research Laboratory and  Office of Naval Research accomplished under cooperative agreement number(s) ARL  W911NF-20-2-0132, ARL W911NF-19-2-0285 and ONR N00014-22-1-2254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The  views and conclusions contained in this document are those of the authors and should  not be interpreted as representing the official policies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' either expressed or implied,  of the Army Research Laboratory, Office of Naval Research, or the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Government.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Government is authorized to reproduce and distribute reprints for Government  purposed notwithstanding any copyright notation herein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  References  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Abbeel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Coates, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ng, Autonomous Helicopter Aerobatics Through  Apprenticeship Learning, The International Journal of Robotics Research 29 (13)  (2010) 1608–1639.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [2] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Kitani, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ziebart, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bagnell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Hebert, Activity Forecasting, in:  European Conference on Computer Vision, Springer, 2012, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 201–214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Hadfield-Menell, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Russell, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Abbeel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Dragan, Cooperative Inverse  Reinforcement Learning, in: NIPS, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Dragan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Srinivasa, A Policy-Blending Formalism for Shared Control,  The International Journal of Robotics Research 32 (7) (2013) 790–805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Osa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Sugita, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Mitsuishi, Online Trajectory Planning in Dynamic Envi-  ronments for Surgical Task Automation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', in: Robotics: Science and Systems,  Citeseer, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  22  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Osa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Sugita, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Mitsuishi, Online Trajectory Planning and Force Control  for Automation of Surgical Tasks, IEEE Transactions on Automation Science and  Engineering 15 (2) (2017) 675–691.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [7] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finn, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Levine, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Abbeel, Guided Cost Learning: Deep Inverse Optimal Con-  trol via Policy Optimization, in: International conference on machine learning,  PMLR, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 49–58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ziebart, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Maas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bagnell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Dey, Maximum Entropy Inverse  Reinforcement Learning, in: AAAI, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 8, 2008, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 1433–1438.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [9] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Zhou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bloem, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bambos, Infinite Time Horizon Maximum Causal Entropy  Inverse Reinforcement Learning, IEEE Transactions on Automatic Control 63 (9)  (2017) 2787–2802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [10] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ziebart, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bagnell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Dey, Modeling Interaction via the Principle of  Maximum Causal Entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Png, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Hsu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Lee, Pomdps for robotic tasks with mixed  observability, in: Robotics: Science and Systems, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 5, 2009, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [12] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bai, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Hsu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Lee, Integrated Perception and Planning in the Continuous  Space: A POMDP Approach, The International Journal of Robotics Research  33 (9) (2014) 1288–1302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Sinapov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Wei, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Stone, Robot Behavioral Exploration and Mul-  timodal Perception using POMDPs, in: AAAI Spring Symposium on Interactive  Multisensory Object Perception for Embodied Agents, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [14] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Akash, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Polson, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Reid, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Jain, Improving Human-Machine Collabora-  tion Through Transparency-based Feedback–Part I: Human Trust and Workload  Model, IFAC-PapersOnLine 51 (34) (2019) 315–321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [15] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Datta, Modeling Context Aware Dynamic Trust Using Hidden Markov  Model, in: Proceedings of the AAAI Conference on Artificial Intelligence,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 26, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [16] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Vlassis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Littman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Barber, On the computational complexity of  stochastic controller optimization in pomdps, ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Theory 4 (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [17] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Madani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Hanks, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Condon, On the Undecidability of Probabilistic Planning  and Infinite-Horizon Partially Observable Markov Decision Problems, in: AAAI,  AAAI Press, 1999, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 541–548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Littman, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Topcu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Fu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Isbell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Wen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' MacGlashan, Environment-  Independent Task Specifications via GLTL, arXiv preprint arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='04341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Baier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Katoen, Principles of Model Checking, The MIT Press, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  23  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Pnueli, The Temporal Logic of Programs, in: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 18th Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Symp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Computer Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', Washington, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', USA, 1977, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 46–57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1109/  SFCS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [21] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Memarian, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Xu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Wu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Wen, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Topcu, Active Task-Inference-Guided  Deep Inverse Reinforcement Learning, in: 2020 59th IEEE Conference on Deci-  sion and Control (CDC), IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 1932–1938.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Wen, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Papusha, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Topcu, Learning from Demonstrations with High-Level  Side Information, in: Proceedings of the Twenty-Sixth International Joint Con-  ference on Artificial Intelligence, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [23] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ziebart, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bagnell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Dey, The Principle of Maximum Causal En-  tropy for Estimating Interacting Processes, IEEE Transactions on Information  Theory 59 (4) (2013) 1966–1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [24] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='-x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Yuan, Recent Advances in Trust Region Algorithms, Mathematical Pro-  gramming 151 (1) (2015) 249–281.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [25] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Mao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Szmuk, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Xu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ac¸ikmese, Successive convexification: A super-  linearly convergent algorithm for non-convex optimal control problems, arXiv  preprint arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='06539.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [26] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Yu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bertsekas, On Near Optimality of the Set of Finite-State Controllers  for Average Cost POMDP, Mathematics of Operations Research 33 (1) (2008)  1–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [27] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Junges, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Jansen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Wimmer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Quatmann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Winterer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Katoen,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Becker, Finite-State Controllers of POMDPs using Parameter Synthesis, in:  Proceedings of UAI, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 519–529.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [28] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Meuleau, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Kim, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Kaelbling, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Cassandra, Solving POMDPs by  searching the space of finite policies, in: UAI, 1999, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 417–426.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [29] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Amato, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bernstein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Zilberstein, Optimizing Fixed-Size Stochastic Con-  trollers for POMDPs and Decentralized POMDPs, AAMAS 21 (3) (2010) 293–  320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ho, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ermon, Generative adversarial imitation learning, Advances in neural  information processing systems 29 (2016) 4565–4573.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [31] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Massey, Causality, feedback and directed information, in: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Symp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Theory Applic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' (ISITA-90), Citeseer, 1990, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 303–305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [32] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Kramer, Directed Information for Channels with Feedback, Citeseer, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [33] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Hansen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Sargent, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Turmuhambetova, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Williams, Robust Control  and Model Misspecification, Journal of Economic Theory 128 (1) (2006) 45–90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Choi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Kim, Inverse Reinforcement Learning in Partially Observable En-  vironments, Journal of Machine Learning Research 12 (2011) 691–730.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  24  [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Junges, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Jansen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Seshia, Enforcing almost-sure reachability in pomdps,  in: International Conference on Computer Aided Verification, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [36] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Walraven, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Spaan, Accelerated Vector Pruning for Optimal POMDP Solvers,  in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 31, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [37] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Kurniawati, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Hsu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Lee, Sarsop: Efficient point-based pomdp planning  by approximating optimally reachable belief spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', in: Robotics: Science and  systems, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 2008, Citeseer, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [38] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Norman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Parker, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Zou, Verification and control of partially observable  probabilistic systems, Real-Time Systems 53 (3) (2017) 354–402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [39] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Osa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Pajarinen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Neumann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bagnell, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Abbeel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Peters, An Algorithmic  Perspective on Imitation Learning, Foundations and Trends in Robotics 7 (1-2)  (2018) 1–179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [40] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ratliff, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bagnell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Zinkevich, Maximum Margin Planning, in:  Proceedings of the 23rd International Conference on Machine Learning, 2006,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 729–736.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [41] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Abbeel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ng, Apprenticeship Learning via Inverse Reinforcement Learn-  ing, in: Proceedings of the 21st International Conference on Machine Learning,  2004, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Russell, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', Algorithms for Inverse Reinforcement Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', in:  Proceedings of the 17th International Conference on Machine Learning, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 1,  2000, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [43] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Ramachandran, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Amir, Bayesian Inverse Reinforcement Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', in: IJ-  CAI, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 7, 2007, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 2586–2591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [44] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Boularias, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Kr¨omer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Peters, Structured Apprenticeship Learning, in:  Joint European Conference on Machine Learning and Knowledge Discovery in  Databases, Springer, 2012, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 227–242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [45] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bogert, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Doshi, Multi-Robot Inverse Reinforcement Learning under Occlu-  sion with Interactions, in: Proceedings of the 2014 International Conference on  Autonomous Agents and Multi-Agent Systems, Citeseer, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 173–180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [46] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bogert, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Doshi, Toward Estimating Others’ Transition Models under Occlu-  sion for Multi-Robot IRL, in: Twenty-Fourth International Joint Conference on  Artificial Intelligence, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  [47] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Bogert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Lin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Doshi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Kulic, Expectation-Maximization for Inverse  Reinforcement Learning with Hidden Data, in: Proceedings of the 2016 Inter-  national Conference on Autonomous Agents & Multiagent Systems, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  1034–1042.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  25  [48] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Papusha, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Wen, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Topcu, Inverse Optimal Control with Regular Language  Specifications, in: 2018 Annual American Control Conference (ACC), IEEE,  2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' 770–777.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Appendices  In this appendix, we provide supplementary derivations for the results in the paper and  more details on the numerical experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Concavity of Causal Entropy and Derivations of the Bellman Constraints  In this section, we first recall the obtained expression of the causal entropy Hγ  σ as a  function of the visitation counts µγ  σ and νγ  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We then prove the concavity of the causal  entropy, which enables convex-optimization-based formulation of the task-guided in-  verse reinforcement learning (IRL) problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, we provide additional details on  the derivation of the affine constraint implied by the Bellman flow constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Concave Causal Entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We first recall the definitions of the state and state-action  visitation counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For a policy σ, state s, and action α, the discounted state visitation  counts are defined by µγ  σ(s) ≜ ESt[�∞  t=1 γt1{St=s}] and the discounted state-action  visitation counts are defined by νγ  σ(s, α) ≜ EAt,St[�∞  t=1 γt1{St=s,At=α}], where 1{·}  is the indicator function and t is the time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' From the definitions of the state and  state-action visitation counts µγ  σ and νγ  σ, it is straightforward to deduce that νγ  σ(s, α) =  σs,αµγ  σ(s), where σs,α = P[At = a|St = s].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We use the visitation counts to prove in  Section 4 that  Hγ  σ =  �  (s,α)∈S×A  −(log πs,α)πs,αµγ  σ(s) =  �  (s,α)∈S×A  − log νγ  σ(s, α)  µγ  σ(s) νγ  σ(s, α),  where the last inequality is obtained by using that πs,α = νγ  σ(s, α)/µγ  σ(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We claim  that Hγ  σ is a concave fucntion of the visitation counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Thus, we want to show that  the function f(νγ  σ, µγ  σ) = �  (s,α)∈S×A − log νγ  σ(s,α)  µγ  σ(s) νγ  σ(s, α) is concave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' To this end,  consider any λ ∈ (0, 1) and the two sets of variables νγ  σ, µγ  σ and ¯νγ  σ, ¯µγ  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' we have  26  the following result:  f(λνγ  σ + (1 − λ)¯νγ  σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' λ¯µγ  σ + (1 − λ)¯µγ  σ)  =  �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A  − log λνγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) + (1 − λ)¯νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  λµγ  σ(s) + (1 − λ)¯µγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) (λνγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) + (1 − λ)¯νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α))  ≥  �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A  −λνγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) log λνγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  λµγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) − (1 − λ)¯νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) log (1 − λ)¯νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  (1 − λ)¯µγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  =  �  (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='α)∈S×A  −λνγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) log νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  µγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) − (1 − λ)¯νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α) log ¯νγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  ¯µγ  σ(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' α)  = λf(νγ  σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' µγ  σ) + (1 − λ)f(¯νγ  σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' ¯µγ  σ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  where the first inequality is obtained by applying to the well-known log-sum inequality,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=',  x1 log x1  y1  + x2 log x2  y2  ≥ (x1 + x2) log x1 + x2  y1 + y2  ,  for nonnegative numbers x1, x2, y1, y2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Specifically, we apply the substitution x1 =  λνγ  σ, y1 = λµγ  σ, x2 = (1 − λ)¯νγ  σ, and y2 = (1 − λ)¯µγ  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Note that the inequality  f(λνγ  σ + (1 − λ)¯νγ  σ, λ¯µγ  σ + (1 − λ)¯µγ  σ) ≥ λf(νγ  σ, µγ  σ) + (1 − λ)f(¯νγ  σ, ¯µγ  σ)  implies that f(νγ  σ, µγ  σ) is concave in νγ  σ, and µγ  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Bellman Flow Constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For the visitation count variables to correspond to a valid  policy generating actions in the POMDP M , νγ  σ and µγ  σ must satisfy the bellman flow  constraint given by  µγ  σ(s) = ESσ  t  � ∞  �  t=0  γt1{Sσ  t =s}  �  = µ0(s) + γESσ  t  � ∞  �  t=0  γt1{Sσ  t+1=s}  �  = µ0(s) + γ  ∞  �  t=0  �  s′∈S  �  α∈A  γtP(s|s′, α)P[Sσ  t = s′, Aσ  t = α]  = µ0(s) + γ  �  s′∈S  �  α∈A  P(s|s′, α)νγ  σ(s′, α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Experimental Tasks  In this section, we first provide a detailed description of the POMDP models used  in the benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The simulations on the benchmark examples empirically demon-  strate that side information alleviates the information asymmetry, and more memory  leads to more performant policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, we provide additional numerical simulations  supporting the claim that SCPForward is sound and yields better scalability than  off-the-shelf solvers for the forward problem, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', computing an optimal policy on a  POMDP for a given reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  27  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Computation Resources and External Assets  All the experiments of this paper were performed on a computer with an Intel Core  i9-9900 CPU 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1GHz ×16 processors and 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='2 Gb of RAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' All the implementations  are written and tested in Python 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='8, and we attach the code with the supplementary  material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Required Tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Our implementation requires Stormpy of Storm [?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' ] and Gurobipy  of Gurobi 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='1 [?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On one hand, we use Storm, a tool for model checking, to parse  POMDP file specifications, to compute the product POMDP with the finite state con-  troller in order to reduce the synthesis problem to the synthesis of memoryless policies,  and to compute the set T of target states satisfying a specification ϕ via graph prepro-  cessing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' On the other hand, we use Gurobi to solve both the linearized problem in (7)  and the feasible solution of the Bellman flow constraint needed for the verification step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Off-The-Shelf Solvers for Forward Problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In order to show the scalability of  the developed algorithm SCPForward, we compare it to state-of-the-art POMDP  solvers SolvePOMDP [36], SARSOP [37], and PRISM-POMDP [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The solver  SolvePOMDP implements both exact and approximate value iterations via incremen-  tal pruning [?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' ] combined with state-of-the-art vector pruning methods [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally,  PrismPOMDP discretizes the belief state and adopts a finite memory strategy to find  an approximate solution of the forward problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For all the solvers above, we use the  default settings except from the timeout enforced to be 3600 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' These solvers  are not provided with our implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, we provide the POMDP models  that each of the solvers can straightforwardly use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Further details are provided in the  readme files of our implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Benchmark Set  We evaluate the proposed learning algorithm on several POMDP instances adapted  from [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' We attached the modified instances in our code with the automatically  generated models for each off-the-shelf solver that the reader can straightforwardly  use to reproduce Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The reader can refer to Table 1 for the number of states,  observations, and transitions of each environment of the benchmark set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In all the  examples, we gather 10 trajectories from an expert that can fully observe its current  state in the environment and an expert having partial observation of the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Our algorithm learns reward functions from these trajectories under different memory  policies and high-level side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  28  Rocks Instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In the environment Rocks, an agent navigates in a gridworld to sam-  ple at least one valuable rock (if a valuable rock is in the grid) over the two possibly  dangerous rocks, without any failures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' When at least one valuable rock has been col-  lected, or the agent realizes that all the rocks are dangerous, it needs to get to an exit  point to terminate the mission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The partial observability is due to the agent can only  observe if its current location is an exit point or a dangerous rock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Furthermore, the  agent has noisy sensors enabling sampling neighbor cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We consider three feature functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The first feature provides a positive reward  when reaching the exit point with at least one valuable rock or no rocks when all of  them are dangerous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The second feature provides a negative reward when the agent  is at the location of a dangerous rock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Finally, the third feature penalizes each action  taken with a negative reward to promote reaching the exit point as soon as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  No information asymmetry  Under information asymmetry  GAIL  0  75  150  225  300  0  50  100  Finite-memory policy  Without side  information  Rφ  σ  0  75  150  225  300  0  50  100  Memoryless policy  Rφ  σ  0  75  150  225  300  0  50  100  Time Steps  With side  information  Rφ  σ  0  75  150  225  300  0  50  100  Time Steps  Rφ  σ  Figure 8: Representative results on the Rock example showing the reward of the policies under the true  reward function (Rφ  σ) versus the time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We compare scenarios with no side information and the a priori knowledge on the  task such as the agent eventually reaches an exit point with a probability greater than  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Figure 8 supports our claim that side information indeed alleviates the informa-  tion asymmetry between the expert and the agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Additionally, we also observe that  incorporating memory leads to more performant policies in terms of the mean accumu-  lated reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  29  Obstacle Instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In the environment Obstacle[n], an agent must find an exit in a  gridworld without colliding with any of the five static obstacles in the grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The agent  only observes whether the current position is an obstacle or an exit state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The parameter  n specifies the dimension of the grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Similar to the Rocks example, the agent receives a positive reward if it successfully  exits the gridworld and a negative reward for every taken action or colliding with an  obstacle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  As for the side information, we specify in temporal logic that while learning the  reward, the agent should not collide any obstacles until it reaches an exit point with a  probability greater than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='No information asymmetry  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Under information asymmetry  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='−200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Finite-memory policy  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Without side  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='information  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Rφ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='σ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='−200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Memoryless policy  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Rφ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='σ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
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+page_content='75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
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+page_content='−200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Time Steps  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='With side  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='information  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Rφ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='σ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='−200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Time Steps  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Rφ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='σ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='Figure 9: Representative results on the Obstacle example showing the reward of the policies under the true  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='reward function (Rφ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='σ) versus the time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Similar to the Maze and Rock examples, Figure 9 supports our claim that side in-  formation alleviates the information asymmetry and memory leads to more performant  policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  30  Evade Instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Evade[n, r, slip] is a turn-based game where the agent must reach a  destination without being intercepted by a faster player.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The player cannot access the  top row of the grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Further, the agent can only observe the player if it is within a fixed  radius from its current location and upon calling the action scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The parameters n, r,  and slip specify the dimension of the grid, the view radius, and the slippery probability,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  The feature functions are defined such that the agent receives a positive reward if  at the destination, a high negative reward if it is intercepted by the player, and a small  negative reward for each action taken, including the scan action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  With side information  Without side information  GAIL  0  25  50  75  100  −10  0  10  20  Time Steps  Mean accumulated reward  Figure 10: Representative results on the Evade example showing the reward of the policies under the true  reward function (Rφ  σ) versus the time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  As for the side information, we specify in temporal logic that while learning the  reward, the agent must reach an exit point with probability greater than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Figure 10 shows that learning with side information provides higher reward than  without side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Besides, there is less randomness in the policy with side  information compared to the policy without side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Specifically, the standard  deviation of the policy with side information is significantly smaller than the policy  without side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We did not discuss the impact of different memory size policies in this example  since the performance of the memoryless policy is already near-optimal, as the policy  obtains the same reward as SARSOP (see Table 1 for a reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Specifically, we  observe that the optimal policy on the underlying MDP yields comparable policies to  the optimal memoryless policy on the POMDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' As a consequence, we observe that the  information asymmetry between the expert and the agent does not hold here either, and  the learned policies obtain a similar performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  31  Intercept Instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Intercept[n, r, slip] is a variant of Evade where the agent must  intercept another player who is trying to exit the gridworld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The agent can move in 8  directions and can only observe the player if it is within a fixed radius from the agent’s  current position when the action scan is performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Besides, the agent has a camera  that enables it to observe all cells from west to east from the center of the gridworld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In  contrast, the player can only move in 4 directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The parameters n, r, and slip specify  the dimension of the grid, the view radius, and the slippery probability, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We consider three feature functions to parameterize the unknown reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The first  feature provides a positive reward to the agent upon intercepting the player.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The second  feature penalizes the agent if the player exits the gridworld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The third feature imposes  a penalty cost for each action taken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  With side information  Without side information  GAIL  0  25  50  75  100  −10  0  10  20  Time Steps  Mean accumulated reward  Figure 11: Representative results on the Intercept example showing the reward of the policies under the  true reward function (Rφ  σ) versus the time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We encode the high-level side information as the temporal logic task specification  Eventually intercept the player with probability greater than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='98, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', the agent should  eventually reach an observation where its location coincides with the player’s location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Figure 11 demonstrates that side information does not improve the performance  of the policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' This result is because memoryless policies are optimal in this example,  and a combination of the given reward features can perfectly encode the temporal logic  specifications, similar to the Evade example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Effects of Side Information  In this section, we provide additional experiments on how the side information  speeds up the learning process in terms of computation time and convergence to the  optimal policy and reward parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Then, we quantify the effects of the side infor-  mation by solving the POMDPs using only the task specifications and no demonstra-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' All these experiments are performed on the Maze example, which is a relatively  low-size POMDP example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  32  Convergence of the Learning With and Without Side Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In the Maze ex-  periments, we empirically observe that side information enables the learning algorithm  to converge with eight times less number of iterations compared to learning without  side information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The number of iterations here denotes both the number of lineariza-  tions in the sequential convex scheme and the number of gradient steps during reward  updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' However, the gain in computation time is not as prominent as the gain in  the number of iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In fact, learning with side information is only approximately  three times faster than learning without side information due to how side information  almost doubles the number of variables in the convex optimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Effects of Side Information Without Any Demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Experiment 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We consider the exact setting of the Maze example with no  demonstrations and the LTL specification Prσ  M(G ¬ bad) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Essentially,  we seek policies that avoid the trapping states with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Without any  additional reward, the optimal policy is exactly what we expect: High probabil-  ity for action enforcing no movements and low probability for the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' With  respect to the true reward, this is clearly suboptimal as the reward will keep de-  creasing due to no minimization of the amount of time spent in the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Now, we optimize the problem for a policy that satisfies the LTL specifications  while penalizing spending time in the environment according to the ground truth  reward for taking more steps in the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The obtained policy has the op-  timal reward of 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='83, which corresponds to optimizing the ground truth reward  in the POMDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Indeed, the fastest way to clear the Maze is to exit through a goal  state while not getting trapped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Experiment 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  We consider the exact setting of the Maze example with no  demonstrations and the LTL specification Prσ  M(E target) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Essentially,  we seek policies that eventually reach the target state (exit of the Maze) with  high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Without any additional reward, the optimal policy is subopti-  mal with respect to the optimal policy on the POMDP, given the ground truth  reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Indeed, the policy can reach the target with an optimal reward of 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='63  due to the amount of time spent to reach the goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' By adding the reward on time  spent in the environment to the LTL specifications, we can obtain the optimal  reward on the POMDP again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Summary of the Results  Side Information Alleviates the Information Asymmetry .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' As mentioned in the sub-  mitted manuscript, side information can indeed alleviate the information asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Specifically, we observe that if there is an information asymmetry in the forward prob-  lem, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=', the obtained reward from an optimal policy on the underlying POMDP is  lower than from an optimal policy on the underlying fully observable MDP, incor-  porating side information in temporal logic specifications alleviates the information  asymmetry between the expert and the agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' For example, we can see the effects of  such information asymmetry in the Maze, Rocks, Obstacle, and Avoid examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In  33  these examples, having partial observability reduces the obtained reward in the for-  ward problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' The policies that do not incorporate side information into the learning  procedure also obtain a lower reward under information asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  Memory Leads to More Performance Policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' Similarly to the side information, we  also observe that if incorporating memory improves the performance of the learned  policies, if it also improves the obtained reward in the forward problem, as seen in the  Maze, Rocks, and Obstacle instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content=' In Table 1, we can also see that incorporating  memory helps to compute a better optimal policy in these examples, unlike computing  a memoryless policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
+page_content='  34' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19AzT4oBgHgl3EQfRvso/content/2301.01219v1.pdf'}
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+An Empirical Investigation into the Use of Image
+Captioning for Automated Software Documentation
+Kevin Moran†, Ali Yachnes∗, George Purnell∗, Junayed Mahmud†,
+Michele Tufano‡, Carlos Bernal Cardenas‡, Denys Poshyvanyk∗, Zach H’Doubler∗
+†George Mason University, VA, USA, ∗William & Mary, VA, USA, ‡Microsoft, WA, USA
+kpmoran@gmu.edu, ayachnes@email.wm.edu, gwpurnell@email.wm.edu, jmahmud@gmu.edu
+michele.tufano@microsoft.com, carlosbe@microsoft.com, denys@cs.wm.edu, pzhdoubler@email.wm.edu
+Abstract—Existing automated techniques for software docu-
+mentation typically attempt to reason between two main sources
+of information: code and natural language. However, this reason-
+ing process is often complicated by the lexical gap between more
+abstract natural language and more structured programming
+languages. One potential bridge for this gap is the Graphical User
+Interface (GUI), as GUIs inherently encode salient information
+about underlying program functionality into rich, pixel-based
+data representations. This paper offers one of the first com-
+prehensive empirical investigations into the connection between
+GUIs and functional, natural language descriptions of software.
+First, we collect, analyze, and open source a large dataset of
+functional GUI descriptions consisting of 45,998 descriptions
+for 10,204 screenshots from popular Android applications. The
+descriptions were obtained from human labelers and underwent
+several quality control mechanisms. To gain insight into the
+representational potential of GUIs, we investigate the ability of
+four Neural Image Captioning models to predict natural language
+descriptions of varying granularity when provided a screenshot
+as input. We evaluate these models quantitatively, using common
+machine translation metrics, and qualitatively through a large-
+scale user study. Finally, we offer learned lessons and a discussion
+of the potential shown by multimodal models to enhance future
+techniques for automated software documentation.
+Index Terms—Software Documentation, Image Captioning,
+Deep Learning
+I. INTRODUCTION & MOTIVATION
+Proper documentation is generally considered to be an inte-
+gral component of building and distributing modern software
+systems. In fact, past studies have illustrated the general ben-
+efits of documentation during the development lifecycle [1],
+[2], [3], [4] and the importance of technical documentation
+to software maintenance and evolution [5]. However, despite
+the value of well-documented systems, modern development
+processes and constraints often lead to the disregard or aban-
+donment of a range of documentation tasks [6], [5], [2], [7],
+[8], [1]. These difficulties have given rise to a wealth of
+research on automated techniques that aim to ease the burden
+on stakeholders by generating various types of documentation
+for a given task. For example, existing approaches have been
+developed to automatically generate natural language sum-
+maries and documentation for code [9], [10], [11], [12], [13],
+[14], [15], APIs [16], [17], unit tests [18], bug reports [19],
+[20], release notes [21], [22], and commit messages [23], [24],
+among other artifacts [25], [26].
+Generally, existing techniques for automated software doc-
+umentation have been concerned with modeling relationships
+that exist between two primary information modalities: code
+and natural language (NL). Unfortunately, reasoning between
+these two information sources is difficult due to the lexical
+gap resulting from the often disparate conceptual associations
+that connect source code lexicon and the more abstract words
+and phrases used in NL descriptions
+[27], [28]. Recently,
+this lexical gap was acknowledged as an information inference
+problem in a report made by Robillard et al. [29], wherein
+key research challenges exist in (i) inferring undocumented
+program properties, and (ii) discovering latent abstractions
+and rationales. These challenges suggest that overcoming the
+semantic disconnect between code and NL may require new
+knowledge sources that encode distinct program properties
+typically absent from traditional software or NL lexicon.
+One source of information which has been left largely
+unexplored for the purposes of automated documentation is
+visual software data encoded into Graphical User Interfaces
+(GUIs). GUI-based applications predominate modern user-
+facing software, as can be readily seen in the popularity of
+desktop and mobile apps [30]. Furthermore, high quality ap-
+plications with well-designed GUIs allow technically-inclined
+users to instinctively understand underlying program features.
+Thus, intuitively, certain functional properties of applications
+are encoded into the visual, pixel-based representation of the
+GUI such that cognitive human processes can determine the
+computing tasks provided by the interface. This suggests that
+there are latent patterns that exist within visual GUI data
+which indicate the presence of natural use cases capturing core
+functionality [31].
+Given the inherent representational power of GUIs in con-
+veying program related information, we set forth the following
+hypothesis that serves as the basis for work in this paper:
+The representational power of graphical user interfaces to
+convey program-related information can be meaningfully
+leveraged to support automated techniques for software doc-
+umentation.
+While most existing work on automated documentation con-
+cerns itself with the dichotomy between code and NL, we posit
+that the latent information encoded within GUIs can aid in
+bridging the existing semantic documentation gap by providing
+arXiv:2301.01224v1  [cs.SE]  3 Jan 2023
+
+an additional source of knowledge that inherently reflects pro-
+gram functionality. In fact, GUI-based representations of soft-
+ware have the potential to address the two challenges set forth
+by Robillard et al. [29]. More specifically, GUIs can aid in
+inferring undocumented program properties that are inherently
+represented within the design of GUI controls or widgets (e.g.,
+capturing a feature which is otherwise poorly represented by
+low-quality code identifiers/comments). Further, GUIs could
+be used as source to mine abstractions or rationales that
+would otherwise remain obscure (e.g., providing a use case-
+based explanation of a block of code connected to a GUI
+screen). In overcoming these challenges, we see GUI-centric
+documentation having an impact on the following types of
+software documentation:
+Technical Documentation: Developers utilize technical docu-
+mentation, such as code comments or READMEs, in order
+to learn about the functionality and interfaces of software
+to support engineering tasks. Automatically generating such
+documentation accurately is a challenging inference problem.
+However, it has been shown that GUI-related code can com-
+prise as much as half of the code in user facing programs [32].
+This means that graphical software data is connected in some
+way to large portions of GUI-based software projects i.e.,
+through GUI-event handlers, or code stipulating GUI layouts
+such as html. Therefore, if automated techniques are able to
+effectively infer salient functionality from the GUIs, they could
+be combined with existing techniques and leveraged to provide
+automation to developers, such as comment generation or code
+summarization with greater feature-based context awareness.
+As we illustrate in this paper, GUI code/metadata appears to
+encode orthogonal information compared to visual GUI data
+(i.e., screenshots), which suggests that we may be able to infer
+documentation information from visual GUI data that likely
+can’t be inferred from GUI code alone.
+User Documentation: Developers typically provide users with
+documentation such as tutorials or walkthroughs to help
+clearly illustrate software features. While some experienced
+users can infer functionality directly from a GUI, end-users
+exhibit a range of technological expertise, and many rely upon
+various forms of end-user documentation [33]. Thus, building
+techniques capable of automatically generating such documen-
+tation would free up development effort for other critical tasks,
+such as bug fixing. Beyond typical user facing software aids,
+GUI-centric program documentation could also enable entirely
+new classes of automated accessibility features, which are
+sorely needed for mobile apps [34]. For example, rather than a
+typical text-to-speech engine, one could envision a screen-to-
+functionality engine that could aid a motor-impaired user with
+navigating the software, without extra development effort.
+To investigate the potential of automated GUI-centric soft-
+ware documentation, we offer one of the first comprehensive
+empirical investigations into this new research direction’s most
+fundamental task: generating a natural language descrip-
+tion given a screenshot (or screen-related information) of
+a software GUI. Given that this task underlies the various
+potential applications discussed above, we view this as a
+logical first step towards investigating the feasibility of fu-
+ture techniques. To accomplish this, we collect and analyze
+a dataset for Comprehending visuaL semAntics to pRedict
+applicatIon functionalTY (the CLARITY dataset) consisting
+of 45,998 functional descriptions of 10,204 screenshots of
+popular Android apps available on Google Play. We provide
+a descriptive analysis of this dataset that investigates the
+“naturalness” and semantic topics of the collected descriptions
+by measuring cross-entropy compared to other corpora and
+performing a topic modeling analysis. To learn functional
+descriptions of the screens from this dataset, we customize,
+train, and test four Deep Learning (DL) models for neural
+image captioning—three that learn from image data and one
+that learns from textual GUI metadata—to predict functional
+descriptions of software at different granularities. We evaluate
+the efficacy of these models both quantitatively, by measuring
+the widely used BLEU metric, and qualitatively through a
+large-scale user study. In summary, this paper’s contributions
+are as follows:
+• We collect the CLARITY dataset of GUIs annotated
+with 45,998 functional, NL descriptions from 10,204
+screenshots of popular Android apps. The NL captions
+were obtained from human labelers, underwent several
+quality control mechanisms, and contain both high- and
+low-level descriptions of screen functionality. While other
+GUI datasets exist [35], [36], the CLARITY dataset differs
+by providing an extensively labeled set of screens, akin
+to Flickr8K [37] or MSCOCO [38];
+• We illustrate the underlying, natural patterns that exist in
+the CLARITY dataset through topic modeling.
+• We provide an extensive quantitative and qualitative eval-
+uation of four tailored DL models for image captioning
+using standard metrics and a large scale user study;
+• We offer an online appendix with examples of model-
+generated descriptions and experimental data [39]. Our
+dataset, trained models, code, and evaluation scripts are
+open source and accessible via the appendix.
+II. BACKGROUND
+A. The Connection between Images and NL
+The task of image captioning is much more difficult than
+that of classification or labeling, as an effective model must
+be able to both learn salient features from images automati-
+cally and semantically equate these features with the proper
+NL words and grammar that describe them. This task of
+semantically aligning two completely different modalities of
+information has led to the development of multimodal DL
+architectures that jointly embed NL and pixel-based infor-
+mation in order to predict an appropriate description of a
+given input image. These techniques are typically trained
+on large-scale datasets that contain images annotated with
+multiple captions, such as MSCOCO [38], and have largely
+drawn inspiration from encoder-decoder neural language mod-
+els traditionally applied to machine translation tasks. In this
+2
+
+…
+…
+…
+Input Image
+CNN or RCNN
+BRNN 
+ or LSTM
+xt
+yt
+W
+st
+v
+Image “Encoder”
+NL “Decoder”
+Fig. 1: Generalized overview of multimodal DL architectures
+for image captioning (with RCNN)
+paper, we adapt three recent architectures for image caption-
+ing, neuraltalk2 [40], the im2txt [41], and the show,
+attend and tell (SAT) [42] frameworks to predict func-
+tional descriptions of software screenshots through the use of
+custom pre-training and fine-tuning procedures. Additionally,
+we explore the seq2seq neural language model.
+DL models for image captioning build upon the success
+of encoder-decoder neural language models. The im2txt
+framework treats image captioning as a machine translation
+problem, wherein the source “sentence” is an image, and
+the target “translation” is a NL description. The generalized
+architecture of such models is shown in Fig. 1. As illustrated,
+these architectures replace the encoder RNN with a Convolu-
+tional Neural Network (CNN), which have been shown to be
+highly capable of learning rich image features [43], [44], [45].
+Google’s implementation of im2txt uses a Long-Short Term
+Memory (LSTM) RNN [46] for the “decoder” module, which
+has also proven extremely effective when applied to machine
+translation tasks. The decoder module of the neuraltalk2
+architecture is composed of a Bidirectional RNN (BRNN) [47]
+as opposed to an LSTM. Finally, the show, attend, &
+tell (SAT) model [42] uses an LSTM decoder but with
+the addition of an attention mechanism that can “attend” to
+salient parts of the image representation by combining “hard”
+and “soft” attention mechanisms.
+III. OVERVIEW
+In this section, we provide an “at-a-glance” overview of the
+data-collection procedures and various analyses performed in
+this paper. Figure 2 illustrates the four major components of
+the paper. The first major task of our study is to derive a
+suitable dataset of screenshot-caption pairs. We describe this
+process in two parts: (i) the collection of screenshots (Sec.
+IV-A), and (ii) the collection of captions from human workers
+(Sec. IV-B). The result of this data-collection effort is the
+CLARITY dataset, which contains 45,998 captions of 10,204
+Android screenshots. Next, we aim to understand the lexical
+properties of our captions through an empirical analysis in
+order to better understand how easily they might be modeled
+(Sec. V). Thus, we perform both a comparison of the the
+cross-entropy of language models trained our caption corpus
+to other popular SE corpora, and perform an LDA-based
+topic analysis. Next, we discuss the process of configuring
+and training three neural image captioning models, and one
+1   Clarity Dataset Collection
+(Screenshots + GUI metadata + Captions)
+2  Naturalness & Topic Analysis
+Cross-Entropy
+Analysis
+LDA-based 
+Topic Analysis
+…
+…
+…
+Input Image
+CNN or RCNN
+BRNN 
+ or LSTM
+xt
+yt
+W
+st
+v
+Image “Encoder”
+NL “Decoder”
+3   Train Image-Captioning and 
+Metadata Captioning Models
+Image-Captioning
+Models
+Metadata-Captioning
+Models
+4  !antitative and !alitative
+Model Evaluations
+“Ground Truth”
+Captions
+“Predicted”
+Captions
++
+Screens
+Large-Scale
+Human Evaluation
+!antitative  
+Evaluation 
+with BLEU
+Fig. 2: Overview of Dataset Collection and Analysis
+sequence-based model to predict functional descriptions of
+software GUIs (Sec. VI). Finally, we conclude our analysis
+by measuring the accuracy of our trained models according to
+both automated reference-based metrics (i.e., BLEU@n) and
+via a large-scale human evaluation. (Sec. VII)
+IV. DATASET COLLECTION
+A. Screen & GUI Metadata Collection
+The first step in deriving the CLARITY dataset is the
+collection of a sizable and diverse dataset of screenshots and
+GUI-metadata. We chose to focus this dataset derivation on the
+Android platform for three main reasons: (i) Android is cur-
+rently the most popular OS in the world [30], (ii) Android apps
+are highly GUI-and gesture driven, making them a suitable
+target for our investigation, and (iii) the Android screencap
+and uiautomator tools facilitate the extraction of screenshots
+and GUI-metadata from running apps. Fortunately, large-scale
+datasets of Android screenshots and metadata are publicly
+available in related literature [48], [35]. For this work, we took
+advantage of the REDRAW [48], [36] dataset which contains
+nearly 17k unique screenshots from 8,655 of the top-rated
+apps from the Google Play Store. It should be noted that
+another large-scale Android GUI dataset that contains a larger
+number of screenshots, RICO, is also available [35]. However,
+we chose to utilize the REDRAW dataset as it aligned with
+one of our primary study objectives. That is, we aim to learn
+latent feature information from both screenshots and GUI-
+metadata. However, for the GUI-metadata to properly align
+with the displayed content on a screen, the app must make use
+of native Android components. Therefore, apps that primarily
+display their information using web technologies, so-called
+hybrid apps, would obscure the GUI-metadata and impact
+our study findings. The REDRAW dataset contains a set of
+screenshots that underwent several stages of filtering to remove
+instances of hybrid apps along with other noise. Furthermore,
+the REDRAW dataset contains a set of GUI-component images
+3
+
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+18.502:04
+Q Search
+Stories
+ Play All
+Add
+Your Story
+George
+Amanda
+Colby
+[因
+What's on your mind?
+Photo
+Guillermo Moreno with Josephine
+Williams and 2 others.
+Yesterday at 10:14 PM · 
+Good friends, good food and a lot of laughs
+Colby Harris and 23 others
+2 Comments000
+</>AHigh Level Caption
+The screen allows the user to 
+look at clothing categories
+Low Level Captions
+The top le! icon allows the user 
+to access the menu
+The top right icon allows the 
+user to access the shopping cart
+The center list of categories allows 
+the user to make a selection
+The heart icon to the le! of the 
+shopping cart allows the user to 
+view favorites
+Fig. 3: Example of captions from the CLARITY dataset.
+labeled with their corresponding types (e.g., Button) which
+we utilize later in our study (Sec. VI). The end result of this
+filtering process was a total set of 17,203 candidate screens for
+labeling. We refer readers to the REDRAW paper for complete
+details of the filtering process [48].
+B. Collection of Functional Descriptions
+Once we derived a suitable set of screens, we needed to
+manually label these screens with functional captions. This
+process occurred in two steps: (i) first, we conducted a pilot
+labeling study in order to develop and prove out a tagging
+methodology suitable for large scale caption collection; (ii)
+second, we performed a full scale data collection study using
+Amazon’s Mechanical Turk Crowd-worker platform to collect
+over 10k screens with functional descriptions.
+1) Caption Granularity: Intuitively, GUIs encode func-
+tional information at multiple levels of granularity. For exam-
+ple, if you were to ask a user or developer what the high-
+level purpose of a given screen is, they might say “This
+screen allows users to browse clothing categories”, as shown
+in Fig. 3. These types of descriptions constitute the “high-
+level” functionality of a given screen. However, a single screen
+rarely implements only one functionality, and there may be
+multiple functional properties that enable the screen’s high-
+level functional purpose. User descriptions of these types
+of functional properties are typically centered around the
+interactive components of a screen, since these represent the
+instances of actions (e.g., users “doing something”) that are
+easily attributed to implemented functions. For example, in
+the screen in Fig. 3, underlying functions include viewing
+favorites, accessing a shopping cart, or selecting an item from
+a list. These types of “low-level” screen properties centered
+around GUI-components describe key constituent functional-
+ity. Hence, in order to capture a holistic functional view of
+each screen, we tasked participants with labeling each screen
+with one “high-level” functional caption, and up to four “low-
+level” functional captions. Fig. 3 shows these two categories
+using actual captions collected as part of the CLARITY dataset.
+2) Pilot Data Collection Study: We developed an initial
+image caption collection platform using a Java-based web
+application. Using this system, the authors manually labeled
+743 screens with the caption granularities described earlier.
+During this study, we discovered some instances of screens
+with relatively little information displayed on them, making
+it difficult to label them with functional attributes, even after
+the filtering techniques discussed previously. Therefore, before
+moving onto the large-scale caption collection with Mechani-
+cal Turk (MTurk), at least one author manually inspected each
+of the 17,203 candidate screens, and discarded those with a
+severe lack of functionality. This resulted in a set of 16,311
+candidate screens for the next phase of the study.
+3) Mechanical Turk Data Collection Study: To set up our
+large-scale data-collection process, we adapted our web ap-
+plication caption collection mechanism to work with MTurk’s
+crowd worker platform. This involved configuring a Human
+Intelligence Task (HIT) that provided workers with a set of
+detailed instructions, displaying a screenshot from our dataset
+alongside text entry boxes for one high-level functional caption
+and up to four low-level functional captions (a limit was
+imposed to normalize the amount of time workers would spend
+on the HIT). This study was approved by the Institutional
+Review Board of the authors’ affiliated institution.
+Given that we aimed to collect high-quality functional
+descriptions of screens in natural English, we targeted MTurk
+users from primarily English speaking countries that had
+completed at least 1,000 HITs and had a HIT approval rate
+of at least 90%. We provided a detailed set of instructions
+for labeling images with captions that clearly explained the
+concept of high-level and low-level captions with examples,
+and provided users with explicit instructions as well as DOs
+and DONTs for the labeling task. The full set of instructions is
+available in our online appendix [39]. With regard to caption
+quality, we specifically had three major requirements: (i) that
+the caption describes the perceived functionality of a screen
+and not simply its appearance, (ii) that spatial references are
+given for low-level captions (e.g., “the button in the top-left
+corner of the screen”), and (iii) that captions be written in
+complete English sentences with reasonably proper grammar.
+We published batches of HIT tasks by sampling unique
+screens from our set of 16,311 candidate screens, ensuring
+that no user was assigned the same screen twice. The quality
+of work from crowd-sourced tasks is not always optimal,
+so as captions were submitted, they needed to be vetted for
+quality. Thus, the captions for each screen were examined by
+at least one author for the three quality attributes mentioned
+above. If an author was unsure about whether a screen met
+these quality attributes, it was reviewed by at least one other
+author to reach a consensus. In total, 2,419 screens were
+rejected and republished as new HITs due to quality issues.
+In summary, 2,150 MTurk workers collected 45,998 captions
+(across granularities) for 10,204 screens (≈5 screens per
+participant), and over $2,400 was paid out.
+V. EMPIRICAL DATASET ANALYSIS
+The CLARITY dataset provides a rich source of data for
+exploring the relationship between GUI-based and lexical
+4
+
+#？
+日9:47
+asos
+三
+HOME
+CATEGORIES
+NEWIN:CLOTHING
+ACTIVEWEAR
+TALL
+JEANS
+SHOES&SNEAKERS
+-SHIRTS
+SUNGIASSESTABLE I: LDA topics learned over high-level captions k = 15
+Assigned Label
+Top 7 Words
+”color options”
+screen show app option color book differ
+”login or create acccount”
+user screen allow account log creat app
+”select image from a list”
+user screen allow select view list imag
+”map search by location”
+screen locat search map user show find
+TABLE II: LDA Topics learned on low-level captions k = 25
+Assigned Label
+Top 7 Words
+”page button”
+page button top center bottom side left
+”select date”
+avail date select one option theme present
+”camera button”
+video imag photo pictur bottom camera
+”privacy policy banner”
+titl just term blue banner privaci polici
+software data. However, it is important to investigate the
+semantic makeup of the collected captions in order to better
+understand: (i) the latent topics they capture as well as (ii)
+their naturalness and, hence, predictability. In this section we
+carry out an empirical analysis of this phenomena guided by
+the following two Research Questions (RQs):
+• RQ1: What are the latent topics captured within the high-
+and low-level captions in the CLARITY dataset?
+• RQ2: How natural (i.e., predictable) are the high- and
+low-level captions in the CLARITY dataset?
+A. Analysis Methodology
+1) RQ1: Investigating Dataset Topics: To investigate the
+latent topics in the CLARITY dataset, we learned topic models
+over caption corpora representing different granularities of
+functional descriptions. More specifically, we applied Latent
+Dirichlet Allocation (LDA) [49] to both segmented high-
+and low- level captions from the CLARITY dataset. In our
+analysis, the set of captions for a specific screenshot in the
+CLARITY dataset represents a document, and the entire set
+of captions across screenshots for a given granularity (i.e.,
+high or low level) constitutes a corpus. LDA has several
+configurable hyper-parameters that impact the smoothing of
+generated topics. These include k, the number of topics,
+n which denotes the number of iterations of the sampling
+algorithm (Gibbs sampling [50], in our case), as well as α
+and β which impact topic distributions. We set α and β to
+standard values for NL corpora, set n to 500, which proved to
+be a sufficient for model convergence, and varied k between
+15, 25, 50, and 75 topics.
+2) RQ2: Analyzing the Naturalness of GUI Descriptions:
+Past work has pioneered the notion of the naturalness of
+software [51], which illustrated the fact that software, even
+more so than NL, exhibits repetitive patterns that make it
+predictable. This finding was recently further investigated and
+the existence of certain natural patterns was confirmed [52]. To
+illustrate naturalness, these past studies have learned statistical
+n-gram language models over software corpora, and measured
+the “perplexity” (or a log-transformed version, cross-entropy)
+of these models, which represents the degree to which a model
+is “surprised” by the patterns on a test corpus when trained on
+a corpus from the same domain. A model with lower measured
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+11
+12
+N-gram order
+Cross-Entropy
+High-Level Captions
+Low-Level Captions
+Java Raw Code
+Java w/o Syntax Tokens
+Stack Overflow
+Guntenberg
+Fig. 4: Cross-entropy of the CLARITY dataset’s high and low-
+Level captions compared to other corpora.
+cross-entropy represents a higher predictive power, and thus,
+a more natural underlying corpus.
+We follow the methodology of these past studies to explore
+the naturalness of the CLARITY dataset captions. Thus, similar
+to the methodology for the previous RQ, we split the collected
+captions into two corpora, one for the high-level descriptions,
+and one for the low-level descriptions. We then learned inter-
+polated n-gram models, using the mitlm [53] implementation
+of Kneser-Ney smoothing [54], which has been shown to be
+the most effective n-gram smoothing method [51], following
+a ten-fold cross-validation procedure. We report the average
+cross-entropy values across these experiments for both the high
+and low-level corpora, compared to prior results [51], [52] for
+other NL and software corpora.
+B. Analysis Results
+1) RQ1: Results of Dataset Topic Modeling: We present
+selected results of some of the most representative topics in
+Tables I & II, complete with descriptive labels that we provide
+for readability, and include all the results in our appendix [39].
+These topics help to provide a descriptive illustration of some
+of the latent patterns that exist in both the high and low level
+CLARITY captions. The high-level captions illustrate several
+screen-level topics, including searching on a map and adjusting
+app settings. The low-level captions conversely capture topics
+that describe component-level functionality, such as date selec-
+tors, camera buttons, and back buttons. These results indicate
+the existence of logical topics specific to the domain of GUIs
+in our collected captions.
+2) RQ2: The Naturalness of Clarity Descriptions: The
+results of our naturalness analysis are illustrated in Figure 4.
+This figure shows the average cross entropy of the high- and
+low- level captions from the CLARITY dataset compared to
+several other corpora as calculated by Rahman et al. [52].
+More specifically, the graph depicts the average ten-fold cross
+entropy for: (i) The Gutenberg corpus containing over 3k
+English books written by over a hundred different authors,
+(ii) Java code from over 134 open source projects on GitHub,
+(iii) Java without Syntax Tokens (i.e., separators, keywords,
+and operators), and (iv) a Stack Overflow corpus consisting of
+only the English descriptions from over 200k posts.
+5
+
+13
+high
+12
+low
+11
+javaraw
+java withoutsyntaxtokens
+10
+stack overflow
+9
+gutenberg
+entropy
+8
+cross
+6
+5
+4
+3
+2
+1
+1
+2
+m
+4
+5
+6
+7
+8
+9
+10
+n-gram lengthAs described earlier, the lower the cross-entropy is for a
+particular dataset, the more natural it is. That is, the corpora
+that exhibit lower cross entropy tend to exhibit stronger latent
+patterns that can be effectively modeled and predicted. As we
+see from Fig. 4, the CLARITY high and low level captions are
+more natural than every dataset excluding raw Java code. It
+should be noted that, comparatively, there are several factors
+that could account for the observed lower cross entropy of the
+CLARITY captions. For instance, such factors could include
+other corpora having a larger size or having a more diverse
+set of human authors and writing styles. However, we mainly
+provide entropy measures of other datasets to provide context
+for the predictability of the CLARITY dataset compared to
+other popular corpora. Regardless of dataset differences, the
+average ≈ 5 bits of entropy measured for the two datasets of
+CLARITY captions signals that our collected descriptions ex-
+hibit strong semantic patterns that can be effectively modeled
+for prediction. Additionally, we observe that the cross-entropy
+for the high and low-level captions are surprisingly similar.
+Intuitively, one might expect that the low-level CLARITY
+captions would exhibit more prevalent patterns due to the
+repetitive use cases of certain GUI-components such as menu
+buttons. This indicates the tendency of both datasets to exhibit
+patterns that can be appropriately modeled. However, as we
+illustrate in Sec. VII the ability for GUI-related information
+to predict captions differs according to granularity.
+VI. DEEP LEARNING FUNCTIONAL DESCRIPTIONS FROM
+SOFTWARE GUIS
+The results of the analysis from the previous section demon-
+strate the presence of the latent patterns in the CLARITY
+dataset of screenshots and captions. In this section, we detail
+our methodology for investigating the capability of different
+customized DL models to learn these patterns to predict
+functional descriptions from two GUI representations.
+A. Clarity Dataset Segmentation
+We collected two different granularities of captions from
+users to derive the CLARITY dataset (Sec. IV-B). For the
+experiments in this section, we want to explore the model’s
+ability to learn both high- and low-level functional descrip-
+tions. Thus, we split the CLARITY dataset into two groups,
+one containing only high level captions, and one containing
+only low level ones. We also created a third dataset combining
+the high and low level captions, in order to explore whether the
+predictive capabilities of the models improved by aggregating
+multiple granularities. It should be noted that each low-level
+caption was treated as a single caption (i.e. each low-level
+caption was treated as a separate data point) as is convention
+with datasets containing multiple captions [38]. Each screen
+in the dataset has both an associated screenshot and a GUI-
+metadata file. In order to make for a fair comparison of
+performance across various model configurations, we created
+consistent training, validation and test partitions (80%, 10%,
+10% according to the number of images/GUI metadata files) to
+be used across models. The NL text used as input to the models
+TABLE III: Image Captioning Model Configs. used in Study
+Model
+Identifier
+Caption Config.
+Model Config.
+im2txt-h-imgnet
+High
+im2txt-l-imgnet
+Low
+im2txt-c-imgnet
+Combined
+inception v3 trained on
+imagenet
+im2txt-h-comp
+High
+im2txt-l-comp
+Low
+im2txt-c-comp
+Combined
+Inception v3 fine-tuned on
+Component Dataset
+im2txt-h-fs
+High
+im2txt-l-fs
+Low
+im2txt
+im2txt-c-fs
+Combined
+Inception v3 fine-tuned on
+Full Screen Dataset
+ntk2-h-imgnet
+High
+ntk2-l-imgnet
+Low
+ntk2-c-imgnet
+Combined
+VGGNet pre-trained on
+ImageNet
+ntk2-h-ft
+High
+ntk2-l-ft
+Low
+NeuralTalk 2
+ntk2-c-ft
+Combined
+VGGNet pre-trained on
+ImageNet with Fine
+Tuning
+sat-h
+High
+sat-l
+Low
+SAT
+sat-c
+Combined
+VGGNet pre-trained on
+ImageNet
+TABLE IV: Subset of Model Hyper-paramters
+Hyperparameter
+im2txt
+NeuralTalk2
+SAT
+Seq2Seq
+Batch Size
+64
+16
+17
+64
+Embedding Size
+512
+512
+512
+128
+Decoder RNN Size/Units
+512
+512
+1024
+128
+Optimizer
+SGD
+SGD
+Adam
+Adam
+Initial Learning Rate
+2
+2
+0.001
+0.0001
+Dropout Probability
+0.7
+0.7
+0.3
+0.8
+was preprocessed according to the specific requirements for
+each model implementation [55], [56], [57].
+B. Image Captioning Model Configurations
+We customize, train, and test the three neural image
+captioning models, im2txt, neuraltalk2, and show,
+attend, & tell (SAT) (Sec. II-A), on the screenshots
+and captions of the CLARITY dataset. We choose to explore
+these three models due to their different underlying design
+decisions related to the type of utilized CNNs and RNNs
+(Sec. II-A), as these differences may affect their performance
+in our domain. It should be noted that in the course of our
+experiments, we make several customizations to these models
+through adaptions to pre-training and fine-tuning procedures.
+However, given the typical number of parameters that consti-
+tute these models, the training time can be quite prohibitive,
+even on modern hardware. Thus, to control our experimental
+complexity and investigate a number of model configurations
+that can be trained in a reasonable amount of time, we fix
+the values of the hyper-parameters for each model in our
+experiments. We derived our utilized hyper-parameter values
+by conducting random searches for optimal values of certain
+parameters, and chose optimal parameters reported in prior
+work for others. While we fix the hyper-parameters for these
+models, we instead customize the configurations of our image
+captioning models at the architectural level. Specifically, we
+investigate how training the “encoder” CNN using different
+datasets and training procedures effects the efficacy of the
+model predictions. This type of analysis allows us to more
+effectively flush out broader patterns related to the benefits and
+drawbacks of model design decisions. In the end, we trained
+more than 15 different configurations of the models (see Table
+III) over several machine months of computation.
+1) im2txt
+Model
+Configurations
+&
+Training:
+For
+im2txt, we adapted Google’s open source implementa-
+6
+
+tion of the model in TensorFlow [55]. Given the incredibly
+large number of parameters that need to be trained for the
+im2txt model, performing even relatively simple hyper-
+paramter searches proved to be computationally prohibitive
+for our experiments. Therefore, for this model we utilized the
+optimal set of parameters reported by Vinyals et al. [41] on
+similarly sized datasets. A subset of these hyper-parameter
+values are given in Table IV, whereas full configuration details
+can be found in our appendix. The publicly available imple-
+mentation of Google’s im2txt model utilizes the Inception
+v3 [58] image captioning architecture as its encoder CNN.
+In past work, the inception model weights were initialized
+by training on the large-scale image classification dataset
+ImageNet [59], which contains “commonplace” image cate-
+goires. However, given that we are applying these models to
+very particular domain (predicting descriptions of software)
+it is unclear if an Inception v3 model trained on the broader
+ImageNet dataset would capture subtle semantic patterns in
+the CLARITY dataset. Therefore, we explored three different
+model configurations to explore this phenomena: one with
+Inception v3 pre-trained on ImageNet, and two with Inception
+v3 fine-tuned on domain specific-datasets. The first domain
+specific image dataset we utilize is the ReDraw cropped
+image dataset outlined in Sec. IV-A, which contains over 190k
+images of native Android GUI-components labeled with their
+type (e.g., Button, TextView). The second domain specific
+image dataset we use consists of the full screenshots from the
+CLARITY dataset, labeled with their Google Play categories.
+2) NeuralTalk2 Model Configurations & Training: For
+neuraltalk2, we adapted Karpathy et al.’s implementation
+written in Torch and lua [56]. We performed a brief random-
+ized hyper-parameter search for this model, given its more
+efficient training time, using the optimal im2txt parameters as
+a starting point. The optimal values resulting from this search
+are provided in Table IV. For its CNN decoder, neuraltalk2
+makes use of a VGGNet [44] architecture pre-trained on
+the ImageNet [59] dataset. Unlike our im2txt configurations,
+we explore the effect of jointly fine-tuning neuraltalk2’s
+CNN and RNN. Thus, we explore two configurations of
+neuraltalk2, one that jointly fine tunes the pre-trained
+VGGNet on the CLARITY dataset, and one that does not
+perform fine-tuning. We followed a training procedure similar
+to that of our im2txt models, in that we trained our models
+on the high, low, and combined CLARITY caption training
+data for 500K iterations, saving model checkpoints every 2K
+iterations.
+3) Show, Attend and Tell Model Configurations & Train-
+ing: For the SAT model, we adapted the open-source imple-
+mentation of the model in Tensorflow [60]. The hyperparam-
+eters that we used to train our model are shown in Table IV.
+The implementation used VGG16 [44] as its encoder CNN.
+We trained the SAT model on the CLARITY dataset for the
+low, high and combined captions for 500K iterations and kept
+the checkpoints after every 1K iterations. Note that due to
+the prohibitive training cost of this model, we did not explore
+using a fine-tuned VGGNet as we did with neuraltalk2.
+TABLE V: Metadata Captioning Model Congfigurations
+Model
+Identifier
+Caption Config.
+Model Config.
+seq2seq-h-type
+High
+seq2seq-l-type
+Low
+seq2seq-c-type
+Combined
+Trained on GUI
+Component Types
+seq2seq-h-text
+High
+seq2seq-l-text
+Low
+seq2seq-c-text
+Combined
+Trained on
+GUI-Component Text
+seq2seq-h-tt
+High
+seq2seq-l-tt
+Low
+seq2seq-c-tt
+Combined
+Trained on
+GUI-Component Type +
+Text
+seq2seq-h-ttl
+High
+seq2seq-l-ttl
+Low
+Seq2Seq
+seq2seq-c-ttl
+Combined
+Trained on
+GUI-component Type +
+Text + Location
+C. Metadata Captioning Model Configurations
+To explore the ability to translate between the lexical
+representations of GUI-metadata and NL functional descrip-
+tions, we train and test an encoder-decoder neural language
+model using Google’s seq2seq [57] framework. Note that
+recent work has proposed new models that take advantage of
+structural text properties [61], however, implementations of
+such models are generally not available, hence we leave the
+study of more advanced models for future work. We chose
+to utilize the default general-purpose architecture and hyper-
+parameters for this model, as they have been shown to be
+effective across a wide-range of machine translation tasks [62].
+More specifically, our encoder network consists of a BRNN
+with Gated Recurrent Units (GRUs) and our decoder network
+consists of an RNN with LSTM units; hyperparameters are
+listed in Table IV.
+To investigate the representative power of different attributes
+included in Android GUI-metadata, we create four config-
+urations of GUI-metadata consisting of different attribute
+combinations (Table V). We chose to utilize these attribute
+combinations as they represent (i) the attributes that are most
+likely to have values, and (ii) represent a wide range of
+information types (e.g., displayed text, component types, and
+spatial information). Note that seq2seq did not consistently
+converge for the high level caption dataset, thus we do not
+report these results. Consistent with the training of the other
+models, our implementation of the seq2seq model was
+trained to 500k iterations, with checkpoints every 2k iterations.
+VII. DEEP LEARNING MODEL EVALUATION
+To explore our core hypothesis set forth at the beginning
+of this paper, and evaluate our DL models described in
+Sec. VI, we perform a comprehensive empirical evaluation
+with two main goals: (i) intrinsically evaluate the predictive
+power of the models according to a well accepted machine
+translation effectiveness metric, and (ii) extrinsically evaluate
+the models by examining and rating the quality of the pred-
+icated functional NL descriptions. The quality focus of this
+evaluation is our studied models’ ability to effectively predict
+accurate, concise, and complete functional descriptions. To aid
+in achieving our study goals, we define the following RQs:
+• RQ3: How accurate are our model’s predicted NL de-
+scriptions?
+• RQ4: How accurate, complete, & understandable are our
+model’s predicted NL descriptions from the viewpoint of
+evaluators?
+7
+
+TABLE VI: BLEU Score Evaluation Results for Models
+Model
+Capt.
+Model Type
+Bc
+B1
+B2
+B3
+B4
+High
+im2txt-h-fs
+12.4
+24.8
+12.6
+6.7
+5.3
+Low
+im2txt-l-comp
+27.0
+45.6
+31.8
+20.0
+10.1
+im2txt
+Comb.
+im2txt-c-comp
+30.3
+51.7
+35.9
+22.1
+11.6
+High
+ntk2-h-imgnet
+13.3
+27.4
+13.5
+7.3
+5.3
+Low
+ntk2-l-ft
+27.4
+47.5
+32.8
+19.5
+9.6
+NeuralTalk2
+Comb.
+ntk2-c-ft
+30.1
+52.1
+36.0
+21.8
+10.8
+Low
+seq2seq-l-type
+18.1
+44.6
+17.0
+7.9
+0.24
+seq2seq
+Comb.
+seq2seq-c-type
+16.9
+38.9
+14.7
+6.0
+0.08
+High
+sat-h
+17.7
+30.1
+18.3
+12.9
+9.8
+Low
+sat-l
+35.0
+52.5
+38.7
+28.1
+20.7
+SAT
+Comb.
+sat-c
+37.7
+56.8
+42.0
+30.5
+22.0
+NeuralTalk2
+Trained on Flickr8K
+34.0
+57.9
+38.3
+24.5
+16.0
+NeuralTalk2
+Trained on MSCOCO
+40.7
+62.5
+45.0
+32.1
+23.0
+im2txt
+42.6
+66.6
+46.1
+32.9
+24.6
+SAT
+45.7
+71.8
+50.4
+35.7
+25.0
+A. Evaluation Methodology
+1) RQ3: Empirically Evaluating Model Accuracy: To
+evaluate the accuracy of our trained model’s generated cap-
+tions, we follow past work [40], [41] and report BLEU
+scores [63] of the predicted captions on the shared CLARITY
+test set of images and GUI-metadata. The BLEU score is a
+standard metric used in machine translation research that mea-
+sures the textual similarity between a predicted caption (the
+output from a model) and a reference caption (the collected
+descriptions from humans in the CLARITY test set). The BLEU
+score can be measured according to the similarity of different
+subsequence lengths (i.e., BLEUn), and we report BLEU1
+through BLEU4, as well as a composite score calculated as the
+average of these, as is convention [40], [41]. For the image
+captioning models, we use the coco-caption implementation
+of the BLEU score adapted for the CLARITY test set. For
+each test image across all image captioning models, three
+captions were generated using a beam width of 3 for the
+beam search across candidate predictions. The seq2seq models
+were evaluated in the same manner. We chose to utilize a
+beam width of 3 as an initial qualitative examination of our
+models’ predictions showed this size to achieve a reasonable
+balance between prediction accuracy and model confidence.
+For the high-level captions, the three candidate captions were
+compared to the reference, and the overall average BLEUn
+scores were calculated for each model. For the low-level and
+combined captions, the predicted captions and reference cap-
+tions were compared in a pairwise manner and overall average
+BLEUn scores were calculated for each model configuration.
+2) RQ4: Human Perceptions of Predicted Captions: To
+qualitatively evaluate our studied model’s generated captions,
+we performed a large-scale study involving an additional 220
+participants recruited from MTurk. We randomly sampled
+220 screens from the CLARITY test set, and then predicted
+high, low, and combined captions for them using the opti-
+mal configurations of im2txt, NeuralTalk2, and seq2seq
+according to the composite BLEU score for each model
+and caption level combination. The SAT captions were not
+included in this study due to time constraints related to the
+model’s training. We created a HIT wherein each participant
+viewed 11 screenshots paired with captions. Two of the 11
+captions were reference high and low to serve as a control,
+while the other 9 captions came from the model predictions.
+Screens and caption pairs were arranged into HITs such that
+1) no single HIT had two of the same screenshot, 2) each
+of the 11 types of captions (2 reference, 9 model) were
+included only once per HIT. The order of these captions was
+randomized per HIT to prevent bias introduced by identical
+caption ordering between HITs. By this arrangement, each
+screen-caption pair was evaluated by 11 participants. After
+viewing these screenshot-caption pairs, participants were asked
+to answer six evaluation questions. Three of these questions
+(EQ1-EQ3) were adapted from prior work that assessed the
+quality of automatically generated code summaries [21], and
+inquired about accuracy, completeness, and understandability,
+respectively. The three remaining questions (EQ4-EQ6), were
+free response and asked participants to explain accuracies,
+inaccuracies, and improvements. The full set of questions and
+HIT are in our online appendix [39]. Similar to the CLARITY
+dataset collection, each participant’s response was thoroughly
+vetted by at least one author, and discarded if the answers
+were incomplete. Responses were collected until 220 HITs
+were completed by unique respondents.
+B. Evaluation Results
+1) RQ3 Results: Evaluating BLEU Scores: We illustrate
+the BLEU score results for the most effective model config-
+uration and checkpoint across all of our trained models in
+Table VI, whereas the results for other model configurations
+can be found in our online appendix [39] in addition to
+caption examples. The cells highlighted in blue illustrate the
+highest performing model configuration for each caption type.
+In general we observe that SAT exhibits the highest overall
+BLEU scores across all caption granularities. We speculate
+that this is attributable to the addition of the advanced attention
+mechanism in this model that is able to “focus” on varying
+image regions or features to effectively handle multiple caption
+granularities. In general, the seq2seq model performed quite
+poorly across the varying caption types, indicating a lower
+tendency for rich representation. Perhaps most interestingly,
+we see that the optimal model configurations for the im2txt
+framework were those where the CNN was conditioned on
+domain specific datasets. More specifically, the best high-level
+caption model was conditioned on full screenshots and the
+best low-level caption was conditioned on the cropped GUI-
+component screenshots.
+Another general trend that emerges is the low-level and
+combined caption models tend to exhibit higher overall BELU
+scores compared to the high-level captions. This is somewhat
+intuitive, as it indicates that there are more natural connections
+between visual GUI and lexical patterns in the low-level
+captions, compared to the high-level captions that reflect more
+abstract functional descriptions. When examining the captions
+generated by the optimal configurations of each model, it is
+clear that im2txt and SAT produces a more diverse set of out-
+put captions than neuraltalk2, which could be considered
+as more useful in many software documentation tasks.
+Finally, it is worth discussing how the BLEU scores of our
+models compare to those of the same models trained on the
+8
+
+None
+Some
+A Lot
+im2txt high
+im2txt low
+im2txt combined
+Easy to Read
+Somewhat
+Readable
+Hard to 
+Read
+im2txt high
+im2txt low
+im2txt combined
+EQ3: Understandability
+EQ2:  Unnecessary Information
+im2txt high
+im2txt low
+im2txt combined
+Strongly 
+Disagree
+ Disagree
+Neutral
+Agree
+Strongly
+Agree
+EQ1: Accuracy
+seq2seq high
+seq2seq low
+seq2seq combined
+Fig. 5: Responses across models for EQ1-EQ3
+more traditional Flickr8k [37] and MSCOCO [38] datasets
+given at the bottom of Table VI. Given the data-intensive
+nature of our DL models, and the much larger size of the
+MSCOCO dataset (≈123k images, each with 5 captions), we
+did not expect our models trained on the CLARITY dataset to
+outperform those trained on MSCOCO. Thus, unsurprisingly,
+we observe that on average, im2txt, neuraltalk2, and SAT
+models trained on the MSCOCO dataset outperform the same
+models trained on the CLARITY datasets by ≈ 10 BLEU score
+points for the combined and low level captions, and ≈ 27
+points on high-level captions. However, when we examine
+the performance of Neuraltalk2 on the more similarly sized
+Flickr8K dataset (≈ 8K images, each with 5 captions) we
+observe comparable performance to the CLARITY low-level
+and combined datasets, with the SAT model narrowly outper-
+forming the Flickr8K neuraltalk2 model, with a slightly
+bigger discrepancy for the high-level captions. Overall, these
+results indicate that when compared with datasets of similar
+size, DL models trained on the CLARITY dataset exhibit
+similar performance.
+2) RQ4 Results: Human Evaluations: The results of EQ1-
+EQ3 for the model configurations with the best performance
+during the human study, in addition to the seq2seq accuracy
+scores, are summarized in Fig. 5. Complete results across all
+model configurations can be found in our online appendix. The
+responses to EQ4-EQ6 varied by the type of caption, and are
+provided in our appendix in full. Generally, im2txt fared the
+best in terms of accuracy, and was followed by neuraltalk2
+and seq2seq respectively. For im2txt, despite mixed reac-
+tions from participants, in many cases respondents verified that
+the caption was accurate (e.g., ”The description accurately
+describes the screen, it is in fact a terms and conditions
+screen.”) and suggested minor improvements similarly to the
+reference captions (e.g., ”It could add specifics about what the
+settings pertain to (i.e. security)”). As illustrated in Fig. 5 the
+im2txt predictions were consistently rated as being readable
+and containing relevant information. It is also interesting to
+note that there appears to a mismatch between the performance
+as indicated by BLEU scores, and human perceptions, with the
+participants consistently rating the im2txt captions better
+than other models across EQ1-EQ3, despite neuraltalk2
+achieving a higher BLEU score for two model configurations.
+VIII. DISCUSSION & LEARNED LESSONS
+Lesson 1: Functional Descriptions of GUIs exhibit a
+high degree of naturalness and can be modeled using DL
+techniques. We observed that DL models trained on the low-
+level and combined datasets exhibit similar performance to
+models trained on general image captioning datasets of similar
+size (e.g., Flickr8K). This indicates that GUI screenshots could
+be used to augment approaches for automated documentation.
+Lesson 2: GUI-centric software documentation mod-
+els benefit from being pre-trained on domain specific
+GUI data, as opposed to general image datasets (e.g.,
+MSCOCO) The qualitative results of our model analysis
+illustrate that for im2txt, the most effective configurations
+were those trained on domain specific CNN datasets. This
+suggests a perceptible difference between the utility of image
+features learned from general datasets, compared to those
+learned on datasets more specific to software. This suggests
+that future work aiming to leverage DL models for GUI-
+centric program documentation should look to collecting and
+extracting features from large-scale GUI-related datasets.
+Lesson 3: Future automated approaches for GUI-centric
+program documentation would likely benefit from com-
+bining the orthogonal semantics of screenshots and GUI-
+metadata. Our evaluation in this paper illustrates that the rep-
+resentational power of screenshots appears to be superior when
+applied to a software documentation task. However, given stark
+differences between these two modalities of information, we
+also observed that they encode orthogonal semantic patterns
+that could be combined for more effective documentation
+generation. One property we observed of certain captions
+generated by the image-based models was the effect of their
+limited vocabulary. For example, certain predicted captions
+similar to the following: “The screen allows the user to select
+a <UNK>”, wherein the UNK token represents missing token,
+which should be mapped to some unobserved app property,
+such as a “album cover” or “store location”. However, such
+predictions could be combined with the vocabulary present in
+GUI metadata to help predict more complete, and accurate
+descriptions. Thus, a promising direction for future work is to
+jointly encode both screenshots and lexical GUI-metadata.
+Lesson 4: Training image captioning models to predict
+specific or diverse pieces of functionality is difficult.
+Practical models for GUI-centric documentation should able
+to predict both specific pieces of information (e.g. the func-
+tionality of a particular button for a given method handler),
+and diverse functionality (being able to generate descriptions
+of functionality anywhere on a given screen). However, one
+aspect we observed across our models is that the most
+common observed types of functionality (e.g., back buttons,
+menu buttons) corresponded to the functionalities that our
+9
+
+seq2seq high
+seq2seq low
+0
+0
+seq2seq combined
+0
+0models predicted most often and most confidently on unseen
+screenshots. This is somewhat expected, as the models saw the
+most examples of such functionalities during training. Thus,
+the diversity of predictions is an open problem for future
+research. This problem can be partially mitigated by larger,
+more diverse datasets with specifically curated descriptions
+(such as extensions to the CLARITY dataset). However, it is
+likely that domain-specific models, or ensembles of models,
+may be required to more effectively predict diverse features.
+Lesson 5: Future studies that evaluate automated GUI-
+centric documentation approaches should include human
+studies, as human perceptions of models may differ from
+automated reference-based metrics. One of the more surpris-
+ing results of our study is that there seems to be a mismatch
+between humans perceptions of the captions generated by our
+DL models and the BLEU score metrics typically used to asses
+the accuracy of model predictions. This signifies that there are
+aspects of human perception that are not effectively captured
+in the BLEU metric, and possibly other translation metrics.
+IX. LIMITATIONS & THREATS TO VALIDITY
+Internal Validity. Threats to internal validity correspond to
+unexpected factors in the experiments that may contribute to
+observed results. To derive our dataset we rely on MTurk and
+its workers to extract the high- and low-level descriptions per
+each screenshot. It should be noted that we did not ask MTurk
+workers to provide technical software documentation descrip-
+tions, but rather general descriptions of screen functionality at
+differing granularities. To minimize low quality captions we
+published the jobs for workers with more than 1k HITS, from
+English speaking countries, and HIT approval rate of more
+than 90%. Also, each successfully completed HIT was vetted
+by at least one of the authors to assure quality. If there was
+any question related to caption quality, at least one of the other
+authors stepped in to resolve the ambiguity. As a result 2,429
+HITs were rejected due to low quality descriptions.
+External Validity. Threats to external validity concern the
+generalization of the results. As with any collected dataset,
+there is a threat to external validity about the generalizability
+of the CLARITY dataset. However, we used a diverse set
+of popular apps from the Android domain, extracted popular
+screenshots from these apps, and the apps were captioned by
+a large and diverse set of MTurk workers. During our data
+collection process, we only collected 4 low-level captions per
+each screen in order to make the task feasible for MTurk
+workers as workers tend to abandon or perform poorly on long
+tasks. This means that, for certain screens with many GUI-
+components, some components may lack natural language
+descriptions. However, given the size of our dataset and the
+diversity of our screenshots and captions, we assert that our
+low-level captions are reasonably representative.
+X. RELATED WORK
+DL for Image Captioning and GUIs. Hossain et al. [64]
+recently performed a wide-ranging study on DL models for
+image captioning, surveying the many different architectures
+and datasets used to evaluate them. However, this survey
+did not examine the ability of any image captioning model
+to predict functional descriptions of software. There have
+been a limited number of papers in the SE community that
+have applied DL techniques to GUI related data. Chen et
+al. [65] designed an approach that uses an NMT to translate
+an Android screenshot into a GUI-skeleton. However, their
+technique is able to predict GUI structure given an image, not
+functional natural language descriptions. Recently, Zhang et.
+al. [66] created a dataset of iOS image captions to train a
+model for captioning accessibility data. However, the authors
+do not make their dataset publicly available and target a
+different goal of accessibility data compared our goal of
+generating functional captions. Chen et al. investigated the
+use of DL image captioning models for applying labels to
+GUI-components in mobile apps [67], however, this approach
+only aims to predict short labels for a limited subset of
+GUI-components, whereas our study focuses upon predicting
+functional descriptions consisting of complete sentences for
+both individual GUI-components and entire screenshots.
+GUI-based Analysis of Mobile Apps. GVT and GCat analyze
+the visual properties of GUIs to detect design violations and
+evolutionary changes [68], [69]. In contrast, we focus solely on
+image captioning techniques to provide functional program de-
+scriptions of screenshots. Approaches such as REMAUI [70],
+REDRAW [48], and pix2code [71] aim to automatically
+generate mobile app code given an app screenshot. Conversely,
+we leverage DL techniques to generate functional descriptions
+rather than source code using a pixel-based image as input.
+Chen et al. [72] introduced StoryDroid, for automatically
+generating visual storyboards of Android apps to help aid
+in the app design process. However, their approach is not
+capable of generating a functional description of an application
+from GUI data. Furthermore, Deka et al. showed how the
+Rico dataset could be navigated via semantic search using
+autoencoders
+[35]. UiRef [73] is an approach for resolving
+security and privacy concerns by considering semantics of
+GUI-components that request user’s inputs. Moreover, Liu et
+al. [74] presented an approach for automatically classifying
+mobile app icons according to semantic GUI patterns. Xiao et
+al. proposed IconIntent that combines program analysis and
+icon classification to detect privacy sensitive GUI-components
+[75]. Different from this body of work, we aim to predict
+functional descriptions of GUIs for software documentation.
+XI. CONCLUSION
+In this paper, we have conducted one of the first com-
+prehensive empirical investigations into the connection be-
+tween GUI-related information, and functional descriptions
+of programs. We have derived the CLARITY dataset of GUI
+screenshots/metadata and NL captions, trained DL models
+on this dataset, and demonstrated their ability to bridge the
+semantic gap between visual and lexical program information.
+ACKNOWLEDGMENT
+This work was supported by the NSF CCF-2007246 &
+CCF-1955853 grants. Any opinions, findings, and conclusions
+expressed herein are the authors’ and do not necessarily reflect
+those of the sponsors.
+10
+
+REFERENCES
+[1] J.-C. Chen and S.-J. Huang, “An empirical analysis of the impact of
+software development problem factors on software maintainability,” J.
+Syst. Softw., vol. 82, pp. 981–992, June 2009.
+[2] M. Kajko-Mattsson, “A survey of documentation practice within correc-
+tive maintenance,” Empirical Software Engineering, vol. 10, pp. 31–55,
+Jan 2005.
+[3] B. Dagenais and M. P. Robillard, “Creating and evolving developer
+documentation: Understanding the decisions of open source contribu-
+tors,” in Proceedings of the Eighteenth ACM SIGSOFT International
+Symposium on Foundations of Software Engineering, FSE ’10, (New
+York, NY, USA), pp. 127–136, ACM, 2010.
+[4] G. Garousi, V. Garousi-Yusifoglu, G. Ruhe, J. Zhi, M. Moussavi, and
+B. Smith, “Usage and usefulness of technical software documentation:
+An industrial case study,” Information and Software Technology, vol. 57,
+pp. 664 – 682, 2015.
+[5] A. Forward and T. C. Lethbridge, “The relevance of software documen-
+tation, tools and technologies: A survey,” in Proceedings of the 2002
+ACM Symposium on Document Engineering, DocEng ’02, (New York,
+NY, USA), pp. 26–33, ACM, 2002.
+[6] “The agile manfiesto http://agilemanifesto.org.”
+[7] J. Zhi, V. Garousi-Yusiflu, B. Sun, G. Garousi, S. Shahnewaz, and
+G. Ruhe, “Cost, benefits and quality of software development docu-
+mentation,” J. Sys. Sof., Jan. 2015.
+[8] B. Fluri, M. Wursch, and H. C. Gall, “Do code and comments co-
+evolve? on the relation between source code and comment changes,” in
+Proceedings of the 14th Working Conference on Reverse Engineering,
+WCRE ’07, (Washington, DC, USA), pp. 70–79, 2007.
+[9] L. Moreno, A. Marcus, L. Pollock, and K. Vijay-Shanker, “JSummarizer:
+An automatic generator of natural language summaries for Java classes,”
+in 2013 21st International Conference on Program Comprehension,
+ICPC’13, pp. 230–232, May 2013.
+[10] L. Moreno, J. Aponte, G. Sridhara, A. Marcus, L. Pollock, and K. Vijay-
+Shanker, “Automatic generation of natural language summaries for Java
+classes,” in 2013 21st International Conference on Program Compre-
+hension, ICPC’13, pp. 23–32, May 2013.
+[11] P. C. Rigby and M. P. Robillard, “Discovering Essential Code Elements
+in Informal Documentation,” in Proceedings of the 2013 International
+Conference on Software Engineering, ICSE’13, (San Francisco, CA,
+USA), pp. 832–841, 2013.
+[12] A. T. T. Ying and M. P. Robillard, “Selection and Presentation Prac-
+tices for Code Example Summarization,” in Proceedings of the 22Nd
+ACM SIGSOFT International Symposium on Foundations of Software
+Engineering, FSE’14, (Hong Kong, China), pp. 460–471, 2014.
+[13] A. T. T. Ying and M. P. Robillard, “Code Fragment Summarization,” in
+Proceedings of the 2013 9th Joint Meeting on Foundations of Software
+Engineering, FSE’13, pp. 655–658, 2013.
+[14] I. K. Ratol and M. P. Robillard, “Detecting fragile comments,” in
+2017 32nd IEEE/ACM International Conference on Automated Software
+Engineering, ASE’17, pp. 112–122, Oct. 2017.
+[15] M. J. Howard, S. Gupta, L. Pollock, and K. Vijay-Shanker, “Automati-
+cally mining software-based, semantically-similar words from comment-
+code mappings,” in 2013 10th Working Conference on Mining Software
+Repositories, MSR’13, pp. 377–386, may 2013.
+[16] C. Treude and M. P. Robillard, “Augmenting API Documentation with
+Insights from Stack Overflow,” in Proceedings of the 38th International
+Conference on Software Engineering, ICSE ’16, (New York, NY, USA),
+pp. 392–403, 2016.
+[17] G. Petrosyan, M. P. Robillard, and R. De Mori, “Discovering Information
+Explaining API Types Using Text Classification,” in Proceedings of
+the 37th International Conference on Software Engineering - Volume
+1, ICSE ’15, (Florence, Italy), pp. 869–879, 2015.
+[18] B. Li, C. Vendome, M. Linares-V´asquez, D. Poshyvanyk, and N. A.
+Kraft, “Automatically Documenting Unit Test Cases,” in 2016 IEEE In-
+ternational Conference on Software Testing, Verification and Validation,
+ICST’16, pp. 341–352, Apr. 2016.
+[19] L. Moreno, W. Bandara, S. Haiduc, and A. Marcus, “On the Relationship
+between the Vocabulary of Bug Reports and Source Code,” in 2013 IEEE
+International Conference on Software Maintenance, ICSM’13, pp. 452–
+455, Sept. 2013.
+[20] K. Moran, M. Linares-V´asquez, C. Bernal-C´ardenas, and D. Poshy-
+vanyk, “Auto-completing Bug Reports for Android Applications,” in
+Proceedings of the 2015 10th Joint Meeting on Foundations of Software
+Engineering, FSE’15, (Bergamo, Italy), pp. 673–686, 2015.
+[21] L. Moreno, G. Bavota, M. D. Penta, R. Oliveto, A. Marcus, and
+G. Canfora, “Arena: An approach for the automated generation of release
+notes,” IEEE Transactions on Software Engineering, vol. 43, pp. 106–
+127, Feb 2017.
+[22] L. Moreno, G. Bavota, M. Di Penta, R. Oliveto, A. Marcus, and
+G. Canfora, “Automatic Generation of Release Notes,” in Proceedings
+of the 22Nd ACM SIGSOFT International Symposium on Foundations
+of Software Engineering, FSE’14, pp. 484–495, 2014.
+[23] S. Jiang, A. Armaly, and C. McMillan, “Automatically generating
+commit messages from diffs using neural machine translation,” in
+2017 32nd IEEE/ACM International Conference on Automated Software
+Engineering, ASE’17, pp. 135–146, oct 2017.
+[24] L. F. Cort´es-Coy, M. Linares-V´asquez, J. Aponte, and D. Poshyvanyk,
+“On automatically generating commit messages via summarization of
+source code changes,” in 2014 IEEE 14th International Working Con-
+ference on Source Code Analysis and Manipulation, SCAM’14, Sep.
+2014.
+[25] P. Chatterjee, B. Gause, H. Hedinger, and L. Pollock, “Extracting
+Code Segments and Their Descriptions from Research Articles,” in
+Proceedings of the 14th International Conference on Mining Software
+Repositories, MSR ’17, (Buenos Aires, Argentina), pp. 91–101, 2017.
+[26] M. Linares-V´asquez, B. Li, C. Vendome, and D. Poshyvanyk, “Doc-
+umenting database usages and schema constraints in database-centric
+applications,” in Proceedings of the 25th International Symposium on
+Software Testing and Analysis, ISSTA 2016, (New York, NY, USA),
+pp. 270–281, 2016.
+[27] T. J. Biggerstaff, B. G. Mitbander, and D. E. Webster, “Program
+understanding and the concept assignment problem,” Commun. ACM,
+vol. 37, pp. 72–82, May 1994.
+[28] J. Guo, J. Cheng, and J. Cleland-Huang, “Semantically enhanced soft-
+ware traceability using deep learning techniques,” in Proceedings of
+the 39th International Conference on Software Engineering, ICSE ’17,
+(Piscataway, NJ, USA), pp. 3–14, 2017.
+[29] M. P. Robillard, A. Marcus, C. Treude, G. Bavota, O. Chaparro, N. Ernst,
+M. A. Gerosa, M. Godfrey, M. Lanza, M. Linares-V´asquez, G. C.
+Murphy, L. Moreno, D. Shepherd, and E. Wong, “On-demand Developer
+Documentation,” in 2017 IEEE International Conference on Software
+Maintenance and Evolution, ICSME’17, pp. 479–483, Sept. 2017.
+[30] “Android inches ahead of windows as most popular os - https://www.
+cnet.com/news/android-most-popular-os-beats-windows-statcounter/.”
+[31] K. Moran, C. Bernal-C´ardenas, M. Linares-V´asquez, and D. Poshy-
+vanyk, “Overcoming lanaguge dichotomies: Toward effective program
+comprehension for mobile app development,” in 26th IEEE International
+Conference on Program Compreehnsion, May 2018. To Appear.
+[32] A. M. Memon, A comprehensive framework for testing graphical user
+interfaces. Ph.D., 2001. Advisors: Mary Lou Soffa and Martha Pol-
+lack; Committee members: Prof. Rajiv Gupta (University of Arizona),
+Prof. Adele E. Howe (Colorado State University), Prof. Lori Pollock
+(University of Delaware).
+[33] A. Solem, “Designing computer documentation that will be used: Un-
+derstanding computer user attitudes,” in Proceedings of the 4th Annual
+International Conference on Systems Documentation, SIGDOC ’85,
+(New York, NY, USA), p. 55–56, Association for Computing Machinery,
+1986.
+[34] A. Alshayban, I. Ahmed, and S. Malek, “Accessibility issues in android
+apps: State of affairs, sentiments, and ways forward,” in Proceedings
+of the 42nd International Conference on Software Engineering, ICSE
+2020, (New York, NY, USA), p. to appear, ACM, 2020.
+[35] B. Deka, Z. Huang, C. Franzen, J. Hibschman, D. Afergan, Y. Li,
+J. Nichols, and R. Kumar, “Rico: A mobile app dataset for building
+data-driven design applications,” in Proceedings of the 30th Annual
+Symposium on User Interface Software and Technology, UIST ’17, 2017.
+[36] K. Moran, C. Bernal-Cardenas, M. Curcio, R. Bonett, and D. Poshy-
+vanyk, “The ReDraw Dataset: A Set of Android Screenshots, GUI Meta-
+data, and Labeled Images of GUI Components,” Jan. 2019. Supported
+by NSF Grant CCF-1815186.
+[37] M. Hodosh, P. Young, and J. Hockenmaier, “Framing image description
+as a ranking task: Data, models and evaluation metrics,” J. Artif. Int.
+Res., vol. 47, no. 1, pp. 853–899, 2013.
+[38] T. Y. Lin, M. Maire, S. Belongie, J. Hays, P. Perona, D. Ramanan,
+P. Doll´ar, and C. L. Zitnick, “Microsoft COCO: Common Objects in
+Context,” in Lecture Notes in Computer Science (including subseries
+Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinfor-
+matics), vol. 8693 LNCS, pp. 740–755, 2014.
+11
+
+[39] “Online appendix http://sagelab.io/Clarity/.”
+[40] A. Karpathy and L. Fei-Fei, “Deep visual-semantic alignments for
+generating image descriptions,” IEEE Trans. Pattern Anal. Mach. Intell.,
+vol. 39, pp. 664–676, Apr. 2017.
+[41] O. Vinyals, A. Toshev, S. Bengio, and D. Erhan, “Show and tell: Lessons
+learned from the 2015 mscoco image captioning challenge,” IEEE Trans.
+Pattern Anal. Mach. Intell., vol. 39, pp. 652–663, Apr. 2017.
+[42] K. Xu, J. Ba, R. Kiros, K. Cho, A. C. Courville, R. Salakhutdinov, R. S.
+Zemel, and Y. Bengio, “Show, attend and tell: Neural image caption
+generation with visual attention,” in ICML, 2015.
+[43] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet Classification
+with Deep Convolutional Neural Networks,” in Advances in Neural In-
+formation Processing Systems 25 (F. Pereira, C. J. C. Burges, L. Bottou,
+and K. Q. Weinberger, eds.), pp. 1097–1105, 2012.
+[44] K. Simonyan and A. Zisserman, “Very deep convolutional networks for
+large-scale image recognition,” International Conference on Learning
+Represen., vol. abs/1409.1556, 2014.
+[45] C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan,
+V. Vanhoucke, and A. Rabinovich, “Going Deeper with Convolutions,”
+in Computer Vision and Pattern Recognition, 2015.
+[46] S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural
+Comput., vol. 9, no. 8, pp. 1735–1780, 1997.
+[47] M. Schuster and K. Paliwal, “Bidirectional recurrent neural networks,”
+Trans. Sig. Proc., vol. 45, pp. 2673–2681, Nov. 1997.
+[48] K. P. Moran, C. Bernal-C´ardenas, M. Curcio, R. Bonett, and D. Poshy-
+vanyk, “Machine learning-based prototyping of graphical user interfaces
+for mobile apps,” IEEE Transactions on Software Engineering, pp. 1–1,
+2018.
+[49] D. M. Blei, A. Y. Ng, and M. I. Jordan, “Latent dirichlet allocation,” J.
+Mach. Learn. Res., vol. 3, pp. 993–1022, Mar. 2003.
+[50] I. Porteous, D. Newman, A. Ihler, A. Asuncion, P. Smyth, and
+M. Welling, “Fast collapsed gibbs sampling for latent dirichlet al-
+location,” in Proceedings of the 14th ACM SIGKDD International
+Conference on Knowledge Discovery and Data Mining, KDD ’08, (New
+York, NY, USA), pp. 569–577, 2008.
+[51] A. Hindle, E. T. Barr, Z. Su, M. Gabel, and P. Devanbu, “On the
+Naturalness of Software,” in International Conference on Software
+Engineering, ICSE’12, pp. 837–847, 2012.
+[52] M. Rahman, D. Palani, and P. Rigby, “Natural software revisted,” in Pro-
+ceedings of the 41st International Conference on Software Engineering
+Companion, ICSE ’19, (Montreal, QC Canada), p. to appear, 2019.
+[53] “Mit language modeling toolkit https://github.com/mitlm/mitlm.”
+[54] P. Koehn, Statistical Machine Translation. 1st ed., 2010.
+[55] “Google’s im2txt implementation https://github.com/tensorflow/models/
+tree/master/research/im2txt.”
+[56] “Neuraltalk2 implementation https://github.com/karpathy/neuraltalk2.”
+[57] “Google seq2seq framework https://github.com/google/seq2seq.”
+[58] C. Szegedy, V. Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna, “Rethinking
+the inception architecture for computer vision,” in 2016 IEEE Confer-
+ence on Computer Vision and Pattern Recognition, June 2016.
+[59] O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma,
+Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, A. C. Berg, and
+L. Fei-Fei, “ImageNet Large Scale Visual Recognition Challenge,”
+International Journal of Computer Vision, vol. 115, no. 3, pp. 211–252,
+2015.
+[60] “Show, attend and tell implementation https://github.com/coldmanck/
+show-attend-and-tell.”
+[61] L. Sha, L. Mou, T. Liu, P. Poupart, S. Li, B. Chang, and Z. Sui,
+“Order-planning neural text generation from structured data,” The
+Thirty-Second AAAI Conference on Artificial Intelligence (AAAI’17),
+vol. abs/1709.00155, 2017.
+[62] D. Britz, A. Goldie, T. Luong, and Q. Le, “Massive Exploration of
+Neural Machine Translation Architectures,” ArXiv e-prints, Mar. 2017.
+[63] K. Papineni, S. Roukos, T. Ward, and W.-J. Zhu, “Bleu: A method for
+automatic evaluation of machine translation,” in Proceedings of the 40th
+Annual Meeting on Association for Computational Linguistics, ACL ’02,
+(Stroudsburg, PA, USA), pp. 311–318, 2002.
+[64] M. Z. Hossain, F. Sohel, M. F. Shiratuddin, and H. Laga, “A compre-
+hensive survey of deep learning for image captioning,” ACM Comput.
+Surv., vol. 51, pp. 118:1–118:36, Feb. 2019.
+[65] S. Chen, L. Fan, C. Chen, T. Su, W. Li, Y. Liu, and L. Xu, “Storydroid:
+Automated generation of storyboard for android apps,” in Proceedings of
+the 41st International Conference on Software Engineering, ICSE ’19,
+(Piscataway, NJ, USA), pp. 596–607, IEEE Press, 2019.
+[66] X. Zhang, L. de Greef, A. Swearngin, S. White, K. Murray, L. Yu,
+Q. Shan, J. Nichols, J. Wu, C. Fleizach, A. Everitt, and J. P. Bigham,
+Screen Recognition: Creating Accessibility Metadata for Mobile Appli-
+cations from Pixels. New York, NY, USA: Association for Computing
+Machinery, 2021.
+[67] J. Chen, C. Chen, Z. Xing, X. Xu, L. Zhu, G. Li, and J. Wang, “Unblind
+your apps: Predicting natural-language labels for mobile gui components
+by deep learning,” in Proceedings of the 42nd International Conference
+on Software Engineering, ICSE 2020, (New York, NY, USA), p. to
+appear, ACM, 2020.
+[68] K. Moran, C. Watson, J. Hoskins, G. Purnell, and D. Poshyvanyk,
+“Detecting and summarizing gui changes in evolving mobile apps,”
+in Proceedings of the 33rd ACM/IEEE International Conference on
+Automated Software Engineering, ASE 2018, (New York, NY, USA),
+pp. 543–553, 2018.
+[69] K. Moran, B. Li, C. Bernal-C´ardenas, D. Jelf, and D. Poshyvanyk,
+“Automated Reporting of GUI Design Violations in Mobile Apps,” in
+Proceedings of the 40th International Conference on Software Engineer-
+ing Companion, ICSE ’18, (Gothenburg, Sweden), p. to appear, 2018.
+[70] T. A. Nguyen and C. Csallner, “Reverse Engineering Mobile Application
+User Interfaces with REMAUI,” in Proceedings of the 2015 30th
+IEEE/ACM International Conference on Automated Software Engineer-
+ing, ASE’15, (Washington, DC, USA), pp. 248–259, 2015.
+[71] T. Beltramelli, “Pix2code: Generating Code from a Graphical User
+Interface Screenshot,” CoRR, vol. abs/1705.07962, 2017.
+[72] Q. Chen and M. Zhou, “A neural framework for retrieval and summariza-
+tion of source code,” in Proceedings of the 33rd ACM/IEEE International
+Conference on Automated Software Engineering, ASE 2018, (New York,
+NY, USA), pp. 826–831, ACM, 2018.
+[73] B. Andow, A. Acharya, D. Li, W. Enck, K. Singh, and T. Xie, “UiRef:
+analysis of sensitive user inputs in Android applications,” in Proceedings
+of the 10th ACM Conference on Security and Privacy in Wireless and
+Mobile Networks, WiSec’17, (New York, New York, USA), pp. 23–34,
+2017.
+[74] T. F. Liu, M. Craft, J. Situ, E. Yumer, R. Mech, and R. Kumar, “Learning
+design semantics for mobile apps,” in The 31st Annual ACM Symposium
+on User Interface Software and Technology, UIST ’18, (New York, NY,
+USA), pp. 569–579, 2018.
+[75] X. Xiao, X. Wang, Z. Cao, H. Wang, and P. Gao, “Iconintent: Automatic
+identification of sensitive ui widgets based on icon classification for
+android apps,” in Proceedings of the 41st International Conference on
+Software Engineering Companion, ICSE ’19, (Montreal, QC Canada),
+p. to appear, 2019.
+12
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf,len=1240
+page_content='An Empirical Investigation into the Use of Image  Captioning for Automated Software Documentation  Kevin Moran†, Ali Yachnes∗, George Purnell∗, Junayed Mahmud†,  Michele Tufano‡, Carlos Bernal Cardenas‡, Denys Poshyvanyk∗, Zach H’Doubler∗  †George Mason University, VA, USA, ∗William & Mary, VA, USA, ‡Microsoft, WA, USA  kpmoran@gmu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='edu, ayachnes@email.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='wm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='edu, gwpurnell@email.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='wm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='edu, jmahmud@gmu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='edu  michele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='tufano@microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='com, carlosbe@microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='com, denys@cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='wm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='edu, pzhdoubler@email.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='wm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='edu  Abstract—Existing automated techniques for software docu-  mentation typically attempt to reason between two main sources  of information: code and natural language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, this reason-  ing process is often complicated by the lexical gap between more  abstract natural language and more structured programming  languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' One potential bridge for this gap is the Graphical User  Interface (GUI), as GUIs inherently encode salient information  about underlying program functionality into rich, pixel-based  data representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This paper offers one of the first com-  prehensive empirical investigations into the connection between  GUIs and functional, natural language descriptions of software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  First, we collect, analyze, and open source a large dataset of  functional GUI descriptions consisting of 45,998 descriptions  for 10,204 screenshots from popular Android applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The  descriptions were obtained from human labelers and underwent  several quality control mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' To gain insight into the  representational potential of GUIs, we investigate the ability of  four Neural Image Captioning models to predict natural language  descriptions of varying granularity when provided a screenshot  as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We evaluate these models quantitatively, using common  machine translation metrics, and qualitatively through a large-  scale user study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Finally, we offer learned lessons and a discussion  of the potential shown by multimodal models to enhance future  techniques for automated software documentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Index Terms—Software Documentation, Image Captioning,  Deep Learning  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' INTRODUCTION & MOTIVATION  Proper documentation is generally considered to be an inte-  gral component of building and distributing modern software  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In fact, past studies have illustrated the general ben-  efits of documentation during the development lifecycle [1],  [2], [3], [4] and the importance of technical documentation  to software maintenance and evolution [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, despite  the value of well-documented systems, modern development  processes and constraints often lead to the disregard or aban-  donment of a range of documentation tasks [6], [5], [2], [7],  [8], [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' These difficulties have given rise to a wealth of  research on automated techniques that aim to ease the burden  on stakeholders by generating various types of documentation  for a given task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For example, existing approaches have been  developed to automatically generate natural language sum-  maries and documentation for code [9], [10], [11], [12], [13],  [14], [15], APIs [16], [17], unit tests [18], bug reports [19],  [20], release notes [21], [22], and commit messages [23], [24],  among other artifacts [25], [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Generally, existing techniques for automated software doc-  umentation have been concerned with modeling relationships  that exist between two primary information modalities: code  and natural language (NL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Unfortunately, reasoning between  these two information sources is difficult due to the lexical  gap resulting from the often disparate conceptual associations  that connect source code lexicon and the more abstract words  and phrases used in NL descriptions  [27], [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Recently,  this lexical gap was acknowledged as an information inference  problem in a report made by Robillard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [29], wherein  key research challenges exist in (i) inferring undocumented  program properties, and (ii) discovering latent abstractions  and rationales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' These challenges suggest that overcoming the  semantic disconnect between code and NL may require new  knowledge sources that encode distinct program properties  typically absent from traditional software or NL lexicon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  One source of information which has been left largely  unexplored for the purposes of automated documentation is  visual software data encoded into Graphical User Interfaces  (GUIs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' GUI-based applications predominate modern user-  facing software, as can be readily seen in the popularity of  desktop and mobile apps [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Furthermore, high quality ap-  plications with well-designed GUIs allow technically-inclined  users to instinctively understand underlying program features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Thus, intuitively, certain functional properties of applications  are encoded into the visual, pixel-based representation of the  GUI such that cognitive human processes can determine the  computing tasks provided by the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This suggests that  there are latent patterns that exist within visual GUI data  which indicate the presence of natural use cases capturing core  functionality [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Given the inherent representational power of GUIs in con-  veying program related information, we set forth the following  hypothesis that serves as the basis for work in this paper:  The representational power of graphical user interfaces to  convey program-related information can be meaningfully  leveraged to support automated techniques for software doc-  umentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  While most existing work on automated documentation con-  cerns itself with the dichotomy between code and NL, we posit  that the latent information encoded within GUIs can aid in  bridging the existing semantic documentation gap by providing  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='01224v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='SE]  3 Jan 2023  an additional source of knowledge that inherently reflects pro-  gram functionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In fact, GUI-based representations of soft-  ware have the potential to address the two challenges set forth  by Robillard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' More specifically, GUIs can aid in  inferring undocumented program properties that are inherently  represented within the design of GUI controls or widgets (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=',  capturing a feature which is otherwise poorly represented by  low-quality code identifiers/comments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Further, GUIs could  be used as source to mine abstractions or rationales that  would otherwise remain obscure (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', providing a use case-  based explanation of a block of code connected to a GUI  screen).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In overcoming these challenges, we see GUI-centric  documentation having an impact on the following types of  software documentation:  Technical Documentation: Developers utilize technical docu-  mentation, such as code comments or READMEs, in order  to learn about the functionality and interfaces of software  to support engineering tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Automatically generating such  documentation accurately is a challenging inference problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  However, it has been shown that GUI-related code can com-  prise as much as half of the code in user facing programs [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  This means that graphical software data is connected in some  way to large portions of GUI-based software projects i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=',  through GUI-event handlers, or code stipulating GUI layouts  such as html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Therefore, if automated techniques are able to  effectively infer salient functionality from the GUIs, they could  be combined with existing techniques and leveraged to provide  automation to developers, such as comment generation or code  summarization with greater feature-based context awareness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  As we illustrate in this paper, GUI code/metadata appears to  encode orthogonal information compared to visual GUI data  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', screenshots), which suggests that we may be able to infer  documentation information from visual GUI data that likely  can’t be inferred from GUI code alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  User Documentation: Developers typically provide users with  documentation such as tutorials or walkthroughs to help  clearly illustrate software features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' While some experienced  users can infer functionality directly from a GUI, end-users  exhibit a range of technological expertise, and many rely upon  various forms of end-user documentation [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, building  techniques capable of automatically generating such documen-  tation would free up development effort for other critical tasks,  such as bug fixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Beyond typical user facing software aids,  GUI-centric program documentation could also enable entirely  new classes of automated accessibility features, which are  sorely needed for mobile apps [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For example, rather than a  typical text-to-speech engine, one could envision a screen-to-  functionality engine that could aid a motor-impaired user with  navigating the software, without extra development effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  To investigate the potential of automated GUI-centric soft-  ware documentation, we offer one of the first comprehensive  empirical investigations into this new research direction’s most  fundamental task: generating a natural language descrip-  tion given a screenshot (or screen-related information) of  a software GUI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Given that this task underlies the various  potential applications discussed above, we view this as a  logical first step towards investigating the feasibility of fu-  ture techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' To accomplish this, we collect and analyze  a dataset for Comprehending visuaL semAntics to pRedict  applicatIon functionalTY (the CLARITY dataset) consisting  of 45,998 functional descriptions of 10,204 screenshots of  popular Android apps available on Google Play.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We provide  a descriptive analysis of this dataset that investigates the  “naturalness” and semantic topics of the collected descriptions  by measuring cross-entropy compared to other corpora and  performing a topic modeling analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' To learn functional  descriptions of the screens from this dataset, we customize,  train, and test four Deep Learning (DL) models for neural  image captioning—three that learn from image data and one  that learns from textual GUI metadata—to predict functional  descriptions of software at different granularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We evaluate  the efficacy of these models both quantitatively, by measuring  the widely used BLEU metric, and qualitatively through a  large-scale user study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In summary, this paper’s contributions  are as follows:  We collect the CLARITY dataset of GUIs annotated  with 45,998 functional, NL descriptions from 10,204  screenshots of popular Android apps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The NL captions  were obtained from human labelers, underwent several  quality control mechanisms, and contain both high- and  low-level descriptions of screen functionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' While other  GUI datasets exist [35], [36], the CLARITY dataset differs  by providing an extensively labeled set of screens, akin  to Flickr8K [37] or MSCOCO [38];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  We illustrate the underlying, natural patterns that exist in  the CLARITY dataset through topic modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  We provide an extensive quantitative and qualitative eval-  uation of four tailored DL models for image captioning  using standard metrics and a large scale user study;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  We offer an online appendix with examples of model-  generated descriptions and experimental data [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Our  dataset, trained models, code, and evaluation scripts are  open source and accessible via the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' BACKGROUND  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The Connection between Images and NL  The task of image captioning is much more difficult than  that of classification or labeling, as an effective model must  be able to both learn salient features from images automati-  cally and semantically equate these features with the proper  NL words and grammar that describe them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This task of  semantically aligning two completely different modalities of  information has led to the development of multimodal DL  architectures that jointly embed NL and pixel-based infor-  mation in order to predict an appropriate description of a  given input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' These techniques are typically trained  on large-scale datasets that contain images annotated with  multiple captions, such as MSCOCO [38], and have largely  drawn inspiration from encoder-decoder neural language mod-  els traditionally applied to machine translation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In this  2  …  …  …  Input Image  CNN or RCNN  BRNN  or LSTM  xt  yt  W  st  v  Image “Encoder”  NL “Decoder”  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 1: Generalized overview of multimodal DL architectures  for image captioning (with RCNN)  paper, we adapt three recent architectures for image caption-  ing, neuraltalk2 [40], the im2txt [41], and the show,  attend and tell (SAT) [42] frameworks to predict func-  tional descriptions of software screenshots through the use of  custom pre-training and fine-tuning procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Additionally,  we explore the seq2seq neural language model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  DL models for image captioning build upon the success  of encoder-decoder neural language models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The im2txt  framework treats image captioning as a machine translation  problem, wherein the source “sentence” is an image, and  the target “translation” is a NL description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The generalized  architecture of such models is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' As illustrated,  these architectures replace the encoder RNN with a Convolu-  tional Neural Network (CNN), which have been shown to be  highly capable of learning rich image features [43], [44], [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Google’s implementation of im2txt uses a Long-Short Term  Memory (LSTM) RNN [46] for the “decoder” module, which  has also proven extremely effective when applied to machine  translation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The decoder module of the neuraltalk2  architecture is composed of a Bidirectional RNN (BRNN) [47]  as opposed to an LSTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Finally, the show, attend, &  tell (SAT) model [42] uses an LSTM decoder but with  the addition of an attention mechanism that can “attend” to  salient parts of the image representation by combining “hard”  and “soft” attention mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' OVERVIEW  In this section, we provide an “at-a-glance” overview of the  data-collection procedures and various analyses performed in  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Figure 2 illustrates the four major components of  the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The first major task of our study is to derive a  suitable dataset of screenshot-caption pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We describe this  process in two parts: (i) the collection of screenshots (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  IV-A), and (ii) the collection of captions from human workers  (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' IV-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The result of this data-collection effort is the  CLARITY dataset, which contains 45,998 captions of 10,204  Android screenshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Next, we aim to understand the lexical  properties of our captions through an empirical analysis in  order to better understand how easily they might be modeled  (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' V).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, we perform both a comparison of the the  cross-entropy of language models trained our caption corpus  to other popular SE corpora, and perform an LDA-based  topic analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Next, we discuss the process of configuring  and training three neural image captioning models, and one  1   Clarity Dataset Collection  (Screenshots + GUI metadata + Captions)  2  Naturalness & Topic Analysis  Cross-Entropy  Analysis  LDA-based  Topic Analysis  …  …  …  Input Image  CNN or RCNN  BRNN  or LSTM  xt  yt  W  st  v  Image “Encoder”  NL “Decoder”  3   Train Image-Captioning and  Metadata Captioning Models  Image-Captioning  Models  Metadata-Captioning  Models  4  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='antitative and !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='alitative  Model Evaluations  “Ground Truth”  Captions  “Predicted”  Captions  +  Screens  Large-Scale  Human Evaluation  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='antitative  Evaluation  with BLEU  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2: Overview of Dataset Collection and Analysis  sequence-based model to predict functional descriptions of  software GUIs (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' VI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Finally, we conclude our analysis  by measuring the accuracy of our trained models according to  both automated reference-based metrics (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', BLEU@n) and  via a large-scale human evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' VII)  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' DATASET COLLECTION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Screen & GUI Metadata Collection  The first step in deriving the CLARITY dataset is the  collection of a sizable and diverse dataset of screenshots and  GUI-metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We chose to focus this dataset derivation on the  Android platform for three main reasons: (i) Android is cur-  rently the most popular OS in the world [30], (ii) Android apps  are highly GUI-and gesture driven, making them a suitable  target for our investigation, and (iii) the Android screencap  and uiautomator tools facilitate the extraction of screenshots  and GUI-metadata from running apps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Fortunately, large-scale  datasets of Android screenshots and metadata are publicly  available in related literature [48], [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For this work, we took  advantage of the REDRAW [48], [36] dataset which contains  nearly 17k unique screenshots from 8,655 of the top-rated  apps from the Google Play Store.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' It should be noted that  another large-scale Android GUI dataset that contains a larger  number of screenshots, RICO, is also available [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However,  we chose to utilize the REDRAW dataset as it aligned with  one of our primary study objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' That is, we aim to learn  latent feature information from both screenshots and GUI-  metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, for the GUI-metadata to properly align  with the displayed content on a screen, the app must make use  of native Android components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Therefore, apps that primarily  display their information using web technologies, so-called  hybrid apps, would obscure the GUI-metadata and impact  our study findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The REDRAW dataset contains a set of  screenshots that underwent several stages of filtering to remove  instances of hybrid apps along with other noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=" Furthermore,  the REDRAW dataset contains a set of GUI-component images  3  2:04  Q Search  Stories  Play All  Add  Your Story  George  Amanda  Colby  [因  What's on your mind?" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Photo  Guillermo Moreno with Josephine  Williams and 2 others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Yesterday at 10:14 PM ·  Good friends, good food and a lot of laughs  Colby Harris and 23 others  2 CommentsHello  4  again!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content="  Password  I forgot  ENTER  Don't have an account?" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Register  wordsearch  Animals-Countries-Cifies  PLAY  Uspresidents-Trademarks0000  三12:34  Kids A-Z  Teacher Username  No Username?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Start Here!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='日#  12:27  The Dollar in Mexico  =  updated: Jun 19, 2017  Order by:  Sell  V  Select the bank of your choice  BAsE  Banco  Buy: 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='4129  Sell: 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='8129  BANCODE MEXICO  Buy: 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='9895  Sell: 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='9945  Interbank dollar to 48 hours  OBANCO AZTECA  Buy:  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='95  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='01  HSBC  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='68  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='17  BANORTE  Buy:  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='85  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='25  Ixe  Buy:  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='85  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='25  monex  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='67  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='28  Banamex  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='50  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='30  INBURSA  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='70  Grupo Financierc  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='30  Santander  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='50  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='30  BBVA  Bancomer  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='16  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='35  B BANCO DEL BAJIO  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='40  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='40  Scotiabank  Buy:  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='80  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='42  Bx+  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='50  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='50  BANREGIO  Buy:  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='40  Sell:  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content="502:04  Q Search  Stories  Play All  Add  Your Story  George  Amanda  Colby  [因  What's on your mind?" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Photo  Guillermo Moreno with Josephine  Williams and 2 others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Yesterday at 10:14 PM ·  Good friends, good food and a lot of laughs  Colby Harris and 23 others  2 Comments000  </>AHigh Level Caption  The screen allows the user to  look at clothing categories  Low Level Captions  The top le!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' icon allows the user  to access the menu  The top right icon allows the  user to access the shopping cart  The center list of categories allows  the user to make a selection  The heart icon to the le!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' of the  shopping cart allows the user to  view favorites  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 3: Example of captions from the CLARITY dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  labeled with their corresponding types (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', Button) which  we utilize later in our study (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' VI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The end result of this  filtering process was a total set of 17,203 candidate screens for  labeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We refer readers to the REDRAW paper for complete  details of the filtering process [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Collection of Functional Descriptions  Once we derived a suitable set of screens, we needed to  manually label these screens with functional captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This  process occurred in two steps: (i) first, we conducted a pilot  labeling study in order to develop and prove out a tagging  methodology suitable for large scale caption collection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' (ii)  second, we performed a full scale data collection study using  Amazon’s Mechanical Turk Crowd-worker platform to collect  over 10k screens with functional descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  1) Caption Granularity: Intuitively, GUIs encode func-  tional information at multiple levels of granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For exam-  ple, if you were to ask a user or developer what the high-  level purpose of a given screen is, they might say “This  screen allows users to browse clothing categories”, as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' These types of descriptions constitute the “high-  level” functionality of a given screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, a single screen  rarely implements only one functionality, and there may be  multiple functional properties that enable the screen’s high-  level functional purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' User descriptions of these types  of functional properties are typically centered around the  interactive components of a screen, since these represent the  instances of actions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', users “doing something”) that are  easily attributed to implemented functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For example, in  the screen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 3, underlying functions include viewing  favorites, accessing a shopping cart, or selecting an item from  a list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' These types of “low-level” screen properties centered  around GUI-components describe key constituent functional-  ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hence, in order to capture a holistic functional view of  each screen, we tasked participants with labeling each screen  with one “high-level” functional caption, and up to four “low-  level” functional captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 3 shows these two categories  using actual captions collected as part of the CLARITY dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  2) Pilot Data Collection Study: We developed an initial  image caption collection platform using a Java-based web  application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Using this system, the authors manually labeled  743 screens with the caption granularities described earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  During this study, we discovered some instances of screens  with relatively little information displayed on them, making  it difficult to label them with functional attributes, even after  the filtering techniques discussed previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Therefore, before  moving onto the large-scale caption collection with Mechani-  cal Turk (MTurk), at least one author manually inspected each  of the 17,203 candidate screens, and discarded those with a  severe lack of functionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This resulted in a set of 16,311  candidate screens for the next phase of the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  3) Mechanical Turk Data Collection Study: To set up our  large-scale data-collection process, we adapted our web ap-  plication caption collection mechanism to work with MTurk’s  crowd worker platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This involved configuring a Human  Intelligence Task (HIT) that provided workers with a set of  detailed instructions, displaying a screenshot from our dataset  alongside text entry boxes for one high-level functional caption  and up to four low-level functional captions (a limit was  imposed to normalize the amount of time workers would spend  on the HIT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This study was approved by the Institutional  Review Board of the authors’ affiliated institution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Given that we aimed to collect high-quality functional  descriptions of screens in natural English, we targeted MTurk  users from primarily English speaking countries that had  completed at least 1,000 HITs and had a HIT approval rate  of at least 90%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We provided a detailed set of instructions  for labeling images with captions that clearly explained the  concept of high-level and low-level captions with examples,  and provided users with explicit instructions as well as DOs  and DONTs for the labeling task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The full set of instructions is  available in our online appendix [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' With regard to caption  quality, we specifically had three major requirements: (i) that  the caption describes the perceived functionality of a screen  and not simply its appearance, (ii) that spatial references are  given for low-level captions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', “the button in the top-left  corner of the screen”), and (iii) that captions be written in  complete English sentences with reasonably proper grammar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  We published batches of HIT tasks by sampling unique  screens from our set of 16,311 candidate screens, ensuring  that no user was assigned the same screen twice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The quality  of work from crowd-sourced tasks is not always optimal,  so as captions were submitted, they needed to be vetted for  quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, the captions for each screen were examined by  at least one author for the three quality attributes mentioned  above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' If an author was unsure about whether a screen met  these quality attributes, it was reviewed by at least one other  author to reach a consensus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In total, 2,419 screens were  rejected and republished as new HITs due to quality issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  In summary, 2,150 MTurk workers collected 45,998 captions  (across granularities) for 10,204 screens (≈5 screens per  participant), and over $2,400 was paid out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' EMPIRICAL DATASET ANALYSIS  The CLARITY dataset provides a rich source of data for  exploring the relationship between GUI-based and lexical  4  #？' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='日9:47  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='asos  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='三  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='HOME  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='CATEGORIES  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='NEWIN:CLOTHING  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='ACTIVEWEAR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='TALL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='JEANS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='SHOES&SNEAKERS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='SHIRTS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='SUNGIASSESTABLE I: LDA topics learned over high-level captions k = 15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Assigned Label  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Top 7 Words  ”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='color options”  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='screen show app option color book differ  ”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='login or create acccount”  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='user screen allow account log creat app  ”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='select image from a list”  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='user screen allow select view list imag  ”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='map search by location”  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='screen locat search map user show find  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='TABLE II: LDA Topics learned on low-level captions k = 25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Assigned Label  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Top 7 Words  ”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='page button”  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='page button top center bottom side left  ”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='select date”  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='avail date select one option theme present  ”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='camera button”  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='video imag photo pictur bottom camera  ”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='privacy policy banner”  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='titl just term blue banner privaci polici  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='software data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, it is important to investigate the  semantic makeup of the collected captions in order to better  understand: (i) the latent topics they capture as well as (ii)  their naturalness and, hence, predictability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In this section we  carry out an empirical analysis of this phenomena guided by  the following two Research Questions (RQs):  RQ1: What are the latent topics captured within the high-  and low-level captions in the CLARITY dataset?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  RQ2: How natural (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', predictable) are the high- and  low-level captions in the CLARITY dataset?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Analysis Methodology  1) RQ1: Investigating Dataset Topics: To investigate the  latent topics in the CLARITY dataset, we learned topic models  over caption corpora representing different granularities of  functional descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' More specifically, we applied Latent  Dirichlet Allocation (LDA) [49] to both segmented high-  and low- level captions from the CLARITY dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In our  analysis, the set of captions for a specific screenshot in the  CLARITY dataset represents a document, and the entire set  of captions across screenshots for a given granularity (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=',  high or low level) constitutes a corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' LDA has several  configurable hyper-parameters that impact the smoothing of  generated topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' These include k, the number of topics,  n which denotes the number of iterations of the sampling  algorithm (Gibbs sampling [50], in our case), as well as α  and β which impact topic distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We set α and β to  standard values for NL corpora, set n to 500, which proved to  be a sufficient for model convergence, and varied k between  15, 25, 50, and 75 topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  2) RQ2: Analyzing the Naturalness of GUI Descriptions:  Past work has pioneered the notion of the naturalness of  software [51], which illustrated the fact that software, even  more so than NL, exhibits repetitive patterns that make it  predictable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This finding was recently further investigated and  the existence of certain natural patterns was confirmed [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' To  illustrate naturalness, these past studies have learned statistical  n-gram language models over software corpora, and measured  the “perplexity” (or a log-transformed version, cross-entropy)  of these models, which represents the degree to which a model  is “surprised” by the patterns on a test corpus when trained on  a corpus from the same domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' A model with lower measured  1  2  3  4  5  6  7  8  9  10  1  2  3  4  5  6  7  8  9  10  11  12  N-gram order  Cross-Entropy  High-Level Captions  Low-Level Captions  Java Raw Code  Java w/o Syntax Tokens  Stack Overflow  Guntenberg  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 4: Cross-entropy of the CLARITY dataset’s high and low-  Level captions compared to other corpora.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  cross-entropy represents a higher predictive power, and thus,  a more natural underlying corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  We follow the methodology of these past studies to explore  the naturalness of the CLARITY dataset captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, similar  to the methodology for the previous RQ, we split the collected  captions into two corpora, one for the high-level descriptions,  and one for the low-level descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We then learned inter-  polated n-gram models, using the mitlm [53] implementation  of Kneser-Ney smoothing [54], which has been shown to be  the most effective n-gram smoothing method [51], following  a ten-fold cross-validation procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We report the average  cross-entropy values across these experiments for both the high  and low-level corpora, compared to prior results [51], [52] for  other NL and software corpora.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Analysis Results  1) RQ1: Results of Dataset Topic Modeling: We present  selected results of some of the most representative topics in  Tables I & II, complete with descriptive labels that we provide  for readability, and include all the results in our appendix [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  These topics help to provide a descriptive illustration of some  of the latent patterns that exist in both the high and low level  CLARITY captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The high-level captions illustrate several  screen-level topics, including searching on a map and adjusting  app settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The low-level captions conversely capture topics  that describe component-level functionality, such as date selec-  tors, camera buttons, and back buttons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' These results indicate  the existence of logical topics specific to the domain of GUIs  in our collected captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  2) RQ2: The Naturalness of Clarity Descriptions: The  results of our naturalness analysis are illustrated in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  This figure shows the average cross entropy of the high- and  low- level captions from the CLARITY dataset compared to  several other corpora as calculated by Rahman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  More specifically, the graph depicts the average ten-fold cross  entropy for: (i) The Gutenberg corpus containing over 3k  English books written by over a hundred different authors,  (ii) Java code from over 134 open source projects on GitHub,  (iii) Java without Syntax Tokens (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', separators, keywords,  and operators), and (iv) a Stack Overflow corpus consisting of  only the English descriptions from over 200k posts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  5  13  high  12  low  11  javaraw  java withoutsyntaxtokens  10  stack overflow  9  gutenberg  entropy  8  cross  6  5  4  3  2  1  1  2  m  4  5  6  7  8  9  10  n-gram lengthAs described earlier, the lower the cross-entropy is for a  particular dataset, the more natural it is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' That is, the corpora  that exhibit lower cross entropy tend to exhibit stronger latent  patterns that can be effectively modeled and predicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' As we  see from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 4, the CLARITY high and low level captions are  more natural than every dataset excluding raw Java code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' It  should be noted that, comparatively, there are several factors  that could account for the observed lower cross entropy of the  CLARITY captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For instance, such factors could include  other corpora having a larger size or having a more diverse  set of human authors and writing styles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, we mainly  provide entropy measures of other datasets to provide context  for the predictability of the CLARITY dataset compared to  other popular corpora.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Regardless of dataset differences, the  average ≈ 5 bits of entropy measured for the two datasets of  CLARITY captions signals that our collected descriptions ex-  hibit strong semantic patterns that can be effectively modeled  for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Additionally, we observe that the cross-entropy  for the high and low-level captions are surprisingly similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Intuitively, one might expect that the low-level CLARITY  captions would exhibit more prevalent patterns due to the  repetitive use cases of certain GUI-components such as menu  buttons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This indicates the tendency of both datasets to exhibit  patterns that can be appropriately modeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, as we  illustrate in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' VII the ability for GUI-related information  to predict captions differs according to granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' DEEP LEARNING FUNCTIONAL DESCRIPTIONS FROM  SOFTWARE GUIS  The results of the analysis from the previous section demon-  strate the presence of the latent patterns in the CLARITY  dataset of screenshots and captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In this section, we detail  our methodology for investigating the capability of different  customized DL models to learn these patterns to predict  functional descriptions from two GUI representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Clarity Dataset Segmentation  We collected two different granularities of captions from  users to derive the CLARITY dataset (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' IV-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For the  experiments in this section, we want to explore the model’s  ability to learn both high- and low-level functional descrip-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, we split the CLARITY dataset into two groups,  one containing only high level captions, and one containing  only low level ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We also created a third dataset combining  the high and low level captions, in order to explore whether the  predictive capabilities of the models improved by aggregating  multiple granularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' It should be noted that each low-level  caption was treated as a single caption (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' each low-level  caption was treated as a separate data point) as is convention  with datasets containing multiple captions [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Each screen  in the dataset has both an associated screenshot and a GUI-  metadata file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In order to make for a fair comparison of  performance across various model configurations, we created  consistent training, validation and test partitions (80%, 10%,  10% according to the number of images/GUI metadata files) to  be used across models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The NL text used as input to the models  TABLE III: Image Captioning Model Configs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' used in Study  Model  Identifier  Caption Config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Model Config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='Combined  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='High  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='im2txt-l-comp  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='im2txt-c-comp  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='Inception v3 fine-tuned on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Component Dataset  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='im2txt-h-fs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='im2txt-l-fs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='im2txt  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='Inception v3 fine-tuned on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Full Screen Dataset  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='ntk2-h-imgnet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='VGGNet pre-trained on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='ImageNet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='NeuralTalk 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='ntk2-c-ft  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='ImageNet with Fine  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Tuning  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='sat-h  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='TABLE IV: Subset of Model Hyper-paramters  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Hyperparameter  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='Seq2Seq  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Batch Size  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='64  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='64  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Embedding Size  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='512  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='512  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='512  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='128  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Decoder RNN Size/Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='512  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='512  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='1024  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='128  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Optimizer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='SGD  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='SGD  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Adam  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Adam  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='Initial Learning Rate  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='0001  Dropout Probability  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='8  was preprocessed according to the specific requirements for  each model implementation [55], [56], [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Image Captioning Model Configurations  We customize, train, and test the three neural image  captioning models, im2txt, neuraltalk2, and show,  attend, & tell (SAT) (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' II-A), on the screenshots  and captions of the CLARITY dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We choose to explore  these three models due to their different underlying design  decisions related to the type of utilized CNNs and RNNs  (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' II-A), as these differences may affect their performance  in our domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' It should be noted that in the course of our  experiments, we make several customizations to these models  through adaptions to pre-training and fine-tuning procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  However, given the typical number of parameters that consti-  tute these models, the training time can be quite prohibitive,  even on modern hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, to control our experimental  complexity and investigate a number of model configurations  that can be trained in a reasonable amount of time, we fix  the values of the hyper-parameters for each model in our  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We derived our utilized hyper-parameter values  by conducting random searches for optimal values of certain  parameters, and chose optimal parameters reported in prior  work for others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' While we fix the hyper-parameters for these  models, we instead customize the configurations of our image  captioning models at the architectural level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Specifically, we  investigate how training the “encoder” CNN using different  datasets and training procedures effects the efficacy of the  model predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This type of analysis allows us to more  effectively flush out broader patterns related to the benefits and  drawbacks of model design decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In the end, we trained  more than 15 different configurations of the models (see Table  III) over several machine months of computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  1) im2txt  Model  Configurations  &  Training:  For  im2txt, we adapted Google’s open source implementa-  6  tion of the model in TensorFlow [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Given the incredibly  large number of parameters that need to be trained for the  im2txt model, performing even relatively simple hyper-  paramter searches proved to be computationally prohibitive  for our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Therefore, for this model we utilized the  optimal set of parameters reported by Vinyals et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [41] on  similarly sized datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' A subset of these hyper-parameter  values are given in Table IV, whereas full configuration details  can be found in our appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The publicly available imple-  mentation of Google’s im2txt model utilizes the Inception  v3 [58] image captioning architecture as its encoder CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  In past work, the inception model weights were initialized  by training on the large-scale image classification dataset  ImageNet [59], which contains “commonplace” image cate-  goires.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, given that we are applying these models to  very particular domain (predicting descriptions of software)  it is unclear if an Inception v3 model trained on the broader  ImageNet dataset would capture subtle semantic patterns in  the CLARITY dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Therefore, we explored three different  model configurations to explore this phenomena: one with  Inception v3 pre-trained on ImageNet, and two with Inception  v3 fine-tuned on domain specific-datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The first domain  specific image dataset we utilize is the ReDraw cropped  image dataset outlined in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' IV-A, which contains over 190k  images of native Android GUI-components labeled with their  type (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', Button, TextView).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The second domain specific  image dataset we use consists of the full screenshots from the  CLARITY dataset, labeled with their Google Play categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  2) NeuralTalk2 Model Configurations & Training: For  neuraltalk2, we adapted Karpathy et al.’s implementation  written in Torch and lua [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We performed a brief random-  ized hyper-parameter search for this model, given its more  efficient training time, using the optimal im2txt parameters as  a starting point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The optimal values resulting from this search  are provided in Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For its CNN decoder, neuraltalk2  makes use of a VGGNet [44] architecture pre-trained on  the ImageNet [59] dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Unlike our im2txt configurations,  we explore the effect of jointly fine-tuning neuraltalk2’s  CNN and RNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, we explore two configurations of  neuraltalk2, one that jointly fine tunes the pre-trained  VGGNet on the CLARITY dataset, and one that does not  perform fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We followed a training procedure similar  to that of our im2txt models, in that we trained our models  on the high, low, and combined CLARITY caption training  data for 500K iterations, saving model checkpoints every 2K  iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  3) Show, Attend and Tell Model Configurations & Train-  ing: For the SAT model, we adapted the open-source imple-  mentation of the model in Tensorflow [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The hyperparam-  eters that we used to train our model are shown in Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  The implementation used VGG16 [44] as its encoder CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  We trained the SAT model on the CLARITY dataset for the  low, high and combined captions for 500K iterations and kept  the checkpoints after every 1K iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Note that due to  the prohibitive training cost of this model, we did not explore  using a fine-tuned VGGNet as we did with neuraltalk2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  TABLE V: Metadata Captioning Model Congfigurations  Model  Identifier  Caption Config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Model Config.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  seq2seq-h-type  High  seq2seq-l-type  Low  seq2seq-c-type  Combined  Trained on GUI  Component Types  seq2seq-h-text  High  seq2seq-l-text  Low  seq2seq-c-text  Combined  Trained on  GUI-Component Text  seq2seq-h-tt  High  seq2seq-l-tt  Low  seq2seq-c-tt  Combined  Trained on  GUI-Component Type +  Text  seq2seq-h-ttl  High  seq2seq-l-ttl  Low  Seq2Seq  seq2seq-c-ttl  Combined  Trained on  GUI-component Type +  Text + Location  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Metadata Captioning Model Configurations  To explore the ability to translate between the lexical  representations of GUI-metadata and NL functional descrip-  tions, we train and test an encoder-decoder neural language  model using Google’s seq2seq [57] framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Note that  recent work has proposed new models that take advantage of  structural text properties [61], however, implementations of  such models are generally not available, hence we leave the  study of more advanced models for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We chose  to utilize the default general-purpose architecture and hyper-  parameters for this model, as they have been shown to be  effective across a wide-range of machine translation tasks [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  More specifically, our encoder network consists of a BRNN  with Gated Recurrent Units (GRUs) and our decoder network  consists of an RNN with LSTM units;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' hyperparameters are  listed in Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  To investigate the representative power of different attributes  included in Android GUI-metadata, we create four config-  urations of GUI-metadata consisting of different attribute  combinations (Table V).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We chose to utilize these attribute  combinations as they represent (i) the attributes that are most  likely to have values, and (ii) represent a wide range of  information types (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', displayed text, component types, and  spatial information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Note that seq2seq did not consistently  converge for the high level caption dataset, thus we do not  report these results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Consistent with the training of the other  models, our implementation of the seq2seq model was  trained to 500k iterations, with checkpoints every 2k iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' DEEP LEARNING MODEL EVALUATION  To explore our core hypothesis set forth at the beginning  of this paper, and evaluate our DL models described in  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' VI, we perform a comprehensive empirical evaluation  with two main goals: (i) intrinsically evaluate the predictive  power of the models according to a well accepted machine  translation effectiveness metric, and (ii) extrinsically evaluate  the models by examining and rating the quality of the pred-  icated functional NL descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The quality focus of this  evaluation is our studied models’ ability to effectively predict  accurate, concise, and complete functional descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' To aid  in achieving our study goals, we define the following RQs:  RQ3: How accurate are our model’s predicted NL de-  scriptions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  RQ4: How accurate, complete, & understandable are our  model’s predicted NL descriptions from the viewpoint of  evaluators?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  7  TABLE VI: BLEU Score Evaluation Results for Models  Model  Capt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Model Type  Bc  B1  B2  B3  B4  High  im2txt-h-fs  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='4  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='8  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='7  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='3  Low  im2txt-l-comp  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='6  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='8  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='  seq2seq-c-type  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='7  SAT  Comb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  sat-c  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='0  NeuralTalk2  Trained on Flickr8K  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='0  NeuralTalk2  Trained on MSCOCO  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='0  im2txt  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
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+page_content='6  SAT  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='7  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='8  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='4  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='7  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='0  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Evaluation Methodology  1) RQ3: Empirically Evaluating Model Accuracy: To  evaluate the accuracy of our trained model’s generated cap-  tions, we follow past work [40], [41] and report BLEU  scores [63] of the predicted captions on the shared CLARITY  test set of images and GUI-metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The BLEU score is a  standard metric used in machine translation research that mea-  sures the textual similarity between a predicted caption (the  output from a model) and a reference caption (the collected  descriptions from humans in the CLARITY test set).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The BLEU  score can be measured according to the similarity of different  subsequence lengths (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', BLEUn), and we report BLEU1  through BLEU4, as well as a composite score calculated as the  average of these, as is convention [40], [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For the image  captioning models, we use the coco-caption implementation  of the BLEU score adapted for the CLARITY test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For  each test image across all image captioning models, three  captions were generated using a beam width of 3 for the  beam search across candidate predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The seq2seq models  were evaluated in the same manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We chose to utilize a  beam width of 3 as an initial qualitative examination of our  models’ predictions showed this size to achieve a reasonable  balance between prediction accuracy and model confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  For the high-level captions, the three candidate captions were  compared to the reference, and the overall average BLEUn  scores were calculated for each model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For the low-level and  combined captions, the predicted captions and reference cap-  tions were compared in a pairwise manner and overall average  BLEUn scores were calculated for each model configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  2) RQ4: Human Perceptions of Predicted Captions: To  qualitatively evaluate our studied model’s generated captions,  we performed a large-scale study involving an additional 220  participants recruited from MTurk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We randomly sampled  220 screens from the CLARITY test set, and then predicted  high, low, and combined captions for them using the opti-  mal configurations of im2txt, NeuralTalk2, and seq2seq  according to the composite BLEU score for each model  and caption level combination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The SAT captions were not  included in this study due to time constraints related to the  model’s training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We created a HIT wherein each participant  viewed 11 screenshots paired with captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Two of the 11  captions were reference high and low to serve as a control,  while the other 9 captions came from the model predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Screens and caption pairs were arranged into HITs such that  1) no single HIT had two of the same screenshot, 2) each  of the 11 types of captions (2 reference, 9 model) were  included only once per HIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The order of these captions was  randomized per HIT to prevent bias introduced by identical  caption ordering between HITs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' By this arrangement, each  screen-caption pair was evaluated by 11 participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' After  viewing these screenshot-caption pairs, participants were asked  to answer six evaluation questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Three of these questions  (EQ1-EQ3) were adapted from prior work that assessed the  quality of automatically generated code summaries [21], and  inquired about accuracy, completeness, and understandability,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The three remaining questions (EQ4-EQ6), were  free response and asked participants to explain accuracies,  inaccuracies, and improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The full set of questions and  HIT are in our online appendix [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Similar to the CLARITY  dataset collection, each participant’s response was thoroughly  vetted by at least one author, and discarded if the answers  were incomplete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Responses were collected until 220 HITs  were completed by unique respondents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Evaluation Results  1) RQ3 Results: Evaluating BLEU Scores: We illustrate  the BLEU score results for the most effective model config-  uration and checkpoint across all of our trained models in  Table VI, whereas the results for other model configurations  can be found in our online appendix [39] in addition to  caption examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The cells highlighted in blue illustrate the  highest performing model configuration for each caption type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  In general we observe that SAT exhibits the highest overall  BLEU scores across all caption granularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We speculate  that this is attributable to the addition of the advanced attention  mechanism in this model that is able to “focus” on varying  image regions or features to effectively handle multiple caption  granularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In general, the seq2seq model performed quite  poorly across the varying caption types, indicating a lower  tendency for rich representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Perhaps most interestingly,  we see that the optimal model configurations for the im2txt  framework were those where the CNN was conditioned on  domain specific datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' More specifically, the best high-level  caption model was conditioned on full screenshots and the  best low-level caption was conditioned on the cropped GUI-  component screenshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Another general trend that emerges is the low-level and  combined caption models tend to exhibit higher overall BELU  scores compared to the high-level captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This is somewhat  intuitive, as it indicates that there are more natural connections  between visual GUI and lexical patterns in the low-level  captions, compared to the high-level captions that reflect more  abstract functional descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' When examining the captions  generated by the optimal configurations of each model, it is  clear that im2txt and SAT produces a more diverse set of out-  put captions than neuraltalk2, which could be considered  as more useful in many software documentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Finally, it is worth discussing how the BLEU scores of our  models compare to those of the same models trained on the  8  None  Some  A Lot  im2txt high  im2txt low  im2txt combined  Easy to Read  Somewhat  Readable  Hard to  Read  im2txt high  im2txt low  im2txt combined  EQ3: Understandability  EQ2:  Unnecessary Information  im2txt high  im2txt low  im2txt combined  Strongly  Disagree  Disagree  Neutral  Agree  Strongly  Agree  EQ1: Accuracy  seq2seq high  seq2seq low  seq2seq combined  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 5: Responses across models for EQ1-EQ3  more traditional Flickr8k [37] and MSCOCO [38] datasets  given at the bottom of Table VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Given the data-intensive  nature of our DL models, and the much larger size of the  MSCOCO dataset (≈123k images, each with 5 captions), we  did not expect our models trained on the CLARITY dataset to  outperform those trained on MSCOCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, unsurprisingly,  we observe that on average, im2txt, neuraltalk2, and SAT  models trained on the MSCOCO dataset outperform the same  models trained on the CLARITY datasets by ≈ 10 BLEU score  points for the combined and low level captions, and ≈ 27  points on high-level captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, when we examine  the performance of Neuraltalk2 on the more similarly sized  Flickr8K dataset (≈ 8K images, each with 5 captions) we  observe comparable performance to the CLARITY low-level  and combined datasets, with the SAT model narrowly outper-  forming the Flickr8K neuraltalk2 model, with a slightly  bigger discrepancy for the high-level captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Overall, these  results indicate that when compared with datasets of similar  size, DL models trained on the CLARITY dataset exhibit  similar performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  2) RQ4 Results: Human Evaluations: The results of EQ1-  EQ3 for the model configurations with the best performance  during the human study, in addition to the seq2seq accuracy  scores, are summarized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Complete results across all  model configurations can be found in our online appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' The  responses to EQ4-EQ6 varied by the type of caption, and are  provided in our appendix in full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Generally, im2txt fared the  best in terms of accuracy, and was followed by neuraltalk2  and seq2seq respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For im2txt, despite mixed reac-  tions from participants, in many cases respondents verified that  the caption was accurate (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', ”The description accurately  describes the screen, it is in fact a terms and conditions  screen.”) and suggested minor improvements similarly to the  reference captions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', ”It could add specifics about what the  settings pertain to (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' security)”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' As illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 5 the  im2txt predictions were consistently rated as being readable  and containing relevant information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' It is also interesting to  note that there appears to a mismatch between the performance  as indicated by BLEU scores, and human perceptions, with the  participants consistently rating the im2txt captions better  than other models across EQ1-EQ3, despite neuraltalk2  achieving a higher BLEU score for two model configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' DISCUSSION & LEARNED LESSONS  Lesson 1: Functional Descriptions of GUIs exhibit a  high degree of naturalness and can be modeled using DL  techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We observed that DL models trained on the low-  level and combined datasets exhibit similar performance to  models trained on general image captioning datasets of similar  size (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', Flickr8K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This indicates that GUI screenshots could  be used to augment approaches for automated documentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Lesson 2: GUI-centric software documentation mod-  els benefit from being pre-trained on domain specific  GUI data, as opposed to general image datasets (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=',  MSCOCO) The qualitative results of our model analysis  illustrate that for im2txt, the most effective configurations  were those trained on domain specific CNN datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This  suggests a perceptible difference between the utility of image  features learned from general datasets, compared to those  learned on datasets more specific to software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This suggests  that future work aiming to leverage DL models for GUI-  centric program documentation should look to collecting and  extracting features from large-scale GUI-related datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Lesson 3: Future automated approaches for GUI-centric  program documentation would likely benefit from com-  bining the orthogonal semantics of screenshots and GUI-  metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Our evaluation in this paper illustrates that the rep-  resentational power of screenshots appears to be superior when  applied to a software documentation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, given stark  differences between these two modalities of information, we  also observed that they encode orthogonal semantic patterns  that could be combined for more effective documentation  generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' One property we observed of certain captions  generated by the image-based models was the effect of their  limited vocabulary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' For example, certain predicted captions  similar to the following: “The screen allows the user to select  a <UNK>”, wherein the UNK token represents missing token,  which should be mapped to some unobserved app property,  such as a “album cover” or “store location”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, such  predictions could be combined with the vocabulary present in  GUI metadata to help predict more complete, and accurate  descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus, a promising direction for future work is to  jointly encode both screenshots and lexical GUI-metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Lesson 4: Training image captioning models to predict  specific or diverse pieces of functionality is difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Practical models for GUI-centric documentation should able  to predict both specific pieces of information (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' the func-  tionality of a particular button for a given method handler),  and diverse functionality (being able to generate descriptions  of functionality anywhere on a given screen).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, one  aspect we observed across our models is that the most  common observed types of functionality (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', back buttons,  menu buttons) corresponded to the functionalities that our  9  seq2seq high  seq2seq low  0  0  seq2seq combined  0  0models predicted most often and most confidently on unseen  screenshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This is somewhat expected, as the models saw the  most examples of such functionalities during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Thus,  the diversity of predictions is an open problem for future  research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This problem can be partially mitigated by larger,  more diverse datasets with specifically curated descriptions  (such as extensions to the CLARITY dataset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, it is  likely that domain-specific models, or ensembles of models,  may be required to more effectively predict diverse features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Lesson 5: Future studies that evaluate automated GUI-  centric documentation approaches should include human  studies, as human perceptions of models may differ from  automated reference-based metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' One of the more surpris-  ing results of our study is that there seems to be a mismatch  between humans perceptions of the captions generated by our  DL models and the BLEU score metrics typically used to asses  the accuracy of model predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This signifies that there are  aspects of human perception that are not effectively captured  in the BLEU metric, and possibly other translation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' LIMITATIONS & THREATS TO VALIDITY  Internal Validity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Threats to internal validity correspond to  unexpected factors in the experiments that may contribute to  observed results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' To derive our dataset we rely on MTurk and  its workers to extract the high- and low-level descriptions per  each screenshot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' It should be noted that we did not ask MTurk  workers to provide technical software documentation descrip-  tions, but rather general descriptions of screen functionality at  differing granularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' To minimize low quality captions we  published the jobs for workers with more than 1k HITS, from  English speaking countries, and HIT approval rate of more  than 90%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Also, each successfully completed HIT was vetted  by at least one of the authors to assure quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' If there was  any question related to caption quality, at least one of the other  authors stepped in to resolve the ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' As a result 2,429  HITs were rejected due to low quality descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  External Validity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Threats to external validity concern the  generalization of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' As with any collected dataset,  there is a threat to external validity about the generalizability  of the CLARITY dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, we used a diverse set  of popular apps from the Android domain, extracted popular  screenshots from these apps, and the apps were captioned by  a large and diverse set of MTurk workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' During our data  collection process, we only collected 4 low-level captions per  each screen in order to make the task feasible for MTurk  workers as workers tend to abandon or perform poorly on long  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' This means that, for certain screens with many GUI-  components, some components may lack natural language  descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, given the size of our dataset and the  diversity of our screenshots and captions, we assert that our  low-level captions are reasonably representative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' RELATED WORK  DL for Image Captioning and GUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hossain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [64]  recently performed a wide-ranging study on DL models for  image captioning, surveying the many different architectures  and datasets used to evaluate them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, this survey  did not examine the ability of any image captioning model  to predict functional descriptions of software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' There have  been a limited number of papers in the SE community that  have applied DL techniques to GUI related data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chen et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [65] designed an approach that uses an NMT to translate  an Android screenshot into a GUI-skeleton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, their  technique is able to predict GUI structure given an image, not  functional natural language descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Recently, Zhang et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [66] created a dataset of iOS image captions to train a  model for captioning accessibility data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, the authors  do not make their dataset publicly available and target a  different goal of accessibility data compared our goal of  generating functional captions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' investigated the  use of DL image captioning models for applying labels to  GUI-components in mobile apps [67], however, this approach  only aims to predict short labels for a limited subset of  GUI-components, whereas our study focuses upon predicting  functional descriptions consisting of complete sentences for  both individual GUI-components and entire screenshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  GUI-based Analysis of Mobile Apps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' GVT and GCat analyze  the visual properties of GUIs to detect design violations and  evolutionary changes [68], [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' In contrast, we focus solely on  image captioning techniques to provide functional program de-  scriptions of screenshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Approaches such as REMAUI [70],  REDRAW [48], and pix2code [71] aim to automatically  generate mobile app code given an app screenshot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Conversely,  we leverage DL techniques to generate functional descriptions  rather than source code using a pixel-based image as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [72] introduced StoryDroid, for automatically  generating visual storyboards of Android apps to help aid  in the app design process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' However, their approach is not  capable of generating a functional description of an application  from GUI data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Furthermore, Deka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' showed how the  Rico dataset could be navigated via semantic search using  autoencoders  [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' UiRef [73] is an approach for resolving  security and privacy concerns by considering semantics of  GUI-components that request user’s inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moreover, Liu et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' [74] presented an approach for automatically classifying  mobile app icons according to semantic GUI patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Xiao et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' proposed IconIntent that combines program analysis and  icon classification to detect privacy sensitive GUI-components  [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Different from this body of work, we aim to predict  functional descriptions of GUIs for software documentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  XI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' CONCLUSION  In this paper, we have conducted one of the first com-  prehensive empirical investigations into the connection be-  tween GUI-related information, and functional descriptions  of programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' We have derived the CLARITY dataset of GUI  screenshots/metadata and NL captions, trained DL models  on this dataset, and demonstrated their ability to bridge the  semantic gap between visual and lexical program information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  ACKNOWLEDGMENT  This work was supported by the NSF CCF-2007246 &  CCF-1955853 grants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Any opinions, findings, and conclusions  expressed herein are the authors’ and do not necessarily reflect  those of the sponsors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  10  REFERENCES  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chen and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Huang, “An empirical analysis of the impact of  software development problem factors on software maintainability,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Softw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 82, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 981–992, June 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Kajko-Mattsson, “A survey of documentation practice within correc-  tive maintenance,” Empirical Software Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 31–55,  Jan 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [3] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Dagenais and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Robillard, “Creating and evolving developer  documentation: Understanding the decisions of open source contribu-  tors,” in Proceedings of the Eighteenth ACM SIGSOFT International  Symposium on Foundations of Software Engineering, FSE ’10, (New  York, NY, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 127–136, ACM, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [4] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Garousi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Garousi-Yusifoglu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ruhe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Zhi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moussavi, and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Smith, “Usage and usefulness of technical software documentation:  An industrial case study,” Information and Software Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 57,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 664 – 682, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Forward and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Lethbridge, “The relevance of software documen-  tation, tools and technologies: A survey,” in Proceedings of the 2002  ACM Symposium on Document Engineering, DocEng ’02, (New York,  NY, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 26–33, ACM, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [6] “The agile manfiesto http://agilemanifesto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='org.”  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Zhi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Garousi-Yusiflu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sun, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Garousi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Shahnewaz, and  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ruhe, “Cost, benefits and quality of software development docu-  mentation,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Fluri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Wursch, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Gall, “Do code and comments co-  evolve?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' on the relation between source code and comment changes,” in  Proceedings of the 14th Working Conference on Reverse Engineering,  WCRE ’07, (Washington, DC, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 70–79, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moreno, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Marcus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Pollock, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Vijay-Shanker, “JSummarizer:  An automatic generator of natural language summaries for Java classes,”  in 2013 21st International Conference on Program Comprehension,  ICPC’13, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 230–232, May 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moreno, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Aponte, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sridhara, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Marcus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Pollock, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Vijay-  Shanker, “Automatic generation of natural language summaries for Java  classes,” in 2013 21st International Conference on Program Compre-  hension, ICPC’13, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 23–32, May 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [11] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Rigby and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Robillard, “Discovering Essential Code Elements  in Informal Documentation,” in Proceedings of the 2013 International  Conference on Software Engineering, ICSE’13, (San Francisco, CA,  USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 832–841, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ying and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Robillard, “Selection and Presentation Prac-  tices for Code Example Summarization,” in Proceedings of the 22Nd  ACM SIGSOFT International Symposium on Foundations of Software  Engineering, FSE’14, (Hong Kong, China), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 460–471, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ying and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Robillard, “Code Fragment Summarization,” in  Proceedings of the 2013 9th Joint Meeting on Foundations of Software  Engineering, FSE’13, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 655–658, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [14] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ratol and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Robillard, “Detecting fragile comments,” in  2017 32nd IEEE/ACM International Conference on Automated Software  Engineering, ASE’17, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 112–122, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Howard, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Gupta, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Pollock, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Vijay-Shanker, “Automati-  cally mining software-based, semantically-similar words from comment-  code mappings,” in 2013 10th Working Conference on Mining Software  Repositories, MSR’13, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 377–386, may 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [16] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Treude and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Robillard, “Augmenting API Documentation with  Insights from Stack Overflow,” in Proceedings of the 38th International  Conference on Software Engineering, ICSE ’16, (New York, NY, USA),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 392–403, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [17] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Petrosyan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Robillard, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' De Mori, “Discovering Information  Explaining API Types Using Text Classification,” in Proceedings of  the 37th International Conference on Software Engineering - Volume  1, ICSE ’15, (Florence, Italy), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 869–879, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [18] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Vendome, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Linares-V´asquez, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshyvanyk, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Kraft, “Automatically Documenting Unit Test Cases,” in 2016 IEEE In-  ternational Conference on Software Testing, Verification and Validation,  ICST’16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 341–352, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [19] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moreno, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bandara, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Haiduc, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Marcus, “On the Relationship  between the Vocabulary of Bug Reports and Source Code,” in 2013 IEEE  International Conference on Software Maintenance, ICSM’13, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 452–  455, Sept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [20] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moran, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Linares-V´asquez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bernal-C´ardenas, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshy-  vanyk, “Auto-completing Bug Reports for Android Applications,” in  Proceedings of the 2015 10th Joint Meeting on Foundations of Software  Engineering, FSE’15, (Bergamo, Italy), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 673–686, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [21] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moreno, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bavota, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Penta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Oliveto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Marcus, and  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Canfora, “Arena: An approach for the automated generation of release  notes,” IEEE Transactions on Software Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 43, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 106–  127, Feb 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [22] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moreno, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bavota, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Di Penta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Oliveto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Marcus, and  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Canfora, “Automatic Generation of Release Notes,” in Proceedings  of the 22Nd ACM SIGSOFT International Symposium on Foundations  of Software Engineering, FSE’14, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 484–495, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Jiang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Armaly, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' McMillan, “Automatically generating  commit messages from diffs using neural machine translation,” in  2017 32nd IEEE/ACM International Conference on Automated Software  Engineering, ASE’17, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 135–146, oct 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [24] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Cort´es-Coy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Linares-V´asquez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Aponte, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshyvanyk,  “On automatically generating commit messages via summarization of  source code changes,” in 2014 IEEE 14th International Working Con-  ference on Source Code Analysis and Manipulation, SCAM’14, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [25] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chatterjee, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Gause, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hedinger, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Pollock, “Extracting  Code Segments and Their Descriptions from Research Articles,” in  Proceedings of the 14th International Conference on Mining Software  Repositories, MSR ’17, (Buenos Aires, Argentina), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 91–101, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Linares-V´asquez, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Vendome, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshyvanyk, “Doc-  umenting database usages and schema constraints in database-centric  applications,” in Proceedings of the 25th International Symposium on  Software Testing and Analysis, ISSTA 2016, (New York, NY, USA),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 270–281, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [27] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Biggerstaff, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Mitbander, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Webster, “Program  understanding and the concept assignment problem,” Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' ACM,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 37, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 72–82, May 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Guo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Cheng, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Cleland-Huang, “Semantically enhanced soft-  ware traceability using deep learning techniques,” in Proceedings of  the 39th International Conference on Software Engineering, ICSE ’17,  (Piscataway, NJ, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 3–14, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [29] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Robillard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Marcus, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Treude, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bavota, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chaparro, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ernst,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Gerosa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Godfrey, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Lanza, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Linares-V´asquez, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Murphy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moreno, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Shepherd, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Wong, “On-demand Developer  Documentation,” in 2017 IEEE International Conference on Software  Maintenance and Evolution, ICSME’17, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 479–483, Sept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [30] “Android inches ahead of windows as most popular os - https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  cnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='com/news/android-most-popular-os-beats-windows-statcounter/.”  [31] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moran, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bernal-C´ardenas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Linares-V´asquez, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshy-  vanyk, “Overcoming lanaguge dichotomies: Toward effective program  comprehension for mobile app development,” in 26th IEEE International  Conference on Program Compreehnsion, May 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' To Appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Memon, A comprehensive framework for testing graphical user  interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Advisors: Mary Lou Soffa and Martha Pol-  lack;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Committee members: Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Rajiv Gupta (University of Arizona),  Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Adele E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Howe (Colorado State University), Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Lori Pollock  (University of Delaware).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Solem, “Designing computer documentation that will be used: Un-  derstanding computer user attitudes,” in Proceedings of the 4th Annual  International Conference on Systems Documentation, SIGDOC ’85,  (New York, NY, USA), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 55–56, Association for Computing Machinery,  1986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [34] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Alshayban, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ahmed, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Malek, “Accessibility issues in android  apps: State of affairs, sentiments, and ways forward,” in Proceedings  of the 42nd International Conference on Software Engineering, ICSE  2020, (New York, NY, USA), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' to appear, ACM, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [35] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Deka, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Franzen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hibschman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Afergan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Li,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Nichols, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Kumar, “Rico: A mobile app dataset for building  data-driven design applications,” in Proceedings of the 30th Annual  Symposium on User Interface Software and Technology, UIST ’17, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [36] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moran, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bernal-Cardenas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Curcio, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bonett, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshy-  vanyk, “The ReDraw Dataset: A Set of Android Screenshots, GUI Meta-  data, and Labeled Images of GUI Components,” Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Supported  by NSF Grant CCF-1815186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [37] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hodosh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Young, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hockenmaier, “Framing image description  as a ranking task: Data, models and evaluation metrics,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Artif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 47, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 853–899, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [38] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Lin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Maire, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Belongie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hays, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Perona, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ramanan,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Doll´ar, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Zitnick, “Microsoft COCO: Common Objects in  Context,” in Lecture Notes in Computer Science (including subseries  Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinfor-  matics), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 8693 LNCS, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 740–755, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  11  [39] “Online appendix http://sagelab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='io/Clarity/.”  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Karpathy and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Fei-Fei, “Deep visual-semantic alignments for  generating image descriptions,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 39, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 664–676, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [41] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Vinyals, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Toshev, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bengio, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Erhan, “Show and tell: Lessons  learned from the 2015 mscoco image captioning challenge,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 39, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 652–663, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [42] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ba, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Kiros, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Cho, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Courville, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Salakhutdinov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Zemel, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bengio, “Show, attend and tell: Neural image caption  generation with visual attention,” in ICML, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Krizhevsky, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sutskever, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hinton, “ImageNet Classification  with Deep Convolutional Neural Networks,” in Advances in Neural In-  formation Processing Systems 25 (F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Pereira, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Burges, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bottou,  and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Weinberger, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' ), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 1097–1105, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [44] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Simonyan and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Zisserman, “Very deep convolutional networks for  large-scale image recognition,” International Conference on Learning  Represen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' abs/1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='1556, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [45] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Szegedy, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Jia, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sermanet, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Reed, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Anguelov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Erhan,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Vanhoucke, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Rabinovich, “Going Deeper with Convolutions,”  in Computer Vision and Pattern Recognition, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [46] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hochreiter and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Schmidhuber, “Long short-term memory,” Neural  Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 1735–1780, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [47] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Schuster and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Paliwal, “Bidirectional recurrent neural networks,”  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 45, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2673–2681, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [48] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moran, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bernal-C´ardenas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Curcio, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bonett, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshy-  vanyk, “Machine learning-based prototyping of graphical user interfaces  for mobile apps,” IEEE Transactions on Software Engineering, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 1–1,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [49] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Blei, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ng, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Jordan, “Latent dirichlet allocation,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 993–1022, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [50] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Porteous, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Newman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ihler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Asuncion, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Smyth, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Welling, “Fast collapsed gibbs sampling for latent dirichlet al-  location,” in Proceedings of the 14th ACM SIGKDD International  Conference on Knowledge Discovery and Data Mining, KDD ’08, (New  York, NY, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 569–577, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [51] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hindle, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Barr, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Su, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Gabel, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Devanbu, “On the  Naturalness of Software,” in International Conference on Software  Engineering, ICSE’12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 837–847, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [52] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Rahman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Palani, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Rigby, “Natural software revisted,” in Pro-  ceedings of the 41st International Conference on Software Engineering  Companion, ICSE ’19, (Montreal, QC Canada), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' to appear, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [53] “Mit language modeling toolkit https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='com/mitlm/mitlm.”  [54] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Koehn, Statistical Machine Translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 1st ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [55] “Google’s im2txt implementation https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='com/tensorflow/models/  tree/master/research/im2txt.”  [56] “Neuraltalk2 implementation https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='com/karpathy/neuraltalk2.”  [57] “Google seq2seq framework https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='com/google/seq2seq.”  [58] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Szegedy, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Vanhoucke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ioffe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Shlens, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Wojna, “Rethinking  the inception architecture for computer vision,” in 2016 IEEE Confer-  ence on Computer Vision and Pattern Recognition, June 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [59] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Russakovsky, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Deng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Su, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Krause, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Satheesh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ma,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Huang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Karpathy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Khosla, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bernstein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Berg, and  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Fei-Fei, “ImageNet Large Scale Visual Recognition Challenge,”  International Journal of Computer Vision, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 115, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 211–252,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [60] “Show, attend and tell implementation https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='com/coldmanck/  show-attend-and-tell.”  [61] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sha, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Mou, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poupart, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chang, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sui,  “Order-planning neural text generation from structured data,” The  Thirty-Second AAAI Conference on Artificial Intelligence (AAAI’17),  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' abs/1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='00155, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [62] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Britz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Goldie, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Luong, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Le, “Massive Exploration of  Neural Machine Translation Architectures,” ArXiv e-prints, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [63] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Papineni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Roukos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Ward, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Zhu, “Bleu: A method for  automatic evaluation of machine translation,” in Proceedings of the 40th  Annual Meeting on Association for Computational Linguistics, ACL ’02,  (Stroudsburg, PA, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 311–318, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [64] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hossain, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Sohel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Shiratuddin, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Laga, “A compre-  hensive survey of deep learning for image captioning,” ACM Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 51, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 118:1–118:36, Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [65] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Fan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Su, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Liu, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Xu, “Storydroid:  Automated generation of storyboard for android apps,” in Proceedings of  the 41st International Conference on Software Engineering, ICSE ’19,  (Piscataway, NJ, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 596–607, IEEE Press, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [66] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' de Greef, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Swearngin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' White, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Murray, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Yu,  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Shan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Nichols, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Fleizach, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Everitt, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bigham,  Screen Recognition: Creating Accessibility Metadata for Mobile Appli-  cations from Pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' New York, NY, USA: Association for Computing  Machinery, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [67] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Xing, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Xu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Zhu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Li, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Wang, “Unblind  your apps: Predicting natural-language labels for mobile gui components  by deep learning,” in Proceedings of the 42nd International Conference  on Software Engineering, ICSE 2020, (New York, NY, USA), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' to  appear, ACM, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [68] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moran, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Watson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Hoskins, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Purnell, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshyvanyk,  “Detecting and summarizing gui changes in evolving mobile apps,”  in Proceedings of the 33rd ACM/IEEE International Conference on  Automated Software Engineering, ASE 2018, (New York, NY, USA),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 543–553, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [69] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Moran, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Bernal-C´ardenas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Jelf, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Poshyvanyk,  “Automated Reporting of GUI Design Violations in Mobile Apps,” in  Proceedings of the 40th International Conference on Software Engineer-  ing Companion, ICSE ’18, (Gothenburg, Sweden), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' to appear, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [70] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Nguyen and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Csallner, “Reverse Engineering Mobile Application  User Interfaces with REMAUI,” in Proceedings of the 2015 30th  IEEE/ACM International Conference on Automated Software Engineer-  ing, ASE’15, (Washington, DC, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 248–259, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [71] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Beltramelli, “Pix2code: Generating Code from a Graphical User  Interface Screenshot,” CoRR, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' abs/1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='07962, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [72] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Chen and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Zhou, “A neural framework for retrieval and summariza-  tion of source code,” in Proceedings of the 33rd ACM/IEEE International  Conference on Automated Software Engineering, ASE 2018, (New York,  NY, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 826–831, ACM, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [73] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Andow, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Acharya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Enck, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Singh, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Xie, “UiRef:  analysis of sensitive user inputs in Android applications,” in Proceedings  of the 10th ACM Conference on Security and Privacy in Wireless and  Mobile Networks, WiSec’17, (New York, New York, USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 23–34,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [74] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Craft, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Situ, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Yumer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Mech, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Kumar, “Learning  design semantics for mobile apps,” in The 31st Annual ACM Symposium  on User Interface Software and Technology, UIST ’18, (New York, NY,  USA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' 569–579, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  [75] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Xiao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Cao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Wang, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' Gao, “Iconintent: Automatic  identification of sensitive ui widgets based on icon classification for  android apps,” in Proceedings of the 41st International Conference on  Software Engineering Companion, ICSE ’19, (Montreal, QC Canada),  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content=' to appear, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
+page_content='  12' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NAzT4oBgHgl3EQfR_tE/content/2301.01224v1.pdf'}
diff --git a/59AyT4oBgHgl3EQf2fl-/vector_store/index.pkl b/59AyT4oBgHgl3EQf2fl-/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..5f2a43445d26fde2dea7a388995894dff4c0ba9d
--- /dev/null
+++ b/59AyT4oBgHgl3EQf2fl-/vector_store/index.pkl
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+Semantic Units 
+ 
+1 
+Semantic Units: Organizing knowledge 
+graphs into semantically meaningful units 
+of representation 
+ 
+Vogt, Lars1; Kuhn, Tobias2; Hoehndorf, Robert3 
+ 
+1 TIB Leibniz Information Centre for Science and Technology, Welfengarten 1B, 30167 Hanover, 
+Germany, 
+orcid.org/0000-0002-8280-0487 
+2 Department of Computer Science, Vrije Universiteit Amsterdam, Netherlands, 
+orcid.org/0000-
+0002-1267-0234 
+3 Computational Bioscience Research Center, Computer, Electrical and Mathematical Sciences & 
+Engineering Division, King Abdullah University of Science and Technology, 4700 KAUST, 23955 Thuwal, 
+Saudi Arabia, 
+orcid.org/0000-0001-8149-5890 
+Correspondence to lars.m.vogt@googlemail.com 
+ 
+ 
+
+Semantic Units 
+ 
+2 
+Abstract 
+Background: Knowledge graphs and ontologies are becoming increasingly important as technical 
+solutions for Findable, Accessible, Interoperable, and Reusable data and metadata (FAIR Guiding 
+Principles). We discuss four challenges that impede the use of FAIR knowledge graphs. 
+Results: Semantic units have the potential to solve the challenges by structuring a knowledge graph 
+into identifiable and semantically meaningful subgraphs. Each semantic unit is represented by its own 
+resource, instantiates a corresponding semantic unit class, and can be implemented as a FAIR Digital 
+Object and a nanopublication in RDF/OWL and property graphs. We distinguish statement and 
+compound units as basic categories of semantic units. Statement units represent smallest, 
+independent propositions that are semantically meaningful for a human reader. They consist of one 
+or more triples and mathematically partition a knowledge graph. We distinguish assertional, 
+contingent (prototypical), and universal statement units as basic types of statement units and propose 
+representational schemes and formal semantics for them (including for absence statements, 
+negations, and cardinality restrictions) that do not involve blank nodes and that translate back to OWL. 
+Compound units, on the other hand, represent semantically meaningful collections of semantic units 
+and we distinguish various types of compound units, representing different levels of representational 
+granularity, different types of granularity trees, and different frames of reference.  
+Conclusions: Semantic units support making statements about statements, can be used for graph-
+alignment, subgraph-matching, knowledge graph profiling, and for managing access restrictions to 
+sensitive data. Organizing the graph into semantic units supports the separation of ontological, 
+diagnostic (i.e., referential), and discursive information, and it also supports the differentiation of 
+multiple frames of reference. 
+ 
+Keywords: FAIR data and metadata, knowledge graph, OWL, RDF, semantic unit, assertional 
+statement, contingent statement, prototypical statement, universal statement, negation 
+ 
+ 
+
+Semantic Units 
+ 
+3 
+Background 
+In times of ever-increasing amounts of data being created every day (1–3), new technical and societal 
+challenges arise (4) that ask for innovative ways of representing and managing data in science and 
+industry. Being able to collect, integrate, and analyze large amounts of data from various sources also 
+represents one of the requirements for facing biodiversity loss and climate change, two major global 
+challenges we are currently facing (5). Solutions to these problems will be driven by sharing data across 
+many stakeholders, needing an effort to help interlink data providers from a diverse range of different 
+areas, often requiring a truly interdisciplinary approach (6), in which data stewardship remains in the 
+hands of the domain experts or institutions, thus ensuring their technical autonomy (following Barend 
+Mons’ data visiting as opposed to data sharing (7)).  
+From a data management and data representation perspective, this requires data and metadata 
+to be FAIR, i.e., readily Findable, Accessible, Interoperable, and Reusable for machines and humans 
+alike (8). If this is not the case, Big Data ultimately turns into Dark Data (9). The establishment of the 
+FAIR Guiding Principles as a general standard in science and industry would also contribute to a 
+solution for the reproducibility crisis in science (10) and the question of the trustworthiness of 
+information in general (see also TRUST Principles of Transparency, Responsibility, User Focus, 
+Sustainability, and Technology (11)). Therefore, we must build something along the lines of the 
+Internet of FAIR Data and Services (12) that scales with Big Data, through which all relevant data-rich 
+institutions, research projects, and citizen-science projects can make their data and metadata 
+accessible following the FAIR Guiding Principles (13,14). This requires providing rich machine-
+actionable data and metadata with human-readable interface outputs and search capabilities, and 
+organizing this data into FAIR Digital Objects (15,16), each of which possesses its own Unique 
+Persistent and Resolvable Identifier (UPRI) for referencing it individually. 
+In this context, knowledge graphs can substantially contribute to the needed technical solutions, 
+providing a suitable framework for managing and representing FAIR data and metadata (17). 
+Knowledge graphs are becoming increasingly popular (18), especially after the 2012 announcement 
+of the Google Knowledge Graph (19) which was followed by further announcements of knowledge 
+graphs being developed from industry and by a growing number of scientific publications on 
+knowledge graphs (20). Besides general applications in industry and research, knowledge graphs are 
+thereby particularly applied in the context of semantic search based on entities and relations, deep 
+reasoning, disambiguation of natural language, machine reading, and entity consolidation for Big Data 
+and text analytics (21).  
+
+Semantic Units 
+ 
+4 
+The graph-based abstractions employed in knowledge graphs have several benefits compared to 
+relational or other NoSQL models, including (i) an intuitive way for modelling relations, (ii) allowing 
+postponing specifications of definitions for data schema so that they can flexibly evolve, which is 
+especially important when dealing with incomplete knowledge, (iii) employing machine-actionable 
+knowledge representation formalisms such as ontologies and rules, (iv) applying graph analytics and 
+machine learning, and (v) utilizing the specialized graph query languages of knowledge graphs that 
+support, in addition to standard relational operators such as joins, unions, and projections, also 
+navigational operators for recursively searching for entities through arbitrary-length paths (20,22–27). 
+Moreover, due to their inherent semantic transparency, knowledge graphs can improve the 
+transparency of data-based decision-making and improve communication in research and science in 
+general. 
+However, although providing a suitable technical framework, using a knowledge graph for 
+documenting data and metadata does not necessarily result in FAIR data and metadata, but requires 
+following specific guidelines such as consistently applying adequate semantic data models and 
+organizing data into FAIR Digital Objects (15,16). Moreover, as it is often the case with new 
+technologies, knowledge graphs bring their own specific technical, conceptual, and societal 
+challenges. This already begins with the concept of a knowledge graph, which is somewhat fuzzy (20) 
+and covers different technical and conceptual incarnations, including property graphs such as Neo4J 
+(https://neo4j.com/) and approaches based on the Resource Description Framework (RDF), the use of 
+RDF-stores, and, with the Web Ontology Language (OWL), also applications of Description Logics.  
+Here, we first briefly discuss four of these challenges, and then we introduce the idea of 
+partitioning and structuring a knowledge graph into identifiable and semantically meaningful units 
+of representation (short: semantic units). The concept of semantic units can significantly contribute 
+to solutions for the four challenges. We introduce the two basic categories of semantic units, i.e., 
+statement units and compound units, as new elements in FAIR knowledge graphs in addition to the 
+well-known triples and the graph as a whole. Statement and compound units can be employed to 
+organize the data graph into five levels of representational granularity, ranging from the level of 
+individual triples to the level of the graph as a whole. We introduce additional subcategories of 
+semantic units that can be used to further organize the data graph. We continue arguing that because 
+each semantic unit can be organized as a FAIR Digital Object that possesses its own UPRI, semantic 
+units can be referred to within triple statements, thus providing a very efficient way of making 
+statements about statements. With the introduction of semantic units, we follow a user-centric 
+approach and add another layer of triples on top of the well established RDF and OWL layer for 
+knowledge graphs (Fig. 1). By simplifying the semantic modelling of empirical data and reducing their 
+
+Semantic Units 
+ 
+5 
+representational complexity and by providing representations (i.e., patterns) and formal semantics for 
+statements for which in OWL no formal semantics exist, semantic units increase the usability of 
+knowledge graphs for domain-experts and developers alike.  
+Figure 1: Semantic units add further layers to a knowledge graph on top of the RDF/OWL layer of triples. The layer of triples 
+is mathematically partitioned into a layer of statement units, so that each triple belongs to exactly one statement unit and 
+each statement unit comprises one or more triples. Statement units can be organized into different types of semantically 
+meaningful collections (i.e., compound units) with which various additional layers can be defined to further structure and 
+organize the knowledge graph in semantically meaningful ways. 
+Box 1 | Conventions 
+In this paper, we refer to FAIR knowledge graphs as machine-actionable semantic graphs for documenting, organizing, 
+and representing assertional (e.g., empirical data), universal, and contingent statements and thus a mixture of ABox and 
+TBox expressions (thereby contrasting knowledge graphs with ontologies, with the latter containing mainly universal 
+statements and thus TBox expressions). We want to point out that we discuss semantic units against the background of 
+RDF-based triple stores, OWL, and Description Logics as a formal framework for inferencing, and labeled property graphs 
+as an alternative to triple stores, because these are the main technologies and logical frameworks used in knowledge 
+graphs that are supported by a broad community of users and developers and for which accepted standards exist. We are 
+aware of the fact that alternative technologies and frameworks exist that support an n-tuples syntax and more advanced 
+logics (e.g., First Order Logic) (28,29), but supporting tools and applications are missing or are not widely used to turn 
+them into well-supported, scalable, and easily usable knowledge graph applications. 
+Throughout this text we use regular underlined to indicate ontology classes, italicsUnderlined when referring to 
+properties (i.e., relations in Neo4j), and use ID numbers to specify each. ID numbers are composed of the ontology prefix 
+followed by a colon and a number, e.g., isAbout (IAO:0000136). If the term is not yet covered in any ontology, we indicate 
+it with *, e.g., the class *metric measurement statement unit*. We use ‘regular underlined’ to indicate instances of classes, 
+
+SemanticUnits
+Knowledge
+different types of
+Graph
+Compound Units
+StatementUnits
+RDF/OWL
+Knowledge
+Triples
+GraphSemantic Units 
+ 
+6 
+with the label referring to the class label and the ID number to the class. Moreover, when we use the term resource, we 
+understand it to be something that is uniquely designated (e.g., a Uniform Resource Identifier, URI) and about which you 
+want to say something. It thus stands for something and represents something you want to talk about. In RDF, the Subject 
+and the Predicate in a triple statement are always resources, whereas the Object can be either a resource or a literal. 
+Resources can be either properties, instances, or classes, with properties taking the Predicate position in a triple and with 
+instances referring to individuals (=particulars) and classes to universals.  
+For reasons of clarity, in the text and in all figures, we represent resources not with their UPRIs but with human-
+readable labels, with the implicit assumption that every property, every instance, and every class has its own UPRI. 
+Challenge 1: FAIR empirical data must specify the graph patterns used 
+for their modelling to prevent schematic interoperability conflicts 
+FAIR is often understood to mean that for data and metadata statements to be interoperable and 
+reusable, all concepts used in them must have identifiers, which in turn are provided by controlled 
+vocabularies such as ontologies. What is frequently overlooked is the fact that to be FAIR, not only the 
+concepts must be standardized (i.e., terminological interoperability), but also the way they are related 
+to one another in data and metadata statements and thus the statements’ underlying semantic graph 
+patterns (i.e., schematic interoperability)―especially when stored and managed in a knowledge 
+graph. In case of universal statements, in RDF-based knowledge graphs this graph pattern is typically 
+well-defined using OWL-specific object properties in class axioms (see also Figure 5B), resulting in TBox 
+expressions.  
+With empirical data, the situation is different. Empirical data should be modelled as ABox 
+expressions (30). However, due to the high general expressivity of RDF and OWL, in a knowledge 
+graph, any given empirical data statement can be modelled in many, usually not directly interoperable 
+ways. A machine would have a hard time to identify two differently structured ABox expressions that 
+actually model the same underlying data statement. As a result, we must deal with such schematic 
+interoperability conflicts, whenever data are modelled using different graph patterns (cf. Fig. 2 and 
+Fig. 3). 
+
+Semantic Units 
+ 
+7 
+Figure 2: Comparison of a human-readable statement with its machine-actionable representation as an ABox semantic 
+graph following the RDF syntax. Top: A human-readable statement about the observation that ObjectX weighs 5 kilograms. 
+Bottom: A representation of the same statement as a graph, using RDF and following the general pattern for measurement 
+data from the Ontology for Biomedical Investigations (OBI; http://obi-ontology.org/) (31) of the Open Biological and 
+Biomedical Ontology Foundry (OBO; http://www.obofoundry.org/).  
+ 
+Figure 3: Alternative machine-actionable representation of the data statement from Fig. 2, following the RDF syntax and 
+the graph-model from the Extensible Observation Ontology (OBOE). This graph represents the same data statement as 
+shown in Figure 2 Top, but applies a different semantic graph model for its representation, which is based on OBOE 
+(http://bioportal.bioontology.org/ontologies/OBOE), an ontology frequently used in the ecology community. 
+Therefore, for an ABox representation of an empirical data statement to be FAIR, one must know 
+which graph pattern has been used for its semantic modelling. Only instance-based graphs (i.e., graphs 
+with instance resources in the Subject and Object positions of their triples; ABoxes) that are modelled 
+using the same template in the form of a graph pattern, for instance specified as a shape using SHACL 
+(32), are guaranteed to meet the minimum requirement for interoperability. Ideally, statements of 
+the same type, e.g., all weight measurements, use the same graph pattern to be potentially 
+interoperable. Therefore, we need identifiers for such graph patterns, and if an empirical datum is 
+documented in the form of an ABox, its metadata should reference the corresponding graph-pattern 
+identifier. With this information, one can identify potentially interoperable ABox expressions by their 
+commonly shared graph-pattern identifiers. 
+
+Observation:
+ObjectX weighs 5 kilograms
+Observation Graph:
+bfo:material entity
+pato:weight
+iao:scalar measurement datum
+obi:scalar value specification
+uo:kilogram
+rdf:type
+rdf:type
+rdf:type
+rdf:type
+rdf:type
+ro:has quality
+lao:isquality
+objectx
+weight
+measured as
+scalar measurement datum
+obi: has value
+scalar value specification
+iao:hasmeasurement
+specification
+unit label
+kilogram
+ro:quality of
+iao:is quality
+measurementof
+iao: has
+measurement
+obi:specifies value of
+value
+class
+instance
+value
+5.00bfo:material entity
+oboe:observation
+oboe:measurement
+rdf:type
+rdf:type
+rdf:type
+objectx
+oboe:ofentity
+observation
+oboe:hasmeasurement
+measurement
+oboe:hasvalue
+5.00
+oboe:ofcharacteristic
+oboe:uses standard
+weight
+kilogram
+class
+instance
+value
+rdf:type
+rdf:type
+pato:weight
+uo:kilogramSemantic Units 
+ 
+8 
+Practically, this implies (i) that all statements in a knowledge graph must be classified into 
+statement classes, with each class having an associated graph pattern specified (e.g., in the form of a 
+shape specification) and (ii) that the subgraph belonging to a particular statement must be identifiable. 
+Only if these two criteria are met, ABox representations of data and metadata truly comply with the 
+FAIR Guiding Principles. Semantic units provide a means to meet these two criteria. 
+Challenge 2: Many software developers do not see the benefit of 
+graph query languages 
+Most knowledge graphs are either directed labeled graphs that are based on RDF/OWL and stored in 
+tuple stores, or they are labeled property graphs such as Neo4j. Directly interacting with these graphs, 
+i.e., conducting CRUD operations for creating (=writing), reading (= searching), updating, and deleting 
+statements in the knowledge graph, requires the use of a query language. For RDF/OWL, this is for 
+example SPARQL (https://www.w3.org/TR/rdf-sparql-query/), and for Neo4j, it is Cypher 
+(https://neo4j.com/developer/cypher/).  
+Whereas these query languages allow detailed and very complex queries, writing queries in 
+SPARQL or Cypher is demanding. Users of knowledge graph applications usually lack the required 
+background for writing such queries themselves. Unfortunately, our personal experiences are that 
+even most developers are not familiar with these languages and struggle with their complexity when 
+attempting to learn them. In other words, having to write SPARQL or Cypher queries represents an 
+entry barrier for interacting with a knowledge graph and hinders their broader usage (33). We thus 
+need technical solutions to mitigate this challenge, such as openly available and reusable query 
+patterns that link to specific graph patterns.  
+The concept of semantic units can contribute to such solutions by allowing experts in Semantics 
+to provide generic CRUD queries for each type of semantic unit that domain experts as users and 
+developers of knowledge graphs that apply semantic units can employ without having to write the 
+queries themselves. Queries of different types of semantic units can be combined via union or 
+intersection to form more complex queries. 
+Challenge 3: Making statements about statements can be challenging 
+The RDF triple syntax of Subject, Predicate, and Object does not natively provide a good method for 
+making statements about statements. In RDF, a statement about a statement is a triple that relates a 
+statement consisting of one or more triples to some value, resource, or some other such statement. 
+
+Semantic Units 
+ 
+9 
+Unfortunately, if you wanted to represent empirical data or the contents of for instance a 
+scholarly publication in a FAIR knowledge graph, you frequently have to model statements about 
+statements. For example, if you want to provide detailed metadata for a measurement datum, you 
+would actually have to relate two subgraphs to one another: the graph representing the measurement 
+itself, documented in a set of triples (e.g., see Fig. 2) and the graph documenting the underlying 
+measuring process, which also involves several triples (e.g., see Fig. 4).  
+In case we only want to refer to a single triple statement in another triple, RDF reification can be 
+used. In RDF reification, a resource is defined to represent a particular triple by describing it via three 
+additional triples that specify its Subject, Predicate, and Object. Alternatively, one can also use the 
+RDF-star approach (34,35). In RDF-star, however, all statements involving the same subject, predicate, 
+and object are understood to reference the same triple and are thus not distinguished, with the 
+consequence that one cannot distinguish different instances of the same statement. Moreover, while 
+using RDF-star is feasible for referring to a single triple, it becomes very inefficient and complicated to 
+query when having to refer to sets of multiple triple statements and thus larger subgraphs. If you 
+wanted to make a statement about the entire graph as depicted in Figure 4 using reification, you would 
+first have to specify a statement for each triple in the graph. Since the graph comprises more than 20 
+triples, you would end up having to create more than 60 triples in this first step. However, because 
+you want to refer to the graph as a whole and not to each of its triples individually, you would have to 
+create more than 20 additional triples that link the resource representing the entire subgraph with 
+the resources you created in the first step for representing each individual triple. While this is 
+technically feasible, it is neither elegant nor easily queried.  
+In cases like this, using Named Graphs is much more efficient than applying RDF reification or 
+RDF-star. Named Graphs can be used in RDF-based knowledge graphs. A Named Graph resource 
+identifies a set of triple statements by adding the UPRI of the subgraph and thus the statement as a 
+fourth element to each triple, turning the triples into quads. Moreover, Named Graphs have the 
+additional benefit to outperform other metadata representation models when conducting more 
+complex queries (36). 
+In labeled property graphs, on the other hand, assigning a resource for identifying subgraphs 
+within the overall data graph is straightforward and can be achieved by adding the resource identifier 
+as the value of a respective property-value pair and add this value pair to all relations and nodes that 
+belong to the same subgraph. 
+ 
+
+Semantic Units 
+ 
+10 
+Figure 4: A detailed machine-actionable representation of the metadata relating to a weight measurement datum 
+documented as an RDF ABox graph. The representation takes the form of an ABox semantic graph following the RDF syntax. 
+The graph documents a mass measurement process using a balance. It relates an instance of mass measurement assay 
+(OBI:0000445) with instances of various other classes from different ontologies, specifying who conducted the 
+measurement, where and when it took place, following which protocol and using which device (i.e., balance). The graph 
+furthermore specifies the particular material entity that served as subject and thus as input of the measurement process 
+(i.e., ‘objectX’), and it specifies the data that is the output of the observation, which is contained in a particular weight 
+measurement assertion.  
+Organizing the overall data graph into different semantic units and thus semantically meaningful 
+subgraphs at different levels of representational granularity provides an efficient way of structuring 
+the graph to allow users to intuitively make statements about statements, and also provides a clear 
+and straightforward implementation schema that is beneficial for developing relevant search 
+schemata. 
+Challenge 4: Conceptual gap between RDF/OWL and property graphs 
+and problems of distinguishing universal, contingent, and assertional 
+statements  
+Some knowledge graphs are based on RDF/OWL, others on labeled property graphs. Each technology 
+has its specific advantages and shortcomings (see table 1).  
+ 
+ 
+
+WHO?
+obi:assay
+INPUT:MATERIALENTITY
+OUTPUT:DATA
+rdfs:subClassOf
+obi:investigation
+objectx
+weightmeasurement
+agentrole
+obi:massmeasurementassay
+assertion
+rdf:type
+rdf:type
+ro:has specified input
+rdf:type
+investigation agent role
+|mass measurement
+ro:has specified output
+weightmeasurement
+bfo:realizes
+assertion
+ro:has role
+ro: has participant
+URIof researcher
+contributingthespecified
+output
+bfo:existsat
+bfo:realizes
+ro:has participant
+bfo:realizes
+obi:device setting
+bfo:occurrsin
+rdf: type
+device setting
+ro: has quality
+| site
+ti:has interval
+ time interval
+startdate
+protocol
+URIof some
+<thebalanceused
+measure function
+publication that
+xsd:dateTime
+describesthe
+ro:has function
+rdf:type
+rdf:type ti:has interval
+rdf:type
+protocol
+rdf:type
+rdf:type
+ro:inheres in
+end date
+jao:isabout
+rdf:type
+xsd:dateTime
+bfo:site
+ti: time interval
+obi:protocol
+iao:publication
+obi:balance
+obi:measure function
+WHERE?
+WHEN?
+FOLLOWINGPROTOCOL?
+USINGWHATDEVICE?Semantic Units 
+ 
+11 
+Table 1: Comparison of the advantages and shortcomings of knowledge graphs based on RDF/OWL and on labeled 
+property graphs (37,38).  
+ 
+RDF 
+labeled property graph 
+query language 
+SPARQL, W3C recommendation 
+various, none has a W3C 
+recommendation 
+formal semantics and 
+reasoning 
+OWL; however: 
+1. 
+when mapped to RDF, OWL is usually very 
+verbose, leading to unnecessarily complex 
+graphs that are not intuitively 
+comprehensible for a human reader and 
+inhibit effective computation; 
+2. 
+OWL is not the only mode of inference, 
+and other frameworks besides Description 
+Logics exist for inferencing 
+no unified set of standards (no W3C 
+recommendation)―a standardized 
+mapping of OWL to a property graph 
+is still lacking; the data model of Neo4j 
+is not based on a formal set theory or 
+first-order-logic 
+relating information 
+directly to edges 
+only indirectly through reification, RDF-star, or 
+named graphs (see Challenge 3) 
+information can be directly related to 
+relations, i.e., edges 
+distinction of universal, 
+contingent, and assertional 
+statements  
+formalized semantic distinction between 
+assertional and universal statements; 
+contingent statements are not modelled in OWL 
+no formalized semantic distinction 
+One of the major differences between an RDF-based graph and a labeled property graph is that 
+OWL can be mapped to RDF and thus provides formal semantics and reasoning following a W3C 
+recommendation. No W3C-recommended standardized mapping exists for property graphs such as 
+Neo4j so far, although proposals have been made (e.g., OWLStar, owl2lpg). OWL is based on 
+Description Logics, and thus strictly separates universal statements1 in the form of class-specifications 
+(terminology box; TBox) from the domain of discourse in the form of assertional statements2 that 
+relate instances (i.e., individuals) to each other (assertion box; ABox) (38). Because, in OWL, classes 
+possess URIs and can thus be referenced, but none of their class axioms do, TBoxes do not belong to 
+the domain of discourse―within a knowledge graph, it is not possible to refer to a particular axiom of 
+a given class but only to the class itself. Therefore, it is not possible to make statements about class 
+ 
+1 A universal statement is a statement that is true for every instance of a specific universal. Universal statements represent 
+commonly accepted domain knowledge and specify what is necessarily the case. Universal statements are based on all-to-
+some relations. Definitions of ontology classes and their class axioms are examples of universal statements, but also many 
+scientific hypotheses and law-like regularities take the form of universal statements. 
+2 An assertional statement is a statement that is true for specific particulars and specifies a fact. Assertional statements are 
+based on one-to-one relations. In a knowledge graph, assertional statements relate particular instances to each other. 
+Empirical data are examples of assertional statements. 
+
+Semantic Units 
+ 
+12 
+definitions (i.e., universal statements) in RDF/OWL-based knowledge graphs. Consequently, 
+documenting statements such as ‘author A asserts universal law X’ is not straightforward in a 
+knowledge graph if the universal law X is modelled as a class.  
+On the other hand, because property graphs typically do not distinguish between ABox and TBox 
+expressions, it is not always clear what their statements actually mean. For instance, the statement 
+‘hand has part thumb’ (Fig. 5A) could refer to a particular hand and its thumb, e.g., the right hand of 
+one of the authors of this paper. As such, the statement would represent an assertional statement. 
+However, the statement could also refer to some unknown hand in the sense that it states that there 
+exists at least one hand that has some thumb as its part, which would represent a contingent 
+statement3. Another possible interpretation of the statement could be that it documents a situation 
+typically found when dealing with hands: a hand typically possesses a thumb. In this case, the 
+statement would represent a prototypical statement4, which is a special case of a contingent 
+statement. Finally, the statement could refer to all instances of a class hand (FMA:9712) and represent 
+a universal statement, indicating that every hand necessarily possesses a thumb. In other words, due 
+to the lack of formal semantics, labeled property graphs provide no standardized way to distinguish 
+between universal, contingent, prototypical, and assertional statements.  
+Regarding universal statements, from a logical point of view, it makes no sense to relate two 
+classes such as hand (FMA:9712) and thumb (FMA:24938) to each other via the property hasPart 
+(BFO:0000051), because classes cannot have other classes as their parts. With few exceptions (e.g., 
+subclassOf (RDFS:subclassOf), type (RDF:type)), object properties model instance-instance and not 
+class-class or instance-class relations. If such object properties are used nevertheless to describe 
+relationships between classes, this leads to semantic inconsistencies that may not cause issues for 
+human readers, but for machines such as reasoners they do. 
+In OWL, the universal statement ‘every instance of a hand has some instance of a thumb as its 
+part’ can be expressed in a semantically proper way using OWL-specific properties, which results in a 
+complex but semantically precise representation of the statement (Fig. 5B). A human reader, however, 
+typically does not want to look at this complex representation but prefers the simpler and still 
+intuitively comprehensible representation provided by a property graph (Fig. 5A). Moreover, the OWL-
+ 
+3 A contingent statement is a statement that is true for some instances of a specific universal and specifies what is possibly 
+the case. Contingent statements are based on some-to-some relations. In a knowledge graph, contingent statements are true 
+for some, but not necessarily every instance of a class.  
+4 A prototypical statement is a statement that is true for all instances of a specific universal as long as not the contrary is 
+explicitly stated, and thus specifies what is typically but not necessarily the case.  
+
+Semantic Units 
+ 
+13 
+based representation involves blank nodes, which makes basic SPARQL querying difficult (38) and has 
+the potential to cause other issues (39).    
+ 
+Figure 
+5: 
+Comparison 
+of 
+a 
+universal statement represented 
+in a property graph and in OWL 
+mapped onto RDF. The statement 
+‘every instance of hand has part 
+some thumb’ represented in A) a 
+labeled property graph and B) in 
+OWL mapped onto RDF.  
+Solutions for representing universal statements in a property graph have been suggested. They 
+involve annotating edges with logical properties such as existential restriction axioms, resulting in an 
+object-property mapping (37,38). A standardized W3C recommendation for a formalism for mapping 
+OWL into a property graph, however, is still lacking.  
+Organizing a knowledge graph into different semantic units, each with its own UPRI and classified 
+as either universal, contingent, or assertional statement, would not only provide a formal conceptual 
+framework that facilitates the application of such object-property mappings, but would allow making 
+statements about universal statements, which would make universal statements accessible to the 
+domain of discourse, meaning formal class definitions (i.e., class axioms) would become referenceable 
+so that one could make statements about them within the graph.  
+Results 
+Organizing knowledge graphs into semantically meaningful units of 
+representation 
+To make knowledge graphs more manageable and provide them with increased levels of structure, 
+their graph must be organized into several layers of partially overlapping, partially enclosed, 
+subgraphs. Approaches for systematically structuring a knowledge graph into subgraphs have been 
+proposed before, e.g., defining a characteristic set as a subgraph consisting of all triples that share the 
+same resource in the Subject position, yielding significant improvements in space and query 
+performance (40,41) (see also the related concept of RDF molecules (42,43)).  
+
+A) Statement modeled in a labeled property graph
+class
+instance
+hand
+haspart
+thumb
+owlspecific
+objectproperty
+class
+B)OWLstatementmappedontoRDF
+owl:restriction
+bfo:haspart
+rdf: type
+owl: on
+property
+fma:hand
+owl:some
+rdfs:subclassof-
+blank node
+fma:thumb
+valuesfromSemantic Units 
+ 
+14 
+However, instead of structuring a knowledge graph into subgraphs based on the rather technical 
+aspects of shared graph-topological properties of its triples, we here propose an approach that focuses 
+on structuring a knowledge graph into identifiable and semantically meaningful sets of triples, i.e., 
+subgraphs that represent units of representation (short: semantic units). The approach builds on an 
+idea suggested in the context of semantic data models for structuring descriptions of phenotypes into 
+smallest semantically meaningful units, i.e., assertions, each of which is organized in its own Named 
+Graph (44). Here, we generalize and extend this idea to the concept of semantic units that can be 
+accessed, searched, and reused as identifiable and reusable data items in their own right, forming 
+units of representation that are FAIR Digital Objects that can be implemented using RDF/OWL-based 
+graphs as well as property graphs.  
+A semantic unit is a subgraph of the overall knowledge graph that represents a unit of 
+information that is semantically meaningful to a human reader. Every semantic unit is represented 
+in the graph by its own resource (i.e., node) and thus possesses its own UPRI. Moreover, it can be 
+classified as an instance of a respective ontology class.  
+In a knowledge graph that is structured into semantic units, two different graph layers are 
+distinguished: a data graph layer and a semantic-units graph layer. The data graph layer contains all 
+the triples of a knowledge graph that semantic units organize into identifiable subgraphs. A knowledge 
+graph that is not structured into semantic units only possesses a data graph layer. The semantic-units 
+graph layer is added to a knowledge graph with organizing it into semantic units and comprises all the 
+triples added to the graph due to organizing and structuring it into semantic units. The resource of 
+each semantic unit and their interrelationships are for instance part of the semantic-units graph layer. 
+Analogously to this general distinction across the knowledge graph, we can distinguish a data graph 
+and a semantic-units graph for each semantic unit. The data graph of a particular semantic unit 
+possesses the same UPRI as its semantic unit resource, so that by referring to the UPRI one refers at 
+the same time to the semantic unit as a resource as well as its corresponding data graph and thus can 
+make statements about the data graph’s content (Fig. 7).  
+Two basic categories of semantic units and their subcategories can be distinguished: statement 
+units and compound units (for a classification of semantic units, see Fig. 6). 
+
+Semantic Units 
+ 
+15 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure 6: Classification of different categories of semantic unit.  
+Statement unit 
+A statement unit is characterized as a unit of information that represents the smallest, independent 
+proposition (i.e., statement) that is semantically meaningful for a human reader (see also (44)). For 
+example, the fact that a population infected with a virus has the quality basic reproduction number 
+(NCIT:C173777) represents a statement unit that is independent of an actual measurement of the 
+basic reproduction number, which represents another statement unit. The measurement statement 
+unit is independent of the quality statement unit because a given population may have more than one 
+measurement for its basic reproduction number for the same point in time, due to measurement 
+errors, measurement inaccuracies, or the application of different measurement methods, 
+instruments, or models. The same applies to all quality measurements. For instance, the weight 
+measurement for ObjectX shown in Figure 2 consists of two statement units. One statement unit 
+specifies that ObjectX has the quality ‘weight’ (PATO:0000128), whereas the other specifies the 
+weight’s measurement. 
+Structuring a knowledge graph into statement units results in a mathematical partition of its data 
+graph layer, with each triple of the data graph layer belonging to exactly one statement unit. It is 
+important to note that only the data graph layer is partitioned into smaller data (sub)graphs. All the 
+
+Semanticunit
+Statementunit
+Qualitativestatementunit
+Quantitativestatementunit
+Assertional statementunit
+Contingent statement unit
+Prototypical contingent statement unit
+Universal statementunit
+Compoundunit
+Typed statement unit
+Qualitymeasurementunit
+Item unit
+-Instance itemunit
+Class itemunit
+Text-resource hybrid item unit
+Itemgroup unit
+Instanceitemgroupunit
+-Classitemgroupunit
+Classaxiomitemgroupunit
+-Dataset unit
+Granularitytreeunit
+Granular itemgroupunit
+Context unit
+List unit
+Unordered list unit
+Set unit
+Ordered list unitSemantic Units 
+ 
+16 
+triples added to the knowledge graph for organizing it into semantic units, i.e., the semantic-units 
+graph layer, are excluded from the partition because otherwise applying semantic units would result 
+in an infinite regression, since adding a semantic unit always adds triples to the semantic-units graph 
+layer, which, if included in the partition, would have to be represented themselves via a statement 
+unit, which would add triples to the semantic-units graph layer again, etc.  
+Following the predicate-argument-structure from linguistics, the main verb of a statement, 
+together with its auxiliaries, represents the statement’s predicate. Each predicate has a valence that 
+determines the number and types of arguments it requires to complete its meaning. Adjuncts can 
+additionally relate to the predicate, but they are not necessary for completing the predicate’s meaning 
+and only provide optional information, such as a time specification in a has-part statement. Subject 
+and object phrases are the most frequently occurring arguments and adjuncts. So, we can say that 
+each statement unit documents a particular proposition by relating a resource that is the subject 
+argument of the predicate of the proposition to some literal or to another resource, which is the object 
+argument or object adjunct of the predicate. The subject argument of a proposition of a statement 
+unit we call subject and the object argument(s) and object adjunct(s) the object(s) of the statement 
+unit. Every statement unit has one such subject and one or more objects.  
+A has-part statement unit (Fig. 7), for instance, has a subject and one object as an argument, 
+whereas a weight measurement statement unit has a subject and two objects as arguments, i.e., the 
+weight value and the weight unit. The resource representing a statement unit in the graph relates to 
+its subject via the property *hasSemanticUnitSubject*, which is documented in the semantic-units 
+graph. 
+If the proposition documented in the data graph is based on a binary relation, and thus a divalent 
+predicate, such as ‘Lars’ right hand has part Lars’ right thumb’, the corresponding statement unit 
+typically consists of a single triple, because in RDF, the properties of triples are binary relations. 
+However, many propositions are based on n-ary relations and thus cannot be modelled with a single 
+triple. For instance, the statements ‘a weight measurement with the value 5 and the unit kilograms’ 
+and ‘Lars’ right hand has part Lars’ right thumb on January 29th 2022’ consist of at least two triples, 
+whereas the statements ‘Anna gives Bob a book’, ‘Carla travels by train from Paris to Berlin on the 
+29th of June 2022’, and ‘Dave buys the car from Eric’ each require more than two triples. Depending 
+on the relation of the underlying proposition and thus the valence of its predicate and depending on 
+the number of optional adjuncts that should be additionally modelled, statement units can thus 
+consist of one or more triples. A specific type of statement unit, i.e., a statement unit class, could thus 
+be defined in reference to the n-ary property that models its underlying relation. Many object 
+
+Semantic Units 
+ 
+17 
+properties of the Basic Formal Ontology 2 are actually ternary relations, as they are time-dependent 
+(45). For instance, ‘b located_in c at t’ requires at least two triples to be modelled in RDF. 
+Figure 7: Example of a statement unit. Example 
+of a semantic unit that models a statement based 
+on a has-part-of relation between two instances. 
+The data graph expressing the statement is shown 
+in the blue box at the bottom, with ‘Lars’ right 
+hand’ being the subject argument and ‘Lars’ right 
+thumb’ the object argument of the statement. 
+The semantic-units graph is shown in the peach-
+colored box and contains the triples representing 
+the semantic unit. It specifies that the resource representing the statement unit (blue box with borders, here shown with its 
+dynamic label), which represents the statement in the data graph (indicated by the blue arrow), is an instance of *has-part-
+of statement unit* and that ‘Lars’ right hand’ is the subject of this semantic unit. The UPRI of *’has-part-of statement unit’* 
+is also the UPRI of the semantic unit’s data graph (the subgraph in the blue box without border).  
+In other words, which triples belong to a statement unit must be specified for each type of 
+underlying predicate on a case-by-case basis by human domain experts. However, by specifying a 
+graph pattern for modelling a given proposition into a graph-based representation that in turn 
+constitutes a statement unit, modelling languages such as LinkML or the Shapes Constraint Language 
+SHACL (32) can be used, and corresponding tools can be applied for identifying instances of this 
+pattern and thus instances of the corresponding type of statement unit. Moreover, the SHACL shapes 
+can be utilized to derive dynamic labels for each statement unit when representing them in 
+visualizations of the knowledge graph in a user interface (UI). Such a label can be generated 
+dynamically by parsing the label from the statement unit’s subject resource and the labels from all of 
+its object resources and literals and creating from them a human-readable statement following a pre-
+defined template. E.g., the template ‘subject travels by A from B to C on the D’, with the input ‘Carla 
+| train | Paris | Berlin | 29th of June’ would read as ‘Carla travels by train from Paris to Berlin on the 
+29th of June 2022’. 
+Each statement unit instantiates a respective statement unit ontology class. Characteristic for the 
+class is the type of relation of the propositions its instances are modelling. Based on the relation of its 
+underlying proposition, one can distinguish two subcategories of statement unit (relation-based 
+criterion): 
+1. Qualitative statement unit: Statement units that document qualitative relations, such as a 
+has-part relation (Fig. 7). The argument objects of a qualitative statement unit are always 
+
+semantic-units graph
+class
+instance
+dynamic label
+Lars'right hand
+haspart
+rdf:type
+has-part statement unit
+Lars'right thumb
+has semantic
+divalent predicate
+unit subject
+Lars' right hand
+bfo:haspart
+Lars'rightthumb
+subjectargument
+data graph
+objectargumentSemantic Units 
+ 
+18 
+resources and not numerical values―only adjunct objects of a qualitative statement unit may 
+be numerical values. 
+2. Quantitative statement unit: Statement units that document quantitative statements, such 
+as a measurement datum. At least one argument object of a quantitative statement unit 
+must be a numerical value. 
+The two categories are exhaustive and disjoint, meaning that any given statement unit is either a 
+qualitative or a quantitative statement unit, but never both. Within these two subcategories, based 
+on the underlying relation, e.g., has part, type, develops from, one can differentiate between further 
+statement unit classes. Additional subtypes of a given relation-based statement unit class, e.g., has-
+part statements about material entities versus has-part statements about information content 
+entities, do not have to be differentiated as classes, but can be identified and distinguished by simply 
+querying for the *hasSemanticUnitSubject* relations that instances of a has-part statement unit class 
+have to their subject. 
+Besides this relation-based criterion, there is another criterion for differentiating classes of 
+statement units. The subject-category-based criterion is based on the category of entity of the 
+statement unit’s subject, resulting in the distinction of assertional, contingent, and universal 
+statement units. These three categories of statement units are exhaustive and disjoint, meaning that 
+any given statement unit is either an assertional, a contingent, or a universal statement unit, but never 
+a combination of them (see also Challenge 4). Since the relation-based and the subject-category-based 
+criterion are mutually independent, a given statement unit can, for instance, be a weight 
+measurement statement unit and an assertional statement unit.  
+Before we discuss the different types of subject-category-based statement units, we first want to 
+point to a convention we want to introduce, which we apply to semantic units to contribute to closing 
+the conceptual gap discussed in challenge 4. This convention involves the introduction of two new 
+types of resources in addition to instances, properties, and classes: some-instance and every-instance 
+resources. Based on these two new types of resources, three different types of qualitative statement 
+units can be distinguished, which model three different types of relations between some-instance, 
+every-instance, named-individual, and class resources in their data graph. 
+ 
+ 
+ 
+ 
+
+Semantic Units 
+ 
+19 
+ 
+ 
+Figure 8: Examples for three different types of identification units. A) 
+Named-individual 
+identification 
+unit. 
+This 
+named-individual 
+identification unit models in its data graph the class-affiliation of the 
+instance ‘Lars’ right hand’ (FMA:9712), which is its subject, through the 
+property type (RDF:type), together with the subject’s label ‘Lars’ right 
+hand’ through the property label (RDFS:label). The blue box without 
+borders shows the data graph that belongs to this named-individual 
+identification unit (blue box with borders). Subjects of named-
+individual identification units are the type of instances that are also the 
+subjects of assertional statement units (cf. Fig. 9A). B) Some-instance 
+identification unit. This some-instance identification unit models in its 
+data graph the class-affiliation of the instance ‘some hand X’ 
+(FMA:9712), which is its subject, through the property *some instance 
+of*, together with the subject’s label ‘some instance of hand’. The blue 
+box without borders shows the data graph that belongs to this some-
+instance identification unit. Subjects of some-instance identification 
+units are the type of instances that are also the subjects of contingent 
+statement units (cf. Fig. 9B). C) Every-instance identification unit. This 
+every-instance identification unit models in its data graph the class-
+affiliation of the instance ‘every hand’ (FMA:9712), which is its subject, 
+through the property *every instance of*, together with the subject’s 
+label ‘every instance of hand’ through the property label (RDFS:label). 
+The blue box without borders shows the data graph that belongs to this 
+every-instance 
+identification 
+unit. 
+Subjects 
+of 
+every-instance 
+identification units are the type of instances that are also the subjects 
+of universal statement units (cf. Fig. 9C). 
+1. Named-individual identification unit: A qualitative statement unit that identifies a resource 
+that is the subject of the statement unit to refer to a named individual, together with its label 
+and its type, i.e., its class membership (Fig. 8A). 
+2. Some-instance identification unit: A qualitative statement unit that identifies a resource that 
+is the subject of the statement unit to refer to some unspecified instances of a given class, 
+together with a label and its class specification (Fig. 8B). When this resource is used in some 
+other statement unit, it is meant as ‘∃i∈C’ (with i = instance and C = class), reading ‘there exists 
+an instance i of class C for which holds …’. A some-instance identification unit may, 
+additionally, also contain information about cardinality restrictions (see Modelling negations, 
+cardinality restrictions, and disagreement below). 
+
+A)Named-lndividualldentificationUnit
+named-individual
+named-individual
+identification unit
+-rdf:type
+identification unit
+hassemantic
+unitsubject
+Lars' right hand
+rdfs:label
+Lars' right hand
+rdf:type
+rdf:type
+fma:hand
+owl:named individual
+class
+instance
+value
+B)Some-lnstanceIdentificationUnit
+some-instance
+Frdf:type
+some-instance
+identification unit
+identification unit
+hassemantic
+unitsubject
+someinstanceof
+somehandx
+rdfs:label
+hand
+someinstance of
+fma:hand
+C)Every-lnstanceIdentificationUnit
+every-instance
+-rdf:typel
+every-instance
+identification unit
+identificationunit
+hassemantic
+unitsubject
+everyhand
+every instanceof
+rdfs:label
+hand
+everyinstanceof
+fma:handSemantic Units 
+ 
+20 
+3. Every-instance identification unit: A qualitative statement unit that identifies a resource that 
+is the subject of the statement unit to refer to every instance of a given class, together with a 
+label and its class specification (Fig. 8C). When this resource is used in some other statement 
+unit, it is meant as ‘∀i∈C’ (with i = instance and C = class), reading ‘for every instance i of class 
+C holds’. 
+Assertional statement unit 
+An assertional statement unit is a statement unit that has a named individual as its subject-resource 
+(e.g., ‘Lars’ right hand’ (FMA:9712) in Fig. 8A), and thus an instance that is known to the knowledge 
+graph. In other words, its subject is also the subject of a named-individual identification unit. If the 
+assertional statement unit possesses an object that is a resource and not a literal, that object also 
+refers to a named individual, resulting in a one-to-one relation (or many such relations in case of an n-
+ary proposition). An assertional statement unit is thus an ABox representation of a relation with at 
+least one particular. 
+As a semantic unit, a particular assertional statement unit refers to a subgraph of a knowledge 
+graph that models a particular assertion. An assertion is a proposition about a particular (the subject) 
+and thus about an individual and not a universal, and this proposition is meant to be either true or 
+false (46,47). In a knowledge graph, a particular assertional statement unit is modelled by a resource 
+that represents the unit’s data graph. This data graph is thus an instance-based subgraph of the 
+knowledge graph and represents an ABox expression. The unit resource is an instance of both the 
+respective type of statement unit and of *assertional statement unit* (Fig. 9A).  
+Contingent statement unit 
+A contingent statement unit is a statement unit that refers to some instances of a specific class as its 
+subject. In other words, its subject is also the subject of a some-instance identification unit. If the 
+contingent statement unit possesses an object that is a resource, that object also refers to some 
+instances of a specific class, resulting in a some-to-some relation (or many such relations in case of an 
+n-ary proposition). For example, if you want to state that some but not necessarily all hands possess 
+a thumb, and you do not want to or simply cannot list all the individual hands to which this applies, 
+you make such a contingent statement unit (Fig. 9B).  
+Contingent statements are propositions that are true for some instances of a specific universal, 
+but not necessarily for every instance (46–48). They are frequently used when expressing prototypical 
+relationships, such as that a human’s hand usually has a thumb as its part, and thus statements about 
+universals that are assumed to be at least typically true in specific contexts, but not necessarily so―a 
+
+Semantic Units 
+ 
+21 
+hand is still a hand, even if it has no thumb5. Other examples are statements about the relationships 
+between diseases and their symptoms or drugs and their effects, which are often expressed in 
+reference to some probability evaluation. These prototypical contingent statements can be 
+documented in prototypical contingent statement units, which form a subcategory of contingent 
+statement units.  
+Description Logics and thus also OWL does not provide the means to state what is typically true, 
+and other logical formalisms that are capable of expressing prototypical knowledge are needed to 
+provide a semantics for such statements (47).  
+In a knowledge graph, a particular contingent statement unit can be modelled as a statement 
+unit, with its resource representing the corresponding data graph. The resource is an instance of both 
+the respective type of statement unit and of *contingent statement unit*. Its subject and, if present, 
+also its object is modelled as a resource that relates to its class through a *some instance of* property 
+in corresponding some-instance identification units (Fig. 8B). Probability values expressing an assumed 
+value of the frequency of instances for which the statement is true can be documented using 
+additional triples, forming in turn an assertional statement unit in its own right, which would have the 
+contingent statement unit’s resource as its subject. 
+ 
+5 Therefore, the example given in Fig. 9C is a statement that human anatomists would not make. They would define a 
+human hand in reference to other properties.  
+
+Semantic Units 
+ 
+22 
+Figure 9: Three subcategories of statement unit. A) 
+Assertional statement unit. An example of a 
+statement unit that is an *assertional statement 
+unit*. It models a has-part relation between two 
+instances. The data graph expressing this relation is 
+shown in the blue box without borders. It is an 
+instance-based data graph and forms an ABox. The 
+subject of this assertional statement unit is an 
+instance resource that is also the subject of a 
+named-individual identification unit (cf. Fig. 8A). The 
+resource representing this data graph, i.e., the 
+assertional statement unit resource (blue box with 
+borders, here shown with its dynamic label), is an 
+instance of *has-part statement unit* and of 
+*assertional statement unit*, which is represented 
+in the semantic-units graph above the blue box 
+without borders. B) Contingent statement unit. An 
+example of a statement unit that is a *contingent 
+statement unit*. It models a has-part relation that 
+exists between some but not necessarily every 
+instance of ‘hand’ (FMA:9712) and some but not 
+necessarily every instance of ‘thumb’ (FMA:24938). 
+The data graph expressing this relation is shown in 
+the blue box without borders. The subject of this 
+contingent statement unit is an instance resource 
+that is also the subject of a some-instance 
+identification unit (cf. Fig. 8B). The resource 
+representing this data graph, i.e., the contingent 
+statement unit resource (blue box with borders, 
+here shown with its dynamic label), is an instance of 
+*has-part statement unit* and of *contingent 
+statement unit*. C) Universal statement unit. An 
+example of a statement unit that is a *universal statement unit*. It models a has-part relation that exists between every 
+instance of ‘hand’ (FMA:9712) and some, but not necessarily every instance of ‘thumb’ (FMA:24938). The data graph 
+expressing this relation is shown in the blue box without borders and can, in principle, be translated into OWL to form a 
+TBox. The subject of this universal statement unit is an instance resource that is also the subject of an every-instance 
+identification unit (cf. Fig. 8C). The resource representing this data graph, i.e., the universal statement unit resource (blue 
+box with borders, here shown with its dynamic label), is an instance of *has-part statement unit* and of *universal statement 
+unit*. D) Conventional OWL model. The example from C) translated into an OWL class-axiom expression mapped to RDF. 
+
+A)AssertionalStatementUnit
+Lars'right hand
+rdf:type
+has-part statement unit
+has part
+Lars'rightthumb
+rdf:type
+hassemantic
+assertionalstatementunit
+unit subject
+Lars' right hand
+bfo:haspart
+Lars'rightthumb
+class
+instance
+B)Contingent Statement Unit
+some hand
+haspart
+rdf:type
+has-part statement unit
+somethumb
+rdf:type,
+hassemantic
+contingent statement unit
+unitsubject
+somehand
+bfo:haspart
+somethumb
+C)UniversalStatementUnit
+everyhand
+haspart
+rdf:type
+has-partstatement unit
+somethumb
+rdf:type
+hassemantic
+universal statementunit
+unitsubject
+every hand
+bfo:haspart
+somethumb
+D)ConventionalOwWLmodel
+owl:restriction
+[bfo:haspart
+rdf: type
+owl:on
+property
+fma:hand
+owl:subclass
+blanknode
+owl:some
+fma:thumb
+of
+valuesfromSemantic Units 
+ 
+23 
+Universal statement unit 
+A universal statement unit is a statement unit that refers to every instance of a specific class as its 
+subject. In other words, its subject is also the subject of an every-instance identification unit. If the 
+universal statement unit possesses an object that is a resource, the object refers to some instances of 
+a specific class, resulting in an all-to-some relation (or many such relations in case of an n-ary 
+proposition). If you want to state that every instance of hand (FMA:9712) necessarily hasPart 
+(BFO:0000051) some thumb (FMA:24938), you make a universal statement (Fig. 9C). Universal 
+statements represent commonly accepted domain knowledge that take the form of, for instance, 
+definitions of terms, expressed as class axioms, or of hypotheses about law-like causal relationships.  
+As a semantic unit, a particular universal statement unit refers to a data graph within a knowledge 
+graph that represents a particular universal statement and thus a proposition that is true for all 
+instances of a specific universal (46,47). In a knowledge graph, a particular universal statement unit is 
+modelled as a statement unit by a resource that represents the corresponding data graph. The 
+resource is an instance of both the respective type of statement unit and of *universal statement unit* 
+(Fig. 9C). Its subject is modelled as a resource that relates to its class through an *every instance of* 
+property in a corresponding every-instance identification unit (Fig. 8C), whereas its resource objects, 
+if present, are modelled as resources that relate to their class through the *some instance of* property 
+in a corresponding some-instance identification unit (Fig. 8B).  
+When compared to the OWL modelling of universal statements, which is rooted in Description 
+Logics (cf. with Fig. 9D), the data graph belonging to a universal statement unit as a semantic unit is 
+less complex and does not include any blank nodes. This improves its querying properties. Moreover, 
+the statement unit’s resource can be used to make statements about a universal statement, making 
+universal statements and thus also particular class axioms available to the general domain of discourse 
+(see Challenge 4). However, because no reasoner yet exists for directly reasoning with this semantic-
+units-based notation, to be able to do reasoning over these statements, they will have to be translated 
+into an OWL-based notation, forming a classical TBox expression (see Logical semantics of semantic 
+units).  
+Compound unit 
+Compound units are semantic units that organize the set of all statement units of a given knowledge 
+graph into larger but still semantically meaningful data graphs. Technically, a compound unit is a 
+container of resources of particular semantic units and thus specifies a collection of associated 
+semantic units. Merging the data graphs of its associated semantic units constitutes the data graph of 
+
+Semantic Units 
+ 
+24 
+the compound unit. Analog to statement units, each compound unit is a semantic unit that is 
+represented in the graph by its own node, possesses its own UPRI, and instantiates a corresponding 
+compound unit ontology class. 
+In the semantic-units graph of a compound unit, the relation between the resource representing 
+the compound unit and the resources representing its associated semantic units is documented via 
+the property *hasAssociatedSemanticUnit* (Fig. 10). The following subcategories of compound unit 
+can be distinguished. 
+Figure 10: Example of a compound unit that comprises 
+several statement units. Compound units possess only 
+indirectly a data graph, through merging the data graphs 
+of their associated statement units. The compound unit 
+resource (here, *’Lars’ right hand item unit’*), however, 
+stands for these merged data graphs (indicated by the 
+blue arrow). Compound units possess a semantic-units 
+graph (shown in the peach-colored box), which 
+documents the semantic units that are associated with it.   
+Typed statement unit 
+In order to be readable for a human being, the URIs of the subject, predicate, and objects of a 
+statement unit must be translated to their respective labels. The dynamic label of a statement unit 
+does exactly that, in a structured way, representing the statement itself in a human-readable plain 
+English sentence. The information contained in a dynamic label, however, goes beyond the 
+information contained in the statement itself, because it includes information from the identification 
+units associated with the statement’s subject and its object resources. Since identification units can 
+be edited independently of the statement units that use their resources as subjects and objects, when 
+referring to a human-readable statement, one is actually referring to the corresponding statement 
+unit and the identification units of its subject and all of its objects. This collection of semantic units is 
+a typed statement unit. A typed statement unit is a compound unit that comprises the following 
+statement units (Fig. 11):  
+1. A statement unit that is not an instance of one of the three types of identification units (see 
+Fig. 8). This statement unit functions then as the reference statement unit of the typed 
+statement unit, and its subject is also the subject of the typed statement unit to which it 
+relates via the property *hasSemanticUnitSubject*.  
+
+semantic-unitsgraph
+class
+instance
+Lars'righthanditemunit
+rdf:type
+materialentityitemunit
+hasassociated
+semantic unit
+Lars'righthandhaspartLars'rightthumb
+has associated
+semantic unit
+hassemantic
+unit subject
+Lars'right handhaspartLars'right index finger
+hasassociated
+semantic unit
+Lars'right hand ispart of Lars'right forearm
+Lars'right hand
+subjectargumentSemantic Units 
+ 
+25 
+2. The identification units that model the class-affiliations of all the resources that are 
+referenced in the data graph of the reference statement unit.  
+Figure 11: Typed statement unit. An example of 
+a typed statement unit, with the data graph 
+shown in the large blue box without borders. 
+This graph results from merging the subgraphs 
+of three statement units: the *‘part-of 
+assertional statement unit’* from Fig. 9A, which 
+is the reference statement unit of this *‘typed 
+part-of statement unit’*, with its data graph 
+shown in the grey box without borders, and two 
+instances of *named-individual identification 
+unit*, with their data graphs in the light-blue 
+box 
+without 
+borders 
+(the 
+resources 
+representing the different data graphs are 
+shown in correspondingly colored boxes with borders and dynamic labels).  
+Typed statement units are important because they contain class-affiliation and label information 
+that human readers usually require for understanding the proposition of the reference statement unit. 
+Since the resource representing a typed statement unit is related to its reference statement unit and 
+all its identification units through the property *hasAssociatedSemanticUnit*, different types of typed 
+statement units can be identified by simply querying these relationships, eliminating the need to 
+further differentiate the class of typed statement units into subclasses. 
+Quality measurement unit 
+A quality measurement unit has one qualitative typed statement unit and one or more quantitative 
+typed statement units associated via the property *hasAssociatedSemanticUnit*. The reference 
+statement unit of its qualitative typed statement unit specifies a quality of a given entity, whereas the 
+statement unit of each of its quantitative typed statement units specifies a measurement of this 
+quality, comprising a value and a unit. A quality measurement unit is thus a collection of typed 
+statement units that describe a specific quality of a given entity together with all quantitative 
+evaluations or measurements of it currently present in the data graph (the graph shown in Figure 2 
+corresponds with a typical data graph of a quality measurement unit). 
+For example, the basic reproduction number of a given population at a given time can be 
+documented in such a quality measurement unit, which would comprise the typed qualitative 
+statement unit that links the population with the quality basic reproduction number (NCIT:C173777) 
+
+class
+instance
+typed statementunit
+rdf:type
+has-part
+assertional
+Lars'righthand
+named-individual
+statementunit
+statement unit
+haspart
+identification unit
+Lars'right thumb
+typed statement unit
+rdf:type
+rdf:type
+rdf:type
+hasassociated
+hasassociated
+rdf:type
+semanticunit
+semanticunit
+hasassociated
+semantic unit
+Lars'right hand
+Lars'right hand
+hassemantic
+Lars'rightthumb
+haspart
+named-individual
+named-individual
+Lars'rightthumb
+unit subject
+identification unit
+identificationunit
+hassemantic
+hassemantic
+hassemantic
+unit subject
+unitsubject
+unit subject
+Lars'right hand
+bfo:haspart
+Lars'rightthumb
+rdf:type
+rdf:type
+fma:hand
+fma:thumbSemantic Units 
+ 
+26 
+and one or more typed quantitative statement units, each of which documents a measurement of this 
+reproduction number, maybe based on different methods and algorithms for its estimation. 
+The basic reproduction number measurement statement unit takes the object resource of the 
+quality statement unit and links the quality statement unit to the basic reproduction number 
+measurement statement unit via the *objectDescribedBySemanticUnit* property. The quality 
+statement unit in its turn has taken the subject of the quality measurement unit it is associated with 
+as its subject and is linked to the respective quality measurement unit via the property 
+*hasAssociatedSemanticUnit*, as is the basic reproduction number measurement statement unit. 
+The subject of the quality statement unit is also the subject of the quality measurement unit, and 
+the resource representing a quality measurement unit in the semantic-units graph relates to this 
+resource via the property *hasSemanticUnitSubject*. 
+Because the resource representing a quality measurement unit in the semantic-units graph is 
+related to its associated typed statement units and their reference statement units through the 
+property *hasAssociatedSemanticUnit*, different types of quality measurement units can be 
+identified by simply querying these relationships, eliminating the need to further differentiate the 
+class of quality measurement units into subclasses. 
+Item unit 
+An item unit comprises all statement units, typed statement units, and all quality measurement units 
+that share the same subject. The corresponding resource is then also the subject of the item unit, and 
+the resource representing an item unit in the semantic-units graph relates to its subject via the 
+property *hasSemanticUnitSubject*. An item unit is thus a collection of semantically related 
+statement units, typed statement units, and quality measurement units that all contain information 
+about the same entity. Conceptually, item units relate to the graph-per-resource data management 
+pattern (49) or to the abovementioned characteristic set or RDF molecule, but applying its idea to 
+statement units instead of triples, similar to Item in the Wikibase data model.  
+The information contained in an item unit is well suited to be presented on the same page in a 
+UI, as the statement units, typed statement units, and quality measurement units belonging to it 
+describe the same entity, i.e., their shared subject. The following subcategories of item unit can be 
+distinguished: 
+1. Instance item unit: An item unit that has a named individual resource as its subject. 
+Consequently, it consists exclusively of all assertional statement units present in the semantic-
+units graph layer of the knowledge graph that share the same subject. Its subject is also 
+
+Semantic Units 
+ 
+27 
+necessarily the subject of a named-individual identification unit. For example, all statements 
+about a particular infected population, such as the population’s location, its qualities, various 
+measurements about it, including basic reproduction number and case fatality rate, as well as 
+the time period to which the information about the population refers, all are typed statement 
+units and quality measurement units that share the same subject, which is a named individual. 
+Together, they therefore constitute an instance item unit. The information contained in an 
+instance item unit can be presented in the same UI page. Another example is the description 
+of the anatomy of a particular specimen, where one could organize all typed statement units 
+and quality measurement units describing a particular part of the specimen in an instance 
+item unit, resulting in several such instance item units―one for each described part of the 
+specimen. 
+2. Class item unit: An item unit that has a some-instance or an every-instance resource of a 
+specific class as its subject. Consequently, it consists exclusively of all universal and all 
+contingent statement units present in the semantic-units graph layer of a knowledge graph 
+that share the same subject. Simple star-shaped class axioms such as the one shown in Figure 
+12 can be organized in such a class item unit. 
+Figure 12: Class item unit. An 
+example of a class item unit (blue 
+box with borders), with its data 
+graph shown in the blue box 
+without borders. The data graph 
+results from merging the data 
+graphs of four universal statement 
+units that have *‘every antenna 
+type 1’* as their semantic unit 
+subject, 
+together 
+with 
+their 
+corresponding identification units. 
+For reasons of clarity of presentation, resources and relations of associated semantic units not shown. 
+3. Text-resource hybrid item unit: Text-resource hybrid item units are used when a resource 
+needs to be described and one does not want to or cannot describe it properly in a formalized 
+machine-actionable semantic way using triple statements and proper terms from ontologies. 
+For instance, in a crowdsourced knowledge graph, when a user wants to describe a specific 
+research objective or the main contribution of a research paper. This user is a domain expert, 
+but most likely with only limited knowledge about semantics, if at all. In such a case, it might 
+be best to specify the research objective or main contribution as a resource that is an instance 
+
+antennatype1
+class
+rdf:type
+class
+instance
+class item unit
+itemunit
+hassemantic
+unitsubject
+bspo:in lateral
+sideof
+everyantenna
+bfo:partof
+some head X
+someinstanceof
+uberon:head
+type1
+bfo:haspart
+somesegement
+uberon:segement
+everyinstance of
+of antennaY
+"someinstanceof
+ofantenna
+bfo:partof
+antennatype1
+some multicellular
+uberon:multicellular
+someinstanceof-
+organismD
+organismSemantic Units 
+ 
+28 
+or subclass of, e.g., objective specification (IAO:0000005), and provide a textual description 
+for it, instead of describing it formally using triples. The textual description can either be 
+documented as the resource’s description through a respective annotation property with a 
+string as its value or, in Neo4j, as a value node that denotes (IAO:0000219) the resource. In a 
+knowledge graph application, this textual description can then be automatically annotated 
+semantically by recognizing mentioned entities that are known to the knowledge graph. These 
+recognized entity resources can be connected to the ‘objective specification’ resource via the 
+relation mentions (IAO:0000142). The resulting set of triples forms a data graph representing 
+a text-resource hybrid item unit. Text-resource hybrid item units provide human-readable 
+information in a textual description that can also be leveraged to some extent by machines 
+via the mentions relations.  
+Item group unit 
+An item group unit consists of at least two item units (or an item unit and a typed statement unit that 
+does not share the same subject) that are semantically related to one another through statement units 
+that relate their subjects in the following way:  
+IF  
+resourceX = subject of itemUnit1, 
+  
+resourceX = subject of statementUnit1,  
+ 
+resourceY = object of statementUnit1, 
+ 
+resourceY = subject of itemUnit2 
+THEN  
+statementUnit1 semantically connects itemUnit1 and itemUnit2 to constitute an item 
+group unit. 
+We refer to statement units that link two item units in the way here described as item links. In 
+the semantic-units graph layer, this is indicated by relating the resource of itemUnit1 to that of 
+itemUnit2 via the property *hasLinkedSemanticUnit* and the linking statement unit to itemUnit2 via 
+the property *objectDescribedBySemanticUnit*. While each individual item link has a specific direction 
+in which it links two item units, two item units can be linked through more than one item link, the 
+directions of which can be opposite. For example, when describing a family with all its members, the 
+item unit describing the father links to that of the daughter as his daughter, whereas the item unit 
+describing the daughter links to that of the father as her father. Consequently, there is no generally 
+applicable rule for identifying a specific resource as the subject of an item group unit, and thus no 
+subject is specified. 
+
+Semantic Units 
+ 
+29 
+In addition to item units, item group units may also consist of individual statement units, typed 
+statement units, and quality measurement units that are not part of any specific item unit, because 
+no other statement unit shares the same subject.  
+In most of the cases, item group units will contain all data about the same object, with some of 
+its item units containing data related to the parts or specific aspects of this object. For example, all 
+data about a particular scholarly publication can be understood to represent the outcome of a 
+research activity. All data relating to that research activity can be organized and represented by a 
+single item group unit, with its item units containing statement units that describe specific parts of 
+that activity, such as smaller research steps, methods that have been applied, materials, instruments, 
+and research agents that have been involved in that research activity. 
+With the information from each item unit being presented in the UI in its own page, item group 
+units can be accessed by a human reader in the UI as a set of linked pages.  
+One can differentiate item group units into instance item group units, class item group units, and 
+class axiom item group units. An instance item group unit has only semantic units associated, whose 
+subjects refer to named individuals. A class item group unit, on the other hand, has only semantic 
+units associated whose subjects refer to some-instance or every-instance resources of a specific class. 
+The semantic units associated with a class item group unit give a formal description of a specific class, 
+which in turn is the subject of the class item group unit. If the subject of the class item group unit is 
+also the subject of an every-instance identification unit, it is a class axiom item group unit. Class axiom 
+item group units are formalized class descriptions that cannot be expressed with a single class item 
+unit because they include chains of relations and thus comprise universal and contingent statement 
+units that do not share the same subject, and thus must be modelled as item group units (Fig. 13).  
+As already discussed above, in Description Logics and thus in OWL, universal statements are 
+modelled in a TBox which, when mapped onto RDF, includes the use of blank nodes (see, e.g., Fig. 5). 
+The use of such blank nodes, which function like anonymous resources in triples (i.e., an instance of 
+anonymous individual (OWL:AnonymousIndividual) in OWL2), is problematic in many contexts, mainly 
+because every entity and property represented in a TBox as an anonymous resource cannot be 
+identified and referenced outside the respective class axiom. This results in substantial practical 
+consequences that significantly affect the overall usability of TBox expressions for modelling empirical 
+data. The consequences impact the findability, accessibility, explorability, comparability, 
+expandability, reusability, and overall machine-actionability of any expression modelled as a TBox, 
+which is why empirical data should be preferably modelled as ABox expressions (for a detailed 
+discussion see (30)). In the context of modelling class axioms, the blank nodes cause problems when 
+
+Semantic Units 
+ 
+30 
+several triples should refer to the same blank node. The Description Logics upon which OWL is based 
+uses a form of tree-model property that restricts OWL axioms to have a tree-shaped structure, so you 
+frequently run into difficulties when describing class axioms that involve triangular relationships when 
+using OWL (50).  
+Figure 13: Class axiom item group unit. An example of a class axiom item group unit (blue box with borders), with its data 
+graph shown in the blue box without borders. The data graph results from merging the data graphs of several universal 
+statement units and their corresponding identification units. The statements cannot be modelled in a single class item unit, 
+because they do not all share the same subject. Contrary to OWL, this notation allows describing triangular relations as the 
+one shown here in red, indicating that every instance of *antenna type 1* is longer than any eye that is part of the same 
+organism. For reasons of clarity of presentation, resources and relations of associated semantic units not shown. 
+For instance, if you want to formally describe a specific type of antenna that is longer than the 
+eyes of its organism, you can try to model a respective *antenna* class in Manchester Syntax (51) with 
+the following expression: 
+‘has part some ((antenna part of some multicellular organism) and has quality some 
+(length and increased in magnitude relative to some (length and inheres in some (eye 
+part of some multicellular organism))))’.  
+However, because the two mentions of ‘some multicellular organism’ are anonymous, the 
+expression does not capture the intended meaning that this should refer to the same multicellular 
+organism, as according to it, to be an instance of the class, an antenna needs to merely be longer than 
+at least one eye of some multicellular organism in the world, not necessarily an eye possessed by the 
+same organism that possesses the antenna (52). Because universal statement units do not use blank 
+nodes, different statements can refer to the same resource ‘some multicellular organism D’ and thus 
+do not run into this restriction of OWL (see Fig. 13, triangular relationship shown in red).  
+
+antennatype1
+rdf:type'
+class
+classitemgroup unit
+instance
+class itemgroupunit
+hassemantic
+unit subject
+bspo:inlateral
+side of
+antenna type1
+everyantenna
+everyinstanceof
+bfo:partof
+someheadX
+someinstanceof
+uberon:head
+type1
+rdfs:sub class of
+bfo:has part
+somesegement
+someinstanceof
+uberon:segement
+uberon:appendage
+of antennaY
+ofantenna
+bfo:partof
+ro: has quality
+somemulticellular
+uberon:multicellular
+pato:length
+someinstanceof
+organismD
+organism
+some instance of
+some instance of
+bfo:partof
+pato:increasedin
+somelengthA
+magnitude
+somelengthB
+ro:has quality
+someeyeC
+someinstanceof
+uberon:eye
+relativetoSemantic Units 
+ 
+31 
+Granularity tree unit 
+Since each statement unit is represented in a knowledge graph by its own resource (i.e., node) and 
+instantiates a corresponding statement unit ontology class that is characterized by the type of relation 
+that underlies the propositions its instances are modelling, we can add further information to that 
+class. We can, for instance, identify types of statement units that depend on partial order relations. A 
+partial order relation is a binary relation p that is transitive (if A has relation p to B and B has relation 
+p to C, then A has relation p to C), reflexive (A has relation p to itself), and asymmetric (if A has relation 
+p to B and B has relation p to A, then A and B are identical). Examples of such partial order relations 
+are the class-subclass relations that can be found in universal statements, or parthood relations found 
+in assertional statements, but many more partial order relations exist, including sequential relations 
+such as before (RO:0002083) that identify timelines in a knowledge graph.  
+Partial order relations can give rise to granular partitions that form granularity trees (53–55) and 
+can be used to define granularity perspectives (56–58). Granularity perspectives identify specific 
+types of semantically meaningful tree-like subgraphs within the data graph layer of a knowledge graph 
+and can be employed for supporting the exploration of the knowledge graph in a way somewhat 
+orthogonally to statement, item, and item group units. By identifying classes of statement units that 
+potentially relate to granularity perspectives, because their characteristic relations are partial order 
+relations, applications can utilize this information for automatically identifying corresponding types of 
+granularity trees within the knowledge graph and make them accessible for the users. 
+Due to the nested structure of a granularity tree and its implicit directionality from root to leaves, 
+one can specify the subject of a granularity tree unit to be the subject of the statement units that 
+share their objects with the subjects but not their subject with the objects of other statement units 
+belonging to that granularity tree unit. The resource representing a granularity tree unit in the 
+semantic-units graph relates to its subject via the property *hasSemanticUnitSubject*.  
+Characteristic of granularity tree units is that their statement units are always instantiating the 
+same statement unit class (because the class is characterized in reference to the underlying partial 
+ordering relation) and subjects and objects are always resources of the same basic type. To make them 
+not only machine-actionable but also better comprehensible for humans, granularity tree units 
+comprise the typed statement units that correspond with the statement units that form the 
+granularity tree. 
+Because the resource representing a granularity tree unit in the semantic-units graph is related 
+to its associated statement units through the property *hasAssociatedSemanticUnit*, different 
+granularity perspectives can be identified and distinguished by simply querying these relationships 
+
+Semantic Units 
+ 
+32 
+and the *hasSemanticUnitSubject* relationship to the subject of the granularity tree unit, eliminating 
+the need to further differentiate the class of granularity tree units into subclasses.  
+Granularity perspectives derived from specific types of statement units thus provide another 
+means for structuring and organizing the overall data graph into semantically meaningful smaller data 
+graphs, and thus provide another category of compound unit. Examples for such granularity 
+perspectives are tree-like hierarchies of has-part relations, for instance between various anatomical 
+structures in an organism, or the temporal sequence of events of a particular process, developmental 
+dependency chains, or more general cause-effect-relation chains, and taxonomies of concepts based 
+on class-subclass relations.  
+Granular item group unit 
+A granular item group unit comprises all statement units, quality measurement units, and item units 
+whose subjects are part of the same granularity tree unit. The subject of the granularity tree unit is 
+then also the subject of the granular item group unit, and the resource representing a granular item 
+group 
+unit 
+in 
+the 
+semantic-units 
+graph 
+relates 
+to 
+its 
+subject 
+via 
+the 
+property 
+*hasSemanticUnitSubject*. 
+A granularity tree provides a nested hierarchical organization of related resources. If these 
+resources are subjects of item units, the corresponding item units can be organized according to the 
+hierarchy provided by the granularity tree, thus organizing several item units in a nested hierarchy. 
+This additional organization and structuring of the data graph layer can be utilized by a knowledge 
+graph application to improve the explorability of its overall data graph for users. Granularity tree units 
+can thus provide additional organizational structure for item group units by organizing their item units 
+into granular item group units. This becomes particularly important when the knowledge graph is 
+highly connected, and its item group units are therefore very large.  
+Because the resource representing a granular item group unit in the semantic-units graph is 
+related to its associated semantic units through the property *hasAssociatedSemanticUnit*, different 
+types of granular item group units can be identified by simply querying these relationships and the 
+*hasSemanticUnitSubject* relation to their respective subjects, eliminating the need to further 
+differentiate the class of granular item group units into subclasses. 
+Context unit 
+A context unit comprises all semantic units for which merging of their data graphs forms a connected 
+graph with no resource or triple being separated from the other resources or triples, i.e. any two 
+
+Semantic Units 
+ 
+33 
+resources in the data graph of the context unit are connected via a series of triple statements that also 
+belong to the data graph of the context unit. The only exception to this rule are triples that have 
+isAbout (IAO:0000136) as their property and which thus belong to an is-about statement unit. The 
+property isAbout relates an information artifact to an entity that the artifact contains information 
+about. It thus always marks a change of frame of reference from the discursive layer to the ontological 
+layer by having a semantic unit resource as its subject and some other non-semantic unit resource 
+from the data graph as its object (for discussion of layers, see Statements about statements and 
+documenting ontological, diagnostic, and discursive information in knowledge graphs using semantic 
+units). In other words, is-about statement units relate resources from the semantic-units graph with 
+resources from the data graph of a knowledge graph and can be used as an index for where in the 
+graph a change of frame of reference occurs. For example, when documenting a research activity 
+with its in- and output and the output being a dataset containing the description of the anatomy of a 
+multicellular organism. The graph will contain the statement *‘description item unit’* isAbout 
+‘multicellular organism’ (UBERON:0000468), which points to a change of frame of reference from the 
+result of the research activity in the form of a description and the multicellular organism it is 
+describing. In short, it indicates a change from the research-activity reference frame to the research-
+subject reference frame (see also Fig. 14 further below). Therefore, an is-about statement unit always 
+indicates the border between the data graphs belonging to two different context units. Similar to item 
+group units, due to the lack of a generally applicable rule for identifying a specific resource as the 
+subject of an item group unit, no subject is specified.  
+Dataset unit 
+A dataset unit is a defined and ordered collection of particular semantic units. This collection can be 
+homogeneous, comprising only semantic units of the same type, but can also be compilations of 
+statement units and compound units of various kinds. Like any other semantic unit, each dataset unit 
+is represented in the semantic-units graph with its own node and its own UPRI. 
+Dataset units can be used in various ways. For instance, for compiling all data contributed by a 
+specific institution within a collaborative project or for documenting the state of a given object in a 
+given time. Also, the results of a particular search query can be stored and made accessible as a dataset 
+unit. Users of knowledge graphs can specify particular dataset units for their own use and use the 
+unit’s UPRI as an identifier to reference it.  
+In addition to such obvious uses of datasets as collections of particular semantic units, dataset 
+units can also be used for managing statements about statements: If users want to point out that a 
+particular measurement datum (assertion statement unit A) from one publication (item group unit X) 
+
+Semantic Units 
+ 
+34 
+supports or directly contradicts a causal theory (universal statement unit B) from another publication 
+(item group unit Y), they could create a respective assertion statement unit C that relates the 
+statement unit A as supporting statement unit B and could create a dataset consisting of these three 
+statement units A, B, and C, without including X and Y. Whereas this might not be communicated as a 
+dataset in the UI, technically it could be structured, stored, and managed as a dataset unit. 
+List unit 
+Sometimes, you need to make a statement about a specific list of particular resources. To do so, such 
+a list can be modelled as a specific type of compound unit, i.e., a list unit. List units can be utilized the 
+same way as the other types of semantic units: each list unit is a semantic unit that is represented in 
+the semantic-units graph by its own node, possesses its own UPRI, and instantiates a corresponding 
+list unit ontology class.  
+We distinguish unordered list units from ordered list units, with the latter having the resources 
+organized in a specific order, for instance the authors of a scholarly publication. A set unit, on the 
+other hand, is an unordered list unit in which every resource is listed only once (uniqueness 
+restriction). 
+Technically, a list unit is a collection of membership statement units, each of which specifies one 
+of the resources belonging to the list by connecting the UPRI of the list unit through a *child* relation 
+to the respective resource. In case of an ordered list unit, each membership statement unit has to be 
+indexed first (by connecting the UPRI of the membership statement unit through a data property index 
+(RDF:index) to a consecutive integer value, starting with 0), resulting in an indexed membership 
+compound unit, which is then associated with the list unit. 
+List units can be used as arrays and may include cardinality restrictions and thus describe a closed 
+collection of entities, making a localized closed-world assumption.  
+Discussion 
+Metadata and Semantic Units as FAIR Digital Objects 
+The concept of a FAIR Digital Object has been suggested by the European Commission Expert Group 
+on FAIR Data as central to the realization of FAIR (16). FAIR Digital Objects must be accompanied by 
+persistent identifiers, metadata, and contextual documentation to enable their reliable discovery, 
+citation, and reuse. Data belonging to a FAIR Digital Object should be stored in a common and ideally 
+
+Semantic Units 
+ 
+35 
+open file format and be richly documented using metadata standards and well-established 
+vocabularies.  
+FAIR Digital Objects also represent the core concept in the interoperability framework of the 
+European Open Science Cloud (EOSC) as atomic entities for a FAIR ecosystem by providing the 
+metadata needed for achieving five layers of interoperability: 1) Information Technology (IT) systems 
+must work with other IT systems in implementation or access without any restrictions or with 
+controlled access for technical interoperability; 2) common data formats and communication 
+protocols for syntactic interoperability; 3) contextual semantics related to common semantic 
+resources for semantic interoperability; 4) contextual processes related to common process resources 
+for organizational interoperability; and 5) contextual licenses related to common license resources for 
+legal interoperability (15). Respective metadata can itself form FAIR Digital Objects that can be linked 
+using their persistent identifiers. Consequently, FAIR Digital Objects can exist at different levels of 
+granularity, and coarser level FAIR Digital Objects may consist of several finer level FAIR Digital Objects.  
+The concept of a semantic unit can be adapted to that of FAIR Digital Objects. Each semantic unit 
+possesses its own UPRI and thus already provides the required persistent identifier. Further, they can 
+be accessed and searched using common protocols such as SPARQL and CYPHER implemented in web 
+interfaces using HTML, with RDF, JSON, and other formats as well-supported data export formats. If a 
+knowledge graph uses well-established controlled vocabularies and ontology terms and organizes its 
+data and metadata following established graph-patterns using tools such as SHACL (32), ShEx (59,60), 
+or OTTR (61,62), all data in the data graphs of semantic units will be semantically interoperable. 
+Additionally, each semantic unit can have its own copyright license assigned, which can either be 
+provided automatically by the knowledge graph application or individually by the creator of a 
+particular semantic unit.  
+Through additional triples, relevant provenance data can be tracked about each particular 
+semantic unit in the form of either corresponding property-value pairs (property graph) or through an 
+additional provenance Named Graph (RDF/OWL) using well-established provenance vocabularies. The 
+provenance metadata of a semantic unit can cover, e.g., creator, creation date, creation application, 
+title of the semantic unit, all contributing users, and last-updated date and are restricted to 
+provenance data about the semantic unit itself—they do not refer to the original process of data 
+production and thus the provenance of the data contents of this unit.  
+Additionally, if the knowledge graph application makes a distinction between published and 
+unpublished data, publication metadata can be tracked separately, covering the date the semantic 
+unit has been published together with its creator and the list of its contributors.  
+
+Semantic Units 
+ 
+36 
+Access control metadata specifies any copyright licenses as well as, in case the knowledge graph 
+application differentiates between different groups or roles of users, a specification of who is allowed 
+to access the semantic unit.  
+With respect to the FAIRness of data, it is also advisable to provide modelling metadata, i.e., 
+information about which data schema or graph pattern has been used for modelling the data in the 
+unit’s data graph. Each instance of a given semantic unit class should ideally apply the same graph 
+pattern. For this purpose, it would be good to have schemata and patterns, each with its own UPRI, 
+stored in some open repository or having the schemata and patterns be documented in the 
+corresponding semantic unit ontology class.  
+Provenance metadata referring to the process of data production (see, e.g., Fig. 4) can be 
+documented in the form of metadata statement units and metadata item and item group units. The 
+provenance of the data production is usually more detailed and complex than the unit’s own 
+provenance and must be documented as semantic units and thus FAIR Digital Objects in their own 
+right.  
+Implementation 
+Semantic Units, Nanopublications, and Micropublications 
+The concept of assertional statement units as FAIR Digital Objects is very similar to that of 
+nanopublications—especially, when implementing them in RDF/OWL. Nanopublications are RDF 
+graphs that represent the smallest units of publishable information extracted from literature and 
+enriched with provenance and attribution information (63–66). They utilize Named Graphs and 
+Semantic Web technologies. Each nanopublication models a particular assertion, e.g., a scientific 
+claim, in machine-readable format and semantics and is accessible and citable through a unique 
+identifier. Nanopublications are used to facilitate the discovery, exploration, and re-use of scholarly 
+assertions (66). Moreover, embedded in a decentralized network of services that employ semantic 
+templates, nanopublications can also be used by users to directly publish small Linked Data statements 
+as nanopublications (65).  
+Each nanopublication is organized into four Named Graphs: 
+1. the head Named Graph, connecting the other three Named Graphs to the 
+nanopublication’s unique identifier; 
+2. the assertion Named Graph, containing the assertion modelled as a graph; 
+
+Semantic Units 
+ 
+37 
+3. the provenance Named Graph, containing metadata about the assertion; and 
+4. the publicationInfo Named Graph, containing metadata about the nanopublication itself.  
+Nanopublications are a natural fit for representing and publishing assertional statement units, 
+with the assertion Named Graph closely corresponding to the data graph and the head Named graph 
+to the semantic-units graph of an assertional statement unit. Triples in the provenance Named Graph 
+can potentially link to other semantic units and thus other nanopublications that contain detailed 
+metadata descriptions (e.g., a graph as shown in Fig. 4). Nanopublications are also suited for publishing 
+the other types of statement units following the same schema. The compound units, on the other 
+hand, correspond to annotated sets of nanopublications, where these sets can either be defined 
+statically (e.g., as nanopublication indexes  (67)) or dynamically (by specifying a query on the 
+knowledge graph). 
+By using dataset units, several such semantic unit nanopublications can be combined to form a 
+micropublication. Micropublications (68) represent scientific arguments, in which a specific assertion 
+represents a claim and additional assertions provide supporting or contradicting scientific evidence in 
+the form of data and its accompanying metadata as well as information about attribution, supporting 
+and contradicting references, links to empirical data and figures, etc. Further assertions can be added, 
+pointing to relations to other claims made by other scientific arguments. This way, micropublications 
+relate scientific claims in the form of nanopublications to all relevant information to turn the claim 
+into a scientific argument (*scientific argument* could constitute a specific type of dataset unit). 
+Structuring a knowledge graph into interrelated semantic units using the Nanopublications-
+schema 
+As a first step for structuring a knowledge graph into interrelated data graphs, each of which is 
+organized as a particular semantic unit, a primary layer of abstraction above the level of triples must 
+be created. This is achieved by partitioning the knowledge graph into a set of statement units, i.e., a 
+mapping of triples to statement units, where each triple belongs to exactly one data graph of a 
+statement unit.  
+When implementing this in RDF/OWL, statement units can be modelled as nanopublications (see 
+above). In Neo4j, as it is a property graph, to identify all triples belonging to the same statement unit, 
+one has to add a ‘statement_unit_URI:upri’ property-value pair to each of its nodes and relations, with 
+the statement unit’s UPRI as the value. 
+Based on this primary abstraction layer of statement units, a secondary abstraction layer of 
+compound units can be organized. Each compound unit is specified as a collection of two or more 
+
+Semantic Units 
+ 
+38 
+semantic units (i.e., statement units and other compound units) by relating the compound unit’s UPRI 
+to the UPRIs of its associated semantic units. In RDF/OWL, this can be implemented by using the 
+compound unit’s semantic-units graph as the head Named Graph of a corresponding nanopublication, 
+while leaving the nanopublication’s assertion Named Graph empty. The head Named Graph thus 
+specifies all basic and compound units that are associated with this compound unit. In contrast, in 
+Neo4j, the nodes and relations of all triples belonging to a compound unit possess a 
+‘compound_unit_URI:upri’ property-value pair with the compound unit’s UPRI as their value. Since a 
+given statement unit can be associated with more than one compound unit, its ‘compound_unit_URI’ 
+property can have an array of UPRIs of different semantic units as its value. 
+Modularity results in increased flexibility of data management 
+“Because human thoughts are combinatorial (simple parts combine) and recursive (parts can be 
+embedded within parts), breathtaking expanses of knowledge can be explored with a finite 
+inventory of mental tools.” ((69), p.360).  
+Just like human thought, structuring a knowledge graph into separate but recursive subgraphs, each 
+of which belongs to a particular semantic unit that, in turn, is classified into different semantic unit 
+classes, organizes the knowledge graph into structured modules that can be (recursively) combined 
+and that encapsulate complexity into manageable units which significantly increases the graph’s 
+expressivity and the flexibility of data management. By allowing the specification of relations between 
+semantic units, a given semantic unit from a finer level of representational granularity can be 
+associated with more than one unit from a coarser level. A given statement unit can thus be associated 
+with more than one compound unit, while having the statement unit itself with all its triples being 
+documented in the graph at a single location.  
+For example, the description of a multicellular organism could contain a has-part statement unit 
+that states that the organism has a head as its part. This statement unit would be associated with the 
+item unit of the organism itself, which would be linked to further item units about the organism’s 
+other parts, constituting an item group unit. Moreover, since has-part is a partial order relation (70), 
+the has-part statement unit would also be associated with a parthood granularity tree unit and its 
+corresponding granular item group unit. Thus, the has-part statement unit would be associated with 
+at least four other semantic units.  
+Due to the modular organization of semantic units, knowledge graphs that implement them can 
+be built as virtual federated knowledge graphs, with data being contributed from several projects 
+and institutions, stored in their own repositories. This way, users with access to all data can utilize the 
+
+Semantic Units 
+ 
+39 
+contents of such a knowledge graph, while data stewardship remains in the hands of the individual 
+contributing projects and institutions, ensuring their technical autonomy. 
+The content modularization brought about by semantic units could also facilitate partitioned-
+based querying of knowledge graphs. This has been successfully done with other approaches for 
+partitioning the graph (71), and we expect that partitioning the graph into semantic units and thus 
+semantically meaningful subgraphs should have a comparable effect on querying tasks. However, the 
+use of semantic units in knowledge graph partitioning and modularity is subject to future research.  
+Organizing a knowledge graph into five levels of representational 
+granularity, into other granularity trees, and into different frames of 
+reference using semantic units 
+With statement unit, item unit, and item group unit as different categories of semantic unit, a 
+knowledge graph can be organized into the following basic representational granularity levels (Fig. 
+14): triples, statement units, item units, item group units, and the knowledge graph as a whole. Triples 
+represent the lowest and thus finest level of abstraction possible in a knowledge graph, with semantic 
+units constituting coarser levels of abstraction and thus coarser levels of representational granularity. 
+Representational granularity organizes the semantic-units graph layer and thus the discursive layer 
+of a knowledge graph into different levels of representational granularity, and with that, indirectly, 
+also the knowledge graph’s data graph layer.  
+Figure 14: Five levels of 
+representational 
+granularity. 
+The 
+introduction of semantic 
+units to a knowledge 
+graph adds a semantic-
+units graph layer to its 
+data graph layer, which 
+adds, among others, a 
+level of statement units, a 
+level of item units, and a 
+level of item group units to the level of triples and the level of the graph as a whole, resulting in five levels of representational 
+granularity. 
+Organizing triples into statement units (which represent the smallest units of semantically 
+meaningful propositions for a human reader), statement units into item units (which can be presented 
+
+ItemGroupUnit
+Semantic-Units
+GraphLayer
+ItemUnit
+Knowledge
+Graph
+StatementUnit
+Data
+GraphLayer
+TripleSemantic Units 
+ 
+40 
+in the UI as individual pages), and item units into item group units (which can be presented as 
+collections of semantically interrelated UI pages) is often necessary to increase the human-readability 
+and usability of a knowledge graph.  
+In addition to the organization and structuring of a knowledge graph into different levels of 
+representational granularity, a given item group unit can be further organized and structured in a 
+somewhat orthogonal way into granular item group units by utilizing granularity tree units present in 
+the item group unit. Granularity trees organize the data graph layer and thus the ontological layer 
+of a knowledge graph into different granularity perspectives. 
+Finally, a given item group unit can be further organized and structured into different context 
+units, each of which covers a specific frame of reference. Points of contact between different frames 
+of reference and thus different context units can be identified via is-about statements: the subject of 
+an is-about statement is a semantic unit resource whose subject belongs to the data graph of one 
+context unit and the object of the is-about statement belongs to the data graph of another context 
+unit (see also Fig. 16). This allows traversing different frames of reference in a knowledge graph via 
+their is-about statement connections. Context units organize the data graph layer and thus the 
+ontological layer of a knowledge graph into different frames of reference. 
+Organizing data into various kinds of semantic units and thus semantically meaningfully 
+subgraphs that can be digested by a human reader as semantically related larger chunks of data is an 
+effective way of presenting data in the UI. With the granular organization of a knowledge graph into 
+different types of semantic units, some of which belong to different levels of representational 
+granularity, and by structuring the knowledge graph into these partially overlapping, partially enclosed 
+subgraphs, data management, data access, data exploration, and graph navigation can be improved 
+significantly.  
+Statements about statements and documenting ontological, 
+diagnostic, and discursive information in knowledge graphs using 
+semantic units 
+Because each semantic unit has its own UPRI and is represented in the semantic-units graph layer of 
+a knowledge graph by its own node, it is straightforward to make assertions about semantic units and 
+thus statements about statements. If semantic units were organized as FAIR Digital Objects, one could 
+also make statements across different databases and knowledge graphs. By structuring the knowledge 
+graph into semantic units, UIs can be developed that provide a very intuitively usable framework for 
+
+Semantic Units 
+ 
+41 
+making statements about statements. The development of such UIs and their accompanying tools and 
+services thereby benefits from semantic units being implemented following a clear and 
+straightforward schema. This way, semantic units can contribute to a solution of the problem that 
+making statements about statements within knowledge graphs can be challenging (see Challenge 3). 
+There is another aspect in knowledge management and knowledge representation, where it is 
+beneficial to be able to make statements about statements in a straightforward way and to have a 
+formalized notation for representing contingent statements.  
+As a scientific realist, one can distinguish between (1) particulars and universals as mind-
+independent real entities, (2) our cognitive representations of real entities in the form of ideas, 
+concepts, and thoughts, and (3) textual and perception-based representations of real entities in the 
+form of words, symbols, images, recordings, etc. (72–74). The latter are usually used for 
+communication and documentation, with the sender having the intention to trigger cognitive 
+representations in the receiver that are maximally similar to their own representations.  
+Meaning and reference are key for the success of communication and condition the duality of a 
+textual representation that must provide both ontological and diagnostic information. The 
+information sent must carry semantic meaning in the sense that it provides answers to questions of 
+the type “What is it?” and thus ontological definitions that carry semantic conceptual content for all 
+referenced entities. Some of this ontological information is provided explicitly, but in most parts the 
+sender relies on the inferential lexical competence (75) of the receiver by using well-known 
+terminology.  
+But communication also has to provide answers to questions of the type “How does it look?” and 
+thus information about the epistemological appearance―information that is required for 
+unambiguously referencing all entities mentioned in the text. This diagnostic, i.e., referential 
+information may not be very important in cases where the receiver already knows the entity, but in 
+all other cases, especially when dealing with theoretical entities whose existence cannot be 
+identified/observed directly and where you often cannot deduce recognition criteria from the 
+ontological definition (e.g., a lead atom, a cell nucleus), diagnostic information is essential for reliably 
+referencing. Therefore, some of this diagnostic information needs to be provided explicitly, but in 
+most parts the sender relies on the referential lexical competence (75) of the receiver.  
+How does that relate to knowledge graphs? Well, sometimes we talk about real entities, 
+sometimes we talk about our cognitive and textual representations of them. Sometimes, this 
+discourse overlaps, and this is where it becomes complicated when having to model this in a 
+knowledge graph. Ideally, ontological definitions and diagnostic operational definitions are provided 
+
+Semantic Units 
+ 
+42 
+by domain ontologies, and assertions in knowledge graphs refer to respective ontology terms and the 
+information linked to them. This way, knowledge graphs would efficiently document, represent, and 
+communicate empirical data.  
+Unfortunately, however, due to limitations of OWL and Description Logics in defining classes, 
+ontologies generally do not provide diagnostic operational definitions. Ontologies define classes in the 
+form of Aristotelian definitions (76) that constitute essentialistic classes. Essentialistic classes are 
+based on universal statements, with class membership being determined in dependence of a set of 
+properties that are individually necessary and jointly sufficient (77). Many diagnostic operational 
+definitions, however, provide method-dependent recognition criteria that require the manipulation 
+of the object to be able to determine its class membership, for instance because the object is too small 
+for the eye, or it can only be identified after it has been stained or when using some test-kit. The 
+defining properties of such operational definitions often refer to properties that are not necessarily 
+present in every instance of a respective class. Instead, they are rather typical and only sufficient in a 
+specific number. Consequently, many recognition criteria cannot be modelled as essentialistic classes 
+but, instead, have to be modelled as cluster classes (74). Contrary to essentialistic classes, an instance 
+of a cluster class does not have to possess all class-defining properties―necessary is that some of 
+them apply, sufficient is a specified percentage threshold, which is the minimum quorum (77). 
+Definitions of cluster classes thus take the form of contingent statements, which cannot be 
+represented in OWL and Description Logics (see discussion above).  
+Diagnostic operational definitions frequently depend not only on cluster class concepts but also 
+on fuzzy sets, since many cluster class definitions rely on terms that refer to fuzzy sets (74). For 
+instance, when recognition criteria refer to coarse inner material, electron-dense clusters, mushroom-
+shaped, ovoid, or hooked to identify class-membership of instances to a specific type of anatomical 
+structure, they refer to terms that specify spatio-structural properties that are better communicated 
+via exemplars or images and thus perceptual contents than textual definitions. Whereas both 
+essentialistic classes and cluster classes are always defined textually, fuzzy sets can be defined 
+ostensively in reference to exemplars and thus to perception-based contents that rely on the human 
+capabilities of pattern recognition.  
+The semantic-units approach provides a formal notation for representing contingent statements 
+and, when combined with semantically annotated exemplary images, a knowledge graph could 
+provide all diagnostic knowledge relevant for answering “How does it look?” questions. Together with 
+the ontological definitions, knowledge graphs could provide any reader of the graph with all relevant 
+knowledge they need to ensure their inferential and referential lexical competence. 
+
+Semantic Units 
+ 
+43 
+In addition to the ontological and the diagnostic layer, knowledge graphs often document a third 
+layer of information, representing discursive contextual information (see also Ingvar Johannson’s 
+distinction between use and mention of linguistic entities (78)). In other words, knowledge graphs not 
+only contain empirical data in the form of assertions like “The melting point of lead is at 327.5 °C”, but 
+also assertions like “author A asserts that the melting point of lead is at 327.5 °C” or “the assertion 
+that the melting point of lead is at 327.5 °C is a result of experiment X”, which address the discursive 
+contextual information. Some assertions may even address the diagnostic aspects of how the 
+reference between textual representation and real entity is achieved by documenting respective 
+methods and diagnostic criteria. Without a good method for making statements about statements, 
+documenting and representing these three layers of information (i.e., ontological, diagnostic, 
+discursive) and expressing their interrelations is not possible.  
+Because semantic units are represented in the graph with their own nodes, they support the 
+documentation and representation of all three layers and their interrelationships. Statement units can 
+provide within their data graphs ontological information that can be gathered within compound units 
+of coarser representational granularity. As propositions, they are represented in their semantic-units 
+graphs, which constitutes a large part of the discursive layer. Moreover, contrary to OWL and 
+Description Logics, the semantic-units approach with its introduction of some-instance and every-
+instance resources and resources that represent individual universal statements and sets of 
+semantically related universal statements, enables differentiated referencing of various entities 
+relating to the ontological layer. Consequently, one can make statements about individual classes 
+(=concepts), their definitions, their individual defining statements, a single instance of a class, a group 
+of instances of a class, and the group of all instances of a class, therewith opening multiple ways to 
+talk about universal statements and their elements. Moreover, with context units, it is even possible 
+to distinguish and explicitly document different frames of reference within the ontological and 
+discursive layer. In other words, the semantic-units approach allows for specifying various 
+interrelationships between the discursive and the ontological layer of its knowledge graph and 
+therefore integrates universal statements in the knowledge graph’s domain of discourse (Challenge 
+4). 
+Since statement units can also relate a particular resource to another statement unit (e.g., 
+‘author_A -asserts-> statement_unit_Y’) or two statement units to each other (e.g., ‘statement_unit_X 
+-hasMetadata-> statement_unit_Z’), relations between the three layers can be easily documented. 
+For instance, an item group unit documents the contents of a particular scholarly publication. Because 
+scholarly publications can be considered in general to represent reports about a scientific investigation 
+or some other research activity, the item group unit will contain information about a research activity 
+
+Semantic Units 
+ 
+44 
+as a process that may have some material entities (i.e., substances, instruments, specimens, etc.) and 
+research agents (i.e., experimenters, patients, test persons, etc.) or some data as its input and some 
+research result as its output. Moreover, the research activity usually realizes a specific plan (i.e., 
+research method) and achieves a specific research objective, which is part of the plan (see Fig. 15). 
+This general model can be applied like a Matryoshka, the russian stacking doll: research activities can 
+have research activities as their parts, i.e., differentiated steps in the overall research process, that 
+again have their own inputs and outputs and realize their own research methods and achieve their 
+own objectives.  
+ 
+Figure 15: A data scheme for modelling the contents of scholarly publications. The relation between a research activity, its 
+input and output and its underlying process plan specification in the form of a research method and research objective 
+(model adapted from (79)).  
+This model can be applied to a knowledge graph of scholarly publications and be adopted to 
+semantic units. The item group unit of the publication is about an instance of *research activity* and 
+has an item unit of the research activity associated with it, of which that *research activity* instance  
+is the subject. The research activity item unit has a research result item unit associated with it that has 
+an instance of *research result* as its subject. The research activity resource is linked to the research 
+result resource via the property hasSpecifiedOutput (OBI:0000299). Now, the research result item unit 
+can be linked to a description item unit that contains several assertional statement units about a 
+particular multicellular organism—the publication describes the anatomy of a specific multicellular 
+organism. This is documented through a triple that relates the *research result item unit* to the 
+*description item unit* via the property *hasLinkedSemanticUnit*. The ‘description’ (SIO:000136) 
+resource is the subject of the *description item unit* and is related to the multicellular organism item 
+unit through the property hasPart (BFO:0000051) and the multicellular organism item unit to the 
+instance 
+of 
+multicellular 
+organism 
+(UBERON:0000468) 
+through 
+the 
+property 
+*hasSemanticUnitSubject*. The resulting set of semantic units thereby cover at least three different 
+frames of reference: the publication itself, the research activity, which the publication is reporting on, 
+
+bfo:has.part
+researchoutput=
+material entity
+-hasachievedresult
+research objective
+bfo:haspart
+research method
+and/ordataitem
+obi:achieves
+bfo: has part
+bfo: has part
+obi:hasspecified
+planned
+bfo:realizes
+objective
+researchparticipant=
+obi:hasspecified
+researchinput=
+researchagent
+ro:hasparticipant
+researchactivity
+material entity
+input
+and/orinstrument
+and/ordataitem
+bfo: has
+instance
+occurrent
+bfo:haspart
+part
+bfo:has partSemantic Units 
+ 
+45 
+and the assertional statements about the research subject, i.e., the multicellular organism, with their 
+boundaries being indicated by the two is-about statements. In Figure 16, you can see how the resulting 
+discursive and the ontological layers, as well as the different frames of reference, are interconnected.  
+ 
+Figure 16: Detail from the graph belonging to an item group unit about the contents of a scholarly publication, represented 
+in an ABox RDF graph. The content is modelled according to a specific data schema (see Fig. 15) that has been adapted to 
+semantic units. All content from the published journal article is organized in its own item group unit instance via various 
+associated semantic units. The publication itself is represented in the data graph as an instance of journal article 
+(IAO:0000013). The item group unit has several item units about the research activity associated with it, that in turn are 
+connected to each other via the property *hasLinkedSemanticUnit*. The item unit describing the research activity has an 
+instance of investigation (OBI:0000066) as its subject, which has as its output an instance of data set (IAO:0000100) that has 
+an instance of description (SIO:000136) as its part. That description instance has the item unit that describes the multicellular 
+organism as its part, the latter of which has an instance of multicellular organism (UBERON:0000468) as its subject. The blue 
+arrow indicates that the data graph (dark blue box without borders) is represented by this item unit (bordered box in the 
+same color). It has a head item unit linked to it, which has an instance of head (UBERON:0000033) as its subject, which is a 
+part of the multicellular organism. The data graphs of the semantic units form the ontological layer, whereas their semantic-
+units graphs form the discursive layer. Three different context units separate the reference frame of a publication from that 
+of a research-activity and that of a research-subject, with is-about statements marking their borders. For reasons of clarity 
+of presentation, the associated statement units are not shown in the discursive layer.  
+Whereas the resources of the semantic units represent and organize the discursive layer, their 
+data graphs represent the ontological (and diagnostic) layer. The same applies to all semantic unit 
+resources. The organization of a knowledge graph into these different layers and into different frames 
+of reference may provide a new framework for the development of innovative visualization and graph 
+exploration methods. 
+
+item group unit
+context unit
+class
+instance
+rdf:type
+rdf:type
+rdf:type
+publication
+research activity
+rdf:type
+research subject
+contextunit
+contextunit
+contextunit
+itemunit
+has associated
+has associated
+has associated
+discursive
+semantic unit
+has associated
+semantic unit
+semantic unit
+has associated
+has associated
+has associated
+semanticunit
+rdt:typo
+rdf:type
+has associated
+semantic unit
+semanticunit
+semanticunit
+rdf:type
+rdf:type
+layer
+has associated
+semanticunit
+semanticunit
+rdf:type
+publication
+has asspclated
+research activity
+has linked
+research result
+has linked
+description
+has linked
+multicellular organism
+has linked
+head
+itemgroupunit
+semanticunit
+itemunit
+semantic unit
+itemunit
+semantic unit
+itemunit
+semantic uni
+itemunit
+semantic unit
+itemunit
+lao:isabout
+has semantic
+iao:is about
+has semantic
+has semantic
+has semantic
+has semantic
+has semantic
+unit subject
+unit subject
+unit subject
+unit subject
+bfo:
+haspart
+layer
+obi:has
+obi:has
+publication
+paupads
+researchactivity
+specified
+researchresult
+bfo:haspart-
+description
+multicellularorganism
+-bfo:haspart-
+head
+output
+output
+rdf:type
+rdf:type
+rdf:type
+rdf:type
+rdf:type
+rdf:type
+lao:journal article
+obi:investigation
+lao:data set
+sio:description
+uberon:mutticellular organism
+uberon:head
+publication
+research-activity
+research-subject
+referenceframe
+reference frame
+referenceframeSemantic Units 
+ 
+46 
+Modelling negations, cardinality restrictions, and disagreement  
+OWL and Description Logics based information systems adhere to what is called the Open World 
+Assumption (OWA). OWA assumes incomplete information by default. Therefore, absence of 
+information about an entity or a fact does not necessarily imply information about the absence of that 
+entity or the negation of that fact. As a consequence, if you for instance want to state that a particular 
+object is a fruit but not a pome fruit, that a particular head of an insect does not possess any antenna, 
+or that this head possesses exactly three eyes, it is not enough to mention that the object is a fruit, 
+the head possesses three eyes, or to not mention any antenna, because due to OWA the fruit could 
+still be a pome fruit and the head could still possess antenna, and it could still possess a fourth eye. 
+Instead, you must explicitly state all these things.  
+Unfortunately, in RDF/OWL, these types of negation and cardinality statements pose tricky 
+modelling challenges, because they cannot be directly expressed as relations between instances and 
+thus ABox expressions. Instead, you must model them in the form of class-expressions as a TBox, e.g., 
+by using OWL Manchester Syntax (51).  
+Regarding negations, one can distinguish two different types of negation statements: negations 
+involving references to classes and negations of relations between instances. An example of the 
+former is the statement ‘this fruit is not a pome fruit’ (Fig. 17A). This can be characterized following 
+the Manchester Syntax as the expression ‘not (type pome fruit)’ (Fig. 17B), which translates to OWL 
+mapped to RDF to a graph in which the given particular entity is an instance of the class fruit 
+(PO:0009001) and an instance of a class that is the complement of the class pome fruit (PO:0030110) 
+(Fig. 17C). Analog to this case are negations that are part of a class axiom. 
+Semantic units can provide an alternative modelling solution by introducing a general *negation 
+unit* class (in Neo4j this could be simply modelled by adding the label ‘:Negation’ to the respective 
+semantic unit node, indicating that this resource is an instance of the class ‘negation’). The statement 
+‘this fruit is not a pome fruit’ can be modelled by two semantic units, both of which would be instances 
+of *named-individual identification unit* and *assertional statement unit*. However, the semantic 
+unit stating that its subject is a pome fruit (PO:0030110) is also an instance of *negation unit*, thereby 
+negating the contents of its data graph (see Fig. 17D).  
+ 
+ 
+ 
+
+Semantic Units 
+ 
+47 
+Figure 
+17: 
+Modelling 
+negations 
+involving 
+instances by applying semantic units. A) A 
+human-readable statement that this fruit is not a 
+pome fruit. The statement can be modelled in two 
+different ways. As an OWL expression that can be 
+specified using B) Manchester Syntax, where the 
+fruit is an instance of a class that is defined as all 
+of its instances are not instances of pome fruit 
+(PO:0030110). Note, how this Manchester Syntax 
+expression translates into C) an OWL expression 
+mapped to RDF, where fruit x is an instance of 
+fruit (PO:0009001) but also of a class that is the 
+complement to 
+pome fruit 
+(PO:0030110). 
+Alternatively, the statement can be modelled as 
+an instance-based graph using semantic units D). 
+The data graph in the blue box states that the 
+entity is a fruit. The data graph belonging to the 
+statement unit stating the negation (red box with borders, here shown with its dynamic label), on the other hand, is shown 
+in the red box without borders and states that the entity is a pome fruit. However, since the latter statement unit not only 
+instantiates the classes *assertional statement unit* and *named-individual identification unit* but also *negation unit*, it 
+actually negates the statement in the data graph, therewith indicating that it is not a pome fruit.  
+Absence statements are another example of negations involving reference to classes. The 
+observation ‘this head has no antenna’ translates to the statement that the head is an instance of a 
+class that is characterized following the Manchester expression as ‘not (‘has part’ some antenna)’, 
+which translates to OWL to a more complex class axiom (see Fig. 18A-C).  
+The same statement can be modelled as the union6 of the subgraphs of two semantic units, with 
+the one having the ‘head x’ (UBERON:0000033) as its subject being an instance of *has-part statement 
+unit*, *assertional statement unit*, and *negation unit*, whereas the one having the ‘some antenna’ 
+(UBERON:0000972) as its subject only being an instance of *some-instance identification unit* (see 
+Fig. 18D). In general, when modelling absence statements this way, all instance resources in the 
+assertion that are supposed to represent types of entities that are absent, would be modelled this 
+way, relating to the respective class via the property *some instance of* within their corresponding 
+some-instance identification units. This notation would be simpler and easier to use and to implement 
+in knowledge graph applications than the OWL-based notation of using a more complex class 
+expression.  
+ 
+6 The union of the subgraphs, but, semantically, the intersection of the statements. 
+
+A)Statement
+Thisfruitisnotapomefruit
+B)OWLManchesterSyntaxexpression
+typenegationclassaxiom:
+not(typepomefruit)
+C)ConventionaloWLmodel
+PO:fruit
+PO:pome fruit
+owl:class
+rdf:type
+owl:complement
+rdf:type
+of
+fruitx
+df:type
+classification
+owl:subclass
+of
+blank node
+negationclass
+class
+owlspecific
+class
+instance
+D)Assertionalstatementunitsmodel
+assertional statementunit
+named-individual
+identificationunit
+rdf:type
+rdf:type
+Fruitxis notapomefruit
+-rdf:type
+negation unit
+hassemantic
+unit subject
+PO:fruit
+rdf:type
+fruitx
+rdf:type
+PO:pome fruitSemantic Units 
+ 
+48 
+Figure 18: Relation between an 
+absence 
+observation, 
+the 
+corresponding assertions, and 
+two alternative ways to model 
+them in a knowledge graph. A) 
+A human-readable statement 
+about the observation that a 
+given head has no antenna. B) 
+Absence statements cannot be 
+expressed as relations between 
+instances. 
+Therefore, 
+the 
+observation from A) must be 
+expressed 
+using 
+a 
+class 
+expression, 
+which 
+can 
+be 
+formulated using Manchester 
+syntax. Following this notation, 
+the head would be an instance 
+of a class that is defined to have 
+only instances that have no 
+antenna as their parts (‘not’ and 
+‘some’ being used as mathematical expressions). C) The translation of the assertion from A) and B) into an OWL expression 
+mapped to RDF. Note how *absence phenotype* is defined as a set of relations of subclass and complement restrictions 
+involving two blank nodes. D) The same statement can be modelled using two semantic units. One of them is modelling the 
+has-part relation and negates it (red box with borders and its dynamic label, with its data graph in the red box without 
+borders). It is therefore an instance of *has-part statement unit* as well as *assertional statement unit* and *negation unit*. 
+The other semantic unit is an instance of *some-instance identification unit* and relates ‘some antenna’ to antenna  
+(UBERON:0000972) via the property *some instance of*. Its data graph is shown in the blue box. Together, they model the 
+observation from A). This notation is comparable to E). E) An alternative notation of the statement ‘this head has no antenna’ 
+and the observation from A). The notation uses Peirce’s predicate logic system of existential graphs. The identity line ― 
+between the two phrases ‘head x’ and ‘has part antenna’ states that head x has some antenna as its part, whereas the red 
+circle surrounding the latter phrase expresses its negation by crossing the line of identity. For reason of clarity of 
+representation, the relation between ‘head x’ and head (UBERON:0000033) is not shown in C) and D). 
+The same approach can also be applied to the case of negations of relations between two 
+instances. The fact that a given fruit is not part of a particular orange plant could be modelled analog 
+to the other negation statements (see Fig. 19). 
+
+A)Observation
+Thisheadhasnoantenna(negatedparthoodassertion)
+B)OWLManchesterSyntaxexpression
+absencephenotypeclassaxiom:
+not（haspartsomeantenna)
+C)ConyentionalOwLmodel
+headx
+owl:class
+owl:restriction
+bfo:has part
+rdf:type
+rdf:type
+owl:on
+rdf:type
+-property
+owl:complement
+owl:some
+absencephenotype
+owl:subclassof-
+blanknode
+blank node
+values
+uberon:antenna
+of
+from
+D)Assertionalstatementunitsmodel
+assertional
+has-part
+statement unit
+statementunit
+class
+instance
+rdf:type
+rdf:type
+owlspecific
+class
+object property
+Headxhasnoantenna
+rdf:type
+negation unit
+hassemantic
+unitsubject
+head x
+bfo:haspart
+someantenna
+someinstanceof
+uberon:antenna
+E)Peirce'spredicatelogicsystemofexistentialgraphs
+head x
+haspartantennaSemantic Units 
+ 
+49 
+Figure 
+19: 
+Modelling 
+negating 
+relations 
+between 
+instances 
+by 
+applying semantic units. A) A human-
+readable statement that this fruit is 
+not part of this organge plant. The 
+statement can be modelled in two 
+different ways: B) as an OWL 
+expression mapped to RDF. Note, how 
+the statement is translated into a 
+negated assertion statement with 
+source, 
+property, 
+and 
+target 
+specification, relating an instance 
+‘fruit x’ (PO:0009001) to an instance 
+‘orange plant y’ (FOODON:03411339) 
+involving a blank node; or C) using 
+three semantic units. The two named-
+individual identification units, with 
+their data graphs shown in the blue boxes, state that one of the objects is a fruit and the other one an orange plant, whereas 
+the part-of statement unit (red bordered box  and its dynamic label, with its data graph shown in the red box without borders) 
+states that fruit x is not part of orange plant y as it instantiates both *part-of statement unit*,  *assertional statement unit*, 
+and *negation unit*.   
+From all these examples, it becomes clear that negations, including absence statements, can be 
+efficiently represented via semantic units by classifying the corresponding semantic unit as a 
+*negation unit*. This general notation can be compared to Peirce’s existential relational graphs 
+(80,81), where a line of identity ‘―’ can be used to express that ‘something is A’ by notating it as ‘―A’. 
+The line of identity can be understood to represent an existential quantifier (Ǝx). By interrupting this 
+line with a circle that encloses A, you express that ‘something is not A’ (see Fig. 18E). The resulting 
+existential relational graphs are sufficiently general to represent full first-order logic with equality (81).  
+Expressing cardinality restrictions is, for the same reasons, also challenging using RDF/OWL and 
+requires the use of a class expression that indicates the cardinality as a class restriction. Instead of 
+using a rather complex class axiom to describe for instance that a given head possesses exactly three 
+eyes (Fig. 20B), the same information could be modelled by two semantic units and allowing for 
+extending the some-instance identification unit to include cardinality restrictions via linking its subject 
+to, for instance, the value 3 via the property qualified cardinality (OWL:qualifiedCardinality) (Fig. 20C). 
+Instead of a simple integer value, a float value range with a unit specification that is constrained to 
+count unit (UO:0000189) and percent (UO:0000187) would even allow the specification of frequencies 
+
+A)Statement
+Thisfruitisnotpartofthisorangeplant
+class
+instance
+owlspecific
+objectproperty
+class
+B)ConventionalOWLmodel
+owl:negativepropertyassertion
+fruitx
+rdf:type
+PO:fruit
+rdf:type
+owl:source individual
+blank node
+owl:assertionproperty
+bfo:partof
+owl:target individual
+orangeplanty
+rdf:type
+FOODON:orangeplant
+C)Assertionalstatementunitsmodel
+part-of
+assertional
+statement unit
+statement unit
+rdf:type
+rdf:type
+Fruitxisnotapartof
+orangeplanty
+rdf:type
+negation unit
+hassemantic
+unitsubject
+PO:fruit
++rdf:type
+fruitx
+bfo:partof
+orangeplanty
+"rdf:type"
+FOODON:orangeplantSemantic Units 
+ 
+50 
+and ranges. The has-part statement unit relates the ‘head x’ to the subject of a semantic unit that 
+instantiates both *some-instance identification unit* and *cardinality restriction unit*.  
+Figure 
+20: 
+Modelling 
+cardinality 
+restrictions 
+involving 
+instances 
+by 
+applying semantic units. A) A human-
+readable statement that this head has 
+exactly three eyes. The statement can be 
+modelled in two different ways: B) as an 
+OWL expression mapped to RDF. Note, 
+how ‘has exactly three eyes’ is translated 
+into being an instance of a class that has a 
+cardinality 
+restriction 
+on 
+the 
+has 
+component property (RO:0002180) and 
+the class eye (UBERON:0000970) with a 
+cardinality value of 3, thereby involving 
+one blank node; or C) using two semantic 
+units, one of which models the has-part 
+relationship, with its data graph shown in 
+the dark blue box. The other semantic unit 
+(light blue bordered box and its dynamic 
+label, with its data graph shown in the light 
+blue box without borders) instantiates 
+*assertional statement unit*, *some-instance identification unit*, and *cardinality restriction unit*. 
+Analog to the approach for modelling negations, semantic units can also be applied for modelling 
+disagreement in a knowledge graph. For instance, if person A asserts ‘This fruit is a pome fruit’ through 
+a named-individual identification unit, and person B disagrees with this statement, the disagreement 
+can be modelled as a semantic unit that instantiates both *assertional statement unit* and 
+*disagreement unit* and its data graph states that the named-individual identification unit asserted 
+by person A instantiates *negation unit* (see Fig. 21).  
+Whereas the here suggested notations result in simpler graphs than their OWL-based RDF 
+equivalents, and these graphs are easier to query due to the lack of blank nodes, reasoners that 
+directly use semantic units would still have to be developed; however, through the translation to OWL 
+(see section Logical semantics of semantic units), standard OWL reasoners will be able to reason over 
+semantic units, including negations, cardinality restrictions, and disagreements. 
+ 
+ 
+
+A)Statement
+Thisheadhasexactly3eyes
+B)ConventionalOwLmodel
+owl: restriction
+ro:hascomponent
+rdf: type
+owl: on
+property
+three-eyed head
+blank node
+owl:qualified
+owl:subclassof-
+cardinality
+3
+rdf:type
+owl: on class
+head x
+uberon:eye
+class
+instance
+owlspecific
+class
+objectproperty
+C)Assertionalstatementunitsmode
+assertional
+some-instance
+cardinality
+statement unit
+identification unit
+restriction unit
+rdf:type
+rdf:type
+rdf:type
+exactly
+3eyes
+hassemantic
+unit subject
+owl:qualified
+3
+cardinality
+head x
+bfo:haspart
+someeye
+some
+uberon:eye
+instanceofSemantic Units 
+ 
+51 
+ 
+ 
+ 
+Figure 21: Modelling disagreement by applying semantic units. 
+A) Person A states that this is a pome fruit and person B 
+disagrees. B) The assertional statement unit (blue bordered box 
+and its dynamic label, with its data graph shown in the blue box 
+without borders) models the statement of person A. C) The 
+disagreement unit (red bordered box and its dynamic label, with 
+its data graph shown in the red box without borders) models the 
+statement of person B and instantiates *assertional statement 
+unit* and *disagreement unit*. Its data graph states that the 
+statement of person A instantiates *negation unit*. 
+Logical semantics of semantic units 
+Semantically, we treat semantic units as translations between ABox and TBox statements, or, 
+alternatively, as translations between logic programs and OWL axioms. For example, ‘Lars’ right hand’ 
+(FMA:9712) has-part (BFO:0000051) ‘Lars’ right thumb’ (FMA:24938) is an ABox statement. It includes, 
+as part of the representation, the information that this expresses a “has part” type axiom (has-part 
+statement unit). Semantically, we treat these statement units as expressions of particular forms of 
+ontology design patterns, where the ABox statement is translated into TBox axioms based on an 
+ontology design pattern dependent on the type of statement unit. We can formalize these translations 
+using expressions of relational ontology design patterns (82), which are OWL axioms involving 
+variables for arbitrary entities. For example, the *’has-part assertional statement unit’* can be 
+translated, in general, as 
+  
+?X SubClassOf: has-part some ?Y, 
+ where ?X is filled by the subject and ?Y by the object of the statement. We can add the pattern 
+as literal, i.e., either as a datatype property or annotation property, to the statement unit class. This 
+will allow use of an OWL reasoner, or, alternatively, a SPARQL query, to retrieve all statements that 
+can be rewritten based on this  design pattern; however, it will be more convenient to specify them 
+separately and use a dual formalism. 
+The dual representation of complex axioms as ABox statements and the translation into TBox (or 
+ABox) axioms enables a dual kind of reasoning. Through the translation to TBox axioms, it becomes 
+possible to apply OWL reasoning and therefore use any OWL reasoner (or reasoners for OWL profiles) 
+
+A)Statements
+PersonA:"This fruit isapomefruit"
+PersonB:"IdisagreewithPersonA,thatthisfruitisapomefruit
+B)TypeAssertionModelforStatementofPersonA
+personA
+class
+instance
+asserted by
+named-individual
+identification unit
+Fruitxisapomefruit
+'rdf:type
+assertional
+statement unit
+hassemantic
+unit subject
+fruit x
+PO:pome fruit
+C)DisagreementAssertionModelforStatementofPersonB
+person B
+asserted by
+assertional
+df:type
+statement unit
+Fruitxisnotapomefruit
+rdf:type
+disagreement unit
+has semantic
+unit subject
+Fruitxisapomefruit
+rdf:type
+negation unitSemantic Units 
+ 
+52 
+to test consistency of the knowledge graph or perform inferences. However, the ABox representation 
+of the axioms as abbreviated patterns also enables a form of reasoning directly on the ABox 
+statements, using the semantics of logic programming; this form of reasoning can exceed the 
+semantics of OWL (83). In particular, it becomes possible to add non-monotonic statements which 
+allow us to model contingent statements, or “defaults”, which may have an exception (84). For 
+example, the statement ‘Typically, a hand has a thumb as part’ can be modelled through a logic 
+program that states that, if there is an instance x of Hand (FMA:9712) and it is not provable that x does 
+not have some instance of Thumb (FMA:24938) as part, then x has some instance of Thumb as part. 
+Formally, this can be expressed as an answer set program such as  
+has-part(x, Thumb) :- rdf:type(x, Hand), not lacks-part(x, Thumb).  
+However, such a statement has several unusual features that need to be explained. First, it is not 
+based on OWL semantics and therefore does not, initially, interact with axioms in the OWL ontology; 
+in particular, the statement unit is not translated into an OWL axiom but rather into a logic rule that 
+is applied to the statement units themselves. Second, under answer set semantics, “not” is weak 
+negation with the intended meaning that lacks-part(x, Thumb) is not provable. It therefore encodes a 
+kind of default knowledge and using this statement results in non-monotonic inference: adding a new 
+statement, such as lacks-part(x, Thumb), will invalidate the previous inference (has-part(x, Thumb)); 
+this is in contrast to the standard semantics of OWL which is monotonic (where adding a new 
+statement will never invalidate an inference). Third, the symbols Hand and Thumb are used here as 
+symbols for individuals and instanceOf is an explicit relation between entities, whereas Hand and 
+Thumb would be classes in OWL (corresponding to unary predicates) and instanceOf is a built-in 
+primitive that relates individuals to classes. 
+To relate the logic programs to OWL, we assume that the logic program is able to use all OWL 
+entities (class symbols, individual symbols, and relation symbols) as individuals. An atomic formula 
+takes the form P (a1 , ..., an ) where P is a predicate symbol and each ai is either an individual symbol 
+or a variable symbol. A formula is called ground if it contains no variable symbol. Several efficient 
+grounders, such as Clingo (85), as well as answer set solvers such as DLV (86) or clasp (87) are available, 
+and allow computation of fully ground answer sets (or stable models of answer set programs). We 
+treat the predicate symbols in the answer set program as ontology design patterns that are translated 
+into a set of OWL axioms. Applying patterns in a forward manner is decidable and can be implemented 
+in a straightforward manner by computing the fully grounded stable models of the answer set program 
+and then applying the forward translation of the design pattern. We can also implement an inverse 
+translation from OWL into these patterns by querying, for each defined ontology design pattern, 
+
+Semantic Units 
+ 
+53 
+whether the pattern is entailed by the OWL axioms; using an OWL reasoner, we can query for the 
+pattern within the deductive closure O⊢ of ontology O and iterating through all OWL entities. However, 
+for a pattern with n variables and |E| entities in the OWL ontology, the complexity will be O(|E|n). 
+Using this approach, a semantic unit is specified by two parts, a statement that takes the form of a 
+logic program, and a pattern to convert predicates into OWL statements. For example, we can express 
+a named-individual identification unit (Figure 8) as: 
+Logic program:  
+rdf:type(Lars’RightHand, fma:hand) 
+Pattern:  
+ 
+rdf:type(Lars’RightHand, fma:hand) 
+In the case of a named-individual identification unit, both statements are identical. More 
+generally, we can formulate all named-individual identification units using a logic program such as:  
+named-individual-identification-unit(x), has-semantic-subject(x,y), rdf:type(y, z), rdfs:label(y, 
+l), owl:named_individual(y);  
+and a pattern that translates each predicate into their corresponding OWL statement. 
+A some-instance identification unit is semantically identical to a named-individual identification 
+unit but does not introduce, explicitly, a name for the individual. This corresponds to the use of an 
+existential quantifier which we can eliminate through “Skolemization”, i.e., we can introduce a new 
+individual name that is not explicitly referred to in the language of the semantic units but exists in the 
+semantic space.  
+The every-instance identification unit requires more elaborate translation into OWL. Here, *every 
+instance of X* refers to the collection of all instances of X, and we may rely on a theory of collections 
+and collectives (88); the example in Figure 8 will then be translated into: 
+• rdf:type(everyHand, Collection) 
+• owl:SubClassOf(fma:Hand, owl:SomeValuesFrom(member-of, owl:oneOf({everyHand}))) 
+• owl:SubClassOf(owl:oneOf(everyHand), owl:AllValuesFrom(has-member, fma:Hand)) 
+In other words, *‘everyHand’* refers to a collection that has as its members all instances of the 
+class Hand (FMA:9712), and that has only instances of that class as members. Analogously, we can 
+translate cardinality restrictions (cardinality restriction units); the example in Figure 20, for example, 
+would be expressed using the following (general) logic program: 
+cardinality-restriction-unit(x), has-semantic-unit-subject(x,y), owl:qualified-cardinality(y,z), 
+some-instance-of(y, w). 
+
+Semantic Units 
+ 
+54 
+with a translation of this pattern into OWL of 
+ 
+rdf:type(cX, owl:intersectionOf(Collection, owl:cardinality(has-member, 3, uberon:eye))) 
+where cX is a new individual name (i.e., a name not used elsewhere). This will then be combined with 
+the ‘part-of assertional statement unit’ for ‘head X’ in the same example to assert the ABox statement 
+ 
+part-of(`head X’, cX). 
+We can use a similar translation to formalize other statements. An assertional statement unit 
+(Fig. 9) is translated directly into an ABox statement, and a universal statement unit follows a similar 
+translation; the statement in Figure 9 will be translated into the OWL ABox axiom  
+hasPart(everyHand, someThumb).  
+Based on OWL semantics and the axioms to formalize *‘everyHand’* and *‘someThumb’* gives 
+rise to the inference of the OWL axiom 
+owl: SubClassOf(fma:Hand, owl:SomeValuesFrom(has-part, Thumb)  
+as expected. The contingent statement unit in Figure 9 is similarly translated into an OWL ABox 
+axiom. However, our formalism also allows us to express a different type of contingent statement, i.e., 
+a statement about prototypes (prototypical contingent statement unit). Such a statement can be used 
+to formulate expressions such as ‘normally, a hand has a thumb as its part’, allowing for the possibility 
+of an exception (such as in the case of loss of a thumb due to an accident). The following statement 
+expresses this prototypical statement:  
+hasPart(x, thumb) :- hasPart(hand, thumb), instanceOf(x, hand), not -hasPart(x, thumb). 
+The use of the logic programming paradigm also allows us to formalize complex statements such 
+as shown in Figure 13 which are not directly expressible in OWL, and the translation into OWL through 
+translation patterns enables inferences within OWL when combined with other OWL axioms. 
+We are also able to model (classical) negation through the use of negation units (Figure 17). A 
+negation is directly added to a semantic unit, and we can use this to define a negated assertional 
+statement unit: 
+ 
+NegatedAssertionalStatementUnit(x) :- NegationUnit(x), AssertionalStatementUnit(x) 
+and then a translation into OWL for NegatedAssertionalStatementUnit with the following logic 
+program as precondition: 
+
+Semantic Units 
+ 
+55 
+NegatedAssertionalStatementUnit(x), has-semantic-unit-subject(x,y), rdf:type(y,z) 
+and the OWL translation 
+ 
+rdf:type(y, owl:complementOf(z)). 
+This 
+example 
+shows 
+the 
+flexibility 
+of 
+our 
+use 
+of 
+logic 
+programming, 
+as 
+the 
+NegatedAssertionalStatementUnit predicate is inferred from the two assertions added to the 
+statement unit and does not have to be asserted. However, this kind of inference, in particular when 
+using negation units, leads to one additional challenge because multiple patterns may apply to 
+statements, and it may not always be clear which translation pattern to apply. For example, in the 
+example in Figure 17, if we ignore the negation unit, we will conclude that the pattern for assertional 
+statement units should apply; applying translations for both statement units will result in an 
+inconsistency. The easiest way to prevent this is to add the weakly negated condition to the logic 
+programs for assertional statement units: not NegatedAssertionalStatementUnit(x), or, even simpler, 
+not NegationUnit(x); this condition will prevent the translation pattern from being triggered in the 
+presence of a negation unit. 
+Furthermore, the logic programming paradigm can be used to translate between statements (treated 
+as individuals) and their content (treated as propositions). The statements, as shown in Figure 21, are 
+units in their own right (assertional statement units) which can be translated to OWL axioms using the 
+patterns we already described. Additionally, the statements are individuals within logic programs 
+where relations between statements can be modelled, which additionally can enable the use of 
+answer set programming to represent arguments (89,90). 
+Semantic units provide a new framework for knowledge graph 
+alignment 
+Semantic units that instantiate the same semantic unit ontology class contain semantically similar 
+information. Therefore, semantic units of the same type are in principle comparable throughout all 
+their instances. Consequently, aligning and comparing different knowledge graphs that are based on 
+the same set of semantic unit ontology classes can be conducted in a step-by-step procedure along 
+the different levels of representational granularity. In a first step, the data graphs belonging to item 
+group units are aligned based on their *hasSemanticUnitSubject* relations to different types of 
+subjects and based on their *hasAssociatedSemanticUnit* relations to different types of associated 
+semantic units. In a next step, for each pair of item group units the data graphs belonging to their 
+associated item units are aligned based on their types of subjects and their types of associated 
+
+Semantic Units 
+ 
+56 
+statement units, which in turn can be aligned by class, and finally their individual triples can be aligned. 
+This would provide a new framework to improve methods for knowledge graph alignment, subgraph-
+matching, graph comparison, and graph similarity measures.  
+Managing restricted access to sensitive data 
+Statement units and their classification into corresponding ontology classes provide a framework for 
+identifying subgraphs within a knowledge graph that can contain sensitive data to which access must 
+be restricted. For example, all information relating to location data of occurrences of endangered 
+species should not be publicly available, and access should be restricted and managed by adequate 
+rules. Respective statement units can be identified by class, and the need to restrict access to them 
+can be based on the threat level of the respective species. If a species is endangered, access to these 
+types of statement units would be automatically restricted, while all other semantic units referring to 
+that species would still be openly accessible. Similarly, any personal data fall under privacy policy 
+restrictions and access to corresponding statement units should depend on specific access rights. This 
+would follow EOSC’s principle of ‘as Open as possible, as closed as necessary’ (16). 
+Conclusions and Future Work 
+With semantic units, we introduce a type of resource that is new to knowledge graphs and that 
+significantly increases their overall expressivity. Semantic units structure a knowledge graph into 
+identifiable and semantically meaningful subgraphs and thus represent an additional type of 
+representational entity (91) besides instances, classes, and properties.  Semantic units represent 
+resources of a higher level of abstraction than the low-level abstraction of the resources used in 
+conventional individual triples. Technically, semantic unit resources are instances of respective 
+ontology classes, but semantically they represent the contents of their data graphs and thus 
+statements or sets of semantically and ontologically related statements. With semantic units, one can 
+thus extract semantically meaningful entities from a knowledge graph that are more abstract than 
+the resources typically used in conventional triples.  
+Regarding the four challenges discussed in the introduction, we can conclude that because every 
+statement is organized in its own statement unit which, in turn, instantiates a corresponding 
+statement unit ontology class, a data schema (e.g., as a shape) and corresponding CRUD query 
+patterns can be specified for each such class. By linking the data schema to the corresponding 
+statement unit class, the UPRI of each statement unit and its affiliation with a corresponding 
+
+Semantic Units 
+ 
+57 
+statement unit class would also reference the underlying data schema and thus contribute to the 
+FAIRness of their data by guaranteeing schematic interoperability. Because statement units partition 
+the knowledge graph so that every triple belongs to exactly one statement unit, all data in the 
+knowledge graph would have information about their underlying data schema. Reference to the 
+underlying data schema represents valuable metadata that guarantees the interoperability of all 
+instances of statement units of the same class because they are all based on the same data schema 
+(Challenge 1).  
+The set of CRUD query patterns would not only provide read queries for domain experts for 
+searching instances of the corresponding class in the overall data graph, but also create, update, and 
+delete queries for developers, who could use them and thus do not have to learn graph query 
+languages anymore (Challenge 2).  
+By organizing the overall data graph into different semantic units and thus semantically 
+meaningful subgraphs at different levels of representational granularity, semantic units also provide 
+a solution to the problem that making statements about statements is challenging in knowledge 
+graphs (Challenge 3). Semantic units provide an efficient way of structuring the graph to allow users 
+to intuitively make statements about statements, and also provides a clear and straightforward 
+implementation schema that supports the development of corresponding queries and related tools. 
+Moreover, contrary to RDF-star, semantic units also allow distinguishing different instances of the 
+same statement by organizing them as different semantic units that instantiate the same semantic 
+unit class. They would have identical subjects and objects, but would differ by their respective 
+semantic unit resource. 
+Finally, by distinguishing between assertional, contingent (including prototypical), and universal 
+statement units as top-level categories of statement units, by introducing some-instance and every-
+instance resources, and by introducing a notation that does not involve blank nodes and that is less 
+complex than the equivalent OWL notation when mapped to RDF, semantic units provide a conceptual 
+framework with which the conceptual gap between RDF/OWL and property graphs can be bridged, 
+formal semantics for contingent and prototypical statements can be provided, and universal 
+statements and thus also particular class axioms can become part of the domain of discourse of a 
+knowledge graph (Challenge 4). In other words, semantic units substantially increase the overall 
+expressivity of knowledge graphs. 
+In the future, we want to expand the concept of a semantic unit to include for each semantic unit 
+class corresponding data schemata and query patterns. Together with further features, this results in 
+what we call a Knowledge Graph Building Block (KGBB) (see also knowledge graph cells (79) for a first 
+
+Semantic Units 
+ 
+58 
+discussion of a similar idea). A KGBB is a small module that is associated with a semantic unit ontology 
+class. Each semantic unit class requires its own associated KGBB. A KGBB provides all information 
+required for managing data belonging to the corresponding type of semantic unit. Each KGBB provides 
+a graph model for storing the data of its associated type of semantic unit, from which CRUD query 
+patterns can be derived, resulting in FAIR data and metadata. KGBBs decouple data storage from data 
+access by providing data access in various formats, and they also decouple data display from data 
+storage by providing different display templates. Ultimately, the idea for KGBBs is that each KGBB 
+functions independently of other KGBBs, that it is made openly available in a repository so that it can 
+be reused by others, and that domain experts can combine multiple KGBBs and define their possible 
+interactions with as little effort as possible to set up their own knowledge graph application, without 
+being a programmer or having knowledge in semantics. A KGBB editor will enable domain experts 
+without background in semantics, in programming, or in graph query languages to describe new 
+KGBBs. A KGBB application engine will use the information provided by the various KGBBs of a 
+knowledge graph application and communicate through respective APIs with the persistence-layer 
+and the presentation-layer, thereby decoupling not only human-readable data display from data 
+storage, but also data access from data storage, and data storage from storage technology.  
+One of the authors has developed a first minimum viable product for how KGBBs and semantic 
+units can be used to manage a knowledge graph (92). It is based on Neo4j and gets its contents through 
+a web interface and user input. It is a small knowledge graph application for documenting assertions 
+from scholarly publications and allows users in an exemplary way to describe some contents that can 
+be found in a scholarly publication (it does not focus on describing the publication’s bibliographic 
+metadata). Each described paper is represented as its own item group unit, with the assertions 
+covered by statement units that are associated with item units and granularity tree units. The 
+showcase 
+is 
+based 
+on 
+Python 
+and 
+flask/Jinja2 
+and 
+is 
+openly 
+available 
+through 
+https://github.com/LarsVogt/Knowledge-Graph-Building-Blocks.  
+We believe that the combination of semantic units with Knowledge Graph Building Blocks will 
+contribute a framework for sharing data across many stakeholders, helping to interlink data providers 
+from a diverse range of different areas, with data stewardship remaining in the hands of the domain 
+experts or institutions, thus ensuring their technical autonomy (following Barend Mons’ data visiting 
+as opposed to data sharing (7)). We also think that due to its modular character, the framework can 
+increase the accessibility of knowledge graphs for software developers and domain experts who lack 
+the expertise in semantics, thus supporting the FAIRification of data and metadata in 
+general―something desperately needed to make all data FAIR, which we believe would increase our 
+chances to fight climate change and biodiversity loss.  
+
+Semantic Units 
+ 
+59 
+Acknowledgements 
+We thank Werner Ceusters, Nico Matentzoglu, Manuel Prinz, Marcel Konrad, Philip Strömert, Roman 
+Baum, Björn Quast, Peter Grobe, István Míko, Manfred Jeusfeld, Manolis Koubarakis, Javad 
+Chamanara, and Kheir Eddine for discussing some of the presented ideas. Lars Vogt received funding 
+by the ERC H2020 Project ‘ScienceGraph’ (819536). We are solely responsible for all the arguments 
+and statements in this paper.  
+Author’s contributions 
+LV: developed the concept of semantic units and wrote the manuscript. TC: contributed to the chapter 
+about nanopublications. RH: contributed the formal semantics. All authors: reviewed the manuscript. 
+References 
+1. Adam, K., Hammad, I., Adam, M., et al. (2015) Big Data Analysis and Storage. Proceedings of the 
+2015 international conference on operations excellence and service engineering, Orlando, 
+Florida, USA, 10-11 Sept 2015, pp. 648–659. 
+2. Marr, B. (2018) How Much Data Do We Create Every Day? The Mind-Blowing Stats Everyone 
+Should Read. How Much Data Do We Create Every Day? The Mind-Blowing Stats Everyone 
+Should Read; (2018) . 
+3. Data never sleeps 5.0 . 
+4. Idrees, S.M., Alam, M.A. and Agarwal, P. (2018) A study of big data and its challenges. Int. J. Inf. 
+Technol., 11, 841–846. 
+5. General Assembly, U.N. (2015) Transforming our world: the 2030 Agenda for Sustainable 
+Development. Transforming our world: the 2030 Agenda for Sustainable Development; (2015) ; 
+pp. 1–35. 
+6. International Science Council (ISC) (2019) Science as a global public good: ISC Action Plan, 2019-
+2021. Science as a global public good: ISC Action Plan, 2019-2021; International Science Council, 
+(2019) . 
+7. Mons, B. (2019) Message from the CODATA President, Barend Mons. Message from the CODATA 
+President, Barend Mons; (2019) . 
+8. Wilkinson, M.D., Dumontier, M., Aalbersberg, I.J., et al. (2016) The FAIR Guiding Principles for 
+scientific data management and stewardship. Sci. Data, 3, 160018. 
+9. P. Bryan Heidorn (2008) Shedding Light on the Dark Data in the Long Tail of Science. Libr. Trends, 
+57, 280–299. 
+10. Baker, M. (2016) 1,500 scientists lift the lid on reproducibility. Nature, 533, 452–454. 
+11. Lin, D., Crabtree, J., Dillo, I., et al. (2020) The TRUST Principles for digital repositories. Sci. Data, 
+7, 144. 
+
+Semantic Units 
+ 
+60 
+12. The Internet of FAIR Data & Services . 
+13. Ayris, P., Berthou, J.-Y., Bruce, R., et al. (2016) Realising the European Open Science Cloud. 
+Realising the European Open Science Cloud; (2016) ; p. 24. 
+14. Hasnain, A. and Rebholz-Schuhmann, D. (2018) Assessing FAIR Data Principles Against the 5-Star 
+Open Data Principles. In Gangemi, A., Gentile, A. L., Nuzzolese, A. G., et al. (eds.), The Semantic 
+Web: ESWC 2018 Satellite Events. ESWC 2018. Lecture Notes in Computer Science, vol 11155., 
+Springer, pp. 469–477. 
+15. European Commission. Directorate General for Research and Innovation. and EOSC Executive 
+Board (2021) EOSC interoperability framework: report from the EOSC Executive Board Working 
+Groups FAIR and Architecture. EOSC interoperability framework: report from the EOSC Executive 
+Board Working Groups FAIR and Architecture.; Publications Office, LU, (2021) . 
+16. European Commission Expert Group on FAIR Data (2018) Turning FAIR into reality. Turning FAIR 
+into reality; (2018) . 
+17. Vogt, L., Baum, R., Bhatty, P., et al. (2019) SOCCOMAS: a FAIR web content management system 
+that uses knowledge graphs and that is based on semantic programming. Database, 2019, 1–22. 
+18. Blumauer, A. (2018) Knowledge Graphs—Connecting the Dots in an Increasingly Complex World. 
+Knowledge Graphs—Connecting the Dots in an Increasingly Complex World; (2018) . 
+19. Singhal, A. (2012) Introducing the Knowledge Graph: things, not strings. Introducing the 
+Knowledge Graph: things, not strings  (2012) . 
+20. Hogan, A., Blomqvist, E., Cochez, M., et al. (2021) Knowledge Graphs. ACM Comput. Surv., 54, 1–
+37. 
+21. Bonatti, P.A., Decker, S., Polleres, A., et al. (2019) Knowledge graphs: new directions for 
+knowledge representation on the semantic web. Rep. Dagstuhl Semin., 8, 29–111. 
+22. Abiteboul, S. (1997) Querying semi-structured data. In Afrati, F., Kolaitis, P. (eds.), Database 
+Theory — ICDT ’97, Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 1–18. 
+23. Angles, R. and Gutierrez, C. (2008) Survey of graph database models. ACM Comput. Surv., 40, 1–
+39. 
+24. Angles, R., Arenas, M., Barceló, P., et al. (2017) Foundations of Modern Query Languages for 
+Graph Databases. ACM Comput. Surv., 50, 1–40. 
+25. Hitzler, P., Krötzsch, M., Parsia, B., et al. (2012) OWL 2 Web Ontology Language Primer (Second 
+Edition), W3C Recommendation 11 December 2012. OWL 2 Web Ontology Language Primer 
+(Second Edition), W3C Recommendation 11 December 2012.  (2012) . 
+26. Stutz, P., Strebel, D. and Bernstein, A. (2016) Signal/Collect12: Processing large graphs in 
+seconds. Semantic Web, 7, 139–166. 
+27. Wang, Q., Mao, Z., Wang, B., et al. (2017) Knowledge Graph Embedding: A Survey of Approaches 
+and Applications. IEEE Trans. Knowl. Data Eng., 29, 2724–2743. 
+28. Ceusters, W. (2020) The place of Referent Tracking in Biomedical Informatics. Terminology, 
+Ontology and their Implementations, Springer Nature, p. 50. 
+29. Ceusters, W., Elkin, P. and Smith, B. (2007) Negative findings in electronic health records and 
+biomedical ontologies: A realist approach. Int. J. Med. Inf., 76, S326–S333. 
+30. Vogt, L. (2021) FAIR data representation in times of eScience: a comparison of instance-based 
+and class-based semantic representations of empirical data using phenotype descriptions as 
+example. J. Biomed. Semant., 12, 20. 
+
+Semantic Units 
+ 
+61 
+31. Bandrowski, A., Brinkman, R., Brochhausen, M., et al. (2016) The Ontology for Biomedical 
+Investigations. PLoS ONE, 11, 1–19. 
+32. Knublauch, H. and Kontokostas, D. (2017) Shapes Contraint Language (SHACL) - W3C 
+Recommendation 20 July 2017. Shapes Contraint Language (SHACL) - W3C Recommendation 20 
+July 2017; (2017) . 
+33. Booth, D. and Wallace, E. (2019) Session X: EasyRDF. Session X: EasyRDF. 2nd US Semantic 
+Technol. Symp. 2019  (2019) . 
+34. Hartig, O. (2017) Foundations of RDF* and SPARQL*. CEUR Workshop Proceedings 1912. 
+35. Arndt, D., Broekstra, J., DuCharme, B., et al. RDF-star and SPARQL-star Draft Community Group 
+Report 01 July 2021. RDF-star and SPARQL-star Draft Community Group Report 01 July 2021. 
+36. Frey, J., Müller, K., Hellmann, S., et al. (2019) Evaluation of metadata representations in RDF 
+stores. Semantic Web J., 10, 205–229. 
+37. Mungall, C.J. (2019) Proposed strategy for semantics in RDF* and Property Graphs. Proposed 
+strategy for semantics in RDF* and Property Graphs  (2019) . 
+38. Mungall, C.J. (2017) Shadowboxing : Mirroring the TBox in the ABox. Shadowboxing : Mirroring 
+the TBox in the ABox  (2017) . 
+39. Hogan, A., Arenas, M., Mallea, A., et al. (2014) Everything you always wanted to know about 
+blank nodes. J. Web Semant., 27–28, 42–69. 
+40. Neumann, T. and Moerkotte, G. (2011) Characteristic sets: Accurate cardinality estimation for 
+RDF queries with multiple joins. 2011 IEEE 27th International Conference on Data Engineering, 
+IEEE, Hannover, Germany, pp. 984–994. 
+41. Papastefanatos, G., Meimaris, M. and Vassiliadis, P. (2021) Relational schema optimization for 
+RDF-based knowledge graphs. Inf. Syst., 101754. 
+42. Collarana, D., Galkin, M., Traverso-Ribón, I., et al. (2017) MINTE: Semantically integrating RDF 
+graphs. Proceedings of the 7th International Conference on Web Intelligence, Mining and 
+Semantics - WIMS ’17, ACM Press, New York, New York, USA, pp. 1–11. 
+43. Endris, K.M., Galkin, M., Lytra, I., et al. (2018) Querying Interlinked Data by Bridging RDF 
+Molecule Templates. Querying Interlinked Data by Bridging RDF Molecule Templates  (2018) . 
+44. Vogt, L. (2019) Organizing phenotypic data—a semantic data model for anatomy. J. Biomed. 
+Semant., 10, 12. 
+45. Smith, B., Almeida, M., Bona, J., et al. (2015) Basic Formal Ontology 2.0. . 
+46. Schulz, S. and Jansen, L. (2013) Formal ontologies in biomedical knowledge representation. IMIA 
+Yearb. Med. Inform. 2013, 8, 132–46. 
+47. Schulz, S., Stenzhorn, H., Boekers, M., et al. (2009) Strengths and limitations of formal ontologies 
+in the biomedical domain. Electron. J. Commun. Inf. Innov. Health, 3, 31–45. 
+48. Rector, A., Stevens, R. and Drummond, N. (2009) What causes pneumonia? The case for a 
+standard semantics for “may” in OWL. CEUR Workshop Proc., 432. 
+49. Dodds, L. and Davis, I. (2011) Linked Data Patterns: A pattern catalogue for modelling, 
+publishing, and consuming Linked Data. Linked Data Patterns: A pattern catalogue for modelling, 
+publishing, and consuming Linked Data; (2011) . 
+50. Stevens, R. and Sattler, U. (2014) Walking your fingers through the trees in OWL: why there are 
+things you want to say but can’t. Walking your fingers through the trees in OWL: why there are 
+things you want to say but can’t. Ontog. - Knowl. Blog  (2014) . 
+
+Semantic Units 
+ 
+62 
+51. W3C: OWL 2 Web Ontology Language Manchester Syntax (Second Edition) . 
+52. Balhoff, J.P., Mikó, I., Yoder, M.J., et al. (2013) A semantic model for species description applied 
+to the ensign wasps (Hymenoptera: Evaniidae) of New Caledonia. Syst. Biol., 62, 639–659. 
+53. Bittner, T. and Smith, B. (2001) A taxonomy of granular partitions. In Montello, D. R. (ed.), 
+Spatial Information Theory: Foundations of Geographic Information Science, volume 2205 of 
+Lecture Notes in Computer Science, Springer, Berlin, p. 16. 
+54. Smith, B. and Bittner, T. (2001) A unified theory of granularity, vagueness and approximation. 
+Proceedings of COSIT Workshop on Spatial Vagueness, Uncertainty, and Granularity., Vol. 102, p. 
+39. 
+55. Bittner, T. and Smith, B. (2003) A theory of granular partitions. In Duckham, M., Goodchild, M. 
+F., Worboys, M. F. (eds.), Foundations of geographic information science, Taylor & Francis Books, 
+London, pp. 117–149. 
+56. Keet, C.M. (2008) A Formal Theory of Granularity - Toward enhancing biological and applied life 
+sciences information system with granularity. PhD Thesis, Free University of Bozen - Bolzano, 
+Bozen. 
+57. Vogt, L. (2010) Spatio-structural granularity of biological material entities. BMC Bioinformatics, 
+11. 
+58. Vogt, L. (2019) Levels and building blocks—toward a domain granularity framework for the life 
+sciences. J. Biomed. Semant., 10, 1–29. 
+59. Gayo, J.E.L., Prud’hommeaux, E., Staworko, S., et al. (2015) Towards an RDF validation language 
+based on regular expression derivatives. CEUR Workshop Proc., 1330, 197–204. 
+60. Staworko, S., Boneva, I., Gayo, J.E.L., et al. Complexity and Expressiveness of ShEx for RDF. 18. 
+61. Lupp, D.P., Hodkiewicz, M. and Skjæveland, M.G. (2020) Template Libraries for Industrial Asset 
+Maintenance: A Methodology for Scalable and Maintainable Ontologies. 13th International 
+Conference on Scalable Semantic Web Knowledge Base Systems (SSWS 2020), colocated with the 
+International Semantic Web Conference (ISWC 2020), pp. 49–64. 
+62. Skjæveland, M.G., Lupp, D.P., Karlsen, L.H., et al. (2018) Practical Ontology Pattern Instantiation, 
+Discovery, and Maintenance with Reasonable Ontology Templates. In Vrandečić, D., Bontcheva, 
+K., Suárez-Figueroa, M. C., et al. (eds.), The Semantic Web – ISWC 2018, Lecture Notes in 
+Computer Science, Springer International Publishing, Cham, Vol. 11136, pp. 477–494. 
+63. Mons, B. and Velterop, J. (2009) Nano-Publication in the e-science era Nano-Publication in the e-
+science era. Workshop on Semantic Web Applications in Scientific Discourse (SWASD 2009). 
+64. Groth, P., Gibson, A. and Velterop, J. (2010) The Anatomy of a Nano-publication. Inf. Serv. Use, 
+30, 51–56. 
+65. Kuhn, T., Taelman, R., Emonet, V., et al. (2021) Semantic micro-contributions with decentralized 
+nanopublication services. PeerJ Comput. Sci., 7, e387. 
+66. Giachelle, F., Dosso, D. and Silvello, G. (2021) Search, access, and explore life science 
+nanopublications on the Web. PeerJ Comput. Sci., 7, e335. 
+67. Kuhn, T., Willighagen, E., Evelo, C., et al. (2017) Reliable Granular References to Changing Linked 
+Data. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial 
+Intelligence and Lecture Notes in Bioinformatics), Vol. 10587 LNCS, pp. 436–451. 
+68. Clark, T., Ciccarese, P.N. and Goble, C.A. (2014) Micropublications: a semantic model for claims, 
+evidence, arguments and annotations in biomedical communications. J. Biomed. Semant., 5, 28. 
+
+Semantic Units 
+ 
+63 
+69. Pinker, S. (1997) How the Mind Works. How the Mind Works; W.W. Norton & Company, Inc., 
+(1997) . 
+70. Herre, H. (2010) The Ontology of Mereological Systems: A Logical Approach. Theory and 
+Applications of Ontology: Philosophical Perspectives, Springer Netherlands, Dordrecht, pp. 57–
+82. 
+71. Azzam, A., Polleres, A., Fernández, J.D., et al. (2022) smart-KG : Partition-Based Linked Data 
+Fragments for Querying Knowledge Graphs. Semantic Web - Interoperability Usability Appl., 
+under revi. 
+72. Vogt, L. (2011) Signs and terminology: science caught between language and perception. 
+Bionomina, 4, 1–41. 
+73. Smith, B., Kusnierczyk, W., Schober, D., et al. (2006) Towards a Reference Terminology for 
+Ontology Research and Development in the Biomedical Domain. In Bodenreider, O. (ed.), 
+Proceedings of KR-MED 2006, Studies in Health Technology and Informatics, Vol. 124, IOS Press, 
+pp. 57–66. 
+74. Vogt, L., Mikó, I. and Bartolomaeus, T. (2022) Anatomy and the type concept in biology show 
+that ontologies must be adapted to the diagnostic needs of research. J. Biomed. Semant., 13, 27. 
+75. Marconi, D. (1995) On the Structure of Lexical Competence. Proc. Aristot. Soc., 95, 131–150. 
+76. Smith, B. (2004) The Logic of Biological Classification and the Foundations of Biomedical 
+Ontology. Spat. Cogn. Comput., 25, 25–29. 
+77. Stamos, D.N. (2005) Pre-Darwinian Taxonomy and Essentialism – A Reply to Mary Winsor. Biol. 
+Philos., 20, 79–96. 
+78. Johansson, I. (2006) Bioinformatics and biological reality. J. Biomed. Inform., 39, 274–287. 
+79. Vogt, L., D’Souza, J., Stocker, M., et al. (2020) Toward Representing Research Contributions in 
+Scholarly Knowledge Graphs Using Knowledge Graph Cells. Proceedings of the ACM/IEEE Joint 
+Conference on Digital Libraries in 2020, ACM, Virtual Event China, pp. 107–116. 
+80. Peirce, C.S. Existential graphs - CP 4.372-417. Existential graphs - CP 4.372-417. 
+81. Sowa, J.F. (2011) Peirce’s tutorial on existential graphs. Semiotica, 2011. 
+82. Hoehndorf, R., Oellrich, A., Dumontier, M., et al. (2010) Relations as patterns: bridging the gap 
+between OBO and OWL. BMC Bioinformatics, 11, 441. 
+83. Lifschitz, V. (2019) Answer Set Programming. Answer Set Programming; Springer International 
+Publishing, Cham, (2019) . 
+84. Hoehndorf, R., Loebe, F., Kelso, J., et al. (2007) Representing default knowledge in biomedical 
+ontologies: application to the integration of anatomy and phenotype ontologies. BMC 
+Bioinformatics, 8, 377. 
+85. Gebser, M., Kaminski, R., Kaufmann, B., et al. (2019) Multi-shot ASP solving with clingo. Theory 
+Pract. Log. Program., 19, 27–82. 
+86. Adrian, W.T., Alviano, M., Calimeri, F., et al. (2018) The ASP System DLV: Advancements and 
+Applications. KI - Künstl. Intell., 32, 177–179. 
+87. Gebser, M., Kaufmann, B., Neumann, A., et al. (2007) clasp: A Conflict-Driven Answer Set Solver. 
+Logic Programming and Nonmonotonic Reasoning, Springer Berlin Heidelberg, Berlin, 
+Heidelberg, pp. 260–265. 
+88. Wood, Z. and Galton, A. (2009) A taxonomy of collective phenomena. Appl. Ontol., 4, 267–292. 
+89. Egly, U., Alice Gaggl, S. and Woltran, S. (2010) Answer-set programming encodings for 
+
+Semantic Units 
+ 
+64 
+argumentation frameworks. Argum. Comput., 1, 147–177. 
+90. Toni, F. and Sergot, M. (2011) Argumentation and Answer Set Programming. pp. 164–180. 
+91. Rector, A., Schulz, S., Rodrigues, J.M., et al. (2019) On beyond Gruber: “Ontologies” in today’s 
+biomedical information systems and the limits of OWL. J. Biomed. Inform. X, 2, 1–15. 
+92. Vogt, L. (2022) FAIR Knowledge Graphs with Semantic Units―a Prototype. FAIR Knowledge 
+Graphs with Semantic Units―a Prototype  (2022) . 
+ 
+
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+page_content='org/0000-0001-8149-5890  Correspondence to lars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='vogt@googlemail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='com  Semantic Units  2  Abstract  Background: Knowledge graphs and ontologies are becoming increasingly important as technical  solutions for Findable, Accessible, Interoperable, and Reusable data and metadata (FAIR Guiding  Principles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We discuss four challenges that impede the use of FAIR knowledge graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Results: Semantic units have the potential to solve the challenges by structuring a knowledge graph  into identifiable and semantically meaningful subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each semantic unit is represented by its own  resource, instantiates a corresponding semantic unit class, and can be implemented as a FAIR Digital  Object and a nanopublication in RDF/OWL and property graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We distinguish statement and  compound units as basic categories of semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Statement units represent smallest,  independent propositions that are semantically meaningful for a human reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' They consist of one  or more triples and mathematically partition a knowledge graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We distinguish assertional,  contingent (prototypical), and universal statement units as basic types of statement units and propose  representational schemes and formal semantics for them (including for absence statements,  negations, and cardinality restrictions) that do not involve blank nodes and that translate back to OWL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Compound units, on the other hand, represent semantically meaningful collections of semantic units  and we distinguish various types of compound units, representing different levels of representational  granularity, different types of granularity trees, and different frames of reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Conclusions: Semantic units support making statements about statements, can be used for graph-  alignment, subgraph-matching, knowledge graph profiling, and for managing access restrictions to  sensitive data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Organizing the graph into semantic units supports the separation of ontological,  diagnostic (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', referential), and discursive information, and it also supports the differentiation of  multiple frames of reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Keywords: FAIR data and metadata, knowledge graph, OWL, RDF, semantic unit, assertional  statement, contingent statement, prototypical statement, universal statement, negation  Semantic Units  3  Background  In times of ever-increasing amounts of data being created every day (1–3), new technical and societal  challenges arise (4) that ask for innovative ways of representing and managing data in science and  industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Being able to collect, integrate, and analyze large amounts of data from various sources also  represents one of the requirements for facing biodiversity loss and climate change, two major global  challenges we are currently facing (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Solutions to these problems will be driven by sharing data across  many stakeholders, needing an effort to help interlink data providers from a diverse range of different  areas, often requiring a truly interdisciplinary approach (6), in which data stewardship remains in the  hands of the domain experts or institutions, thus ensuring their technical autonomy (following Barend  Mons’ data visiting as opposed to data sharing (7)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  From a data management and data representation perspective, this requires data and metadata  to be FAIR, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', readily Findable, Accessible, Interoperable, and Reusable for machines and humans  alike (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If this is not the case, Big Data ultimately turns into Dark Data (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The establishment of the  FAIR Guiding Principles as a general standard in science and industry would also contribute to a  solution for the reproducibility crisis in science (10) and the question of the trustworthiness of  information in general (see also TRUST Principles of Transparency, Responsibility, User Focus,  Sustainability, and Technology (11)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Therefore, we must build something along the lines of the  Internet of FAIR Data and Services (12) that scales with Big Data, through which all relevant data-rich  institutions, research projects, and citizen-science projects can make their data and metadata  accessible following the FAIR Guiding Principles (13,14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This requires providing rich machine-  actionable data and metadata with human-readable interface outputs and search capabilities, and  organizing this data into FAIR Digital Objects (15,16), each of which possesses its own Unique  Persistent and Resolvable Identifier (UPRI) for referencing it individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In this context, knowledge graphs can substantially contribute to the needed technical solutions,  providing a suitable framework for managing and representing FAIR data and metadata (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Knowledge graphs are becoming increasingly popular (18), especially after the 2012 announcement  of the Google Knowledge Graph (19) which was followed by further announcements of knowledge  graphs being developed from industry and by a growing number of scientific publications on  knowledge graphs (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Besides general applications in industry and research, knowledge graphs are  thereby particularly applied in the context of semantic search based on entities and relations, deep  reasoning, disambiguation of natural language, machine reading, and entity consolidation for Big Data  and text analytics (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  4  The graph-based abstractions employed in knowledge graphs have several benefits compared to  relational or other NoSQL models,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' including (i) an intuitive way for modelling relations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (ii) allowing  postponing specifications of definitions for data schema so that they can flexibly evolve,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' which is  especially important when dealing with incomplete knowledge,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (iii) employing machine-actionable  knowledge representation formalisms such as ontologies and rules,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (iv) applying graph analytics and  machine learning,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and (v) utilizing the specialized graph query languages of knowledge graphs that  support,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' in addition to standard relational operators such as joins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' unions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and projections,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' also  navigational operators for recursively searching for entities through arbitrary-length paths (20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='22–27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Moreover, due to their inherent semantic transparency, knowledge graphs can improve the  transparency of data-based decision-making and improve communication in research and science in  general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  However, although providing a suitable technical framework, using a knowledge graph for  documenting data and metadata does not necessarily result in FAIR data and metadata, but requires  following specific guidelines such as consistently applying adequate semantic data models and  organizing data into FAIR Digital Objects (15,16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, as it is often the case with new  technologies, knowledge graphs bring their own specific technical, conceptual, and societal  challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This already begins with the concept of a knowledge graph, which is somewhat fuzzy (20)  and covers different technical and conceptual incarnations, including property graphs such as Neo4J  (https://neo4j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='com/) and approaches based on the Resource Description Framework (RDF), the use of  RDF-stores, and, with the Web Ontology Language (OWL), also applications of Description Logics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Here, we first briefly discuss four of these challenges, and then we introduce the idea of  partitioning and structuring a knowledge graph into identifiable and semantically meaningful units  of representation (short: semantic units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The concept of semantic units can significantly contribute  to solutions for the four challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We introduce the two basic categories of semantic units, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  statement units and compound units, as new elements in FAIR knowledge graphs in addition to the  well-known triples and the graph as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Statement and compound units can be employed to  organize the data graph into five levels of representational granularity, ranging from the level of  individual triples to the level of the graph as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We introduce additional subcategories of  semantic units that can be used to further organize the data graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We continue arguing that because  each semantic unit can be organized as a FAIR Digital Object that possesses its own UPRI, semantic  units can be referred to within triple statements, thus providing a very efficient way of making  statements about statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' With the introduction of semantic units, we follow a user-centric  approach and add another layer of triples on top of the well established RDF and OWL layer for  knowledge graphs (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' By simplifying the semantic modelling of empirical data and reducing their  Semantic Units  5  representational complexity and by providing representations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', patterns) and formal semantics for  statements for which in OWL no formal semantics exist, semantic units increase the usability of  knowledge graphs for domain-experts and developers alike.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 1: Semantic units add further layers to a knowledge graph on top of the RDF/OWL layer of triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The layer of triples  is mathematically partitioned into a layer of statement units, so that each triple belongs to exactly one statement unit and  each statement unit comprises one or more triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Statement units can be organized into different types of semantically  meaningful collections (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', compound units) with which various additional layers can be defined to further structure and  organize the knowledge graph in semantically meaningful ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Box 1 | Conventions  In this paper, we refer to FAIR knowledge graphs as machine-actionable semantic graphs for documenting, organizing,  and representing assertional (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', empirical data), universal, and contingent statements and thus a mixture of ABox and  TBox expressions (thereby contrasting knowledge graphs with ontologies, with the latter containing mainly universal  statements and thus TBox expressions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We want to point out that we discuss semantic units against the background of  RDF-based triple stores, OWL, and Description Logics as a formal framework for inferencing, and labeled property graphs  as an alternative to triple stores, because these are the main technologies and logical frameworks used in knowledge  graphs that are supported by a broad community of users and developers and for which accepted standards exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We are  aware of the fact that alternative technologies and frameworks exist that support an n-tuples syntax and more advanced  logics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', First Order Logic) (28,29), but supporting tools and applications are missing or are not widely used to turn  them into well-supported, scalable, and easily usable knowledge graph applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Throughout this text we use regular underlined to indicate ontology classes, italicsUnderlined when referring to  properties (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', relations in Neo4j), and use ID numbers to specify each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ID numbers are composed of the ontology prefix  followed by a colon and a number, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', isAbout (IAO:0000136).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If the term is not yet covered in any ontology, we indicate  it with *, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the class *metric measurement statement unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We use ‘regular underlined’ to indicate instances of classes,  SemanticUnits  Knowledge  different types of  Graph  Compound Units  StatementUnits  RDF/OWL  Knowledge  Triples  GraphSemantic Units  6  with the label referring to the class label and the ID number to the class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, when we use the term resource, we  understand it to be something that is uniquely designated (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', a Uniform Resource Identifier, URI) and about which you  want to say something.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It thus stands for something and represents something you want to talk about.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In RDF, the Subject  and the Predicate in a triple statement are always resources, whereas the Object can be either a resource or a literal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Resources can be either properties, instances, or classes, with properties taking the Predicate position in a triple and with  instances referring to individuals (=particulars) and classes to universals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  For reasons of clarity, in the text and in all figures, we represent resources not with their UPRIs but with human-  readable labels, with the implicit assumption that every property, every instance, and every class has its own UPRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Challenge 1: FAIR empirical data must specify the graph patterns used  for their modelling to prevent schematic interoperability conflicts  FAIR is often understood to mean that for data and metadata statements to be interoperable and  reusable, all concepts used in them must have identifiers, which in turn are provided by controlled  vocabularies such as ontologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' What is frequently overlooked is the fact that to be FAIR, not only the  concepts must be standardized (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', terminological interoperability), but also the way they are related  to one another in data and metadata statements and thus the statements’ underlying semantic graph  patterns (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', schematic interoperability)―especially when stored and managed in a knowledge  graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In case of universal statements, in RDF-based knowledge graphs this graph pattern is typically  well-defined using OWL-specific object properties in class axioms (see also Figure 5B), resulting in TBox  expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  With empirical data, the situation is different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Empirical data should be modelled as ABox  expressions (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, due to the high general expressivity of RDF and OWL, in a knowledge  graph, any given empirical data statement can be modelled in many, usually not directly interoperable  ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A machine would have a hard time to identify two differently structured ABox expressions that  actually model the same underlying data statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' As a result, we must deal with such schematic  interoperability conflicts, whenever data are modelled using different graph patterns (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 2 and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  7  Figure 2: Comparison of a human-readable statement with its machine-actionable representation as an ABox semantic  graph following the RDF syntax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Top: A human-readable statement about the observation that ObjectX weighs 5 kilograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Bottom: A representation of the same statement as a graph, using RDF and following the general pattern for measurement  data from the Ontology for Biomedical Investigations (OBI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' http://obi-ontology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='org/) (31) of the Open Biological and  Biomedical Ontology Foundry (OBO;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='obofoundry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='org/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 3: Alternative machine-actionable representation of the data statement from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 2, following the RDF syntax and  the graph-model from the Extensible Observation Ontology (OBOE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This graph represents the same data statement as  shown in Figure 2 Top, but applies a different semantic graph model for its representation, which is based on OBOE  (http://bioportal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bioontology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='org/ontologies/OBOE), an ontology frequently used in the ecology community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Therefore, for an ABox representation of an empirical data statement to be FAIR, one must know  which graph pattern has been used for its semantic modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Only instance-based graphs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', graphs  with instance resources in the Subject and Object positions of their triples;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ABoxes) that are modelled  using the same template in the form of a graph pattern, for instance specified as a shape using SHACL  (32), are guaranteed to meet the minimum requirement for interoperability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Ideally, statements of  the same type, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', all weight measurements, use the same graph pattern to be potentially  interoperable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Therefore, we need identifiers for such graph patterns, and if an empirical datum is  documented in the form of an ABox, its metadata should reference the corresponding graph-pattern  identifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' With this information, one can identify potentially interoperable ABox expressions by their  commonly shared graph-pattern identifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Observation:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='ObjectX weighs 5 kilograms  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Observation Graph:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:material entity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='pato:weight  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='iao:scalar measurement datum  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='obi:scalar value specification  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='uo:kilogram  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='ro:has quality  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='lao:isquality  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='objectx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='weight  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='measured as  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='scalar measurement datum  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='obi: has value  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='scalar value specification  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='iao:hasmeasurement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='specification  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit label  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='kilogram  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='ro:quality of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='iao:is quality  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='measurementof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='iao: has  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='measurement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='obi:specifies value of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='value  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='value  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='00bfo:material entity  oboe:observation  oboe:measurement  rdf:type  rdf:type  rdf:type  objectx  oboe:ofentity  observation  oboe:hasmeasurement  measurement  oboe:hasvalue  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='00  oboe:ofcharacteristic  oboe:uses standard  weight  kilogram  class  instance  value  rdf:type  rdf:type  pato:weight  uo:kilogramSemantic Units  8  Practically, this implies (i) that all statements in a knowledge graph must be classified into  statement classes, with each class having an associated graph pattern specified (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', in the form of a  shape specification) and (ii) that the subgraph belonging to a particular statement must be identifiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Only if these two criteria are met, ABox representations of data and metadata truly comply with the  FAIR Guiding Principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semantic units provide a means to meet these two criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Challenge 2: Many software developers do not see the benefit of  graph query languages  Most knowledge graphs are either directed labeled graphs that are based on RDF/OWL and stored in  tuple stores, or they are labeled property graphs such as Neo4j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Directly interacting with these graphs,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', conducting CRUD operations for creating (=writing), reading (= searching), updating, and deleting  statements in the knowledge graph, requires the use of a query language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For RDF/OWL, this is for  example SPARQL (https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='w3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='org/TR/rdf-sparql-query/), and for Neo4j, it is Cypher  (https://neo4j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='com/developer/cypher/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Whereas these query languages allow detailed and very complex queries, writing queries in  SPARQL or Cypher is demanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Users of knowledge graph applications usually lack the required  background for writing such queries themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Unfortunately, our personal experiences are that  even most developers are not familiar with these languages and struggle with their complexity when  attempting to learn them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, having to write SPARQL or Cypher queries represents an  entry barrier for interacting with a knowledge graph and hinders their broader usage (33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We thus  need technical solutions to mitigate this challenge, such as openly available and reusable query  patterns that link to specific graph patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The concept of semantic units can contribute to such solutions by allowing experts in Semantics  to provide generic CRUD queries for each type of semantic unit that domain experts as users and  developers of knowledge graphs that apply semantic units can employ without having to write the  queries themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Queries of different types of semantic units can be combined via union or  intersection to form more complex queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Challenge 3: Making statements about statements can be challenging  The RDF triple syntax of Subject, Predicate, and Object does not natively provide a good method for  making statements about statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In RDF, a statement about a statement is a triple that relates a  statement consisting of one or more triples to some value, resource, or some other such statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  9  Unfortunately, if you wanted to represent empirical data or the contents of for instance a  scholarly publication in a FAIR knowledge graph, you frequently have to model statements about  statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, if you want to provide detailed metadata for a measurement datum, you  would actually have to relate two subgraphs to one another: the graph representing the measurement  itself, documented in a set of triples (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 2) and the graph documenting the underlying  measuring process, which also involves several triples (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In case we only want to refer to a single triple statement in another triple, RDF reification can be  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In RDF reification, a resource is defined to represent a particular triple by describing it via three  additional triples that specify its Subject, Predicate, and Object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Alternatively, one can also use the  RDF-star approach (34,35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In RDF-star, however, all statements involving the same subject, predicate,  and object are understood to reference the same triple and are thus not distinguished, with the  consequence that one cannot distinguish different instances of the same statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, while  using RDF-star is feasible for referring to a single triple, it becomes very inefficient and complicated to  query when having to refer to sets of multiple triple statements and thus larger subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If you  wanted to make a statement about the entire graph as depicted in Figure 4 using reification, you would  first have to specify a statement for each triple in the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Since the graph comprises more than 20  triples, you would end up having to create more than 60 triples in this first step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, because  you want to refer to the graph as a whole and not to each of its triples individually, you would have to  create more than 20 additional triples that link the resource representing the entire subgraph with  the resources you created in the first step for representing each individual triple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' While this is  technically feasible, it is neither elegant nor easily queried.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In cases like this, using Named Graphs is much more efficient than applying RDF reification or  RDF-star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Named Graphs can be used in RDF-based knowledge graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A Named Graph resource  identifies a set of triple statements by adding the UPRI of the subgraph and thus the statement as a  fourth element to each triple, turning the triples into quads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, Named Graphs have the  additional benefit to outperform other metadata representation models when conducting more  complex queries (36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In labeled property graphs, on the other hand, assigning a resource for identifying subgraphs  within the overall data graph is straightforward and can be achieved by adding the resource identifier  as the value of a respective property-value pair and add this value pair to all relations and nodes that  belong to the same subgraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  10  Figure 4: A detailed machine-actionable representation of the metadata relating to a weight measurement datum  documented as an RDF ABox graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The representation takes the form of an ABox semantic graph following the RDF syntax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The graph documents a mass measurement process using a balance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It relates an instance of mass measurement assay  (OBI:0000445) with instances of various other classes from different ontologies, specifying who conducted the  measurement, where and when it took place, following which protocol and using which device (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', balance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The graph  furthermore specifies the particular material entity that served as subject and thus as input of the measurement process  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', ‘objectX’), and it specifies the data that is the output of the observation, which is contained in a particular weight  measurement assertion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Organizing the overall data graph into different semantic units and thus semantically meaningful  subgraphs at different levels of representational granularity provides an efficient way of structuring  the graph to allow users to intuitively make statements about statements, and also provides a clear  and straightforward implementation schema that is beneficial for developing relevant search  schemata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Challenge 4: Conceptual gap between RDF/OWL and property graphs  and problems of distinguishing universal, contingent, and assertional  statements  Some knowledge graphs are based on RDF/OWL, others on labeled property graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each technology  has its specific advantages and shortcomings (see table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  WHO?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='INPUT:MATERIALENTITY  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='OUTPUT:DATA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdfs:subClassOf  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='WHERE?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  WHEN?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  FOLLOWINGPROTOCOL?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  USINGWHATDEVICE?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Semantic Units  11  Table 1: Comparison of the advantages and shortcomings of knowledge graphs based on RDF/OWL and on labeled  property graphs (37,38).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  RDF  labeled property graph  query language  SPARQL, W3C recommendation  various, none has a W3C  recommendation  formal semantics and  reasoning  OWL;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' however:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  when mapped to RDF, OWL is usually very  verbose, leading to unnecessarily complex  graphs that are not intuitively  comprehensible for a human reader and  inhibit effective computation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  OWL is not the only mode of inference,  and other frameworks besides Description  Logics exist for inferencing  no unified set of standards (no W3C  recommendation)―a standardized  mapping of OWL to a property graph  is still lacking;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the data model of Neo4j  is not based on a formal set theory or  first-order-logic  relating information  directly to edges  only indirectly through reification, RDF-star, or  named graphs (see Challenge 3)  information can be directly related to  relations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', edges  distinction of universal,  contingent, and assertional  statements  formalized semantic distinction between  assertional and universal statements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  contingent statements are not modelled in OWL  no formalized semantic distinction  One of the major differences between an RDF-based graph and a labeled property graph is that  OWL can be mapped to RDF and thus provides formal semantics and reasoning following a W3C  recommendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' No W3C-recommended standardized mapping exists for property graphs such as  Neo4j so far, although proposals have been made (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', OWLStar, owl2lpg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' OWL is based on  Description Logics, and thus strictly separates universal statements1 in the form of class-specifications  (terminology box;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' TBox) from the domain of discourse in the form of assertional statements2 that  relate instances (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', individuals) to each other (assertion box;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ABox) (38).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Because, in OWL, classes  possess URIs and can thus be referenced, but none of their class axioms do, TBoxes do not belong to  the domain of discourse―within a knowledge graph, it is not possible to refer to a particular axiom of  a given class but only to the class itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Therefore, it is not possible to make statements about class  1 A universal statement is a statement that is true for every instance of a specific universal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Universal statements represent  commonly accepted domain knowledge and specify what is necessarily the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Universal statements are based on all-to-  some relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Definitions of ontology classes and their class axioms are examples of universal statements, but also many  scientific hypotheses and law-like regularities take the form of universal statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  2 An assertional statement is a statement that is true for specific particulars and specifies a fact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Assertional statements are  based on one-to-one relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In a knowledge graph, assertional statements relate particular instances to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Empirical data are examples of assertional statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  12  definitions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', universal statements) in RDF/OWL-based knowledge graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Consequently,  documenting statements such as ‘author A asserts universal law X’ is not straightforward in a  knowledge graph if the universal law X is modelled as a class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  On the other hand, because property graphs typically do not distinguish between ABox and TBox  expressions, it is not always clear what their statements actually mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For instance, the statement  ‘hand has part thumb’ (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 5A) could refer to a particular hand and its thumb, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the right hand of  one of the authors of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' As such, the statement would represent an assertional statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  However, the statement could also refer to some unknown hand in the sense that it states that there  exists at least one hand that has some thumb as its part, which would represent a contingent  statement3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Another possible interpretation of the statement could be that it documents a situation  typically found when dealing with hands: a hand typically possesses a thumb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In this case, the  statement would represent a prototypical statement4, which is a special case of a contingent  statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Finally, the statement could refer to all instances of a class hand (FMA:9712) and represent  a universal statement, indicating that every hand necessarily possesses a thumb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, due  to the lack of formal semantics, labeled property graphs provide no standardized way to distinguish  between universal, contingent, prototypical, and assertional statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Regarding universal statements, from a logical point of view, it makes no sense to relate two  classes such as hand (FMA:9712) and thumb (FMA:24938) to each other via the property hasPart  (BFO:0000051), because classes cannot have other classes as their parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' With few exceptions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  subclassOf (RDFS:subclassOf), type (RDF:type)), object properties model instance-instance and not  class-class or instance-class relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If such object properties are used nevertheless to describe  relationships between classes, this leads to semantic inconsistencies that may not cause issues for  human readers, but for machines such as reasoners they do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In OWL, the universal statement ‘every instance of a hand has some instance of a thumb as its  part’ can be expressed in a semantically proper way using OWL-specific properties, which results in a  complex but semantically precise representation of the statement (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 5B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A human reader, however,  typically does not want to look at this complex representation but prefers the simpler and still  intuitively comprehensible representation provided by a property graph (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 5A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, the OWL-  3 A contingent statement is a statement that is true for some instances of a specific universal and specifies what is possibly  the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Contingent statements are based on some-to-some relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In a knowledge graph, contingent statements are true  for some, but not necessarily every instance of a class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  4 A prototypical statement is a statement that is true for all instances of a specific universal as long as not the contrary is  explicitly stated, and thus specifies what is typically but not necessarily the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  13  based representation involves blank nodes, which makes basic SPARQL querying difficult (38) and has  the potential to cause other issues (39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure  5:  Comparison  of  a  universal statement represented  in a property graph and in OWL  mapped onto RDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The statement  ‘every instance of hand has part  some thumb’ represented in A) a  labeled property graph and B) in  OWL mapped onto RDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Solutions for representing universal statements in a property graph have been suggested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' They  involve annotating edges with logical properties such as existential restriction axioms, resulting in an  object-property mapping (37,38).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A standardized W3C recommendation for a formalism for mapping  OWL into a property graph, however, is still lacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Organizing a knowledge graph into different semantic units, each with its own UPRI and classified  as either universal, contingent, or assertional statement, would not only provide a formal conceptual  framework that facilitates the application of such object-property mappings, but would allow making  statements about universal statements, which would make universal statements accessible to the  domain of discourse, meaning formal class definitions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', class axioms) would become referenceable  so that one could make statements about them within the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Results  Organizing knowledge graphs into semantically meaningful units of  representation  To make knowledge graphs more manageable and provide them with increased levels of structure,  their graph must be organized into several layers of partially overlapping, partially enclosed,  subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Approaches for systematically structuring a knowledge graph into subgraphs have been  proposed before, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', defining a characteristic set as a subgraph consisting of all triples that share the  same resource in the Subject position, yielding significant improvements in space and query  performance (40,41) (see also the related concept of RDF molecules (42,43)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  A) Statement modeled in a labeled property graph  class  instance  hand  haspart  thumb  owlspecific  objectproperty  class  B)OWLstatementmappedontoRDF  owl:restriction  bfo:haspart  rdf: type  owl: on  property  fma:hand  owl:some  rdfs:subclassof-  blank node  fma:thumb  valuesfromSemantic Units  14  However,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' instead of structuring a knowledge graph into subgraphs based on the rather technical  aspects of shared graph-topological properties of its triples,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' we here propose an approach that focuses  on structuring a knowledge graph into identifiable and semantically meaningful sets of triples,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  subgraphs that represent units of representation (short: semantic units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The approach builds on an  idea suggested in the context of semantic data models for structuring descriptions of phenotypes into  smallest semantically meaningful units, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', assertions, each of which is organized in its own Named  Graph (44).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Here, we generalize and extend this idea to the concept of semantic units that can be  accessed, searched, and reused as identifiable and reusable data items in their own right, forming  units of representation that are FAIR Digital Objects that can be implemented using RDF/OWL-based  graphs as well as property graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  A semantic unit is a subgraph of the overall knowledge graph that represents a unit of  information that is semantically meaningful to a human reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Every semantic unit is represented  in the graph by its own resource (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', node) and thus possesses its own UPRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, it can be  classified as an instance of a respective ontology class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In a knowledge graph that is structured into semantic units, two different graph layers are  distinguished: a data graph layer and a semantic-units graph layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The data graph layer contains all  the triples of a knowledge graph that semantic units organize into identifiable subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A knowledge  graph that is not structured into semantic units only possesses a data graph layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The semantic-units  graph layer is added to a knowledge graph with organizing it into semantic units and comprises all the  triples added to the graph due to organizing and structuring it into semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resource of  each semantic unit and their interrelationships are for instance part of the semantic-units graph layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Analogously to this general distinction across the knowledge graph, we can distinguish a data graph  and a semantic-units graph for each semantic unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The data graph of a particular semantic unit  possesses the same UPRI as its semantic unit resource, so that by referring to the UPRI one refers at  the same time to the semantic unit as a resource as well as its corresponding data graph and thus can  make statements about the data graph’s content (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Two basic categories of semantic units and their subcategories can be distinguished: statement  units and compound units (for a classification of semantic units, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  15  Figure 6: Classification of different categories of semantic unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Statement unit  A statement unit is characterized as a unit of information that represents the smallest, independent  proposition (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', statement) that is semantically meaningful for a human reader (see also (44)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For  example, the fact that a population infected with a virus has the quality basic reproduction number  (NCIT:C173777) represents a statement unit that is independent of an actual measurement of the  basic reproduction number, which represents another statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The measurement statement  unit is independent of the quality statement unit because a given population may have more than one  measurement for its basic reproduction number for the same point in time, due to measurement  errors, measurement inaccuracies, or the application of different measurement methods,  instruments, or models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The same applies to all quality measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For instance, the weight  measurement for ObjectX shown in Figure 2 consists of two statement units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' One statement unit  specifies that ObjectX has the quality ‘weight’ (PATO:0000128), whereas the other specifies the  weight’s measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Structuring a knowledge graph into statement units results in a mathematical partition of its data  graph layer, with each triple of the data graph layer belonging to exactly one statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It is  important to note that only the data graph layer is partitioned into smaller data (sub)graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' All the  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Semanticunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Statementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Qualitativestatementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Quantitativestatementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Assertional statementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Contingent statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Prototypical contingent statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Universal statementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Compoundunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Typed statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Qualitymeasurementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Item unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Instance itemunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Class itemunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Text-resource hybrid item unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Itemgroup unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Instanceitemgroupunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Classitemgroupunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Classaxiomitemgroupunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Dataset unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Granularitytreeunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Granular itemgroupunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Context unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='List unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Unordered list unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Set unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Ordered list unitSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='triples added to the knowledge graph for organizing it into semantic units,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the semantic-units  graph layer, are excluded from the partition because otherwise applying semantic units would result  in an infinite regression, since adding a semantic unit always adds triples to the semantic-units graph  layer, which, if included in the partition, would have to be represented themselves via a statement  unit, which would add triples to the semantic-units graph layer again, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Following the predicate-argument-structure from linguistics, the main verb of a statement,  together with its auxiliaries, represents the statement’s predicate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each predicate has a valence that  determines the number and types of arguments it requires to complete its meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Adjuncts can  additionally relate to the predicate, but they are not necessary for completing the predicate’s meaning  and only provide optional information, such as a time specification in a has-part statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Subject  and object phrases are the most frequently occurring arguments and adjuncts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' So, we can say that  each statement unit documents a particular proposition by relating a resource that is the subject  argument of the predicate of the proposition to some literal or to another resource, which is the object  argument or object adjunct of the predicate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The subject argument of a proposition of a statement  unit we call subject and the object argument(s) and object adjunct(s) the object(s) of the statement  unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Every statement unit has one such subject and one or more objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  A has-part statement unit (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 7), for instance, has a subject and one object as an argument,  whereas a weight measurement statement unit has a subject and two objects as arguments, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the  weight value and the weight unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resource representing a statement unit in the graph relates to  its subject via the property *hasSemanticUnitSubject*, which is documented in the semantic-units  graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  If the proposition documented in the data graph is based on a binary relation, and thus a divalent  predicate, such as ‘Lars’ right hand has part Lars’ right thumb’, the corresponding statement unit  typically consists of a single triple, because in RDF, the properties of triples are binary relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  However, many propositions are based on n-ary relations and thus cannot be modelled with a single  triple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For instance, the statements ‘a weight measurement with the value 5 and the unit kilograms’  and ‘Lars’ right hand has part Lars’ right thumb on January 29th 2022’ consist of at least two triples,  whereas the statements ‘Anna gives Bob a book’, ‘Carla travels by train from Paris to Berlin on the  29th of June 2022’, and ‘Dave buys the car from Eric’ each require more than two triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Depending  on the relation of the underlying proposition and thus the valence of its predicate and depending on  the number of optional adjuncts that should be additionally modelled, statement units can thus  consist of one or more triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A specific type of statement unit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', a statement unit class, could thus  be defined in reference to the n-ary property that models its underlying relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Many object  Semantic Units  17  properties of the Basic Formal Ontology 2 are actually ternary relations, as they are time-dependent  (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For instance, ‘b located_in c at t’ requires at least two triples to be modelled in RDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 7: Example of a statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Example  of a semantic unit that models a statement based  on a has-part-of relation between two instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The data graph expressing the statement is shown  in the blue box at the bottom, with ‘Lars’ right  hand’ being the subject argument and ‘Lars’ right  thumb’ the object argument of the statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The semantic-units graph is shown in the peach-  colored box and contains the triples representing  the semantic unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It specifies that the resource representing the statement unit (blue box with borders, here shown with its  dynamic label), which represents the statement in the data graph (indicated by the blue arrow), is an instance of *has-part-  of statement unit* and that ‘Lars’ right hand’ is the subject of this semantic unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The UPRI of *’has-part-of statement unit’*  is also the UPRI of the semantic unit’s data graph (the subgraph in the blue box without border).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In other words, which triples belong to a statement unit must be specified for each type of  underlying predicate on a case-by-case basis by human domain experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, by specifying a  graph pattern for modelling a given proposition into a graph-based representation that in turn  constitutes a statement unit, modelling languages such as LinkML or the Shapes Constraint Language  SHACL (32) can be used, and corresponding tools can be applied for identifying instances of this  pattern and thus instances of the corresponding type of statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, the SHACL shapes  can be utilized to derive dynamic labels for each statement unit when representing them in  visualizations of the knowledge graph in a user interface (UI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Such a label can be generated  dynamically by parsing the label from the statement unit’s subject resource and the labels from all of  its object resources and literals and creating from them a human-readable statement following a pre-  defined template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the template ‘subject travels by A from B to C on the D’, with the input ‘Carla  | train | Paris | Berlin | 29th of June’ would read as ‘Carla travels by train from Paris to Berlin on the  29th of June 2022’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Each statement unit instantiates a respective statement unit ontology class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Characteristic for the  class is the type of relation of the propositions its instances are modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Based on the relation of its  underlying proposition, one can distinguish two subcategories of statement unit (relation-based  criterion):  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Qualitative statement unit: Statement units that document qualitative relations, such as a  has-part relation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=" The argument objects of a qualitative statement unit are always  semantic-units graph  class  instance  dynamic label  Lars'right hand  haspart  rdf:type  has-part statement unit  Lars'right thumb  has semantic  divalent predicate  unit subject  Lars' right hand  bfo:haspart  Lars'rightthumb  subjectargument  data graph  objectargumentSemantic Units  18  resources and not numerical values―only adjunct objects of a qualitative statement unit may  be numerical values." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Quantitative statement unit: Statement units that document quantitative statements, such  as a measurement datum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' At least one argument object of a quantitative statement unit  must be a numerical value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The two categories are exhaustive and disjoint, meaning that any given statement unit is either a  qualitative or a quantitative statement unit, but never both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Within these two subcategories, based  on the underlying relation, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', has part, type, develops from, one can differentiate between further  statement unit classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Additional subtypes of a given relation-based statement unit class, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', has-  part statements about material entities versus has-part statements about information content  entities, do not have to be differentiated as classes, but can be identified and distinguished by simply  querying for the *hasSemanticUnitSubject* relations that instances of a has-part statement unit class  have to their subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Besides this relation-based criterion, there is another criterion for differentiating classes of  statement units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The subject-category-based criterion is based on the category of entity of the  statement unit’s subject, resulting in the distinction of assertional, contingent, and universal  statement units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' These three categories of statement units are exhaustive and disjoint, meaning that  any given statement unit is either an assertional, a contingent, or a universal statement unit, but never  a combination of them (see also Challenge 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Since the relation-based and the subject-category-based  criterion are mutually independent, a given statement unit can, for instance, be a weight  measurement statement unit and an assertional statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Before we discuss the different types of subject-category-based statement units, we first want to  point to a convention we want to introduce, which we apply to semantic units to contribute to closing  the conceptual gap discussed in challenge 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This convention involves the introduction of two new  types of resources in addition to instances, properties, and classes: some-instance and every-instance  resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Based on these two new types of resources, three different types of qualitative statement  units can be distinguished, which model three different types of relations between some-instance,  every-instance, named-individual, and class resources in their data graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  19  Figure 8: Examples for three different types of identification units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A)  Named-individual  identification  unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  This  named-individual  identification unit models in its data graph the class-affiliation of the  instance ‘Lars’ right hand’ (FMA:9712), which is its subject, through the  property type (RDF:type), together with the subject’s label ‘Lars’ right  hand’ through the property label (RDFS:label).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The blue box without  borders shows the data graph that belongs to this named-individual  identification unit (blue box with borders).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Subjects of named-  individual identification units are the type of instances that are also the  subjects of assertional statement units (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' B) Some-instance  identification unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This some-instance identification unit models in its  data graph the class-affiliation of the instance ‘some hand X’  (FMA:9712), which is its subject, through the property *some instance  of*, together with the subject’s label ‘some instance of hand’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The blue  box without borders shows the data graph that belongs to this some-  instance identification unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Subjects of some-instance identification  units are the type of instances that are also the subjects of contingent  statement units (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' C) Every-instance identification unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This  every-instance identification unit models in its data graph the class-  affiliation of the instance ‘every hand’ (FMA:9712), which is its subject,  through the property *every instance of*, together with the subject’s  label ‘every instance of hand’ through the property label (RDFS:label).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The blue box without borders shows the data graph that belongs to this  every-instance  identification  unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Subjects  of  every-instance  identification units are the type of instances that are also the subjects  of universal statement units (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Named-individual identification unit: A qualitative statement unit that identifies a resource  that is the subject of the statement unit to refer to a named individual, together with its label  and its type, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', its class membership (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Some-instance identification unit: A qualitative statement unit that identifies a resource that  is the subject of the statement unit to refer to some unspecified instances of a given class,  together with a label and its class specification (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' When this resource is used in some  other statement unit, it is meant as ‘∃i∈C’ (with i = instance and C = class), reading ‘there exists  an instance i of class C for which holds …’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A some-instance identification unit may,  additionally, also contain information about cardinality restrictions (see Modelling negations,  cardinality restrictions, and disagreement below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A)Named-lndividualldentificationUnit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='named-individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='named-individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars' right hand  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdfs:label  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars' right hand  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fma:hand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:named individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='value  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='B)Some-lnstanceIdentificationUnit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='some-instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Frdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='some-instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='someinstanceof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='somehandx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdfs:label  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='someinstance of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fma:hand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='C)Every-lnstanceIdentificationUnit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='every-instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:typel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='every-instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identificationunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='everyhand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='every instanceof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdfs:label  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='everyinstanceof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fma:handSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Every-instance identification unit: A qualitative statement unit that identifies a resource that  is the subject of the statement unit to refer to every instance of a given class, together with a  label and its class specification (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' When this resource is used in some other statement  unit, it is meant as ‘∀i∈C’ (with i = instance and C = class), reading ‘for every instance i of class  C holds’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Assertional statement unit  An assertional statement unit is a statement unit that has a named individual as its subject-resource  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', ‘Lars’ right hand’ (FMA:9712) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8A), and thus an instance that is known to the knowledge  graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, its subject is also the subject of a named-individual identification unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If the  assertional statement unit possesses an object that is a resource and not a literal, that object also  refers to a named individual, resulting in a one-to-one relation (or many such relations in case of an n-  ary proposition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An assertional statement unit is thus an ABox representation of a relation with at  least one particular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  As a semantic unit, a particular assertional statement unit refers to a subgraph of a knowledge  graph that models a particular assertion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An assertion is a proposition about a particular (the subject)  and thus about an individual and not a universal, and this proposition is meant to be either true or  false (46,47).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In a knowledge graph, a particular assertional statement unit is modelled by a resource  that represents the unit’s data graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This data graph is thus an instance-based subgraph of the  knowledge graph and represents an ABox expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The unit resource is an instance of both the  respective type of statement unit and of *assertional statement unit* (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Contingent statement unit  A contingent statement unit is a statement unit that refers to some instances of a specific class as its  subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, its subject is also the subject of a some-instance identification unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If the  contingent statement unit possesses an object that is a resource, that object also refers to some  instances of a specific class, resulting in a some-to-some relation (or many such relations in case of an  n-ary proposition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, if you want to state that some but not necessarily all hands possess  a thumb, and you do not want to or simply cannot list all the individual hands to which this applies,  you make such a contingent statement unit (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Contingent statements are propositions that are true for some instances of a specific universal,  but not necessarily for every instance (46–48).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' They are frequently used when expressing prototypical  relationships, such as that a human’s hand usually has a thumb as its part, and thus statements about  universals that are assumed to be at least typically true in specific contexts, but not necessarily so―a  Semantic Units  21  hand is still a hand, even if it has no thumb5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Other examples are statements about the relationships  between diseases and their symptoms or drugs and their effects, which are often expressed in  reference to some probability evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' These prototypical contingent statements can be  documented in prototypical contingent statement units, which form a subcategory of contingent  statement units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Description Logics and thus also OWL does not provide the means to state what is typically true,  and other logical formalisms that are capable of expressing prototypical knowledge are needed to  provide a semantics for such statements (47).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In a knowledge graph, a particular contingent statement unit can be modelled as a statement  unit, with its resource representing the corresponding data graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resource is an instance of both  the respective type of statement unit and of *contingent statement unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Its subject and, if present,  also its object is modelled as a resource that relates to its class through a *some instance of* property  in corresponding some-instance identification units (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Probability values expressing an assumed  value of the frequency of instances for which the statement is true can be documented using  additional triples, forming in turn an assertional statement unit in its own right, which would have the  contingent statement unit’s resource as its subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  5 Therefore, the example given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9C is a statement that human anatomists would not make.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' They would define a  human hand in reference to other properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  22  Figure 9: Three subcategories of statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A)  Assertional statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An example of a  statement unit that is an *assertional statement  unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It models a has-part relation between two  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The data graph expressing this relation is  shown in the blue box without borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It is an  instance-based data graph and forms an ABox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  subject of this assertional statement unit is an  instance resource that is also the subject of a  named-individual identification unit (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  resource representing this data graph, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the  assertional statement unit resource (blue box with  borders, here shown with its dynamic label), is an  instance of *has-part statement unit* and of  assertional statement unit*, which is represented  in the semantic-units graph above the blue box  without borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' B) Contingent statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An  example of a statement unit that is a *contingent  statement unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It models a has-part relation that  exists between some but not necessarily every  instance of ‘hand’ (FMA:9712) and some but not  necessarily every instance of ‘thumb’ (FMA:24938).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The data graph expressing this relation is shown in  the blue box without borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The subject of this  contingent statement unit is an instance resource  that is also the subject of a some-instance  identification unit (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resource  representing this data graph, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the contingent  statement unit resource (blue box with borders,  here shown with its dynamic label), is an instance of  has-part statement unit* and of *contingent  statement unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' C) Universal statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An  example of a statement unit that is a *universal statement unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It models a has-part relation that exists between every  instance of ‘hand’ (FMA:9712) and some, but not necessarily every instance of ‘thumb’ (FMA:24938).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The data graph  expressing this relation is shown in the blue box without borders and can, in principle, be translated into OWL to form a  TBox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The subject of this universal statement unit is an instance resource that is also the subject of an every-instance  identification unit (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resource representing this data graph, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the universal statement unit resource (blue  box with borders, here shown with its dynamic label), is an instance of *has-part statement unit* and of *universal statement  unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' D) Conventional OWL model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The example from C) translated into an OWL class-axiom expression mapped to RDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="  A)AssertionalStatementUnit  Lars'right hand  rdf:type  has-part statement unit  has part  Lars'rightthumb  rdf:type  hassemantic  assertionalstatementunit  unit subject  Lars' right hand  bfo:haspart  Lars'rightthumb  class  instance  B)Contingent Statement Unit  some hand  haspart  rdf:type  has-part statement unit  somethumb  rdf:type," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='contingent statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='somehand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='somethumb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='C)UniversalStatementUnit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='everyhand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has-partstatement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='somethumb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='universal statementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='every hand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='somethumb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='D)ConventionalOwWLmodel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:restriction  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='[bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf: type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='property  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fma:hand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:subclass  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='blanknode  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:some  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fma:thumb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='valuesfromSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Universal statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A universal statement unit is a statement unit that refers to every instance of a specific class as its  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, its subject is also the subject of an every-instance identification unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If the  universal statement unit possesses an object that is a resource, the object refers to some instances of  a specific class, resulting in an all-to-some relation (or many such relations in case of an n-ary  proposition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If you want to state that every instance of hand (FMA:9712) necessarily hasPart  (BFO:0000051) some thumb (FMA:24938), you make a universal statement (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Universal  statements represent commonly accepted domain knowledge that take the form of, for instance,  definitions of terms, expressed as class axioms, or of hypotheses about law-like causal relationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  As a semantic unit, a particular universal statement unit refers to a data graph within a knowledge  graph that represents a particular universal statement and thus a proposition that is true for all  instances of a specific universal (46,47).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In a knowledge graph, a particular universal statement unit is  modelled as a statement unit by a resource that represents the corresponding data graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  resource is an instance of both the respective type of statement unit and of *universal statement unit*  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Its subject is modelled as a resource that relates to its class through an *every instance of*  property in a corresponding every-instance identification unit (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8C), whereas its resource objects,  if present, are modelled as resources that relate to their class through the *some instance of* property  in a corresponding some-instance identification unit (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  When compared to the OWL modelling of universal statements, which is rooted in Description  Logics (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9D), the data graph belonging to a universal statement unit as a semantic unit is  less complex and does not include any blank nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This improves its querying properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover,  the statement unit’s resource can be used to make statements about a universal statement, making  universal statements and thus also particular class axioms available to the general domain of discourse  (see Challenge 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, because no reasoner yet exists for directly reasoning with this semantic-  units-based notation, to be able to do reasoning over these statements, they will have to be translated  into an OWL-based notation, forming a classical TBox expression (see Logical semantics of semantic  units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Compound unit  Compound units are semantic units that organize the set of all statement units of a given knowledge  graph into larger but still semantically meaningful data graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Technically, a compound unit is a  container of resources of particular semantic units and thus specifies a collection of associated  semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Merging the data graphs of its associated semantic units constitutes the data graph of  Semantic Units  24  the compound unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Analog to statement units, each compound unit is a semantic unit that is  represented in the graph by its own node, possesses its own UPRI, and instantiates a corresponding  compound unit ontology class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In the semantic-units graph of a compound unit, the relation between the resource representing  the compound unit and the resources representing its associated semantic units is documented via  the property *hasAssociatedSemanticUnit* (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The following subcategories of compound unit  can be distinguished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 10: Example of a compound unit that comprises  several statement units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Compound units possess only  indirectly a data graph, through merging the data graphs  of their associated statement units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The compound unit  resource (here, *’Lars’ right hand item unit’*), however,  stands for these merged data graphs (indicated by the  blue arrow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Compound units possess a semantic-units  graph (shown in the peach-colored box), which  documents the semantic units that are associated with it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Typed statement unit  In order to be readable for a human being, the URIs of the subject, predicate, and objects of a  statement unit must be translated to their respective labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The dynamic label of a statement unit  does exactly that, in a structured way, representing the statement itself in a human-readable plain  English sentence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The information contained in a dynamic label, however, goes beyond the  information contained in the statement itself, because it includes information from the identification  units associated with the statement’s subject and its object resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Since identification units can  be edited independently of the statement units that use their resources as subjects and objects, when  referring to a human-readable statement, one is actually referring to the corresponding statement  unit and the identification units of its subject and all of its objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This collection of semantic units is  a typed statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A typed statement unit is a compound unit that comprises the following  statement units (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 11):  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A statement unit that is not an instance of one of the three types of identification units (see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This statement unit functions then as the reference statement unit of the typed  statement unit, and its subject is also the subject of the typed statement unit to which it  relates via the property *hasSemanticUnitSubject*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="  semantic-unitsgraph  class  instance  Lars'righthanditemunit  rdf:type  materialentityitemunit  hasassociated  semantic unit  Lars'righthandhaspartLars'rightthumb  has associated  semantic unit  hassemantic  unit subject  Lars'right handhaspartLars'right index finger  hasassociated  semantic unit  Lars'right hand ispart of Lars'right forearm  Lars'right hand  subjectargumentSemantic Units  25  2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The identification units that model the class-affiliations of all the resources that are  referenced in the data graph of the reference statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 11: Typed statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An example of  a typed statement unit, with the data graph  shown in the large blue box without borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  This graph results from merging the subgraphs  of three statement units: the *‘part-of  assertional statement unit’* from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9A, which  is the reference statement unit of this *‘typed  part-of statement unit’*, with its data graph  shown in the grey box without borders, and two  instances of *named-individual identification  unit*, with their data graphs in the light-blue  box  without  borders  (the  resources  representing the different data graphs are  shown in correspondingly colored boxes with borders and dynamic labels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Typed statement units are important because they contain class-affiliation and label information  that human readers usually require for understanding the proposition of the reference statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Since the resource representing a typed statement unit is related to its reference statement unit and  all its identification units through the property *hasAssociatedSemanticUnit*, different types of typed  statement units can be identified by simply querying these relationships, eliminating the need to  further differentiate the class of typed statement units into subclasses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Quality measurement unit  A quality measurement unit has one qualitative typed statement unit and one or more quantitative  typed statement units associated via the property *hasAssociatedSemanticUnit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The reference  statement unit of its qualitative typed statement unit specifies a quality of a given entity, whereas the  statement unit of each of its quantitative typed statement units specifies a measurement of this  quality, comprising a value and a unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A quality measurement unit is thus a collection of typed  statement units that describe a specific quality of a given entity together with all quantitative  evaluations or measurements of it currently present in the data graph (the graph shown in Figure 2  corresponds with a typical data graph of a quality measurement unit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  For example,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the basic reproduction number of a given population at a given time can be  documented in such a quality measurement unit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' which would comprise the typed qualitative  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statement unit that links the population with the quality basic reproduction number (NCIT:C173777)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='typed statementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has-part  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='assertional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars'righthand  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='named-individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars'right thumb  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='typed statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hasassociated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hasassociated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='semanticunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='semanticunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hasassociated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='semantic unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars'right hand  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars'right hand  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars'rightthumb  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='named-individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='named-individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars'rightthumb  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identificationunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars'right hand  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="Lars'rightthumb  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fma:hand  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fma:thumbSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='and one or more typed quantitative statement units,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' each of which documents a measurement of this  reproduction number,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' maybe based on different methods and algorithms for its estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The basic reproduction number measurement statement unit takes the object resource of the  quality statement unit and links the quality statement unit to the basic reproduction number  measurement statement unit via the *objectDescribedBySemanticUnit* property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The quality  statement unit in its turn has taken the subject of the quality measurement unit it is associated with  as its subject and is linked to the respective quality measurement unit via the property  hasAssociatedSemanticUnit*, as is the basic reproduction number measurement statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The subject of the quality statement unit is also the subject of the quality measurement unit, and  the resource representing a quality measurement unit in the semantic-units graph relates to this  resource via the property *hasSemanticUnitSubject*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Because the resource representing a quality measurement unit in the semantic-units graph is  related to its associated typed statement units and their reference statement units through the  property *hasAssociatedSemanticUnit*, different types of quality measurement units can be  identified by simply querying these relationships, eliminating the need to further differentiate the  class of quality measurement units into subclasses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Item unit  An item unit comprises all statement units, typed statement units, and all quality measurement units  that share the same subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The corresponding resource is then also the subject of the item unit, and  the resource representing an item unit in the semantic-units graph relates to its subject via the  property *hasSemanticUnitSubject*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An item unit is thus a collection of semantically related  statement units, typed statement units, and quality measurement units that all contain information  about the same entity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Conceptually, item units relate to the graph-per-resource data management  pattern (49) or to the abovementioned characteristic set or RDF molecule, but applying its idea to  statement units instead of triples, similar to Item in the Wikibase data model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The information contained in an item unit is well suited to be presented on the same page in a  UI, as the statement units, typed statement units, and quality measurement units belonging to it  describe the same entity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', their shared subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The following subcategories of item unit can be  distinguished:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Instance item unit: An item unit that has a named individual resource as its subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Consequently, it consists exclusively of all assertional statement units present in the semantic-  units graph layer of the knowledge graph that share the same subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Its subject is also  Semantic Units  27  necessarily the subject of a named-individual identification unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, all statements  about a particular infected population, such as the population’s location, its qualities, various  measurements about it, including basic reproduction number and case fatality rate, as well as  the time period to which the information about the population refers, all are typed statement  units and quality measurement units that share the same subject, which is a named individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Together, they therefore constitute an instance item unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The information contained in an  instance item unit can be presented in the same UI page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Another example is the description  of the anatomy of a particular specimen, where one could organize all typed statement units  and quality measurement units describing a particular part of the specimen in an instance  item unit, resulting in several such instance item units―one for each described part of the  specimen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Class item unit: An item unit that has a some-instance or an every-instance resource of a  specific class as its subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Consequently, it consists exclusively of all universal and all  contingent statement units present in the semantic-units graph layer of a knowledge graph  that share the same subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Simple star-shaped class axioms such as the one shown in Figure  12 can be organized in such a class item unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 12: Class item unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An  example of a class item unit (blue  box with borders), with its data  graph shown in the blue box  without borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The data graph  results from merging the data  graphs of four universal statement  units that have *‘every antenna  type 1’* as their semantic unit  subject,  together  with  their  corresponding identification units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  For reasons of clarity of presentation, resources and relations of associated semantic units not shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Text-resource hybrid item unit: Text-resource hybrid item units are used when a resource  needs to be described and one does not want to or cannot describe it properly in a formalized  machine-actionable semantic way using triple statements and proper terms from ontologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  For instance, in a crowdsourced knowledge graph, when a user wants to describe a specific  research objective or the main contribution of a research paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This user is a domain expert,  but most likely with only limited knowledge about semantics, if at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In such a case,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' it might  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='be best to specify the research objective or main contribution as a resource that is an instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='antennatype1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class item unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='itemunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bspo:in lateral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='sideof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='everyantenna  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:partof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='some head X  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='someinstanceof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='uberon:head  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='type1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='somesegement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='uberon:segement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='everyinstance of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='of antennaY  "' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='someinstanceof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='ofantenna  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:partof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='antennatype1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='some multicellular  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='uberon:multicellular  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='someinstanceof-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='organismD  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='organismSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='or subclass of,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', objective specification (IAO:0000005), and provide a textual description  for it, instead of describing it formally using triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The textual description can either be  documented as the resource’s description through a respective annotation property with a  string as its value or, in Neo4j, as a value node that denotes (IAO:0000219) the resource.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In a  knowledge graph application, this textual description can then be automatically annotated  semantically by recognizing mentioned entities that are known to the knowledge graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' These  recognized entity resources can be connected to the ‘objective specification’ resource via the  relation mentions (IAO:0000142).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resulting set of triples forms a data graph representing  a text-resource hybrid item unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Text-resource hybrid item units provide human-readable  information in a textual description that can also be leveraged to some extent by machines  via the mentions relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Item group unit  An item group unit consists of at least two item units (or an item unit and a typed statement unit that  does not share the same subject) that are semantically related to one another through statement units  that relate their subjects in the following way:  IF  resourceX = subject of itemUnit1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  resourceX = subject of statementUnit1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  resourceY = object of statementUnit1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  resourceY = subject of itemUnit2  THEN  statementUnit1 semantically connects itemUnit1 and itemUnit2 to constitute an item  group unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  We refer to statement units that link two item units in the way here described as item links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In  the semantic-units graph layer, this is indicated by relating the resource of itemUnit1 to that of  itemUnit2 via the property *hasLinkedSemanticUnit* and the linking statement unit to itemUnit2 via  the property *objectDescribedBySemanticUnit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' While each individual item link has a specific direction  in which it links two item units, two item units can be linked through more than one item link, the  directions of which can be opposite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, when describing a family with all its members, the  item unit describing the father links to that of the daughter as his daughter, whereas the item unit  describing the daughter links to that of the father as her father.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Consequently, there is no generally  applicable rule for identifying a specific resource as the subject of an item group unit, and thus no  subject is specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  29  In addition to item units, item group units may also consist of individual statement units, typed  statement units, and quality measurement units that are not part of any specific item unit, because  no other statement unit shares the same subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In most of the cases, item group units will contain all data about the same object, with some of  its item units containing data related to the parts or specific aspects of this object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, all  data about a particular scholarly publication can be understood to represent the outcome of a  research activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' All data relating to that research activity can be organized and represented by a  single item group unit, with its item units containing statement units that describe specific parts of  that activity, such as smaller research steps, methods that have been applied, materials, instruments,  and research agents that have been involved in that research activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  With the information from each item unit being presented in the UI in its own page, item group  units can be accessed by a human reader in the UI as a set of linked pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  One can differentiate item group units into instance item group units, class item group units, and  class axiom item group units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An instance item group unit has only semantic units associated, whose  subjects refer to named individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A class item group unit, on the other hand, has only semantic  units associated whose subjects refer to some-instance or every-instance resources of a specific class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The semantic units associated with a class item group unit give a formal description of a specific class,  which in turn is the subject of the class item group unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If the subject of the class item group unit is  also the subject of an every-instance identification unit, it is a class axiom item group unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Class axiom  item group units are formalized class descriptions that cannot be expressed with a single class item  unit because they include chains of relations and thus comprise universal and contingent statement  units that do not share the same subject, and thus must be modelled as item group units (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  As already discussed above, in Description Logics and thus in OWL, universal statements are  modelled in a TBox which, when mapped onto RDF, includes the use of blank nodes (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The use of such blank nodes, which function like anonymous resources in triples (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', an instance of  anonymous individual (OWL:AnonymousIndividual) in OWL2), is problematic in many contexts, mainly  because every entity and property represented in a TBox as an anonymous resource cannot be  identified and referenced outside the respective class axiom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This results in substantial practical  consequences that significantly affect the overall usability of TBox expressions for modelling empirical  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The consequences impact the findability, accessibility, explorability, comparability,  expandability, reusability, and overall machine-actionability of any expression modelled as a TBox,  which is why empirical data should be preferably modelled as ABox expressions (for a detailed  discussion see (30)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In the context of modelling class axioms, the blank nodes cause problems when  Semantic Units  30  several triples should refer to the same blank node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The Description Logics upon which OWL is based  uses a form of tree-model property that restricts OWL axioms to have a tree-shaped structure, so you  frequently run into difficulties when describing class axioms that involve triangular relationships when  using OWL (50).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 13: Class axiom item group unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An example of a class axiom item group unit (blue box with borders), with its data  graph shown in the blue box without borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The data graph results from merging the data graphs of several universal  statement units and their corresponding identification units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The statements cannot be modelled in a single class item unit,  because they do not all share the same subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Contrary to OWL, this notation allows describing triangular relations as the  one shown here in red, indicating that every instance of *antenna type 1* is longer than any eye that is part of the same  organism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For reasons of clarity of presentation, resources and relations of associated semantic units not shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  For instance, if you want to formally describe a specific type of antenna that is longer than the  eyes of its organism, you can try to model a respective *antenna* class in Manchester Syntax (51) with  the following expression:  ‘has part some ((antenna part of some multicellular organism) and has quality some  (length and increased in magnitude relative to some (length and inheres in some (eye  part of some multicellular organism))))’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  However, because the two mentions of ‘some multicellular organism’ are anonymous, the  expression does not capture the intended meaning that this should refer to the same multicellular  organism, as according to it, to be an instance of the class, an antenna needs to merely be longer than  at least one eye of some multicellular organism in the world, not necessarily an eye possessed by the  same organism that possesses the antenna (52).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Because universal statement units do not use blank  nodes, different statements can refer to the same resource ‘some multicellular organism D’ and thus  do not run into this restriction of OWL (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 13, triangular relationship shown in red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='antennatype1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="rdf:type'  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='classitemgroup unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class itemgroupunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bspo:inlateral  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='relativetoSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Granularity tree unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Since each statement unit is represented in a knowledge graph by its own resource (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', node) and  instantiates a corresponding statement unit ontology class that is characterized by the type of relation  that underlies the propositions its instances are modelling, we can add further information to that  class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We can, for instance, identify types of statement units that depend on partial order relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A  partial order relation is a binary relation p that is transitive (if A has relation p to B and B has relation  p to C, then A has relation p to C), reflexive (A has relation p to itself), and asymmetric (if A has relation  p to B and B has relation p to A, then A and B are identical).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Examples of such partial order relations  are the class-subclass relations that can be found in universal statements, or parthood relations found  in assertional statements, but many more partial order relations exist, including sequential relations  such as before (RO:0002083) that identify timelines in a knowledge graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Partial order relations can give rise to granular partitions that form granularity trees (53–55) and  can be used to define granularity perspectives (56–58).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Granularity perspectives identify specific  types of semantically meaningful tree-like subgraphs within the data graph layer of a knowledge graph  and can be employed for supporting the exploration of the knowledge graph in a way somewhat  orthogonally to statement, item, and item group units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' By identifying classes of statement units that  potentially relate to granularity perspectives, because their characteristic relations are partial order  relations, applications can utilize this information for automatically identifying corresponding types of  granularity trees within the knowledge graph and make them accessible for the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Due to the nested structure of a granularity tree and its implicit directionality from root to leaves,  one can specify the subject of a granularity tree unit to be the subject of the statement units that  share their objects with the subjects but not their subject with the objects of other statement units  belonging to that granularity tree unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resource representing a granularity tree unit in the  semantic-units graph relates to its subject via the property *hasSemanticUnitSubject*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Characteristic of granularity tree units is that their statement units are always instantiating the  same statement unit class (because the class is characterized in reference to the underlying partial  ordering relation) and subjects and objects are always resources of the same basic type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' To make them  not only machine-actionable but also better comprehensible for humans, granularity tree units  comprise the typed statement units that correspond with the statement units that form the  granularity tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Because the resource representing a granularity tree unit in the semantic-units graph is related  to its associated statement units through the property *hasAssociatedSemanticUnit*,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' different  granularity perspectives can be identified and distinguished by simply querying these relationships  Semantic Units  32  and the *hasSemanticUnitSubject* relationship to the subject of the granularity tree unit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' eliminating  the need to further differentiate the class of granularity tree units into subclasses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Granularity perspectives derived from specific types of statement units thus provide another  means for structuring and organizing the overall data graph into semantically meaningful smaller data  graphs, and thus provide another category of compound unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Examples for such granularity  perspectives are tree-like hierarchies of has-part relations, for instance between various anatomical  structures in an organism, or the temporal sequence of events of a particular process, developmental  dependency chains, or more general cause-effect-relation chains, and taxonomies of concepts based  on class-subclass relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Granular item group unit  A granular item group unit comprises all statement units, quality measurement units, and item units  whose subjects are part of the same granularity tree unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The subject of the granularity tree unit is  then also the subject of the granular item group unit, and the resource representing a granular item  group  unit  in  the  semantic-units  graph  relates  to  its  subject  via  the  property  hasSemanticUnitSubject*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  A granularity tree provides a nested hierarchical organization of related resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If these  resources are subjects of item units, the corresponding item units can be organized according to the  hierarchy provided by the granularity tree, thus organizing several item units in a nested hierarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  This additional organization and structuring of the data graph layer can be utilized by a knowledge  graph application to improve the explorability of its overall data graph for users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Granularity tree units  can thus provide additional organizational structure for item group units by organizing their item units  into granular item group units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This becomes particularly important when the knowledge graph is  highly connected, and its item group units are therefore very large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Because the resource representing a granular item group unit in the semantic-units graph is  related to its associated semantic units through the property *hasAssociatedSemanticUnit*, different  types of granular item group units can be identified by simply querying these relationships and the  hasSemanticUnitSubject* relation to their respective subjects, eliminating the need to further  differentiate the class of granular item group units into subclasses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Context unit  A context unit comprises all semantic units for which merging of their data graphs forms a connected  graph with no resource or triple being separated from the other resources or triples, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' any two  Semantic Units  33  resources in the data graph of the context unit are connected via a series of triple statements that also  belong to the data graph of the context unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The only exception to this rule are triples that have  isAbout (IAO:0000136) as their property and which thus belong to an is-about statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  property isAbout relates an information artifact to an entity that the artifact contains information  about.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It thus always marks a change of frame of reference from the discursive layer to the ontological  layer by having a semantic unit resource as its subject and some other non-semantic unit resource  from the data graph as its object (for discussion of layers, see Statements about statements and  documenting ontological, diagnostic, and discursive information in knowledge graphs using semantic  units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, is-about statement units relate resources from the semantic-units graph with  resources from the data graph of a knowledge graph and can be used as an index for where in the  graph a change of frame of reference occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, when documenting a research activity  with its in- and output and the output being a dataset containing the description of the anatomy of a  multicellular organism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The graph will contain the statement *‘description item unit’* isAbout  ‘multicellular organism’ (UBERON:0000468), which points to a change of frame of reference from the  result of the research activity in the form of a description and the multicellular organism it is  describing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In short, it indicates a change from the research-activity reference frame to the research-  subject reference frame (see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 14 further below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Therefore, an is-about statement unit always  indicates the border between the data graphs belonging to two different context units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Similar to item  group units, due to the lack of a generally applicable rule for identifying a specific resource as the  subject of an item group unit, no subject is specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Dataset unit  A dataset unit is a defined and ordered collection of particular semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This collection can be  homogeneous, comprising only semantic units of the same type, but can also be compilations of  statement units and compound units of various kinds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Like any other semantic unit, each dataset unit  is represented in the semantic-units graph with its own node and its own UPRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Dataset units can be used in various ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For instance, for compiling all data contributed by a  specific institution within a collaborative project or for documenting the state of a given object in a  given time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Also, the results of a particular search query can be stored and made accessible as a dataset  unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Users of knowledge graphs can specify particular dataset units for their own use and use the  unit’s UPRI as an identifier to reference it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In addition to such obvious uses of datasets as collections of particular semantic units,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' dataset  units can also be used for managing statements about statements: If users want to point out that a  particular measurement datum (assertion statement unit A) from one publication (item group unit X)  Semantic Units  34  supports or directly contradicts a causal theory (universal statement unit B) from another publication  (item group unit Y),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' they could create a respective assertion statement unit C that relates the  statement unit A as supporting statement unit B and could create a dataset consisting of these three  statement units A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' without including X and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Whereas this might not be communicated as a  dataset in the UI, technically it could be structured, stored, and managed as a dataset unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  List unit  Sometimes, you need to make a statement about a specific list of particular resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' To do so, such  a list can be modelled as a specific type of compound unit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', a list unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' List units can be utilized the  same way as the other types of semantic units: each list unit is a semantic unit that is represented in  the semantic-units graph by its own node, possesses its own UPRI, and instantiates a corresponding  list unit ontology class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  We distinguish unordered list units from ordered list units, with the latter having the resources  organized in a specific order, for instance the authors of a scholarly publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A set unit, on the  other hand, is an unordered list unit in which every resource is listed only once (uniqueness  restriction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Technically, a list unit is a collection of membership statement units, each of which specifies one  of the resources belonging to the list by connecting the UPRI of the list unit through a *child* relation  to the respective resource.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In case of an ordered list unit, each membership statement unit has to be  indexed first (by connecting the UPRI of the membership statement unit through a data property index  (RDF:index) to a consecutive integer value, starting with 0), resulting in an indexed membership  compound unit, which is then associated with the list unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  List units can be used as arrays and may include cardinality restrictions and thus describe a closed  collection of entities, making a localized closed-world assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Discussion  Metadata and Semantic Units as FAIR Digital Objects  The concept of a FAIR Digital Object has been suggested by the European Commission Expert Group  on FAIR Data as central to the realization of FAIR (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' FAIR Digital Objects must be accompanied by  persistent identifiers, metadata, and contextual documentation to enable their reliable discovery,  citation, and reuse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Data belonging to a FAIR Digital Object should be stored in a common and ideally  Semantic Units  35  open file format and be richly documented using metadata standards and well-established  vocabularies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  FAIR Digital Objects also represent the core concept in the interoperability framework of the  European Open Science Cloud (EOSC) as atomic entities for a FAIR ecosystem by providing the  metadata needed for achieving five layers of interoperability: 1) Information Technology (IT) systems  must work with other IT systems in implementation or access without any restrictions or with  controlled access for technical interoperability;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 2) common data formats and communication  protocols for syntactic interoperability;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 3) contextual semantics related to common semantic  resources for semantic interoperability;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 4) contextual processes related to common process resources  for organizational interoperability;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and 5) contextual licenses related to common license resources for  legal interoperability (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Respective metadata can itself form FAIR Digital Objects that can be linked  using their persistent identifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Consequently, FAIR Digital Objects can exist at different levels of  granularity, and coarser level FAIR Digital Objects may consist of several finer level FAIR Digital Objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The concept of a semantic unit can be adapted to that of FAIR Digital Objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each semantic unit  possesses its own UPRI and thus already provides the required persistent identifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Further, they can  be accessed and searched using common protocols such as SPARQL and CYPHER implemented in web  interfaces using HTML, with RDF, JSON, and other formats as well-supported data export formats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If a  knowledge graph uses well-established controlled vocabularies and ontology terms and organizes its  data and metadata following established graph-patterns using tools such as SHACL (32), ShEx (59,60),  or OTTR (61,62), all data in the data graphs of semantic units will be semantically interoperable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Additionally, each semantic unit can have its own copyright license assigned, which can either be  provided automatically by the knowledge graph application or individually by the creator of a  particular semantic unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Through additional triples, relevant provenance data can be tracked about each particular  semantic unit in the form of either corresponding property-value pairs (property graph) or through an  additional provenance Named Graph (RDF/OWL) using well-established provenance vocabularies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  provenance metadata of a semantic unit can cover, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', creator, creation date, creation application,  title of the semantic unit, all contributing users, and last-updated date and are restricted to  provenance data about the semantic unit itself—they do not refer to the original process of data  production and thus the provenance of the data contents of this unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Additionally, if the knowledge graph application makes a distinction between published and  unpublished data, publication metadata can be tracked separately, covering the date the semantic  unit has been published together with its creator and the list of its contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  36  Access control metadata specifies any copyright licenses as well as, in case the knowledge graph  application differentiates between different groups or roles of users, a specification of who is allowed  to access the semantic unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  With respect to the FAIRness of data, it is also advisable to provide modelling metadata, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  information about which data schema or graph pattern has been used for modelling the data in the  unit’s data graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each instance of a given semantic unit class should ideally apply the same graph  pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For this purpose, it would be good to have schemata and patterns, each with its own UPRI,  stored in some open repository or having the schemata and patterns be documented in the  corresponding semantic unit ontology class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Provenance metadata referring to the process of data production (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 4) can be  documented in the form of metadata statement units and metadata item and item group units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  provenance of the data production is usually more detailed and complex than the unit’s own  provenance and must be documented as semantic units and thus FAIR Digital Objects in their own  right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Implementation  Semantic Units, Nanopublications, and Micropublications  The concept of assertional statement units as FAIR Digital Objects is very similar to that of  nanopublications—especially, when implementing them in RDF/OWL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Nanopublications are RDF  graphs that represent the smallest units of publishable information extracted from literature and  enriched with provenance and attribution information (63–66).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' They utilize Named Graphs and  Semantic Web technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each nanopublication models a particular assertion, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', a scientific  claim, in machine-readable format and semantics and is accessible and citable through a unique  identifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Nanopublications are used to facilitate the discovery, exploration, and re-use of scholarly  assertions (66).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, embedded in a decentralized network of services that employ semantic  templates, nanopublications can also be used by users to directly publish small Linked Data statements  as nanopublications (65).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Each nanopublication is organized into four Named Graphs:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the head Named Graph, connecting the other three Named Graphs to the  nanopublication’s unique identifier;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the assertion Named Graph, containing the assertion modelled as a graph;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  37  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the provenance Named Graph, containing metadata about the assertion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the publicationInfo Named Graph, containing metadata about the nanopublication itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Nanopublications are a natural fit for representing and publishing assertional statement units,  with the assertion Named Graph closely corresponding to the data graph and the head Named graph  to the semantic-units graph of an assertional statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Triples in the provenance Named Graph  can potentially link to other semantic units and thus other nanopublications that contain detailed  metadata descriptions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', a graph as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Nanopublications are also suited for publishing  the other types of statement units following the same schema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The compound units, on the other  hand, correspond to annotated sets of nanopublications, where these sets can either be defined  statically (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', as nanopublication indexes  (67)) or dynamically (by specifying a query on the  knowledge graph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  By using dataset units, several such semantic unit nanopublications can be combined to form a  micropublication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Micropublications (68) represent scientific arguments, in which a specific assertion  represents a claim and additional assertions provide supporting or contradicting scientific evidence in  the form of data and its accompanying metadata as well as information about attribution, supporting  and contradicting references, links to empirical data and figures, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Further assertions can be added,  pointing to relations to other claims made by other scientific arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This way, micropublications  relate scientific claims in the form of nanopublications to all relevant information to turn the claim  into a scientific argument (*scientific argument* could constitute a specific type of dataset unit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Structuring a knowledge graph into interrelated semantic units using the Nanopublications-  schema  As a first step for structuring a knowledge graph into interrelated data graphs, each of which is  organized as a particular semantic unit, a primary layer of abstraction above the level of triples must  be created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This is achieved by partitioning the knowledge graph into a set of statement units, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', a  mapping of triples to statement units, where each triple belongs to exactly one data graph of a  statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  When implementing this in RDF/OWL, statement units can be modelled as nanopublications (see  above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In Neo4j, as it is a property graph, to identify all triples belonging to the same statement unit,  one has to add a ‘statement_unit_URI:upri’ property-value pair to each of its nodes and relations, with  the statement unit’s UPRI as the value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Based on this primary abstraction layer of statement units, a secondary abstraction layer of  compound units can be organized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each compound unit is specified as a collection of two or more  Semantic Units  38  semantic units (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', statement units and other compound units) by relating the compound unit’s UPRI  to the UPRIs of its associated semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In RDF/OWL, this can be implemented by using the  compound unit’s semantic-units graph as the head Named Graph of a corresponding nanopublication,  while leaving the nanopublication’s assertion Named Graph empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The head Named Graph thus  specifies all basic and compound units that are associated with this compound unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In contrast, in  Neo4j, the nodes and relations of all triples belonging to a compound unit possess a  ‘compound_unit_URI:upri’ property-value pair with the compound unit’s UPRI as their value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Since a  given statement unit can be associated with more than one compound unit, its ‘compound_unit_URI’  property can have an array of UPRIs of different semantic units as its value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Modularity results in increased flexibility of data management  “Because human thoughts are combinatorial (simple parts combine) and recursive (parts can be  embedded within parts), breathtaking expanses of knowledge can be explored with a finite  inventory of mental tools.” ((69), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='360).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Just like human thought, structuring a knowledge graph into separate but recursive subgraphs, each  of which belongs to a particular semantic unit that, in turn, is classified into different semantic unit  classes, organizes the knowledge graph into structured modules that can be (recursively) combined  and that encapsulate complexity into manageable units which significantly increases the graph’s  expressivity and the flexibility of data management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' By allowing the specification of relations between  semantic units, a given semantic unit from a finer level of representational granularity can be  associated with more than one unit from a coarser level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A given statement unit can thus be associated  with more than one compound unit, while having the statement unit itself with all its triples being  documented in the graph at a single location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  For example, the description of a multicellular organism could contain a has-part statement unit  that states that the organism has a head as its part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This statement unit would be associated with the  item unit of the organism itself, which would be linked to further item units about the organism’s  other parts, constituting an item group unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, since has-part is a partial order relation (70),  the has-part statement unit would also be associated with a parthood granularity tree unit and its  corresponding granular item group unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Thus, the has-part statement unit would be associated with  at least four other semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Due to the modular organization of semantic units, knowledge graphs that implement them can  be built as virtual federated knowledge graphs, with data being contributed from several projects  and institutions, stored in their own repositories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This way, users with access to all data can utilize the  Semantic Units  39  contents of such a knowledge graph, while data stewardship remains in the hands of the individual  contributing projects and institutions, ensuring their technical autonomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The content modularization brought about by semantic units could also facilitate partitioned-  based querying of knowledge graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This has been successfully done with other approaches for  partitioning the graph (71), and we expect that partitioning the graph into semantic units and thus  semantically meaningful subgraphs should have a comparable effect on querying tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, the  use of semantic units in knowledge graph partitioning and modularity is subject to future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Organizing a knowledge graph into five levels of representational  granularity, into other granularity trees, and into different frames of  reference using semantic units  With statement unit, item unit, and item group unit as different categories of semantic unit, a  knowledge graph can be organized into the following basic representational granularity levels (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  14): triples, statement units, item units, item group units, and the knowledge graph as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Triples  represent the lowest and thus finest level of abstraction possible in a knowledge graph, with semantic  units constituting coarser levels of abstraction and thus coarser levels of representational granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Representational granularity organizes the semantic-units graph layer and thus the discursive layer  of a knowledge graph into different levels of representational granularity, and with that, indirectly,  also the knowledge graph’s data graph layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 14: Five levels of  representational  granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The  introduction of semantic  units to a knowledge  graph adds a semantic-  units graph layer to its  data graph layer, which  adds, among others, a  level of statement units, a  level of item units, and a  level of item group units to the level of triples and the level of the graph as a whole, resulting in five levels of representational  granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Organizing triples into statement units (which represent the smallest units of semantically  meaningful propositions for a human reader),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' statement units into item units (which can be presented  ItemGroupUnit  Semantic-Units  GraphLayer  ItemUnit  Knowledge  Graph  StatementUnit  Data  GraphLayer  TripleSemantic Units  40  in the UI as individual pages),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and item units into item group units (which can be presented as  collections of semantically interrelated UI pages) is often necessary to increase the human-readability  and usability of a knowledge graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In addition to the organization and structuring of a knowledge graph into different levels of  representational granularity, a given item group unit can be further organized and structured in a  somewhat orthogonal way into granular item group units by utilizing granularity tree units present in  the item group unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Granularity trees organize the data graph layer and thus the ontological layer  of a knowledge graph into different granularity perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Finally, a given item group unit can be further organized and structured into different context  units, each of which covers a specific frame of reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Points of contact between different frames  of reference and thus different context units can be identified via is-about statements: the subject of  an is-about statement is a semantic unit resource whose subject belongs to the data graph of one  context unit and the object of the is-about statement belongs to the data graph of another context  unit (see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This allows traversing different frames of reference in a knowledge graph via  their is-about statement connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Context units organize the data graph layer and thus the  ontological layer of a knowledge graph into different frames of reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Organizing data into various kinds of semantic units and thus semantically meaningfully  subgraphs that can be digested by a human reader as semantically related larger chunks of data is an  effective way of presenting data in the UI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' With the granular organization of a knowledge graph into  different types of semantic units, some of which belong to different levels of representational  granularity, and by structuring the knowledge graph into these partially overlapping, partially enclosed  subgraphs, data management, data access, data exploration, and graph navigation can be improved  significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Statements about statements and documenting ontological,  diagnostic, and discursive information in knowledge graphs using  semantic units  Because each semantic unit has its own UPRI and is represented in the semantic-units graph layer of  a knowledge graph by its own node, it is straightforward to make assertions about semantic units and  thus statements about statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If semantic units were organized as FAIR Digital Objects, one could  also make statements across different databases and knowledge graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' By structuring the knowledge  graph into semantic units, UIs can be developed that provide a very intuitively usable framework for  Semantic Units  41  making statements about statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The development of such UIs and their accompanying tools and  services thereby benefits from semantic units being implemented following a clear and  straightforward schema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This way, semantic units can contribute to a solution of the problem that  making statements about statements within knowledge graphs can be challenging (see Challenge 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  There is another aspect in knowledge management and knowledge representation, where it is  beneficial to be able to make statements about statements in a straightforward way and to have a  formalized notation for representing contingent statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  As a scientific realist, one can distinguish between (1) particulars and universals as mind-  independent real entities, (2) our cognitive representations of real entities in the form of ideas,  concepts, and thoughts, and (3) textual and perception-based representations of real entities in the  form of words, symbols, images, recordings, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (72–74).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The latter are usually used for  communication and documentation, with the sender having the intention to trigger cognitive  representations in the receiver that are maximally similar to their own representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Meaning and reference are key for the success of communication and condition the duality of a  textual representation that must provide both ontological and diagnostic information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  information sent must carry semantic meaning in the sense that it provides answers to questions of  the type “What is it?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and thus ontological definitions that carry semantic conceptual content for all  referenced entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Some of this ontological information is provided explicitly, but in most parts the  sender relies on the inferential lexical competence (75) of the receiver by using well-known  terminology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  But communication also has to provide answers to questions of the type “How does it look?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and  thus information about the epistemological appearance―information that is required for  unambiguously referencing all entities mentioned in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This diagnostic, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', referential  information may not be very important in cases where the receiver already knows the entity, but in  all other cases, especially when dealing with theoretical entities whose existence cannot be  identified/observed directly and where you often cannot deduce recognition criteria from the  ontological definition (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', a lead atom, a cell nucleus), diagnostic information is essential for reliably  referencing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Therefore, some of this diagnostic information needs to be provided explicitly, but in  most parts the sender relies on the referential lexical competence (75) of the receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  How does that relate to knowledge graphs?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Well, sometimes we talk about real entities,  sometimes we talk about our cognitive and textual representations of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Sometimes, this  discourse overlaps, and this is where it becomes complicated when having to model this in a  knowledge graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Ideally, ontological definitions and diagnostic operational definitions are provided  Semantic Units  42  by domain ontologies, and assertions in knowledge graphs refer to respective ontology terms and the  information linked to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This way, knowledge graphs would efficiently document, represent, and  communicate empirical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Unfortunately, however, due to limitations of OWL and Description Logics in defining classes,  ontologies generally do not provide diagnostic operational definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Ontologies define classes in the  form of Aristotelian definitions (76) that constitute essentialistic classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Essentialistic classes are  based on universal statements, with class membership being determined in dependence of a set of  properties that are individually necessary and jointly sufficient (77).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Many diagnostic operational  definitions, however, provide method-dependent recognition criteria that require the manipulation  of the object to be able to determine its class membership, for instance because the object is too small  for the eye, or it can only be identified after it has been stained or when using some test-kit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  defining properties of such operational definitions often refer to properties that are not necessarily  present in every instance of a respective class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Instead, they are rather typical and only sufficient in a  specific number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Consequently, many recognition criteria cannot be modelled as essentialistic classes  but, instead, have to be modelled as cluster classes (74).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Contrary to essentialistic classes, an instance  of a cluster class does not have to possess all class-defining properties―necessary is that some of  them apply, sufficient is a specified percentage threshold, which is the minimum quorum (77).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Definitions of cluster classes thus take the form of contingent statements, which cannot be  represented in OWL and Description Logics (see discussion above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Diagnostic operational definitions frequently depend not only on cluster class concepts but also  on fuzzy sets, since many cluster class definitions rely on terms that refer to fuzzy sets (74).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For  instance, when recognition criteria refer to coarse inner material, electron-dense clusters, mushroom-  shaped, ovoid, or hooked to identify class-membership of instances to a specific type of anatomical  structure, they refer to terms that specify spatio-structural properties that are better communicated  via exemplars or images and thus perceptual contents than textual definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Whereas both  essentialistic classes and cluster classes are always defined textually, fuzzy sets can be defined  ostensively in reference to exemplars and thus to perception-based contents that rely on the human  capabilities of pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The semantic-units approach provides a formal notation for representing contingent statements  and, when combined with semantically annotated exemplary images, a knowledge graph could  provide all diagnostic knowledge relevant for answering “How does it look?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Together with  the ontological definitions, knowledge graphs could provide any reader of the graph with all relevant  knowledge they need to ensure their inferential and referential lexical competence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  43  In addition to the ontological and the diagnostic layer, knowledge graphs often document a third  layer of information, representing discursive contextual information (see also Ingvar Johannson’s  distinction between use and mention of linguistic entities (78)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, knowledge graphs not  only contain empirical data in the form of assertions like “The melting point of lead is at 327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='5 °C”, but  also assertions like “author A asserts that the melting point of lead is at 327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='5 °C” or “the assertion  that the melting point of lead is at 327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='5 °C is a result of experiment X”, which address the discursive  contextual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Some assertions may even address the diagnostic aspects of how the  reference between textual representation and real entity is achieved by documenting respective  methods and diagnostic criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Without a good method for making statements about statements,  documenting and representing these three layers of information (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', ontological, diagnostic,  discursive) and expressing their interrelations is not possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Because semantic units are represented in the graph with their own nodes, they support the  documentation and representation of all three layers and their interrelationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Statement units can  provide within their data graphs ontological information that can be gathered within compound units  of coarser representational granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' As propositions, they are represented in their semantic-units  graphs, which constitutes a large part of the discursive layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, contrary to OWL and  Description Logics, the semantic-units approach with its introduction of some-instance and every-  instance resources and resources that represent individual universal statements and sets of  semantically related universal statements, enables differentiated referencing of various entities  relating to the ontological layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Consequently, one can make statements about individual classes  (=concepts), their definitions, their individual defining statements, a single instance of a class, a group  of instances of a class, and the group of all instances of a class, therewith opening multiple ways to  talk about universal statements and their elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, with context units, it is even possible  to distinguish and explicitly document different frames of reference within the ontological and  discursive layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, the semantic-units approach allows for specifying various  interrelationships between the discursive and the ontological layer of its knowledge graph and  therefore integrates universal statements in the knowledge graph’s domain of discourse (Challenge  4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Since statement units can also relate a particular resource to another statement unit (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  ‘author_A -asserts-> statement_unit_Y’) or two statement units to each other (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', ‘statement_unit_X  hasMetadata-> statement_unit_Z’), relations between the three layers can be easily documented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  For instance, an item group unit documents the contents of a particular scholarly publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Because  scholarly publications can be considered in general to represent reports about a scientific investigation  or some other research activity, the item group unit will contain information about a research activity  Semantic Units  44  as a process that may have some material entities (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', substances, instruments, specimens, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=') and  research agents (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', experimenters, patients, test persons, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=') or some data as its input and some  research result as its output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Moreover, the research activity usually realizes a specific plan (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  research method) and achieves a specific research objective, which is part of the plan (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  This general model can be applied like a Matryoshka, the russian stacking doll: research activities can  have research activities as their parts, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', differentiated steps in the overall research process, that  again have their own inputs and outputs and realize their own research methods and achieve their  own objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 15: A data scheme for modelling the contents of scholarly publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The relation between a research activity, its  input and output and its underlying process plan specification in the form of a research method and research objective  (model adapted from (79)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  This model can be applied to a knowledge graph of scholarly publications and be adopted to  semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The item group unit of the publication is about an instance of *research activity* and  has an item unit of the research activity associated with it, of which that *research activity* instance  is the subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The research activity item unit has a research result item unit associated with it that has  an instance of *research result* as its subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The research activity resource is linked to the research  result resource via the property hasSpecifiedOutput (OBI:0000299).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Now, the research result item unit  can be linked to a description item unit that contains several assertional statement units about a  particular multicellular organism—the publication describes the anatomy of a specific multicellular  organism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This is documented through a triple that relates the *research result item unit* to the  description item unit* via the property *hasLinkedSemanticUnit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The ‘description’ (SIO:000136)  resource is the subject of the *description item unit* and is related to the multicellular organism item  unit through the property hasPart (BFO:0000051) and the multicellular organism item unit to the  instance  of  multicellular  organism  (UBERON:0000468)  through  the  property  hasSemanticUnitSubject*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resulting set of semantic units thereby cover at least three different  frames of reference: the publication itself, the research activity, which the publication is reporting on,  bfo:has.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='part  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='researchoutput=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='material entity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hasachievedresult  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='research objective  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='research method  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='and/ordataitem  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='obi:achieves  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo: has part  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo: has part  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='obi:hasspecified  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='planned  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:realizes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='objective  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='researchparticipant=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='obi:hasspecified  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='researchinput=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='researchagent  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='ro:hasparticipant  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='researchactivity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='material entity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='input  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='and/orinstrument  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='and/ordataitem  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo: has  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='occurrent  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='part  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:has partSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='45  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='and the assertional statements about the research subject,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', the multicellular organism, with their  boundaries being indicated by the two is-about statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In Figure 16, you can see how the resulting  discursive and the ontological layers, as well as the different frames of reference, are interconnected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure 16: Detail from the graph belonging to an item group unit about the contents of a scholarly publication, represented  in an ABox RDF graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The content is modelled according to a specific data schema (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 15) that has been adapted to  semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' All content from the published journal article is organized in its own item group unit instance via various  associated semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The publication itself is represented in the data graph as an instance of journal article  (IAO:0000013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The item group unit has several item units about the research activity associated with it, that in turn are  connected to each other via the property *hasLinkedSemanticUnit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The item unit describing the research activity has an  instance of investigation (OBI:0000066) as its subject, which has as its output an instance of data set (IAO:0000100) that has  an instance of description (SIO:000136) as its part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' That description instance has the item unit that describes the multicellular  organism as its part, the latter of which has an instance of multicellular organism (UBERON:0000468) as its subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The blue  arrow indicates that the data graph (dark blue box without borders) is represented by this item unit (bordered box in the  same color).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It has a head item unit linked to it, which has an instance of head (UBERON:0000033) as its subject, which is a  part of the multicellular organism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The data graphs of the semantic units form the ontological layer, whereas their semantic-  units graphs form the discursive layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Three different context units separate the reference frame of a publication from that  of a research-activity and that of a research-subject, with is-about statements marking their borders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For reasons of clarity  of presentation, the associated statement units are not shown in the discursive layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Whereas the resources of the semantic units represent and organize the discursive layer, their  data graphs represent the ontological (and diagnostic) layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The same applies to all semantic unit  resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The organization of a knowledge graph into these different layers and into different frames  of reference may provide a new framework for the development of innovative visualization and graph  exploration methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='item group unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='context unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='publication  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='research activity  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='research subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='contextunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='contextunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='contextunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='itemunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has associated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has associated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has associated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='discursive  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='semantic unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has associated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='semantic unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='semantic unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='has associated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has associated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='semanticunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdt:typo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='46  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Modelling negations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' cardinality restrictions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and disagreement  OWL and Description Logics based information systems adhere to what is called the Open World  Assumption (OWA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' OWA assumes incomplete information by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Therefore, absence of  information about an entity or a fact does not necessarily imply information about the absence of that  entity or the negation of that fact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' As a consequence, if you for instance want to state that a particular  object is a fruit but not a pome fruit, that a particular head of an insect does not possess any antenna,  or that this head possesses exactly three eyes, it is not enough to mention that the object is a fruit,  the head possesses three eyes, or to not mention any antenna, because due to OWA the fruit could  still be a pome fruit and the head could still possess antenna, and it could still possess a fourth eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Instead, you must explicitly state all these things.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Unfortunately, in RDF/OWL, these types of negation and cardinality statements pose tricky  modelling challenges, because they cannot be directly expressed as relations between instances and  thus ABox expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Instead, you must model them in the form of class-expressions as a TBox, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  by using OWL Manchester Syntax (51).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Regarding negations, one can distinguish two different types of negation statements: negations  involving references to classes and negations of relations between instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An example of the  former is the statement ‘this fruit is not a pome fruit’ (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 17A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This can be characterized following  the Manchester Syntax as the expression ‘not (type pome fruit)’ (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 17B), which translates to OWL  mapped to RDF to a graph in which the given particular entity is an instance of the class fruit  (PO:0009001) and an instance of a class that is the complement of the class pome fruit (PO:0030110)  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 17C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Analog to this case are negations that are part of a class axiom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic units can provide an alternative modelling solution by introducing a general *negation  unit* class (in Neo4j this could be simply modelled by adding the label ‘:Negation’ to the respective  semantic unit node, indicating that this resource is an instance of the class ‘negation’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The statement  ‘this fruit is not a pome fruit’ can be modelled by two semantic units, both of which would be instances  of *named-individual identification unit* and *assertional statement unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, the semantic  unit stating that its subject is a pome fruit (PO:0030110) is also an instance of *negation unit*, thereby  negating the contents of its data graph (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 17D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  47  Figure  17:  Modelling  negations  involving  instances by applying semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A) A  human-readable statement that this fruit is not a  pome fruit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The statement can be modelled in two  different ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' As an OWL expression that can be  specified using B) Manchester Syntax, where the  fruit is an instance of a class that is defined as all  of its instances are not instances of pome fruit  (PO:0030110).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Note, how this Manchester Syntax  expression translates into C) an OWL expression  mapped to RDF, where fruit x is an instance of  fruit (PO:0009001) but also of a class that is the  complement to  pome fruit  (PO:0030110).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Alternatively, the statement can be modelled as  an instance-based graph using semantic units D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The data graph in the blue box states that the  entity is a fruit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The data graph belonging to the  statement unit stating the negation (red box with borders, here shown with its dynamic label), on the other hand, is shown  in the red box without borders and states that the entity is a pome fruit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, since the latter statement unit not only  instantiates the classes *assertional statement unit* and *named-individual identification unit* but also *negation unit*, it  actually negates the statement in the data graph, therewith indicating that it is not a pome fruit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Absence statements are another example of negations involving reference to classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  observation ‘this head has no antenna’ translates to the statement that the head is an instance of a  class that is characterized following the Manchester expression as ‘not (‘has part’ some antenna)’,  which translates to OWL to a more complex class axiom (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 18A-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The same statement can be modelled as the union6 of the subgraphs of two semantic units, with  the one having the ‘head x’ (UBERON:0000033) as its subject being an instance of *has-part statement  unit*, *assertional statement unit*, and *negation unit*, whereas the one having the ‘some antenna’  (UBERON:0000972) as its subject only being an instance of *some-instance identification unit* (see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 18D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In general, when modelling absence statements this way, all instance resources in the  assertion that are supposed to represent types of entities that are absent, would be modelled this  way, relating to the respective class via the property *some instance of* within their corresponding  some-instance identification units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This notation would be simpler and easier to use and to implement  in knowledge graph applications than the OWL-based notation of using a more complex class  expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  6 The union of the subgraphs, but, semantically, the intersection of the statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A)Statement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Thisfruitisnotapomefruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='B)OWLManchesterSyntaxexpression  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='typenegationclassaxiom:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='not(typepomefruit)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='C)ConventionaloWLmodel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='PO:fruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='PO:pome fruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:complement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fruitx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='df:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='classification  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:subclass  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='blank node  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='negationclass  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owlspecific  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='D)Assertionalstatementunitsmodel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='assertional statementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='named-individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identificationunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Fruitxis notapomefruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='negation unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='PO:fruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fruitx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='PO:pome fruitSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='48  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Figure 18: Relation between an  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='absence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='observation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  the  corresponding assertions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and  two alternative ways to model  them in a knowledge graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A)  A human-readable statement  about the observation that a  given head has no antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' B)  Absence statements cannot be  expressed as relations between  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Therefore,  the  observation from A) must be  expressed  using  a  class  expression,  which  can  be  formulated using Manchester  syntax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Following this notation,  the head would be an instance  of a class that is defined to have  only instances that have no  antenna as their parts (‘not’ and  ‘some’ being used as mathematical expressions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' C) The translation of the assertion from A) and B) into an OWL expression  mapped to RDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Note how *absence phenotype* is defined as a set of relations of subclass and complement restrictions  involving two blank nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' D) The same statement can be modelled using two semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' One of them is modelling the  has-part relation and negates it (red box with borders and its dynamic label, with its data graph in the red box without  borders).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It is therefore an instance of *has-part statement unit* as well as *assertional statement unit* and *negation unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The other semantic unit is an instance of *some-instance identification unit* and relates ‘some antenna’ to antenna  (UBERON:0000972) via the property *some instance of*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Its data graph is shown in the blue box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Together, they model the  observation from A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This notation is comparable to E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' E) An alternative notation of the statement ‘this head has no antenna’  and the observation from A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The notation uses Peirce’s predicate logic system of existential graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The identity line ―  between the two phrases ‘head x’ and ‘has part antenna’ states that head x has some antenna as its part, whereas the red  circle surrounding the latter phrase expresses its negation by crossing the line of identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For reason of clarity of  representation, the relation between ‘head x’ and head (UBERON:0000033) is not shown in C) and D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The same approach can also be applied to the case of negations of relations between two  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The fact that a given fruit is not part of a particular orange plant could be modelled analog  to the other negation statements (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A)Observation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Thisheadhasnoantenna(negatedparthoodassertion)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='B)OWLManchesterSyntaxexpression  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='absencephenotypeclassaxiom:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='not（haspartsomeantenna)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='C)ConyentionalOwLmodel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='headx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:restriction  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:has part  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='property  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:complement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:some  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='absencephenotype  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:subclassof-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='blanknode  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='blank node  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='values  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='uberon:antenna  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='from  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='D)Assertionalstatementunitsmodel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='assertional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has-part  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statementunit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owlspecific  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='object property  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Headxhasnoantenna  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='negation unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='head x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='someantenna  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='someinstanceof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='uberon:antenna  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="E)Peirce'spredicatelogicsystemofexistentialgraphs  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='head x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='haspartantennaSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='49  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Figure  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='19:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Modelling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='negating  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='relations  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='between  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instances  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='by  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='applying semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A) A human-  readable statement that this fruit is  not part of this organge plant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  statement can be modelled in two  different ways: B) as an OWL  expression mapped to RDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Note, how  the statement is translated into a  negated assertion statement with  source,  property,  and  target  specification, relating an instance  ‘fruit x’ (PO:0009001) to an instance  ‘orange plant y’ (FOODON:03411339)  involving a blank node;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' or C) using  three semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The two named-  individual identification units, with  their data graphs shown in the blue boxes, state that one of the objects is a fruit and the other one an orange plant, whereas  the part-of statement unit (red bordered box  and its dynamic label, with its data graph shown in the red box without borders)  states that fruit x is not part of orange plant y as it instantiates both *part-of statement unit*,  *assertional statement unit*,  and *negation unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  From all these examples, it becomes clear that negations, including absence statements, can be  efficiently represented via semantic units by classifying the corresponding semantic unit as a  negation unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This general notation can be compared to Peirce’s existential relational graphs  (80,81), where a line of identity ‘―’ can be used to express that ‘something is A’ by notating it as ‘―A’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The line of identity can be understood to represent an existential quantifier (Ǝx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' By interrupting this  line with a circle that encloses A, you express that ‘something is not A’ (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 18E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The resulting  existential relational graphs are sufficiently general to represent full first-order logic with equality (81).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Expressing cardinality restrictions is, for the same reasons, also challenging using RDF/OWL and  requires the use of a class expression that indicates the cardinality as a class restriction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Instead of  using a rather complex class axiom to describe for instance that a given head possesses exactly three  eyes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 20B), the same information could be modelled by two semantic units and allowing for  extending the some-instance identification unit to include cardinality restrictions via linking its subject  to, for instance, the value 3 via the property qualified cardinality (OWL:qualifiedCardinality) (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 20C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Instead of a simple integer value,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' a float value range with a unit specification that is constrained to  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='count unit (UO:0000189) and percent (UO:0000187) would even allow the specification of frequencies  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A)Statement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Thisfruitisnotpartofthisorangeplant  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owlspecific  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='objectproperty  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='B)ConventionalOWLmodel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:negativepropertyassertion  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fruitx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='PO:fruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:source individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='blank node  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:assertionproperty  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:partof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:target individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='orangeplanty  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='FOODON:orangeplant  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='C)Assertionalstatementunitsmodel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='part-of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='assertional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Fruitxisnotapartof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='orangeplanty  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='negation unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unitsubject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='PO:fruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='+rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fruitx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:partof  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='orangeplanty  "' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type"  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='FOODON:orangeplantSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='and ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The has-part statement unit relates the ‘head x’ to the subject of a semantic unit that  instantiates both *some-instance identification unit* and *cardinality restriction unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Figure  20:  Modelling  cardinality  restrictions  involving  instances  by  applying semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A) A human-  readable statement that this head has  exactly three eyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The statement can be  modelled in two different ways: B) as an  OWL expression mapped to RDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Note,  how ‘has exactly three eyes’ is translated  into being an instance of a class that has a  cardinality  restriction  on  the  has  component property (RO:0002180) and  the class eye (UBERON:0000970) with a  cardinality value of 3, thereby involving  one blank node;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' or C) using two semantic  units, one of which models the has-part  relationship, with its data graph shown in  the dark blue box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The other semantic unit  (light blue bordered box and its dynamic  label, with its data graph shown in the light  blue box without borders) instantiates  assertional statement unit*, *some-instance identification unit*, and *cardinality restriction unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Analog to the approach for modelling negations, semantic units can also be applied for modelling  disagreement in a knowledge graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For instance, if person A asserts ‘This fruit is a pome fruit’ through  a named-individual identification unit, and person B disagrees with this statement, the disagreement  can be modelled as a semantic unit that instantiates both *assertional statement unit* and  disagreement unit* and its data graph states that the named-individual identification unit asserted  by person A instantiates *negation unit* (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Whereas the here suggested notations result in simpler graphs than their OWL-based RDF  equivalents, and these graphs are easier to query due to the lack of blank nodes, reasoners that  directly use semantic units would still have to be developed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' however, through the translation to OWL  (see section Logical semantics of semantic units), standard OWL reasoners will be able to reason over  semantic units, including negations, cardinality restrictions, and disagreements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A)Statement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Thisheadhasexactly3eyes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='B)ConventionalOwLmodel  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl: restriction  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='ro:hascomponent  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf: type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl: on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='property  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='three-eyed head  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='blank node  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='C)Assertionalstatementunitsmode  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='cardinality  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='restriction unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='exactly  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='3eyes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='owl:qualified  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='cardinality  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='head x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='bfo:haspart  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='someeye  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='some  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='uberon:eye  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instanceofSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='51  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Figure 21: Modelling disagreement by applying semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  A) Person A states that this is a pome fruit and person B  disagrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' B) The assertional statement unit (blue bordered box  and its dynamic label, with its data graph shown in the blue box  without borders) models the statement of person A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' C) The  disagreement unit (red bordered box and its dynamic label, with  its data graph shown in the red box without borders) models the  statement of person B and instantiates *assertional statement  unit* and *disagreement unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Its data graph states that the  statement of person A instantiates *negation unit*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Logical semantics of semantic units  Semantically, we treat semantic units as translations between ABox and TBox statements, or,  alternatively, as translations between logic programs and OWL axioms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, ‘Lars’ right hand’  (FMA:9712) has-part (BFO:0000051) ‘Lars’ right thumb’ (FMA:24938) is an ABox statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It includes,  as part of the representation, the information that this expresses a “has part” type axiom (has-part  statement unit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semantically, we treat these statement units as expressions of particular forms of  ontology design patterns, where the ABox statement is translated into TBox axioms based on an  ontology design pattern dependent on the type of statement unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We can formalize these translations  using expressions of relational ontology design patterns (82), which are OWL axioms involving  variables for arbitrary entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, the *’has-part assertional statement unit’* can be  translated, in general, as  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='X SubClassOf: has-part some ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Y,  where ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='X is filled by the subject and ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Y by the object of the statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We can add the pattern  as literal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', either as a datatype property or annotation property, to the statement unit class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This  will allow use of an OWL reasoner, or, alternatively, a SPARQL query, to retrieve all statements that  can be rewritten based on this  design pattern;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' however, it will be more convenient to specify them  separately and use a dual formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The dual representation of complex axioms as ABox statements and the translation into TBox (or  ABox) axioms enables a dual kind of reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Through the translation to TBox axioms,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' it becomes  possible to apply OWL reasoning and therefore use any OWL reasoner (or reasoners for OWL profiles)  A)Statements  PersonA:"This fruit isapomefruit"  PersonB:"IdisagreewithPersonA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='thatthisfruitisapomefruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='B)TypeAssertionModelforStatementofPersonA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='personA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='class  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='instance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='asserted by  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='named-individual  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='identification unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Fruitxisapomefruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content="'rdf:type  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='assertional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='hassemantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='fruit x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='PO:pome fruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='C)DisagreementAssertionModelforStatementofPersonB  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='person B  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='asserted by  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='assertional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='df:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='statement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Fruitxisnotapomefruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='disagreement unit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='has semantic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='unit subject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='Fruitxisapomefruit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='rdf:type  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='negation unitSemantic Units  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='52  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='to test consistency of the knowledge graph or perform inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, the ABox representation  of the axioms as abbreviated patterns also enables a form of reasoning directly on the ABox  statements, using the semantics of logic programming;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' this form of reasoning can exceed the  semantics of OWL (83).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In particular, it becomes possible to add non-monotonic statements which  allow us to model contingent statements, or “defaults”, which may have an exception (84).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For  example, the statement ‘Typically, a hand has a thumb as part’ can be modelled through a logic  program that states that, if there is an instance x of Hand (FMA:9712) and it is not provable that x does  not have some instance of Thumb (FMA:24938) as part, then x has some instance of Thumb as part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Formally, this can be expressed as an answer set program such as  has-part(x, Thumb) :- rdf:type(x, Hand), not lacks-part(x, Thumb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  However, such a statement has several unusual features that need to be explained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' First, it is not  based on OWL semantics and therefore does not, initially, interact with axioms in the OWL ontology;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  in particular, the statement unit is not translated into an OWL axiom but rather into a logic rule that  is applied to the statement units themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Second, under answer set semantics, “not” is weak  negation with the intended meaning that lacks-part(x, Thumb) is not provable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It therefore encodes a  kind of default knowledge and using this statement results in non-monotonic inference: adding a new  statement, such as lacks-part(x, Thumb), will invalidate the previous inference (has-part(x, Thumb));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  this is in contrast to the standard semantics of OWL which is monotonic (where adding a new  statement will never invalidate an inference).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Third, the symbols Hand and Thumb are used here as  symbols for individuals and instanceOf is an explicit relation between entities, whereas Hand and  Thumb would be classes in OWL (corresponding to unary predicates) and instanceOf is a built-in  primitive that relates individuals to classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  To relate the logic programs to OWL, we assume that the logic program is able to use all OWL  entities (class symbols, individual symbols, and relation symbols) as individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An atomic formula  takes the form P (a1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', an ) where P is a predicate symbol and each ai is either an individual symbol  or a variable symbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A formula is called ground if it contains no variable symbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Several efficient  grounders, such as Clingo (85), as well as answer set solvers such as DLV (86) or clasp (87) are available,  and allow computation of fully ground answer sets (or stable models of answer set programs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We  treat the predicate symbols in the answer set program as ontology design patterns that are translated  into a set of OWL axioms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Applying patterns in a forward manner is decidable and can be implemented  in a straightforward manner by computing the fully grounded stable models of the answer set program  and then applying the forward translation of the design pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We can also implement an inverse  translation from OWL into these patterns by querying, for each defined ontology design pattern,  Semantic Units  53  whether the pattern is entailed by the OWL axioms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' using an OWL reasoner, we can query for the  pattern within the deductive closure O⊢ of ontology O and iterating through all OWL entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However,  for a pattern with n variables and |E| entities in the OWL ontology, the complexity will be O(|E|n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Using this approach, a semantic unit is specified by two parts, a statement that takes the form of a  logic program, and a pattern to convert predicates into OWL statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, we can express  a named-individual identification unit (Figure 8) as:  Logic program:  rdf:type(Lars’RightHand, fma:hand)  Pattern:  rdf:type(Lars’RightHand, fma:hand)  In the case of a named-individual identification unit, both statements are identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' More  generally, we can formulate all named-individual identification units using a logic program such as:  named-individual-identification-unit(x), has-semantic-subject(x,y), rdf:type(y, z), rdfs:label(y,  l), owl:named_individual(y);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  and a pattern that translates each predicate into their corresponding OWL statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  A some-instance identification unit is semantically identical to a named-individual identification  unit but does not introduce, explicitly, a name for the individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This corresponds to the use of an  existential quantifier which we can eliminate through “Skolemization”, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', we can introduce a new  individual name that is not explicitly referred to in the language of the semantic units but exists in the  semantic space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The every-instance identification unit requires more elaborate translation into OWL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Here, *every  instance of X* refers to the collection of all instances of X, and we may rely on a theory of collections  and collectives (88);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the example in Figure 8 will then be translated into:  rdf:type(everyHand, Collection)  owl:SubClassOf(fma:Hand, owl:SomeValuesFrom(member-of, owl:oneOf({everyHand})))  owl:SubClassOf(owl:oneOf(everyHand), owl:AllValuesFrom(has-member, fma:Hand))  In other words, *‘everyHand’* refers to a collection that has as its members all instances of the  class Hand (FMA:9712), and that has only instances of that class as members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Analogously, we can  translate cardinality restrictions (cardinality restriction units);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the example in Figure 20, for example,  would be expressed using the following (general) logic program:  cardinality-restriction-unit(x), has-semantic-unit-subject(x,y), owl:qualified-cardinality(y,z),  some-instance-of(y, w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  54  with a translation of this pattern into OWL of  rdf:type(cX, owl:intersectionOf(Collection, owl:cardinality(has-member, 3, uberon:eye)))  where cX is a new individual name (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', a name not used elsewhere).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This will then be combined with  the ‘part-of assertional statement unit’ for ‘head X’ in the same example to assert the ABox statement  part-of(`head X’, cX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  We can use a similar translation to formalize other statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' An assertional statement unit  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 9) is translated directly into an ABox statement, and a universal statement unit follows a similar  translation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' the statement in Figure 9 will be translated into the OWL ABox axiom  hasPart(everyHand, someThumb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Based on OWL semantics and the axioms to formalize *‘everyHand’* and *‘someThumb’* gives  rise to the inference of the OWL axiom  owl: SubClassOf(fma:Hand, owl:SomeValuesFrom(has-part, Thumb)  as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The contingent statement unit in Figure 9 is similarly translated into an OWL ABox  axiom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, our formalism also allows us to express a different type of contingent statement, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  a statement about prototypes (prototypical contingent statement unit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Such a statement can be used  to formulate expressions such as ‘normally, a hand has a thumb as its part’, allowing for the possibility  of an exception (such as in the case of loss of a thumb due to an accident).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The following statement  expresses this prototypical statement:  hasPart(x, thumb) :- hasPart(hand, thumb), instanceOf(x, hand), not -hasPart(x, thumb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The use of the logic programming paradigm also allows us to formalize complex statements such  as shown in Figure 13 which are not directly expressible in OWL, and the translation into OWL through  translation patterns enables inferences within OWL when combined with other OWL axioms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  We are also able to model (classical) negation through the use of negation units (Figure 17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A  negation is directly added to a semantic unit, and we can use this to define a negated assertional  statement unit:  NegatedAssertionalStatementUnit(x) :- NegationUnit(x), AssertionalStatementUnit(x)  and then a translation into OWL for NegatedAssertionalStatementUnit with the following logic  program as precondition:  Semantic Units  55  NegatedAssertionalStatementUnit(x), has-semantic-unit-subject(x,y), rdf:type(y,z)  and the OWL translation  rdf:type(y, owl:complementOf(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  This  example  shows  the  flexibility  of  our  use  of  logic  programming,  as  the  NegatedAssertionalStatementUnit predicate is inferred from the two assertions added to the  statement unit and does not have to be asserted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' However, this kind of inference, in particular when  using negation units, leads to one additional challenge because multiple patterns may apply to  statements, and it may not always be clear which translation pattern to apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, in the  example in Figure 17, if we ignore the negation unit, we will conclude that the pattern for assertional  statement units should apply;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' applying translations for both statement units will result in an  inconsistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The easiest way to prevent this is to add the weakly negated condition to the logic  programs for assertional statement units: not NegatedAssertionalStatementUnit(x), or, even simpler,  not NegationUnit(x);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' this condition will prevent the translation pattern from being triggered in the  presence of a negation unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Furthermore, the logic programming paradigm can be used to translate between statements (treated  as individuals) and their content (treated as propositions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The statements, as shown in Figure 21, are  units in their own right (assertional statement units) which can be translated to OWL axioms using the  patterns we already described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Additionally, the statements are individuals within logic programs  where relations between statements can be modelled, which additionally can enable the use of  answer set programming to represent arguments (89,90).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic units provide a new framework for knowledge graph  alignment  Semantic units that instantiate the same semantic unit ontology class contain semantically similar  information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Therefore, semantic units of the same type are in principle comparable throughout all  their instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Consequently, aligning and comparing different knowledge graphs that are based on  the same set of semantic unit ontology classes can be conducted in a step-by-step procedure along  the different levels of representational granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In a first step, the data graphs belonging to item  group units are aligned based on their *hasSemanticUnitSubject* relations to different types of  subjects and based on their *hasAssociatedSemanticUnit* relations to different types of associated  semantic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In a next step, for each pair of item group units the data graphs belonging to their  associated item units are aligned based on their types of subjects and their types of associated  Semantic Units  56  statement units, which in turn can be aligned by class, and finally their individual triples can be aligned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  This would provide a new framework to improve methods for knowledge graph alignment, subgraph-  matching, graph comparison, and graph similarity measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Managing restricted access to sensitive data  Statement units and their classification into corresponding ontology classes provide a framework for  identifying subgraphs within a knowledge graph that can contain sensitive data to which access must  be restricted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' For example, all information relating to location data of occurrences of endangered  species should not be publicly available, and access should be restricted and managed by adequate  rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Respective statement units can be identified by class, and the need to restrict access to them  can be based on the threat level of the respective species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' If a species is endangered, access to these  types of statement units would be automatically restricted, while all other semantic units referring to  that species would still be openly accessible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Similarly, any personal data fall under privacy policy  restrictions and access to corresponding statement units should depend on specific access rights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' This  would follow EOSC’s principle of ‘as Open as possible, as closed as necessary’ (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Conclusions and Future Work  With semantic units, we introduce a type of resource that is new to knowledge graphs and that  significantly increases their overall expressivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semantic units structure a knowledge graph into  identifiable and semantically meaningful subgraphs and thus represent an additional type of  representational entity (91) besides instances, classes, and properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semantic units represent  resources of a higher level of abstraction than the low-level abstraction of the resources used in  conventional individual triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Technically, semantic unit resources are instances of respective  ontology classes, but semantically they represent the contents of their data graphs and thus  statements or sets of semantically and ontologically related statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' With semantic units, one can  thus extract semantically meaningful entities from a knowledge graph that are more abstract than  the resources typically used in conventional triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Regarding the four challenges discussed in the introduction, we can conclude that because every  statement is organized in its own statement unit which, in turn, instantiates a corresponding  statement unit ontology class, a data schema (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', as a shape) and corresponding CRUD query  patterns can be specified for each such class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' By linking the data schema to the corresponding  statement unit class, the UPRI of each statement unit and its affiliation with a corresponding  Semantic Units  57  statement unit class would also reference the underlying data schema and thus contribute to the  FAIRness of their data by guaranteeing schematic interoperability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Because statement units partition  the knowledge graph so that every triple belongs to exactly one statement unit, all data in the  knowledge graph would have information about their underlying data schema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Reference to the  underlying data schema represents valuable metadata that guarantees the interoperability of all  instances of statement units of the same class because they are all based on the same data schema  (Challenge 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  The set of CRUD query patterns would not only provide read queries for domain experts for  searching instances of the corresponding class in the overall data graph, but also create, update, and  delete queries for developers, who could use them and thus do not have to learn graph query  languages anymore (Challenge 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  By organizing the overall data graph into different semantic units and thus semantically  meaningful subgraphs at different levels of representational granularity, semantic units also provide  a solution to the problem that making statements about statements is challenging in knowledge  graphs (Challenge 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semantic units provide an efficient way of structuring the graph to allow users  to intuitively make statements about statements, and also provides a clear and straightforward  implementation schema that supports the development of corresponding queries and related tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Moreover, contrary to RDF-star, semantic units also allow distinguishing different instances of the  same statement by organizing them as different semantic units that instantiate the same semantic  unit class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' They would have identical subjects and objects, but would differ by their respective  semantic unit resource.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Finally,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' by distinguishing between assertional,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' contingent (including prototypical),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and universal  statement units as top-level categories of statement units,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' by introducing some-instance and every-  instance resources,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and by introducing a notation that does not involve blank nodes and that is less  complex than the equivalent OWL notation when mapped to RDF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' semantic units provide a conceptual  framework with which the conceptual gap between RDF/OWL and property graphs can be bridged,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  formal semantics for contingent and prototypical statements can be provided,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and universal  statements and thus also particular class axioms can become part of the domain of discourse of a  knowledge graph (Challenge 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In other words, semantic units substantially increase the overall  expressivity of knowledge graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  In the future, we want to expand the concept of a semantic unit to include for each semantic unit  class corresponding data schemata and query patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Together with further features, this results in  what we call a Knowledge Graph Building Block (KGBB) (see also knowledge graph cells (79) for a first  Semantic Units  58  discussion of a similar idea).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A KGBB is a small module that is associated with a semantic unit ontology  class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each semantic unit class requires its own associated KGBB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A KGBB provides all information  required for managing data belonging to the corresponding type of semantic unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each KGBB provides  a graph model for storing the data of its associated type of semantic unit, from which CRUD query  patterns can be derived, resulting in FAIR data and metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' KGBBs decouple data storage from data  access by providing data access in various formats, and they also decouple data display from data  storage by providing different display templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Ultimately, the idea for KGBBs is that each KGBB  functions independently of other KGBBs, that it is made openly available in a repository so that it can  be reused by others, and that domain experts can combine multiple KGBBs and define their possible  interactions with as little effort as possible to set up their own knowledge graph application, without  being a programmer or having knowledge in semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A KGBB editor will enable domain experts  without background in semantics, in programming, or in graph query languages to describe new  KGBBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' A KGBB application engine will use the information provided by the various KGBBs of a  knowledge graph application and communicate through respective APIs with the persistence-layer  and the presentation-layer, thereby decoupling not only human-readable data display from data  storage, but also data access from data storage, and data storage from storage technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  One of the authors has developed a first minimum viable product for how KGBBs and semantic  units can be used to manage a knowledge graph (92).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It is based on Neo4j and gets its contents through  a web interface and user input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' It is a small knowledge graph application for documenting assertions  from scholarly publications and allows users in an exemplary way to describe some contents that can  be found in a scholarly publication (it does not focus on describing the publication’s bibliographic  metadata).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Each described paper is represented as its own item group unit, with the assertions  covered by statement units that are associated with item units and granularity tree units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The  showcase  is  based  on  Python  and  flask/Jinja2  and  is  openly  available  through  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='com/LarsVogt/Knowledge-Graph-Building-Blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  We believe that the combination of semantic units with Knowledge Graph Building Blocks will  contribute a framework for sharing data across many stakeholders, helping to interlink data providers  from a diverse range of different areas, with data stewardship remaining in the hands of the domain  experts or institutions, thus ensuring their technical autonomy (following Barend Mons’ data visiting  as opposed to data sharing (7)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We also think that due to its modular character, the framework can  increase the accessibility of knowledge graphs for software developers and domain experts who lack  the expertise in semantics, thus supporting the FAIRification of data and metadata in  general―something desperately needed to make all data FAIR, which we believe would increase our  chances to fight climate change and biodiversity loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  59  Acknowledgements  We thank Werner Ceusters, Nico Matentzoglu, Manuel Prinz, Marcel Konrad, Philip Strömert, Roman  Baum, Björn Quast, Peter Grobe, István Míko, Manfred Jeusfeld, Manolis Koubarakis, Javad  Chamanara, and Kheir Eddine for discussing some of the presented ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Lars Vogt received funding  by the ERC H2020 Project ‘ScienceGraph’ (819536).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' We are solely responsible for all the arguments  and statements in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Author’s contributions  LV: developed the concept of semantic units and wrote the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' TC: contributed to the chapter  about nanopublications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' RH: contributed the formal semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' All authors: reviewed the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Adam, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Hammad, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Adam, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2015) Big Data Analysis and Storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Proceedings of the  2015 international conference on operations excellence and service engineering, Orlando,  Florida, USA, 10-11 Sept 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 648–659.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Marr, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) How Much Data Do We Create Every Day?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The Mind-Blowing Stats Everyone  Should Read.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' How Much Data Do We Create Every Day?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The Mind-Blowing Stats Everyone  Should Read;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Data never sleeps 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Idrees, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Alam, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Agarwal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) A study of big data and its challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 11, 841–846.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' General Assembly, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2015) Transforming our world: the 2030 Agenda for Sustainable  Development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Transforming our world: the 2030 Agenda for Sustainable Development;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2015) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 1–35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' International Science Council (ISC) (2019) Science as a global public good: ISC Action Plan, 2019-  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Science as a global public good: ISC Action Plan, 2019-2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' International Science Council,  (2019) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Mons, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) Message from the CODATA President, Barend Mons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Message from the CODATA  President, Barend Mons;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Wilkinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Dumontier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Aalbersberg, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2016) The FAIR Guiding Principles for  scientific data management and stewardship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Data, 3, 160018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Bryan Heidorn (2008) Shedding Light on the Dark Data in the Long Tail of Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Libr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Trends,  57, 280–299.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Baker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2016) 1,500 scientists lift the lid on reproducibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Nature, 533, 452–454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Lin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Crabtree, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Dillo, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2020) The TRUST Principles for digital repositories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Data,  7, 144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  60  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The Internet of FAIR Data & Services .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Ayris, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Berthou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Bruce, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2016) Realising the European Open Science Cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Realising the European Open Science Cloud;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2016) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Hasnain, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Rebholz-Schuhmann, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) Assessing FAIR Data Principles Against the 5-Star  Open Data Principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In Gangemi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Gentile, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Nuzzolese, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ), The Semantic  Web: ESWC 2018 Satellite Events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ESWC 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Lecture Notes in Computer Science, vol 11155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  Springer, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 469–477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' European Commission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Directorate General for Research and Innovation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and EOSC Executive  Board (2021) EOSC interoperability framework: report from the EOSC Executive Board Working  Groups FAIR and Architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' EOSC interoperability framework: report from the EOSC Executive  Board Working Groups FAIR and Architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Publications Office, LU, (2021) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' European Commission Expert Group on FAIR Data (2018) Turning FAIR into reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Turning FAIR  into reality;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Baum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Bhatty, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) SOCCOMAS: a FAIR web content management system  that uses knowledge graphs and that is based on semantic programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Database, 2019, 1–22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Blumauer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) Knowledge Graphs—Connecting the Dots in an Increasingly Complex World.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' (2018) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Singhal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2012) Introducing the Knowledge Graph: things, not strings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Introducing the  Knowledge Graph: things, not strings  (2012) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Hogan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Blomqvist, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Cochez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2021) Knowledge Graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ACM Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 54, 1–  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Bonatti, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Decker, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Polleres, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) Knowledge graphs: new directions for  knowledge representation on the semantic web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Dagstuhl Semin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 8, 29–111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Abiteboul, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (1997) Querying semi-structured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In Afrati, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Kolaitis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ), Database  Theory — ICDT ’97, Springer Berlin Heidelberg, Berlin, Heidelberg, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 1–18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Angles, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Gutierrez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2008) Survey of graph database models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ACM Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 40, 1–  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Angles, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Arenas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Barceló, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2017) Foundations of Modern Query Languages for  Graph Databases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ACM Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 50, 1–40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Hitzler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Krötzsch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Parsia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2012) OWL 2 Web Ontology Language Primer (Second  Edition), W3C Recommendation 11 December 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' OWL 2 Web Ontology Language Primer  (Second Edition), W3C Recommendation 11 December 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2012) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Stutz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Strebel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Bernstein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2016) Signal/Collect12: Processing large graphs in  seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semantic Web, 7, 139–166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Mao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2017) Knowledge Graph Embedding: A Survey of Approaches  and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Knowl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Data Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 29, 2724–2743.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Ceusters, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2020) The place of Referent Tracking in Biomedical Informatics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Terminology,  Ontology and their Implementations, Springer Nature, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Ceusters, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Elkin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Smith, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2007) Negative findings in electronic health records and  biomedical ontologies: A realist approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Med.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 76, S326–S333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2021) FAIR data representation in times of eScience: a comparison of instance-based  and class-based semantic representations of empirical data using phenotype descriptions as  example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 12, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  61  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Bandrowski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Brinkman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Brochhausen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2016) The Ontology for Biomedical  Investigations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' PLoS ONE, 11, 1–19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Knublauch, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Kontokostas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2017) Shapes Contraint Language (SHACL) - W3C  Recommendation 20 July 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Shapes Contraint Language (SHACL) - W3C Recommendation 20  July 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2017) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Booth, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Wallace, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) Session X: EasyRDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Session X: EasyRDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 2nd US Semantic  Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Symp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 2019  (2019) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Hartig, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2017) Foundations of RDF* and SPARQL*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' CEUR Workshop Proceedings 1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Arndt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Broekstra, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', DuCharme, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' RDF-star and SPARQL-star Draft Community Group  Report 01 July 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' RDF-star and SPARQL-star Draft Community Group Report 01 July 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Frey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Müller, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Hellmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) Evaluation of metadata representations in RDF  stores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semantic Web J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 10, 205–229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Mungall, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) Proposed strategy for semantics in RDF* and Property Graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Proposed  strategy for semantics in RDF* and Property Graphs  (2019) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Mungall, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2017) Shadowboxing : Mirroring the TBox in the ABox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Shadowboxing : Mirroring  the TBox in the ABox  (2017) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Hogan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Arenas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Mallea, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2014) Everything you always wanted to know about  blank nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Web Semant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 27–28, 42–69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Neumann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Moerkotte, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2011) Characteristic sets: Accurate cardinality estimation for  RDF queries with multiple joins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 2011 IEEE 27th International Conference on Data Engineering,  IEEE, Hannover, Germany, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 984–994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Papastefanatos, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Meimaris, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Vassiliadis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2021) Relational schema optimization for  RDF-based knowledge graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 101754.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Collarana, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Galkin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Traverso-Ribón, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2017) MINTE: Semantically integrating RDF  graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Proceedings of the 7th International Conference on Web Intelligence, Mining and  Semantics - WIMS ’17, ACM Press, New York, New York, USA, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 1–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Endris, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Galkin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Lytra, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) Querying Interlinked Data by Bridging RDF  Molecule Templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Querying Interlinked Data by Bridging RDF Molecule Templates  (2018) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) Organizing phenotypic data—a semantic data model for anatomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 10, 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Smith, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Almeida, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Bona, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2015) Basic Formal Ontology 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' and Jansen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=', Stenzhorn, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2009) Strengths and limitations of formal ontologies  in the biomedical domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Rector, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Stevens, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Drummond, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2009) What causes pneumonia?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' The case for a  standard semantics for “may” in OWL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' CEUR Workshop Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 432.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Dodds, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Davis, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2011) Linked Data Patterns: A pattern catalogue for modelling,  publishing, and consuming Linked Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' (2011) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Stevens, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Sattler, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2014) Walking your fingers through the trees in OWL: why there are  things you want to say but can’t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' Ontog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' - Knowl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Blog  (2014) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  62  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' W3C: OWL 2 Web Ontology Language Manchester Syntax (Second Edition) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Balhoff, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Mikó, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Yoder, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2013) A semantic model for species description applied  to the ensign wasps (Hymenoptera: Evaniidae) of New Caledonia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 62, 639–659.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Bittner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Smith, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2001) A taxonomy of granular partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In Montello, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ),  Spatial Information Theory: Foundations of Geographic Information Science, volume 2205 of  Lecture Notes in Computer Science, Springer, Berlin, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Smith, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Bittner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2001) A unified theory of granularity, vagueness and approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Proceedings of COSIT Workshop on Spatial Vagueness, Uncertainty, and Granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 102, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Bittner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Smith, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2003) A theory of granular partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In Duckham, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Goodchild, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Worboys, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ), Foundations of geographic information science, Taylor & Francis Books,  London, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 117–149.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Keet, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2008) A Formal Theory of Granularity - Toward enhancing biological and applied life  sciences information system with granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' PhD Thesis, Free University of Bozen - Bolzano,  Bozen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2010) Spatio-structural granularity of biological material entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' BMC Bioinformatics,  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) Levels and building blocks—toward a domain granularity framework for the life  sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 10, 1–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Gayo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Prud’hommeaux, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Staworko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2015) Towards an RDF validation language  based on regular expression derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' CEUR Workshop Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 1330, 197–204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Staworko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Boneva, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Gayo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Complexity and Expressiveness of ShEx for RDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Lupp, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Hodkiewicz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Skjæveland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2020) Template Libraries for Industrial Asset  Maintenance: A Methodology for Scalable and Maintainable Ontologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 13th International  Conference on Scalable Semantic Web Knowledge Base Systems (SSWS 2020), colocated with the  International Semantic Web Conference (ISWC 2020), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 49–64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Skjæveland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Lupp, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Karlsen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) Practical Ontology Pattern Instantiation,  Discovery, and Maintenance with Reasonable Ontology Templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In Vrandečić, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Bontcheva,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Suárez-Figueroa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ), The Semantic Web – ISWC 2018, Lecture Notes in  Computer Science, Springer International Publishing, Cham, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 11136, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 477–494.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Mons, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Velterop, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2009) Nano-Publication in the e-science era Nano-Publication in the e-  science era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Workshop on Semantic Web Applications in Scientific Discourse (SWASD 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Groth, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Gibson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Velterop, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2010) The Anatomy of a Nano-publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Serv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Use,  30, 51–56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Kuhn, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Taelman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Emonet, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2021) Semantic micro-contributions with decentralized  nanopublication services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' PeerJ Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 7, e387.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Giachelle, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Dosso, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Silvello, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2021) Search, access, and explore life science  nanopublications on the Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' PeerJ Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 7, e335.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Kuhn, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Willighagen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Evelo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2017) Reliable Granular References to Changing Linked  Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial  Intelligence and Lecture Notes in Bioinformatics), Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 10587 LNCS, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 436–451.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Clark, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Ciccarese, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Goble, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2014) Micropublications: a semantic model for claims,  evidence, arguments and annotations in biomedical communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 5, 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Semantic Units  63  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Pinker, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (1997) How the Mind Works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' How the Mind Works;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Norton & Company, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  (1997) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Herre, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2010) The Ontology of Mereological Systems: A Logical Approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Theory and  Applications of Ontology: Philosophical Perspectives, Springer Netherlands, Dordrecht, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 57–  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Azzam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Polleres, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Fernández, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2022) smart-KG : Partition-Based Linked Data  Fragments for Querying Knowledge Graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Semantic Web - Interoperability Usability Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=',  under revi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2011) Signs and terminology: science caught between language and perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  Bionomina, 4, 1–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Smith, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Kusnierczyk, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Schober, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2006) Towards a Reference Terminology for  Ontology Research and Development in the Biomedical Domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' In Bodenreider, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' ),  Proceedings of KR-MED 2006, Studies in Health Technology and Informatics, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 124, IOS Press,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 57–66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Mikó, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Bartolomaeus, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2022) Anatomy and the type concept in biology show  that ontologies must be adapted to the diagnostic needs of research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=', 13, 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' (1995) On the Structure of Lexical Competence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Aristot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=', 95, 131–150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Smith, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=', 25, 25–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2005) Pre-Darwinian Taxonomy and Essentialism – A Reply to Mary Winsor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=', 39, 274–287.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', D’Souza, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Stocker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2020) Toward Representing Research Contributions in  Scholarly Knowledge Graphs Using Knowledge Graph Cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Proceedings of the ACM/IEEE Joint  Conference on Digital Libraries in 2020, ACM, Virtual Event China, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 107–116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Peirce, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Existential graphs - CP 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='372-417.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Existential graphs - CP 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='372-417.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Sowa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2011) Peirce’s tutorial on existential graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content='  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Hoehndorf, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Oellrich, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Dumontier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2010) Relations as patterns: bridging the gap  between OBO and OWL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' BMC Bioinformatics, 11, 441.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' Answer Set Programming;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Springer International  Publishing, Cham, (2019) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Hoehndorf, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Loebe, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Kelso, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2007) Representing default knowledge in biomedical  ontologies: application to the integration of anatomy and phenotype ontologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' BMC  Bioinformatics, 8, 377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Gebser, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Kaminski, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Kaufmann, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) Multi-shot ASP solving with clingo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Theory  Pract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=', 19, 27–82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Adrian, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Alviano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Calimeri, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2018) The ASP System DLV: Advancements and  Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' KI - Künstl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', 32, 177–179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Gebser, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Kaufmann, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Neumann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2007) clasp: A Conflict-Driven Answer Set Solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' 260–265.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Wood, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Galton, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2009) A taxonomy of collective phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' Egly, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Alice Gaggl, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Woltran, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2010) Answer-set programming encodings for  Semantic Units  64  argumentation frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+page_content=' Toni, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' and Sergot, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2011) Argumentation and Answer Set Programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' 164–180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Rector, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Schulz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', Rodrigues, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2019) On beyond Gruber: “Ontologies” in today’s  biomedical information systems and the limits of OWL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' X, 2, 1–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content='  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' Vogt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' (2022) FAIR Knowledge Graphs with Semantic Units―a Prototype.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
+page_content=' FAIR Knowledge  Graphs with Semantic Units―a Prototype  (2022) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7tAzT4oBgHgl3EQfSPsA/content/2301.01227v1.pdf'}
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+arXiv:2301.08636v1  [math.NA]  20 Jan 2023
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE
+PROBLEM
+Hajri Imen 1 Fethi Ben Belgacem 2
+Abstract. In this article, we introduce and study three numerical methods for the Dirichlet
+Monge-Ampère equation in two dimensions. The approaches consist in considering new equivalent
+problems. The latter are discretized by a wide stencil finite difference discretization and monotone
+schemes are obtained. Hence, we apply the Barles-Souganidis theory to prove the convergence of
+the schemes and the Damped Newtons method is used to compute the solutions of the schemes.
+Finally, some numerical results are illustrated.
+Monge-Ampere, Monotone scheme, Newton method.
+1. Introduction
+We are interested in the numerical solution of the Monge-Ampère equation with Dirichlet bound-
+ary condition
+(1.1)
+(MAD)
+
+
+
+
+
+det
+�
+D2u (x)
+�
+= f (x) , for x in Ω,
+u (x) = ϕ (x) , for x on ∂Ω,
+u is convex.
+Where Ω is a convex bounded domain in R2, with boundary ∂Ω, (D2u) , is the Hessian of the
+function u, f and ϕ are given functions.
+We take the simplest boundary conditions. For more general operator of Monge-Ampère and
+other boundary conditions, we mention for instance [12]. The convexity constraint is crucial for
+the (MAD). It is required for the Monge-Ampère equation to be degenerate elliptic and for (MAD)
+to have a unique solution. It is also needed for numerical stability. The Monge-Ampère equation,
+has extensive applications, it is strictly related to the “prescribed Gauss curvature” problem, see
+for instance [12]. It appears also in affine geometry, precisely, in the affine sphere problem and the
+affine maximal surfaces problem, this was discussed in [5, 6, 25, 27, 28, 29]. Other applications
+appear in fluid mechanics, geometric optics, and meteorology : for example, in semigeostrophic
+equations, the Monge-Ampère equation is coupled with a transport equation, this is pointed out
+in [12]. The analysis of the regularity of the Monge-Ampere equation is essential in the study
+1Higher
+Institute
+of
+Applied
+Studies
+in
+Humanities
+of
+Mahdia,5121
+Mahdia,
+Tunisia,
+Email:hajri.imene2017@gmail.com.
+2Laboratory of partial differential equations (LR03ES04), ISIMM, University of Monastir, El Manar, TUNISIA.
+Email: fethi.benbelgacem@isimm.rnu.tn
+1
+
+2
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+of the regularity of the transp ort problem. This, latter, has been employed in many areas. We
+only briefly mention [8, 9, 4] for mesh geneartion,[15, 16, 17]for image registration, and [12] for
+reflector design. Developing an efficient numerical method has aroused a lot of interest, and large
+standard techniques have been proposed. A first method to do so was introduced in [24] by using
+a discretization of the geometric Alexandrov-Bakelman interpretation of solutions. Variational
+approaches have been presented in [10, 11], more precisely, the augmented Lagrangian approach
+and the least-squares approach. But these methods needed more regularity than can be predicted
+for solutions. A different approach was studied in [18], using the vanishing moment method. The
+periodic case was treated in [14].
+Although, the standard techniques, mentioned above, work well for smooth solutions, and they
+fail for singular solutions, for more details, see, for instance, the discussion in [2]. To overcome
+these difficulties, we have to use the notion of viscosity solution or Alexsandrov solution. In two
+dimension, a numerical method was introduced in [24], which is geometric in nature, and converges
+to the Alexsandrov solution. The method introduced in [22]„ in two dimension and improved in
+[19] for higher dimension, uses the wide stencil scheme that converges to the viscosity solution,
+which we briefly describe for this reason in the end of this section.
+The following variant of the AM-GM inequalities, is the keystone of our formulation introduced
+here.
+For A and B two symmetric matrices, such that, A, B ≥ 0. We have the following inequality
+2
+�
+det (AB) ≤ Tr (AB) .
+Where for symmetric matrices M ≥ 0 means xT Mx ≥ 0.
+Remark 1. We can deduce from the above inequality that for a smooth convex solution u of (1.1),
+one can deduce the following inequality
+∆u − 2
+�
+f ≥ 0.
+Let us define the function
+˜g := ∆u − 2
+�
+f.
+It is then straightforward to check that if u is a smooth solution of (1.1), then is indeed a solution
+of the linear Dirichlet Poisson problem
+(1.2)
+�
+P˜g� �
+∆u = 2√f + ˜g,
+u|Γ = ϕ,
+which can be easily descretized by any method of choice if the function ˜g is known.
+We finish this remark by mentioning that the convexity constraint is essential to ensure unique-
+ness (for example, u and −u are both solution of the Monge Ampère equation). For viscosity
+solution, this constraint can be required by the equation
+(1.3)
+λ1
+�
+D2u
+�
+≥ 0,
+
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+3
+in the viscosity sense, see for instance [21, 22], where λ1 (D2u) is the smallest eigenvalue of the
+Hessian of u. However, for a twice continuously differentiable function u, the convexity restriction
+is equivalent to requiring that the eigenvalues of the Hessian, D2u, are positives, which is approved
+by considering the linear Poisson Dirichlet problem
+�
+P˜g�
+.
+The approaches that we follow, in the present paper, are inspired by the idea developed in [3]
+and the wide stencil finite difference discretization introduced in [22] and [19] for viscosity solution
+of M-A equation in two and higher dimensions that relies on a framework developed in [1]. For
+clarity, we recall the full result in the next section.
+2. Viscosity solution and convergence theory of approximation schemes
+2.1. Degenerate elliptic equations. Let F (x, r, p, X) be a continuous real valued function de-
+fined on Ω × R × Rn × Sn, with Sn being the space of symmetric n × n matrices. Consider the
+nonlinear, partial differential equation with Dirichlet boundary conditions,
+�
+F (x, u (x) , Du (x) , D2u (x)) (x) = 0
+for x in Ω
+u (x) = g (x)
+for x in ∂Ω.
+Where Ω is a domain in Rn, Du and D2u denote the gradient and Hessian of u, respectively.
+Definition 2. [19]The equation F is degenerate elliptic if
+F (x, r, p, X) ≤ F (x, s, p, Y ) whenever r ≤ s and Y ≤ X.
+Where Y ≤ X means that Y − X is a nonnegative definite symmetric matrix.
+The viscosity solution for the Monge-Ampère equation is defined in [22].
+Definition 3. Let u ∈ C (Ω) be convex and f ≥ 0 be continuous. The function u is a viscosity
+subsolution (supersolution) of the Monge-Ampère equation in Ω if whenever convex ϕ ∈ C2 (Ω)
+and x0 ∈ Ω are such that (u − ϕ) (x) ≤ (≥) (u − ϕ) (x0) for all x in a neighborhood of x0, then we
+must have
+det
+�
+D2φ (x0)
+�
+≥ (≤) f (x0) .
+The function u is a viscosity solution if it is both a viscosity subsolution and supersolution.
+For the existence and uniqueness of viscosity solution for (1.1), we mention the next result in
+[7],
+Theorem 4. Let Ω ⊆ Rd be abounded and strictly convex, g ∈ C (∂Ω) , f ∈ C (Ω) , with f ≥ 0.
+Then there exists a unique convex viscosity solution u ∈ C
+� ¯Ω
+�
+of the problem (1.1).
+The advantage of considering viscosity solutions come from the following fundamental theorem,
+obtained in [1], which gives conditions for convergence of approximation schemes to viscosity
+solution.
+
+4
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+Theorem 5. (Convergence of Approximation Schemes). Consider a degenerate elliptic equation,
+for which there exist unique viscosity solutions. A consistent, stable approximation scheme con-
+verges uniformly on compact subsets to the viscosity solution, provided it is monotone.
+By the previous theorem, we need just a way to build a monotone finite difference schemes,
+which represents a new challenge. In the sequel, we recall here the basic framework introduced in
+[20], for building a monotone scheme.
+Firstly, a finite difference equation take the form
+F i [u] = F i (ui, ui − uj|i̸=j) .
+We say that a scheme is degenerate elliptic if the following holds [20]:
+Definition 6. The scheme F is degenerate elliptic if F i is non-decreasing in each variable.
+We are now ready to present the following theorem in [20]:
+Theorem 7. Under mild analytic conditions, degenerate elliptic schemes are monotone, and non-
+expansive in the uniform norm. The iteration
+(2.1)
+um+1 = um + dtF (um) ,
+is a contraction in L∞ provided dt ≤ K (F)−1 , where K (F) is the Lipschitz constant of the scheme,
+regarded as a function from RN −→ RN.
+We end this paragraphre by the next result, proven in [20]
+Theorem 8. A proper, locally Lipschitz continuous degenerate elliptic scheme has a unique solu-
+tion which is stable in the l∞ norm.
+2.2. Wide stencil schemes. We finish this section by noting that wide stencil schemes are re-
+quired to build consistent, monotone schemes of degenerate second order PDEs (see discussion in
+[22]). Wide stencil schemes were built for the two-dimensional Monge-Ampère equation in [22]
+and for the convex envelope in [21]. Each approach considered here is a function of eigenvalues of
+the Hessian. To fully discretize the equation (4.1) for the eigenvalues of the Hessian on a finite
+difference grid, we approximate the second derivatives by centered finite differences; this is the
+spatial discretization, with parameter h. We consider also a finite number of possible directions ν
+that lie on the grid; this is the directional discretization, with parameter dθ. The spatial resolution
+is improved by using more grid points, the directional resolution is improved by increasing the size
+of the stencil. So, a wide stencil is needed (see Fig 2.2)
+3. First Formulation of the (MAD) in two dimensions (method A)
+3.1. An equivalent problem. Let us begin with a simple approach to illustrate the ideas. We
+can rephrase, for instance, the (MAD) as the following:
+(3.1)
+�
+Find a positive function g, such that
+det (D2ug) = λ1 [D2ug] × λ2 [D2ug] = f,
+
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+5
+Figure 2.1. Grid for wide stencil 17 points, in two dimension
+where: ug is the solution of�
+∆ug = λ1 [D2ug] + λ2 [D2ug]
+= 2√f + g,
+ug
+|Γ
+= ϕ.
+We are now ready to state a first example of our approches.
+Lemma 9. Provided the solution, u, of (1.1) is in H2, there exists a unique positive function
+˜g ∈ L2, such that u = u˜g, where u˜g is the solution of (P˜g). Conversely, if u¯g is solution of (3.1)
+for some ¯g > 0, then u¯g = u.
+Proof. Let u be a solution of (1.1). From the above, one can see easily, that u = u˜g.
+Conversely, if u¯g is a solution of (3.1), we can clearly see that
+�
+det (D2u¯g) = f > 0
+∆u¯g ≥ 0.
+It follows that u¯g is convex and satisfies (1.1).
+□
+Remark 10. We notice that according to the result in [26], we have equivalence of viscosity and
+weak solutions for the Poisson problem. This motivates us to build a convergent scheme to the
+viscosity solution of Poisson problem
+�
+P˜g�
+through the discretization of the (MAD) problem. The
+viscosity solution u˜g of
+�
+P˜g�
+will be equivalent to the weak solution of (MAD) problem in the
+distributional sense.
+4. Discretization of the problem (3.1)
+Let us consider a regular and uniform cartesian grid, consider the stencil at the reference point
+x0 consist of the neighbors x1, ..., xN (as in Figure 1). We can define vi in polar coordinates by
+vi = xi − x0 = hivθi.
+
+6
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+We assume that the stencil is symetric and we define the local spatial resolution and the directional
+resolution respectively by
+¯h (x0) = max
+i
+hi
+and
+dθ = max
+θ∈[−π,π] min
+i
+|θ − θi|.
+First, the problem (3.1) can be written as function of the eigenvalues of the Hessian. We will
+then start by discretizing λ1 and λ2. Hence by a simple substitution we obtain the scheme for (3.1).
+We recall that the smallest and the largest eigenvalues of a symmetric matrix can be represented
+respectively by the Rayleigh-Ritz formula
+(4.1)
+λ1
+�
+D2u
+�
+(x) = min
+θ
+d2u
+dν2
+θ
+,
+λ2
+�
+D2u
+�
+(x) = max
+θ
+d2u
+dν2
+θ
+,
+where νθ = (cos θ, sin θ)is the unit vector in the direction of the angle θ.
+This formula was used in [22] to build a monotone scheme in two dimension for the (MAD).
+We begin by building monotone schemes for λ1 and λ2 on a wide stencil uniform grid. These
+operators are used to give schemes for all formulations in this paper.
+We discretize the eigenvalues of the Hessian by the following formula.
+(4.2)
+λh,dθ
+1
+�
+D2ug�
+(x) = min
+i
+ug (x + vi) − 2ug (x) + ug (x − vi)
+|vi|2
+and
+(4.3)
+λh,dθ
+2
+�
+D2ug�
+(x) = max
+i
+ug (x + vi) − 2ug (x) + ug (x − vi)
+|vi|2
+.
+Lemma 11. The schemes (4.2) and (4.3) are degenerate elliptic.
+Proof. We follow the same as in [22].
+Since each discrete second derivative in the direction vi is the average of the terms which have
+the form ug
+j − ug
+i , they are non-decreasing in ug
+j − ug
+i . Taking a minimum (or maximum) of non-
+decreasing functions furnishes a non-decreasing function.
+□
+We finally substitute (4.2) and (4.3) in (3.1) to obtain the wide stencil finite difference scheme
+of (3.1)
+(4.4)
+�
+Find a positive function gi, such that
+λh,dθ
+1
+�
+D2ugi�
+× λh,dθ
+2
+�
+D2ugi�
+= f i,
+
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+7
+with
+�
+λh,dθ
+1
+�
+D2ugi�
++ λh,dθ
+2
+�
+D2ugi�
+= 2
+�
+f i + gi.
+ug
+|Γ
+= ϕ.
+Where f i = f (xi) and gi = g (xi) .
+Lemma 12. The scheme (4.4) is degenerate elliptic.
+Proof. From the properties of nondecreasing functions, obtained in [22],
+that if G : R2 → R is a nondecreasing function, and if F1 and F2 are degenerate elliptic finite
+difference schemes, then so is F = G (F1, F2) . It is also clear that the discretization f i = f (xi)
+and gi = g (xi) does affect the ordering properties. We conclude that (4.4) is degenerate elliptic.
+□
+In the following, for simplicity, we omit the index i when there is no ambiguity.
+Definition 13. We say the scheme Hh,dθ is consistent with the equation (MAD) at x0 if for every
+twice continuously differentiable function ϕ (x) defined in a neighborhood of x0, Hh,dθ(ϕ) (x0) →
+H (ϕ) (x0) as h, dθ → 0. The global scheme defined on Ω is consistent if the limit above holds
+uniformly for all x ∈ Ω. (The domain is assumed to be closed and bounded).
+Lemma 14. The consistency holds for (4.2) and (4.3) and so for (4.4).
+Proof. Let x0 be a reference point with neighbors x1, ..., xN, and direction vectors vi = xi − x0, for
+i = 1, ..., N, arranged symmetrically, if vi is a direction vector, then so is −vi. By Taylor series one
+has
+ug (x0 + vi) − 2ug (x0) + ug (x0 − vi)
+|vi|2
+= d2ug
+dv2
+i
++ O
+�
+h2
+i
+�
+.
+Let M given symetric 2 × 2 matrix, that we can take it diagonal. Set vθ a unit vector. It follows
+from [22] (Lemma 3) that
+min
+θ∈{θ1,...,θN} vT
+θ Mvθ = λ1 + (λ2 − λ1) O
+�
+θ2�
+.
+Which implies that
+λ1 (ϕ) (x0) − λh,dθ
+1
+(ϕ) (x0) = O
+�¯h2 + (λ2 − λ1) dθ2�
+and thus consistency holds for (4.2).
+Similar argument gives consistency for (4.3) and so for
+(4.4).
+□
+Theorem 15. Suppose that unique viscosity solutions exist for the equation (3.1) Then the finite
+difference scheme given by (4.4) converges uniformly on compacts subsets of Ω to the unique
+viscosity solution of the equation.
+Proof. We need to verify consistency and monotonicity. Consistency follows from Lemma 14 and
+monotonicity follows from Lemma 12.
+□
+
+8
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+Finally, the scheme yields a fully nonlinear equation defined on grid functions. We perform the
+iteration (2.1) and by Theorem 7 will converge to a fixed point which is a solution of the equation.
+This approach is used in [22].
+5. TWO METHODS OF FIXED POINT
+5.1. The first method (Method B). Notice that from Lemma 9 if u is a solution of (1.1)
+u (x, y) = u˜g (x, y) it follows that det (D2u) = det
+�
+D2u˜g�
+, where u˜g is the solution of (1.2) for
+˜g ∈ L2.
+By writing
+△u˜g = 2
+�
+f + ˜g =
+�
+(∆u˜g)2 + 2 (f − det (D2u˜g))
+and expanding
+�
+∆u˜g�2 =
+�
+u˜g
+xx
+�2 +
+�
+u˜g
+yy
+�2 + 2u˜g
+xxu˜g
+yy we have
+△u˜g =
+��
+u˜g
+xx
+�2
++
+�
+u˜g
+yy
+�2
++ 2
+�
+u˜g
+xy
+�2
++ 2f = 2
+�
+f + ˜g
+Let us define the operator Q : L2 (Ω) → L2 (Ω) for Ω ⊂ R2 by
+Q (g) :=
+�
+(ug
+xx)2 + (ug
+yy)2 + 2 (ug
+xy)2 + 2f − 2
+�
+f,
+with ug solution of (Pg) . So, one has
+Lemma 16. ˜g is a fixed point of Q.
+Proof. It follows from above expansions.
+□
+5.1.1. The scheme. We consider the following scheme
+gn+1 = Q (gn) =
+�
+(ugn
+xx)2 + (ugn
+yy)2 + 2 (ugn
+xy)2 + 2f − 2
+�
+f.
+With initial value g0 > 0 close to zero and ug0 is the solution of (P g0) .
+Remark 17. The advantage of this method by comparing it to that in [19] and [2] is that it
+guarantees, at least, at each iteration that tr (D2ugn (x)) > 0, which is necessary to check the
+convexity.
+Although this method turns out to be simple to implement is well suited in the case where ug
+is in H2 (Ω) . If not, the method may not converge.
+5.1.2. Algorithm.
+• g0 ≥ 0 (close to 0), solve (P g0) , ((ug)0 = ug0being known),
+• For n ≥ 0, compute gn+1 and (ug)n+1 as follows
+gn+1 = Q (gn) ,
+(ug)n+1 solution of
+�
+P gn+1�
+.
+
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+9
+Where, the method involves simply discretising the second derivatives using standard central dif-
+ferences on a uniform Cartesian grid, as a result
+D2
+xxuij
+=
+1
+h2 (ui+1,,j + ui−1,j−, 2ui,,j) ,
+D2
+yyuij
+=
+1
+h2 (ui,,j+1 + ui,,j−1 − 2ui,,j) ,
+D2
+xxuij
+=
+1
+4h2 (ui+1,,j+1 + ui−1,,j−1 − ui−1,,j+1 − ui+1,,j−1) .
+5.2. The second method (Method C). In the same setting we define the next operator.
+Definition 18. Let Ω a bounded domain in R2. Define the operator F : L2 (Ω) → L2 (Ω) ,
+by
+(5.1)
+F (g) =
+�
+|det [D2ug] − f| + g,
+where ug is a solution of
+(5.2)
+(Pg)
+�
+∆u = 2√f + g,
+u|Γ = ϕ.
+For g ∈ L2 (Ω), the operator F is well defined and it is easy to verify that
+Lemma 19. �g is a fixed point of the operator F.
+Proof. Let u a smooth solution of (1.1). It follows from Lemma 9 that u = u�g. Which implies that
+det
+�
+D2u�g�
+= det [D2u] = f and therefore, F (�g) = �g.
+□
+5.3. The scheme. We define the following scheme
+gn+1 = F (gn) =
+�
+|det [D2ugn] − f| + gn.
+With initial value g0 > 0 close to zero and ug0 is the solution of (P g0) .
+Remark 20. The method is advantageous, it simply involves evaluating derivatives and solving the
+Poisson equation that preserves the convexity constraint.
+5.3.1. Algorithm.
+• g0 ≥ 0 (close to 0), solve (P g0) , ((ug)0 = ug0being known),
+• For n ≥ 0, compute gn+1 and (ug)n+1 as follows
+gn+1 = α
+�
+|det [D2ugn] − f| + gn,
+with 0 < α < 1.
+(ug)n+1 solution of
+�
+P gn+1�
+.
+As in the above method, second derivatives are descretized using standard central differences on a
+uniform Cartesian grid.
+
+10
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+N
+Results in [19]
+Method A
+Method B
+Method C
+31
+2.44 × 10−4
+2.965 × 10−4
+4.226 × 10−4
+18 × 10−4
+45
+1.52 × 10−4
+3.052 × 10−4
+2.202 × 10−4
+18 × 10−4
+63
+9.06 × 10−5
+2.801 × 10−4
+1.190 × 10−4
+17 × 10−4
+89
+5.32 × 10−5
+8.035 × 10−4
+6.494 × 10−5
+17 × 10−4
+127
+3.06 × 10−5
+2.015 × 10−4
+3.888 × 10−5
+17 × 10−4
+Table 1. Errors
+��u − uN��
+∞ for the exact solution of the first example on an N ×N
+grid. We include results from the wide stencil methods of [19] on seventeen point
+stencils.
+−1
+−0.5
+0
+0.5
+1
+−1
+−0.5
+0
+0.5
+1
+1
+1.5
+2
+2.5
+3
+30
+40
+50
+60
+70
+80
+90
+100
+110
+120
+130
+0
+20
+40
+60
+80
+100
+120
+140
+160
+180
+N
+CPU Time
+ 
+ 
+Method A
+Method B
+Method C
+Figure 6.1. Results for example 1 on an N × N grid and total CPU time versus
+N for the methods A, B and C.
+6. Numerical experiments
+The three methods are tested on three different examples (smooth or singular solutions). The
+discretization is done in the wide stencil Finite Difference method with 17- points (see Figure 2.2).
+The number of noeuds meshing is equal to N ∗ N with N = 31, 45, 63, 89, 127, the step of meshing
+h = L/N, with L is the length of the side of the rectangular domain Ω. The results obtained are
+compared with those in [19].
+In the first example we study the regular solution given by :
+u (x, y) = exp
+�(x2 + y2)
+2
+�
+with f (x, y) =
+�
+x2 + y2 + 1
+�
+exp
+�
+x2 + y2�
+.
+The Table 1 summarizes the obtained results for different meshing.
+In Figure 6 we show the surface plot of the solution and the total CPU time versus N for the
+methods A, B and C.
+
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+11
+N
+Results in [19]
+Method A
+Method B
+Method C
+31
+1.22 × 10−3
+5.806 × 10−4
+6.853 × 10−4
+8.794 × 10−4
+45
+5.9 × 10−4
+4.92 × 10−4
+6.719 × 10−4
+8.727 × 10−4
+63
+4.2 × 10−4
+4.914 × 10−4
+2.733 × 10−4
+8.601 × 10−4
+89
+2.6 × 10−4
+4.085 × 10−4
+2.09 × 10−5
+8.173 × 10−4
+127
+2.0 × 10−4
+4.056 × 10−4
+1.08 × 10−5
+8.164 × 10−4
+Table 2. Errors
+��u − uN��
+∞ for the exact solution of the second example on an
+N × N grid. We include results from the wide stencil methods of [19] on seventeen
+point stencils.
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+0.5
+1
+0
+0.05
+0.1
+0.15
+0.2
+30
+40
+50
+60
+70
+80
+90
+100
+110
+120
+130
+0
+50
+100
+150
+200
+250
+300
+N
+CPU Time
+ 
+ 
+Method A
+Method B
+Method C
+Figure 6.2. Results for example 2 on an N × N grid and total CPU time versus
+N for the methods A, B and C.
+As a second example, which is C1 , we take the one considered in [19] which is given by
+u(x, y) = 1
+2((
+�
+(x − 0.5)2 + (y − 0.5)2 − 0.2)+)2 with f(x, y) = (1 −
+0.2
+�
+(x − 0.5)2 + (y − 0.5)2)+.
+The results are in Table 2.
+Finally, we consider a third example which is singular at the bord of the domain Ω = [0, 1] ×
+[0.1] ,defined by
+u(x, y) = −
+�
+(2 − x2 − y2) where f(x, y) =
+2
+(2 − x2 − y2)2.
+.
+The results are illustrated in Table 3 and
+
+12
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+N
+Results in [19]
+Method A
+Method B
+Method C
+31
+1.74 × 10−3
+1.7 × 10−3
+5.1 × 10−3
+5.7 × 10−3
+45
+9.8 × 10−4
+1.5 × 10−3
+4.8 × 10−3
+5.5 × 10−3
+63
+5.9 × 10−4
+8.9 × 10−4
+3.9 × 10−3
+5.5 × 10−3
+89
+3.5 × 10−4
+8.9 × 10−4
+3.1 × 10−3
+5.5 × 10−3
+127
+2.0 × 10−4
+8.2 × 10−4
+2.4 × 10−3
+5.5 × 10−3
+Table 3. Errors
+��u − uN��
+∞ for the exact solution of the third example on an N ×N
+grid. We include results from the wide stencil methods of [19] on seventeen point
+stencils.
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+0.5
+1
+−1.5
+−1
+−0.5
+0
+30
+40
+50
+60
+70
+80
+90
+100
+110
+120
+130
+0
+200
+400
+600
+800
+1000
+1200
+1400
+1600
+1800
+N
+CPU Time 
+ 
+ 
+Method A
+Method B
+Method C
+Figure 6.3. Results for example 2 on an N × N grid and total CPU time versus
+N for the methods A, B and C.
+Acknowledgments
+We are indebted to Pr. Pierre-Emmanuelle Jabin for his relevant remarks and his impressive
+comments which have greatly improved this work.
+References
+[1] Guy Barles and Panagiotis E. Souganidis. Convergence of approximation schemes for fully nonlinear second
+order equations. Asymptotic Anal., 4(3):271–283, 1991.
+[2] Jean-David Benamou, Brittany D. Froese, and Adam M. Oberman. Two numerical methods for the elliptic
+Monge-Ampère equation. ESAIM: Math. Model. Numer. Anal., 44(4), 2010.
+[3] Fethi Ben Belgacem, Optimization approach for the Monge-Ampère equation, Acta Mathematica Scientia, Vol.
+38, Issu 4 (2018), 1285-1295.
+[4] C. J. Budd and J. F. Williams. Moving mesh generation using the parabolic Monge-Ampère equation. SIAM
+J. Sci. Comput., 31(5):3438–3465, 2009.
+[5] Eugenio Calabi, Complete affine hyperspheres. I, Symposia Mathematica, Vol. X (Convegno di Geometria
+Differenziale, INDAM, Rome, 1971), Academic Press, London, 1972, pp. 19–38. MR0365607 (51 #1859)
+
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+13
+[6] Shiu Yuen Cheng and Shing-Tung Yau, Complete affine hypersurfaces. I. The com- pleteness of affine metrics,
+Comm. Pure Appl. Math. 39 (1986), no. 6, 839–866, DOI 10.1002/cpa.3160390606. MR859275 (87k:53127)
+[7] Cristian E. Gutiérrez. The Monge-Ampère equation. Progress in Nonlinear Differential Equations and their
+Applications, 44. Birkhäuser Boston Inc., Boston, MA, 2001.
+[8] G. L. Delzanno, L. Chacón, J. M. Finn, Y. Chung, and G. Lapenta. An optimal robust equidistribution
+method for two-dimensional grid adaptation based on Monge-Kantorovich optimization. J. Comput. Phys.,
+227(23):9841–9864, 2008
+[9]
+J. M. Finn, G. L. Delzanno, and L. Chacón. Grid generation and adaptation by Monge- Kantorovich opti-
+mization in two and three dimensions. In Proceedings of the 17th Interna- tional Meshing Roundtable, pages
+551–568, 2008
+[10] E. J. Dean and R. Glowinski. An augmented Lagrangian approach to the numerical solution of the Dirichlet
+problem for the elliptic Monge-Ampère equation in two dimensions. Electron. Trans. Numer. Anal., 22:71–96
+(electronic), 2006.
+[11] E. J. Dean and Roland Glowinski. On the numerical solution of the elliptic Monge- Ampère equation in
+dimension two: a least-squares approach. In Partial differential equations, volume 16 of Comput. Methods
+Appl. Sci., pages 43–63. Springer, Dordrecht, 2008.
+[12] G. De Philippis and A. Figalli, The Monge-Ampère equation and its link to optimal trans- portation, Bull.
+Amer. Math. Soc. (N.S.) 51 (2014), no. 4, 527–580. MR3237759
+[13] T. Glimm and V. Oliker. Optical design of single reflector systems and the Monge-Kantorovich mass transfer
+problem. J. Math. Sci. (N. Y.), 117(3):4096–4108, 2003. Nonlinear problems and function theory.
+[14] Grégoire Loeper and Francesca Rapetti. Numerical solution of the Monge-Ampére equation by a Newton’s
+algorithm. C. R. Math. Acad. Sci. Paris, 340(4):319–324, 2005.
+[15] T. ur Rehman, E. Haber, G. Pryor, J. Melonakos, and A. Tannenbaum. 3D nonrigid regis- tration via optimal
+mass transport on the GPU. Med Image Anal, 13(6):931–40, 12 2009.
+[16]
+Steven Haker, Allen Tannenbaum, and Ron Kikinis. Mass preserving mappings and image registration. In
+MICCAI ’01: Proceedings of the 4th International Conference on Medical Image Computing and Computer-
+Assisted Intervention, pages 120–127, London, UK, 2001. Springer-Verlag
+[17] . Steven Haker, Lei Zhu, Allen Tannenbaum, and Sigurd Angenent. Optimal mass transport for registration
+and warping. Int. J. Comput. Vision, 60(3):225–240, 2004.
+[18] X. Feng and Michael Neilan. Mixed finite element methods for the fully nonlinear Monge-Ampère equation
+based on the vanishing moment method. SIAM J. Numer. Anal., 47(2):1226–1250, 2009.
+[19] B. D. Froese and A. M. Oberman, Convergent finite difference solvers for viscosity solutions of the elliptic
+Monge-Ampère equation in dimensions two and higher, SIAM J. Numer. Anal. 49 (2011), no. 4, 1692–1714.
+MR2831067
+[20] Adam M. Oberman. Convergent difference schemes for degenerate elliptic and parabolic equations: Hamilton-
+Jacobi equations and free boundary problems. SIAM J. Numer. Anal., 44(2):879–895 (electronic), 2006.
+[21] Adam M. Oberman. Computing the convex envelope using a nonlinear partial differential equation. Math.
+Models Methods Appl. Sci., 18(5):759–780, 2008.
+[22] Adam M. Oberman. Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions
+of the eigenvalues of the Hessian. Discrete Contin. Dyn. Syst. Ser. B, 10(1):221–238, 2008
+[23] Adam M. Oberman and Luis Silvestre. The Dirichlet problem for the convex envelope. Trans. Amer. Math.
+Soc. (to appear), 2010 http://arxiv.org/abs/1007.0773
+[24] V. I. Oliker and L. D. Prussner. On the numerical solution of the equation (∂ 2 z/∂x 2 )(∂ 2 z/∂y 2 ) − (∂ 2
+z/∂x∂y) 2 = f and its discretizations, I. Numer. Math., 54(3):271– 293, 1988.
+[25] A. V. Pogorelov, On the improper convex affine hyperspheres, Geometriae Dedicata 1 (1972), no. 1, 33–46.
+MR0319126 (47 #7672)
+
+14
+CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM
+[26] Siltakoski, J. Equivalence of viscosity and weak solutions for the normalized p(x)-Laplacian. Calc. Var. 57, 95
+(2018). https://doi.org/10.1007/s00526-018-1375-1
+[27] Neil S. Trudinger and Xu-Jia Wang, The Bernstein problem for affine maximal hypersur- faces, Invent. Math.
+140 (2000), no. 2, 399–422, DOI 10.1007/s002220000059. MR1757001 (2001h:53016)
+[28] Neil S. Trudinger and Xu-Jia Wang, Affine complete locally convex hypersurfaces, Invent. Math. 150 (2002),
+no. 1, 45–60, DOI 10.1007/s00222-002-0229-8. MR1930881 (2003h:53012)
+[29] Neil S. Trudinger and Xu-Jia Wang, The affine Plateau problem, J. Amer. Math. Soc. 18 (2005), no. 2, 253–289,
+DOI 10.1090/S0894-0347-05-00475-3. MR2137978 (2006e:53071)
+[30] V. Zheligovsky, O. Podvigina, and U. Frisch. The Monge-Ampère equation: Various forms and numerical
+solution. J. Comput. Phys., 229(13):5043–5061, 2010.
+.
+
+40
+50
+60
+70
+80
+90
+100
+110
+N
+
+40
+50
+60
+70
+80
+90
+100
+110
+N
+
+40
+50
+60
+70
+80
+90
+100
+110
+N
+
+40
+50
+60
+70
+80
+90
+100
+110
+N
+
+10
+20
+30
+40
+50
+60
+70
+
+40
+50
+60
+70
+80
+90
+100
+110
+N
+
+40
+50
+60
+70
+80
+90
+100
+110
+N
+
+20
+40
+60
+80
+100
+
+20
+40
+60
+80
+100
+
+40
+50
+60
+70
+80
+90
+100
+110
+N
+
diff --git a/8NFAT4oBgHgl3EQfox1h/content/tmp_files/load_file.txt b/8NFAT4oBgHgl3EQfox1h/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..52eec5a151f27bef5058b07e40a3e3276fe7eba4
--- /dev/null
+++ b/8NFAT4oBgHgl3EQfox1h/content/tmp_files/load_file.txt
@@ -0,0 +1,620 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf,len=619
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='08636v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='NA]  20 Jan 2023  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE  PROBLEM  Hajri Imen 1 Fethi Ben Belgacem 2  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' In this article, we introduce and study three numerical methods for the Dirichlet  Monge-Ampère equation in two dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The approaches consist in considering new equivalent  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The latter are discretized by a wide stencil finite difference discretization and monotone  schemes are obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Hence, we apply the Barles-Souganidis theory to prove the convergence of  the schemes and the Damped Newtons method is used to compute the solutions of the schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Finally, some numerical results are illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Monge-Ampere, Monotone scheme, Newton method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Introduction  We are interested in the numerical solution of the Monge-Ampère equation with Dirichlet bound-  ary condition  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  (MAD)  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  det  �  D2u (x)  �  = f (x) , for x in Ω,  u (x) = ϕ (x) , for x on ∂Ω,  u is convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Where Ω is a convex bounded domain in R2, with boundary ∂Ω, (D2u) , is the Hessian of the  function u, f and ϕ are given functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We take the simplest boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' For more general operator of Monge-Ampère and  other boundary conditions, we mention for instance [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The convexity constraint is crucial for  the (MAD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' It is required for the Monge-Ampère equation to be degenerate elliptic and for (MAD)  to have a unique solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' It is also needed for numerical stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The Monge-Ampère equation,  has extensive applications, it is strictly related to the “prescribed Gauss curvature” problem, see  for instance [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' It appears also in affine geometry, precisely, in the affine sphere problem and the  affine maximal surfaces problem, this was discussed in [5, 6, 25, 27, 28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Other applications  appear in fluid mechanics, geometric optics, and meteorology : for example, in semigeostrophic  equations, the Monge-Ampère equation is coupled with a transport equation, this is pointed out  in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The analysis of the regularity of the Monge-Ampere equation is essential in the study  1Higher  Institute  of  Applied  Studies  in  Humanities  of  Mahdia,5121  Mahdia,  Tunisia,  Email:hajri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='imene2017@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  2Laboratory of partial differential equations (LR03ES04), ISIMM, University of Monastir, El Manar, TUNISIA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Email: fethi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='benbelgacem@isimm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='rnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='tn  1  2  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  of the regularity of the transp ort problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' This, latter, has been employed in many areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We  only briefly mention [8, 9, 4] for mesh geneartion,[15, 16, 17]for image registration, and [12] for  reflector design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Developing an efficient numerical method has aroused a lot of interest, and large  standard techniques have been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' A first method to do so was introduced in [24] by using  a discretization of the geometric Alexandrov-Bakelman interpretation of solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Variational  approaches have been presented in [10, 11], more precisely, the augmented Lagrangian approach  and the least-squares approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' But these methods needed more regularity than can be predicted  for solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' A different approach was studied in [18], using the vanishing moment method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The  periodic case was treated in [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Although, the standard techniques, mentioned above, work well for smooth solutions, and they  fail for singular solutions, for more details, see, for instance, the discussion in [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' To overcome  these difficulties, we have to use the notion of viscosity solution or Alexsandrov solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' In two  dimension, a numerical method was introduced in [24], which is geometric in nature, and converges  to the Alexsandrov solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The method introduced in [22]„ in two dimension and improved in  [19] for higher dimension, uses the wide stencil scheme that converges to the viscosity solution,  which we briefly describe for this reason in the end of this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The following variant of the AM-GM inequalities, is the keystone of our formulation introduced  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  For A and B two symmetric matrices, such that, A, B ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We have the following inequality  2  �  det (AB) ≤ Tr (AB) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Where for symmetric matrices M ≥ 0 means xT Mx ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We can deduce from the above inequality that for a smooth convex solution u of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1),  one can deduce the following inequality  ∆u − 2  �  f ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Let us define the function  ˜g := ∆u − 2  �  f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  It is then straightforward to check that if u is a smooth solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1), then is indeed a solution  of the linear Dirichlet Poisson problem  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2)  �  P˜g� �  ∆u = 2√f + ˜g,  u|Γ = ϕ,  which can be easily descretized by any method of choice if the function ˜g is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We finish this remark by mentioning that the convexity constraint is essential to ensure unique-  ness (for example, u and −u are both solution of the Monge Ampère equation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' For viscosity  solution, this constraint can be required by the equation  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3)  λ1  �  D2u  �  ≥ 0,  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  3  in the viscosity sense, see for instance [21, 22], where λ1 (D2u) is the smallest eigenvalue of the  Hessian of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' However, for a twice continuously differentiable function u, the convexity restriction  is equivalent to requiring that the eigenvalues of the Hessian, D2u, are positives, which is approved  by considering the linear Poisson Dirichlet problem  �  P˜g�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The approaches that we follow, in the present paper, are inspired by the idea developed in [3]  and the wide stencil finite difference discretization introduced in [22] and [19] for viscosity solution  of M-A equation in two and higher dimensions that relies on a framework developed in [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' For  clarity, we recall the full result in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Viscosity solution and convergence theory of approximation schemes  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Degenerate elliptic equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Let F (x, r, p, X) be a continuous real valued function de-  fined on Ω × R × Rn × Sn, with Sn being the space of symmetric n × n matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Consider the  nonlinear, partial differential equation with Dirichlet boundary conditions,  �  F (x, u (x) , Du (x) , D2u (x)) (x) = 0  for x in Ω  u (x) = g (x)  for x in ∂Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Where Ω is a domain in Rn, Du and D2u denote the gradient and Hessian of u, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' [19]The equation F is degenerate elliptic if  F (x, r, p, X) ≤ F (x, s, p, Y ) whenever r ≤ s and Y ≤ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Where Y ≤ X means that Y − X is a nonnegative definite symmetric matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The viscosity solution for the Monge-Ampère equation is defined in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Let u ∈ C (Ω) be convex and f ≥ 0 be continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The function u is a viscosity  subsolution (supersolution) of the Monge-Ampère equation in Ω if whenever convex ϕ ∈ C2 (Ω)  and x0 ∈ Ω are such that (u − ϕ) (x) ≤ (≥) (u − ϕ) (x0) for all x in a neighborhood of x0, then we  must have  det  �  D2φ (x0)  �  ≥ (≤) f (x0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The function u is a viscosity solution if it is both a viscosity subsolution and supersolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  For the existence and uniqueness of viscosity solution for (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1), we mention the next result in  [7],  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Let Ω ⊆ Rd be abounded and strictly convex, g ∈ C (∂Ω) , f ∈ C (Ω) , with f ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Then there exists a unique convex viscosity solution u ∈ C  � ¯Ω  �  of the problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The advantage of considering viscosity solutions come from the following fundamental theorem,  obtained in [1], which gives conditions for convergence of approximation schemes to viscosity  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  4  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' (Convergence of Approximation Schemes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Consider a degenerate elliptic equation,  for which there exist unique viscosity solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' A consistent, stable approximation scheme con-  verges uniformly on compact subsets to the viscosity solution, provided it is monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  By the previous theorem, we need just a way to build a monotone finite difference schemes,  which represents a new challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' In the sequel, we recall here the basic framework introduced in  [20], for building a monotone scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Firstly, a finite difference equation take the form  F i [u] = F i (ui, ui − uj|i̸=j) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We say that a scheme is degenerate elliptic if the following holds [20]:  Definition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The scheme F is degenerate elliptic if F i is non-decreasing in each variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We are now ready to present the following theorem in [20]:  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Under mild analytic conditions, degenerate elliptic schemes are monotone, and non-  expansive in the uniform norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The iteration  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  um+1 = um + dtF (um) ,  is a contraction in L∞ provided dt ≤ K (F)−1 , where K (F) is the Lipschitz constant of the scheme,  regarded as a function from RN −→ RN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We end this paragraphre by the next result, proven in [20]  Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' A proper, locally Lipschitz continuous degenerate elliptic scheme has a unique solu-  tion which is stable in the l∞ norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Wide stencil schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We finish this section by noting that wide stencil schemes are re-  quired to build consistent, monotone schemes of degenerate second order PDEs (see discussion in  [22]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Wide stencil schemes were built for the two-dimensional Monge-Ampère equation in [22]  and for the convex envelope in [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Each approach considered here is a function of eigenvalues of  the Hessian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' To fully discretize the equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1) for the eigenvalues of the Hessian on a finite  difference grid, we approximate the second derivatives by centered finite differences;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' this is the  spatial discretization, with parameter h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We consider also a finite number of possible directions ν  that lie on the grid;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' this is the directional discretization, with parameter dθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The spatial resolution  is improved by using more grid points, the directional resolution is improved by increasing the size  of the stencil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' So, a wide stencil is needed (see Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' First Formulation of the (MAD) in two dimensions (method A)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' An equivalent problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Let us begin with a simple approach to illustrate the ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We  can rephrase, for instance, the (MAD) as the following:  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  �  Find a positive function g, such that  det (D2ug) = λ1 [D2ug] × λ2 [D2ug] = f,  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  5  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Grid for wide stencil 17 points, in two dimension  where: ug is the solution of�  ∆ug = λ1 [D2ug] + λ2 [D2ug]  = 2√f + g,  ug  |Γ  = ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We are now ready to state a first example of our approches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Lemma 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Provided the solution, u, of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1) is in H2, there exists a unique positive function  ˜g ∈ L2, such that u = u˜g, where u˜g is the solution of (P˜g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Conversely, if u¯g is solution of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  for some ¯g > 0, then u¯g = u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Let u be a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' From the above, one can see easily, that u = u˜g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Conversely, if u¯g is a solution of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1), we can clearly see that  �  det (D2u¯g) = f > 0  ∆u¯g ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  It follows that u¯g is convex and satisfies (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  □  Remark 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We notice that according to the result in [26], we have equivalence of viscosity and  weak solutions for the Poisson problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' This motivates us to build a convergent scheme to the  viscosity solution of Poisson problem  �  P˜g�  through the discretization of the (MAD) problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The  viscosity solution u˜g of  �  P˜g�  will be equivalent to the weak solution of (MAD) problem in the  distributional sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Discretization of the problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  Let us consider a regular and uniform cartesian grid, consider the stencil at the reference point  x0 consist of the neighbors x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', xN (as in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We can define vi in polar coordinates by  vi = xi − x0 = hivθi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  6  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  We assume that the stencil is symetric and we define the local spatial resolution and the directional  resolution respectively by  ¯h (x0) = max  i  hi  and  dθ = max  θ∈[−π,π] min  i  |θ − θi|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  First, the problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1) can be written as function of the eigenvalues of the Hessian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We will  then start by discretizing λ1 and λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Hence by a simple substitution we obtain the scheme for (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We recall that the smallest and the largest eigenvalues of a symmetric matrix can be represented  respectively by the Rayleigh-Ritz formula  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  λ1  �  D2u  �  (x) = min  θ  d2u  dν2  θ  ,  λ2  �  D2u  �  (x) = max  θ  d2u  dν2  θ  ,  where νθ = (cos θ, sin θ)is the unit vector in the direction of the angle θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  This formula was used in [22] to build a monotone scheme in two dimension for the (MAD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We begin by building monotone schemes for λ1 and λ2 on a wide stencil uniform grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' These  operators are used to give schemes for all formulations in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  We discretize the eigenvalues of the Hessian by the following formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2)  λh,dθ  1  �  D2ug�  (x) = min  i  ug (x + vi) − 2ug (x) + ug (x − vi)  |vi|2  and  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3)  λh,dθ  2  �  D2ug�  (x) = max  i  ug (x + vi) − 2ug (x) + ug (x − vi)  |vi|2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Lemma 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The schemes (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3) are degenerate elliptic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We follow the same as in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Since each discrete second derivative in the direction vi is the average of the terms which have  the form ug  j − ug  i , they are non-decreasing in ug  j − ug  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Taking a minimum (or maximum) of non-  decreasing functions furnishes a non-decreasing function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  □  We finally substitute (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3) in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1) to obtain the wide stencil finite difference scheme  of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4)  �  Find a positive function gi, such that  λh,dθ  1  �  D2ugi�  × λh,dθ  2  �  D2ugi�  = f i,  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  7  with  �  λh,dθ  1  �  D2ugi�  + λh,dθ  2  �  D2ugi�  = 2  �  f i + gi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  ug  |Γ  = ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Where f i = f (xi) and gi = g (xi) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Lemma 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The scheme (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4) is degenerate elliptic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' From the properties of nondecreasing functions, obtained in [22],  that if G : R2 → R is a nondecreasing function, and if F1 and F2 are degenerate elliptic finite  difference schemes, then so is F = G (F1, F2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' It is also clear that the discretization f i = f (xi)  and gi = g (xi) does affect the ordering properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We conclude that (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4) is degenerate elliptic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  □  In the following, for simplicity, we omit the index i when there is no ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Definition 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We say the scheme Hh,dθ is consistent with the equation (MAD) at x0 if for every  twice continuously differentiable function ϕ (x) defined in a neighborhood of x0, Hh,dθ(ϕ) (x0) →  H (ϕ) (x0) as h, dθ → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The global scheme defined on Ω is consistent if the limit above holds  uniformly for all x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' (The domain is assumed to be closed and bounded).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Lemma 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The consistency holds for (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3) and so for (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Let x0 be a reference point with neighbors x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', xN, and direction vectors vi = xi − x0, for  i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', N, arranged symmetrically, if vi is a direction vector, then so is −vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' By Taylor series one  has  ug (x0 + vi) − 2ug (x0) + ug (x0 − vi)  |vi|2  = d2ug  dv2  i  + O  �  h2  i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Let M given symetric 2 × 2 matrix, that we can take it diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Set vθ a unit vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' It follows  from [22] (Lemma 3) that  min  θ∈{θ1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=',θN} vT  θ Mvθ = λ1 + (λ2 − λ1) O  �  θ2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Which implies that  λ1 (ϕ) (x0) − λh,dθ  1  (ϕ) (x0) = O  �¯h2 + (λ2 − λ1) dθ2�  and thus consistency holds for (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Similar argument gives consistency for (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3) and so for  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  □  Theorem 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Suppose that unique viscosity solutions exist for the equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1) Then the finite  difference scheme given by (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4) converges uniformly on compacts subsets of Ω to the unique  viscosity solution of the equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We need to verify consistency and monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Consistency follows from Lemma 14 and  monotonicity follows from Lemma 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  □  8  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  Finally, the scheme yields a fully nonlinear equation defined on grid functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We perform the  iteration (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1) and by Theorem 7 will converge to a fixed point which is a solution of the equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  This approach is used in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' TWO METHODS OF FIXED POINT  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The first method (Method B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Notice that from Lemma 9 if u is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  u (x, y) = u˜g (x, y) it follows that det (D2u) = det  �  D2u˜g�  , where u˜g is the solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2) for  ˜g ∈ L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  By writing  △u˜g = 2  �  f + ˜g =  �  (∆u˜g)2 + 2 (f − det (D2u˜g))  and expanding  �  ∆u˜g�2 =  �  u˜g  xx  �2 +  �  u˜g  yy  �2 + 2u˜g  xxu˜g  yy we have  △u˜g =  ��  u˜g  xx  �2  +  �  u˜g  yy  �2  + 2  �  u˜g  xy  �2  + 2f = 2  �  f + ˜g  Let us define the operator Q : L2 (Ω) → L2 (Ω) for Ω ⊂ R2 by  Q (g) :=  �  (ug  xx)2 + (ug  yy)2 + 2 (ug  xy)2 + 2f − 2  �  f,  with ug solution of (Pg) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' So, one has  Lemma 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' ˜g is a fixed point of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' It follows from above expansions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  □  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We consider the following scheme  gn+1 = Q (gn) =  �  (ugn  xx)2 + (ugn  yy)2 + 2 (ugn  xy)2 + 2f − 2  �  f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  With initial value g0 > 0 close to zero and ug0 is the solution of (P g0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Remark 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The advantage of this method by comparing it to that in [19] and [2] is that it  guarantees, at least, at each iteration that tr (D2ugn (x)) > 0, which is necessary to check the  convexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Although this method turns out to be simple to implement is well suited in the case where ug  is in H2 (Ω) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' If not, the method may not converge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  g0 ≥ 0 (close to 0), solve (P g0) , ((ug)0 = ug0being known),  For n ≥ 0, compute gn+1 and (ug)n+1 as follows  gn+1 = Q (gn) ,  (ug)n+1 solution of  �  P gn+1�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  9  Where, the method involves simply discretising the second derivatives using standard central dif-  ferences on a uniform Cartesian grid, as a result  D2  xxuij  =  1  h2 (ui+1,,j + ui−1,j−, 2ui,,j) ,  D2  yyuij  =  1  h2 (ui,,j+1 + ui,,j−1 − 2ui,,j) ,  D2  xxuij  =  1  4h2 (ui+1,,j+1 + ui−1,,j−1 − ui−1,,j+1 − ui+1,,j−1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The second method (Method C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' In the same setting we define the next operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Definition 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Let Ω a bounded domain in R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Define the operator F : L2 (Ω) → L2 (Ω) ,  by  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1)  F (g) =  �  |det [D2ug] − f| + g,  where ug is a solution of  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2)  (Pg)  �  ∆u = 2√f + g,  u|Γ = ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  For g ∈ L2 (Ω), the operator F is well defined and it is easy to verify that  Lemma 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' �g is a fixed point of the operator F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Let u a smooth solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' It follows from Lemma 9 that u = u�g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Which implies that  det  �  D2u�g�  = det [D2u] = f and therefore, F (�g) = �g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  □  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We define the following scheme  gn+1 = F (gn) =  �  |det [D2ugn] − f| + gn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  With initial value g0 > 0 close to zero and ug0 is the solution of (P g0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Remark 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The method is advantageous, it simply involves evaluating derivatives and solving the  Poisson equation that preserves the convexity constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  g0 ≥ 0 (close to 0), solve (P g0) , ((ug)0 = ug0being known),  For n ≥ 0, compute gn+1 and (ug)n+1 as follows  gn+1 = α  �  |det [D2ugn] − f| + gn,  with 0 < α < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  (ug)n+1 solution of  �  P gn+1�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  As in the above method, second derivatives are descretized using standard central differences on a  uniform Cartesian grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  10  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  N  Results in [19]  Method A  Method B  Method C  31  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='44 × 10−4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='965 × 10−4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='226 × 10−4  18 × 10−4  45  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='52 × 10−4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='052 × 10−4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='202 × 10−4  18 × 10−4  63  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='06 × 10−5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='801 × 10−4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='190 × 10−4  17 × 10−4  89  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='32 × 10−5  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='035 × 10−4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='494 × 10−5  17 × 10−4  127  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='06 × 10−5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='015 × 10−4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='888 × 10−5  17 × 10−4  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Errors  ��u − uN��  ∞ for the exact solution of the first example on an N ×N  grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We include results from the wide stencil methods of [19] on seventeen point  stencils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  −1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  1  −1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  1  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  3  30  40  50  60  70  80  90  100  110  120  130  0  20  40  60  80  100  120  140  160  180  N  CPU Time  Method A  Method B  Method C  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Results for example 1 on an N × N grid and total CPU time versus  N for the methods A, B and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Numerical experiments  The three methods are tested on three different examples (smooth or singular solutions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The  discretization is done in the wide stencil Finite Difference method with 17- points (see Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The number of noeuds meshing is equal to N ∗ N with N = 31, 45, 63, 89, 127, the step of meshing  h = L/N, with L is the length of the side of the rectangular domain Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The results obtained are  compared with those in [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  In the first example we study the regular solution given by :  u (x, y) = exp  �(x2 + y2)  2  �  with f (x, y) =  �  x2 + y2 + 1  �  exp  �  x2 + y2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The Table 1 summarizes the obtained results for different meshing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  In Figure 6 we show the surface plot of the solution and the total CPU time versus N for the  methods A, B and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  11  N  Results in [19]  Method A  Method B  Method C  31  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='22 × 10−3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='806 × 10−4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='853 × 10−4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='794 × 10−4  45  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='9 × 10−4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='92 × 10−4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='719 × 10−4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='727 × 10−4  63  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2 × 10−4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='914 × 10−4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='733 × 10−4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='601 × 10−4  89  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='6 × 10−4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='085 × 10−4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='09 × 10−5  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='173 × 10−4  127  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='0 × 10−4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='056 × 10−4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='08 × 10−5  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='164 × 10−4  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Errors  ��u − uN��  ∞ for the exact solution of the second example on an  N × N grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We include results from the wide stencil methods of [19] on seventeen  point stencils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='8  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2  30  40  50  60  70  80  90  100  110  120  130  0  50  100  150  200  250  300  N  CPU Time  Method A  Method B  Method C  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Results for example 2 on an N × N grid and total CPU time versus  N for the methods A, B and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  As a second example, which is C1 , we take the one considered in [19] which is given by  u(x, y) = 1  2((  �  (x − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5)2 + (y − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5)2 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2)+)2 with f(x, y) = (1 −  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2  �  (x − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5)2 + (y − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5)2)+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The results are in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Finally, we consider a third example which is singular at the bord of the domain Ω = [0, 1] ×  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1] ,defined by  u(x, y) = −  �  (2 − x2 − y2) where f(x, y) =  2  (2 − x2 − y2)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  The results are illustrated in Table 3 and  12  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  N  Results in [19]  Method A  Method B  Method C  31  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='74 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='7 × 10−3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1 × 10−3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='7 × 10−3  45  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='8 × 10−4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5 × 10−3  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='8 × 10−3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5 × 10−3  63  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='9 × 10−4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='9 × 10−4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='9 × 10−3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5 × 10−3  89  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5 × 10−4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='9 × 10−4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1 × 10−3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5 × 10−3  127  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='0 × 10−4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2 × 10−4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4 × 10−3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5 × 10−3  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Errors  ��u − uN��  ∞ for the exact solution of the third example on an N ×N  grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' We include results from the wide stencil methods of [19] on seventeen point  stencils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='8  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  1  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  −1  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='5  0  30  40  50  60  70  80  90  100  110  120  130  0  200  400  600  800  1000  1200  1400  1600  1800  N  CPU Time  Method A  Method B  Method C  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Results for example 2 on an N × N grid and total CPU time versus  N for the methods A, B and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Acknowledgments  We are indebted to Pr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Pierre-Emmanuelle Jabin for his relevant remarks and his impressive  comments which have greatly improved this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  References  [1] Guy Barles and Panagiotis E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Souganidis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Convergence of approximation schemes for fully nonlinear second  order equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Asymptotic Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 4(3):271–283, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [2] Jean-David Benamou, Brittany D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Froese, and Adam M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Oberman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Two numerical methods for the elliptic  Monge-Ampère equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' ESAIM: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Numer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 44(4), 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [3] Fethi Ben Belgacem, Optimization approach for the Monge-Ampère equation, Acta Mathematica Scientia, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  38, Issu 4 (2018), 1285-1295.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [4] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Budd and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Moving mesh generation using the parabolic Monge-Ampère equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' SIAM  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 31(5):3438–3465, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [5] Eugenio Calabi, Complete affine hyperspheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' I, Symposia Mathematica, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' X (Convegno di Geometria  Differenziale, INDAM, Rome, 1971), Academic Press, London, 1972, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 19–38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' MR0365607 (51 #1859)  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  13  [6] Shiu Yuen Cheng and Shing-Tung Yau, Complete affine hypersurfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The com- pleteness of affine metrics,  Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 39 (1986), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 6, 839–866, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1002/cpa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='3160390606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' MR859275 (87k:53127)  [7] Cristian E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Gutiérrez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The Monge-Ampère equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Progress in Nonlinear Differential Equations and their  Applications, 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Birkhäuser Boston Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', Boston, MA, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [8] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Delzanno, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Chacón, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Finn, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Chung, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Lapenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' An optimal robust equidistribution  method for two-dimensional grid adaptation based on Monge-Kantorovich optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=',  227(23):9841–9864, 2008  [9]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Finn, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Delzanno, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Chacón.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Grid generation and adaptation by Monge- Kantorovich opti-  mization in two and three dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' In Proceedings of the 17th Interna- tional Meshing Roundtable, pages  551–568, 2008  [10] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Dean and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Glowinski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' An augmented Lagrangian approach to the numerical solution of the Dirichlet  problem for the elliptic Monge-Ampère equation in two dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Numer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 22:71–96  (electronic), 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [11] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Dean and Roland Glowinski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' On the numerical solution of the elliptic Monge- Ampère equation in  dimension two: a least-squares approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' In Partial differential equations, volume 16 of Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Methods  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', pages 43–63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Springer, Dordrecht, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [12] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' De Philippis and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Figalli, The Monge-Ampère equation and its link to optimal trans- portation, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' (N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=') 51 (2014), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 4, 527–580.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' MR3237759  [13] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Glimm and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Oliker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Optical design of single reflector systems and the Monge-Kantorovich mass transfer  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' (N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' ), 117(3):4096–4108, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Nonlinear problems and function theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [14] Grégoire Loeper and Francesca Rapetti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Numerical solution of the Monge-Ampére equation by a Newton’s  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Paris, 340(4):319–324, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [15] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' ur Rehman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Haber, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Pryor, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Melonakos, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Tannenbaum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 3D nonrigid regis- tration via optimal  mass transport on the GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Med Image Anal, 13(6):931–40, 12 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [16]  Steven Haker, Allen Tannenbaum, and Ron Kikinis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Mass preserving mappings and image registration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' In  MICCAI ’01: Proceedings of the 4th International Conference on Medical Image Computing and Computer-  Assisted Intervention, pages 120–127, London, UK, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Springer-Verlag  [17] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Steven Haker, Lei Zhu, Allen Tannenbaum, and Sigurd Angenent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Optimal mass transport for registration  and warping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Vision, 60(3):225–240, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [18] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Feng and Michael Neilan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Mixed finite element methods for the fully nonlinear Monge-Ampère equation  based on the vanishing moment method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Numer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 47(2):1226–1250, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Froese and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Oberman, Convergent finite difference solvers for viscosity solutions of the elliptic  Monge-Ampère equation in dimensions two and higher, SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Numer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 49 (2011), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 4, 1692–1714.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  MR2831067  [20] Adam M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Oberman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Convergent difference schemes for degenerate elliptic and parabolic equations: Hamilton-  Jacobi equations and free boundary problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Numer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 44(2):879–895 (electronic), 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [21] Adam M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Oberman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Computing the convex envelope using a nonlinear partial differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Models Methods Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 18(5):759–780, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [22] Adam M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Oberman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions  of the eigenvalues of the Hessian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Discrete Contin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' B, 10(1):221–238, 2008  [23] Adam M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Oberman and Luis Silvestre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The Dirichlet problem for the convex envelope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' (to appear), 2010 http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='org/abs/1007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='0773  [24] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Oliker and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Prussner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' On the numerical solution of the equation (∂ 2 z/∂x 2 )(∂ 2 z/∂y 2 ) − (∂ 2  z/∂x∂y) 2 = f and its discretizations, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Numer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 54(3):271– 293, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Pogorelov, On the improper convex affine hyperspheres, Geometriae Dedicata 1 (1972), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 1, 33–46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  MR0319126 (47 #7672)  14  CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM  [26] Siltakoski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Equivalence of viscosity and weak solutions for the normalized p(x)-Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Calc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Var.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 57, 95  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1007/s00526-018-1375-1  [27] Neil S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Trudinger and Xu-Jia Wang, The Bernstein problem for affine maximal hypersur- faces, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  140 (2000), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 2, 399–422, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1007/s002220000059.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' MR1757001 (2001h:53016)  [28] Neil S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Trudinger and Xu-Jia Wang, Affine complete locally convex hypersurfaces, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 150 (2002),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 1, 45–60, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1007/s00222-002-0229-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' MR1930881 (2003h:53012)  [29] Neil S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Trudinger and Xu-Jia Wang, The affine Plateau problem, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 18 (2005), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' 2, 253–289,  DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='1090/S0894-0347-05-00475-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' MR2137978 (2006e:53071)  [30] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Zheligovsky, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Podvigina, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Frisch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' The Monge-Ampère equation: Various forms and numerical  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content=', 229(13):5043–5061, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
+page_content='  40  50  60  70  80  90  100  110  N  40  50  60  70  80  90  100  110  N  40  50  60  70  80  90  100  110  N  40  50  60  70  80  90  100  110  N  10  20  30  40  50  60  70  40  50  60  70  80  90  100  110  N  40  50  60  70  80  90  100  110  N  20  40  60  80  100  20  40  60  80  100  40  50  60  70  80  90  100  110  N' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NFAT4oBgHgl3EQfox1h/content/2301.08636v1.pdf'}
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+arXiv:2301.11595v1  [math-ph]  27 Jan 2023
+Exact solutions of Maxwell equations in homogeneous
+spaces with group of motions G3(IX)
+V. V. Obukhov
+Institute of Scietific Research and Development, Tomsk State Pedagogical University
+(TSPU). Tomsk State Pedagogical University, 60 Kievskaya St., Tomsk, 634041, Russia;
+Laboratory for Theoretical Cosmology, International Center of Gravity and Cosmos, Tomsk
+State University of Control Systems and Radio Electronics (TUSUR), 36, Lenin Avenue, Tomsk,
+634050, Russia
+Keywords: Maxwell equations, Klein-Gordon-Fock equation, algebra of symmetry operators,
+theory of symmetry, linear partial differential equations.
+Exact solutions of Maxwell equations in homogeneous spaces with group of motions G3(IX)
+1
+Introduction
+All known methods of integration of main differential equations of mathematical physics are
+based on complete reduction of these equations to a system of ordinary differential equations.
+Reduction is carried out using symmetry operators. For the equations of motion of classical
+or quantum sample particle in external electromagnetic and gravitational fields the symmetry
+operators are integrals of motion. It is known that a necessary condition for the existence of
+integrals of motion is the existence of spacetime symmetry given by the Killing fields.
+Thus the problem of exact integration is closely related to the study of space-time symmetry.
+At present two methods of exact integration of equations of motion are known. These are
+methods of commutative (CIM) and noncommutative (NCIM) integration. The first method is
+based on the theory of complete separation of variables, and it is applicable in stackel spaces.
+Stackel spaces admit complete sets consisting of mutually commuting Killing fields. Theory
+of Stackel spaces was developed in [1], [2], [3], [4], [5], [6],[7].
+A description of the theory
+and a detailed bibliography can be found in [8], [9] [10], [13] (see also [12]). Solutions of field
+equations, which are still used widely in the theory of gravitation, have been constructed on
+the basis of Stackel spaces. These solutions are often used in the study of various effects in
+gravitational fields (see, for example,[14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25],
+[26]).
+The second method (NCI method) is based on the use of noncommutative algebras of
+symmetry operators linear in moments and constructed using vector Killing fields. The method
+was proposed in [27]. The development of the method and its application to gravity theory can
+be found in [28], [29], [30], [31].
+1
+
+As in stackel spaces in the spaces with a noncommutative group of motions the equations
+of motion of a test particle admit the complete reduction to a system of ordinary differential
+equations.
+Therefore, we will call space-time manifolds admitting noncommutative groups
+Gr, r ≥ 3 as post-Stackel spaces (PSS).
+By analogy with stackel spaces we will call the PSS non-isotropic if a group Gr (or its
+subgroup of rank 3) acts transitive on a non-isotropic hypersurface of spacetime, or isotropic,
+if the hypersurface is isotropic. For non-isotropic post-stackel spaces we will also use the term
+”homogeneous post-stackel space (HPSS)”.
+The same classification problems can be considered for the PSS as for the stackel spaces.
+For example, in the papers [9] [10], [11] a complete classification is given for the case when
+the Hamilton-Jacobi equation for a charged test particle admits the complete separation of
+variables in the external electromagnetic field. A similar classification problem has been solved
+for PSS-spaces as well. In [32] PSS-spaces with transitive four-parameter groups of motions
+are considered; in [33] HPSS-spaces are considered (see also [34]); in [35] PSS-spaces with
+groups acting on isotropic hypersurfaces of transitivity are considered. PSS-spaces with four-
+parameter groups of motions are considered in [36], provided that these groups have transitive
+three-parameter subgroups. Thus, one has found the potentials of all admissible electromag-
+netic fields, for which the Hamilton-Jacobi and Klein-Gordon-Fock equations have algebras of
+symmetry operators given by groups of motions of post-stackel spaces. It was proved, that
+the Klein-Gordon-Fock equation admits the algebra of symmetry operators given by groups of
+motions of PSS if and only if the Hamilton-Jacobi equations admits the appropriate algebra of
+integrals of motion.
+Next classification problem is the classification of electrovacuum solutions of the Einstein-
+Maxwell equations for the case, when CIM and NCIM methods are applicable. During the
+century-long history of General relativity, many exact solutions of the vacuum and electrovac-
+uum Einstein equations have been found (see, for example,[42] ). Nevertheless, this problem has
+not lost its relevance up to now. The main purpose of the classification is not so much to find
+new exact solutions, as to list all gravitational and electromagnetic fields, in which equations
+of motion of test particles can be exactly integrated or at least reduced to systems of ordinary
+differential equations. This problem divided into two stages.
+At the first stage all non-equivalent classes of solutions of the vacuum Maxwell equations for
+the potentials of admissible electromagnetic fields are found. At the second stage the obtained
+classification is used to classify the corresponding electrovacuum spaces. Historically, for Stackel
+spaces this problem was solved before the problem of the first stage (see the bibliography given
+in [9], [10], [11]). The present article is devoted to solving the first stage of this classification
+problem. All non-equivalent solutions of empty Maxwell equations in homogeneous spaces of
+type IX according to Bianchi’s classification are found.
+2
+Admissible electromagnetic fields in homogeneous spaces
+There are two definitions of homogeneous spaces.
+According to the first a spacetime
+V4
+is homogeneous if its subspace
+V3,
+endowed with the Euclidean space signature, admits
+coordinate transformations (forming the group G3(N) of motions of spaces V4), that allow to
+connect any two points in
+V3
+(see [38]). This definition directly implies that metric of the
+2
+
+V4 in the semi-geodesic coordinate system
+[ui]
+can be represented as follows:
+ds2 = −du02 + ηabla
+αlb
+βduαduβ,
+gij = −δ0
+i δ0
+j + δa
+i δb
+jea
+αeb
+βηab(u0),
+det|ηab| > 0
+ea
+α,0 = 0.
+(1)
+The coordinate indices of the variables of the semi-geodesic coordinate system are denoted
+by lower case Latin letters:
+i, j, k = 0, 1 . . . 3.
+The coordinate indices of the variables of the
+local coordinate system on the hypersurface
+V3
+are denoted by lower case Greek letters:
+α, β, γ = 1, . . . 3.
+the time variable is denoted by a 0 index. Group indices and indices of
+nonholonomic frame are denoted by
+a, b, c = 1, . . . 3.
+Summation is performed over repeated
+upper and lower indices within the index range.
+The 1-form
+ea
+αduα
+is invariant under the acting of the group G3(N). The vectors of the
+frame ea
+α define a non-holonomic coordinate system in V3. The dual triplet of vectors
+eα
+a,
+eα
+aeb
+α = δb
+a,
+eα
+aea
+β = δα
+β
+defines the operators of the group algebra:
+ˆYa = eα
+a∂a,
+[ ˆYa, ˆYb] = Cc
+ab ˆYc.
+(2)
+According to another definition, space-time
+V4
+is homogeneous if it admits a three-parameter
+group of motions
+G3(N),
+whose hypersurface
+V3
+of transitivity has the Euclidean space
+signature. The Killing vector fields ξα
+a
+and their dual vector fields
+ξa
+α
+form another frame
+of the space V3 and another representation of the algebra of the group G3. The vector fields
+ξα
+a
+satisfy the Killing equations:
+gαβ
+,γ ξγ
+a = gαγξβ
+a,γ + gβγξα
+a,γ,
+(3)
+and sets the infinitesimal group operators of the algebra G3
+ˆXa = ξα
+a ∂α,
+[ ˆXa, ˆXb] = Cc
+ab ˆXc.
+(4)
+Let us consider electromagnetic field with potential Ai. For a charged test particle, moving in
+this external electromagnetic field, it has been proved, that the Hamilton-Jacobi equation:
+gijPiPj = m,
+Pi = pi + Ai.
+(5)
+and the Klein-Gordon-Fock equation:
+ˆHϕ = (gij ˆPi ˆPj)ϕ = m2ϕ,
+ˆPk = ˆpk + Ak.
+(6)
+admit the integrals of motion, which are given by Killing vectors:
+˜Xα = ξi
+αpi
+(or
+ˆ˜Xα = ξi
+αˆpi),
+if and only if the conditions:
+ξα
+a ( ˜A),α = Cc
+ab ˜A
+(7)
+are satisfied (see papers [33]). Here
+pi = ∂iϕ;
+ˆpk = −ı ˆ∇k;
+( ˆ∇k is the covariant deriva-
+tive operator corresponding to the partial derivative operator -
+ˆ∂i
+in the coordinate field
+ui),
+ϕ
+is a scalar function of particle with mass
+m;
+˜Aa = ξα
+a Aα.
+3
+
+The electromagnetic field whose potential satisfies condition (7) is called admissible. All
+admissible electromagnetic fields for groups of motion
+Gr(N)
+(r ≤ 4),
+acting transitively
+on hypersurfaces of the spacetime, have been found in [33], [35], [36].
+Solutions of the set of equations (7) for HPSS of type IX have the form:
+Aα = αa(u0)la
+α ⇒ Aa = lα
+aAα = αa(u0).
+(8)
+To prove this let’s find the frame vector. We will use the metric tensor of IX-type space by
+Bianchi, found in Petrov’s book [39]. As it is known, the Bianchi type IX metric contains as
+a special case the space of constant positive curvature and therefore is of special interest for
+cosmology.
+ds2 = du12[a11 − (a12 cos 2u3 + a22 sin 2u3)] + 2du1du3((a13 cos u3 − a23 sin u3)+
+(9)
++2du1du2[(a13 cos u3 − a23 sin u3) cos u1 + (a12 cos 2u3 − a22 sin 2u3) sin u1]
++du22[a33cos u12 + (a23 cos u3 + a13 sin u3) sin 2u1 + (a12 sin 2u3 + a22 cos 2u3 + a11)sin u12]
+2du2du3(a33 cos u1 + (a23 cos u3 + a13 sin u3) sin u1) + du32a33 + edu02.
+aab are arbitrary functions on u0.
+To obtain the functions
+lα
+a
+, it is sufficient to consider the components
+g13, g23
+from the system (3). The solution has the form:
+la
+α = δp
+αla
+p(u1, u3) + δ3
+αδa
+3
+.
+From the equations:
+g13 = a13 cos u3 − a23 sin u3 = η3ala
+1,
+g23 = a33 cos u1 + (a23 cos u3 + a13 sin u3) sin u1 = η3ala
+1
+it follows:
+la
+α =
+�
+�
+cos u3
+− sin u3
+0
+sin u1 sin u3
+sin u1 cos u3
+cos u1
+0
+0
+1
+�
+� , lα
+a =
+�
+�
+cos u3
+sin u3
+sin u1
+−cos u1 sin u3
+sin u1
+− sin u3
+cos u3
+sin u1
+−cos u1 cos u3
+sin u1
+0
+0
+1
+�
+� ,
+(10)
+la
+αlα
+b = δa
+b .
+The lower index numbers the lines. One can show that the vector fields (10) satisfy the
+equations (1), (2): We present the components of the vectors ξα
+a in the form of a matrix:
+||ξα
+a || =
+�
+�
+0
+1
+0
+cos u2
+−cos u1 sin u2
+sin u1
+sin u2
+sin u1
+− sin u2
+−cos u1 cos u2
+sin u1
+cos u2
+sin u1
+�
+�
+The components ˜Aα can be expressed through Aα as follows:
+˜Aa = Zb
+aAb,
+4
+
+where
+||Zb
+a = ξα
+a lb
+α|| =
+�
+�
+sin u1 sin u3
+sin u1 cos u3
+cos u1
+(cos u2 cos u3 − sin u2 sin u3 cos u1)
+−(cos u2 sin u3 + sin u2 cos u3 cos u1)
+sin u1 sin u2
+−(sin u2 cos u3 + cos u2 sin u3 cos u1)
+(sin u2 sin u3 − cos u2 cos u3 cos u1)
+cos u2 sin u1
+�
+� .
+It can be shown by direct calculation that the elements of the matrix Zb
+a satisfy the equation:
+Zb
+a|c = Ca1
+caZb
+a1,
+|a = lα
+a∂α.
+(11)
+Therefore, the equation (7) can be reduced to the form:
+ξα
+a Ab,α = 0 ⇒ Aa = αa(u0).
+(12)
+3
+Maxwell’s equations with zero electromagnetic field
+sources in a homogeneous spacetime
+All exact solutions of vacuum Maxwell equations for solvable groups have been found in the
+papers [40], [41]. In the present paper the problem is solved for the group G3(IX).
+We will use the first definition of homogeneous spaces. Note, that for the space-time with
+the groups of motions G3(I) − G3(V I), G3(IX) both definitions are equivalent
+Consider the Maxwell equations with zero electromagnetic field sources in homogeneous
+space in the presence of an electromagnetic field invariant with respect to the group Gr:
+1
+√−g(√−gF ij),j = 0,
+(13)
+The metric tensor is defined by relations (1), the electromagnetic potential by the relations (7).
+When i = 0, from the set of equations (13) it follows:
+1
+√−g(√−ggαβF0β)α = 1
+l (llα
+aηab ˙αb),α = ηabρa ˙αb = 0.
+(14)
+Here it is denoted g = − det ||gαβ|| = −(ηl)2,
+where
+η2 = det ||ηαβ||,
+l = det ||la
+α||,
+ρa =
+lα
+a,α + l|a/l,
+the dots means the time derivatives. Let
+i = α.
+Then from the equation (13)
+it follows:
+1
+η(ηgαβF0β),0 = 1
+l (lgνβgαγFβγ),ν ⇒ 1
+η(ηηablα
+a ˙αb),0 = 1
+l (llν
+alβ
+b ηablα
+˜alγ
+˜b η˜a˜bFβγ),ν ⇒
+(15)
+(ηηab ˙αb),0 = ηla
+α
+l (llβ
+b lα
+˜a1lγ
+˜b Fβγ)|a1ηa1bη˜a˜b.
+(16)
+Let us find components of Fαβ, using the relations (8).
+Fαβ = (la
+β,α − la
+β,α)αa = lc
+βlγ
+c ld
+αlν
+d(la
+γ,ν − la
+ν,γ)αa = lb
+βla
+αlc
+γ(lγ
+a|b − lγ
+b|a)αc = lb
+βla
+αCc
+baαc.
+(17)
+Then
+(lF αβ),β = ηabη˜a˜bCd
+˜bbαd((llα
+a)|˜a + llα
+alγ
+˜a,γ).
+(18)
+5
+
+Structural constants of a group
+G3
+can be present in the form:
+Cc
+ab = Cc
+12ε12
+˜a˜b + Cc
+13ε13
+˜a˜b + Cc
+23ε23
+˜a˜b,
+εAB
+ab = δA
+a δB
+b − δA
+b δB
+a .
+(19)
+Using the notations:
+σ1 = Ca
+23αa,
+σ2 = Ca
+31αa,
+σ3 = Ca
+12αa,
+γ1 = σ1η11 + σ2η12 + σ3η13,
+γ2 = σ1η12 + σ2η22 + σ3η23,
+γ3 = σ1η13 + σ2η23 + σ3η33,
+let us reduce Maxwell’s equations (13) to the form:
+η(ηab ˙αb),0 = δa
+1(γ1(C1
+32) − γ2(C1
+31 + ρ3) + γ3(C1
+21 + ρ2)) + δa
+2(γ1(C2
+32 + ρ3)+
+(20)
+γ2C2
+13 − γ3(C2
+12ρ1)) + δa
+3(−γ1(C3
+23 + ρ2) + γ2(C3
+13 + ρ1) + γ3C3
+21),
+The order of the equations (20) can be decreased by introducing a new independent functions:
+βa = βa = ηηab ˙αb
+⇒
+η ˙αa = ηabβb.
+(21)
+Let us consider the Maxwell equations for the group G3(IX). As in this case
+non zero
+structural constants are following:
+C3
+12 = C2
+31 = C1
+23 = 1,
+functions
+σa, γ1
+have the form:
+σ1 = α1,
+σ2 = α2,
+σ3 = α3.
+γ1 = α1η11 + α2η12 + α3η13,
+γ2 = α1η12 + α2η22 + α3η23,
+γ1 = α1η13 + α2η23 + α3η33.
+Using these relations, we obtain Maxwell’s equations (14), (20) as a system of linear algebraic
+equations on the unknown functions
+nab:
+nab = ηab
+η ⇒ η =
+1
+det nab
+.
+(22)
+ˆW ˆn = ˆω,
+(23)
+where
+ˆW =
+�
+�
+�
+�
+�
+�
+�
+�
+α1
+α2
+α3
+0
+0
+0
+β1
+β2
+β3
+0
+0
+0
+0
+α1
+0
+α2
+α3
+0
+0
+β1
+0
+β2
+β3
+0
+0
+0
+α1
+0
+α2
+α3
+0
+0
+β1
+0
+β2
+β3
+�
+�
+�
+�
+�
+�
+�
+�
+,
+(24)
+ˆnT = (n11, n12, n13, n22, n23, n33);
+ˆωT = (− ˙β1, ˙α1, − ˙β2, ˙α2, − ˙β3, ˙α3),
+6
+
+index T means the transposition of a matrix. Let us find the algebraic complement of the
+matrix ˆW :
+ˆV =
+�
+�
+�
+�
+�
+�
+�
+�
+β1V 2
+1
+−α1V 2
+1
+β2V 2
+1
+−α2V 2
+1
+β3V 2
+1
+−α3V 2
+1
+β1V1V2
+−α1V1V2
+β2V1V2
+−α2V1V2
+β3V1V2
+−α3V1V2
+β1V1V3
+−α1V1V3
+β2V1V3
+−α2V1V3
+β3V1V3
+−α3V1V3
+β1V 2
+2
+−α1V 2
+2
+β2V 2
+2
+−α2V 2
+2
+β3V 2
+2
+−α3V 2
+2
+β1V2V3
+−α1V2V3
+β2V2V3
+−α2V2V3
+β3V2V3
+−α3V2V3
+β1V 2
+3
+−α1V 2
+3
+β2V 2
+3
+−α2V 2
+3
+β3V 2
+3
+−α3V 2
+3
+�
+�
+�
+�
+�
+�
+�
+�
+(25)
+As ˆW is singular matrix, ˆV is the annulling matrix for ˆW:
+ˆV ˆW = 0.
+(26)
+Therefore, one of the equations from the system (23) can be replaced by the equation:
+δab( ˙αa ˙αb + ˙βa ˙βb) ⇒ δab(αaαb + βaβb) = c2 = const.
+(27)
+Depending on the rank of the matrix ˆW, one or more functions nab are independent. The
+remaining functions nab can be expressed through them and through the functions αa, βa. For
+classification it is necessary to find non-equivalent solutions of the system (23). Obviously, this
+system are symmetric with respect to the transposition
+lα
+1 ↔ lα
+2 . Therefore the reference
+indices a = 1 and a = 2 can be interchanged. Taking this observation into account, let us
+consider all non-equivalent options.
+4
+Solutions of Maxwell equations
+1.
+a1V1 ̸= 0 ⇒ the minor ˆW12 and its inverse matrix ˆΩ = ˆW −1
+12 have the form:
+ˆW12 =
+�
+�
+�
+�
+�
+�
+α2
+α3
+0
+0
+0
+α1
+0
+α2
+α3
+0
+β1
+0
+β2
+β3
+0
+0
+α1
+0
+α2
+α3
+0
+β1
+0
+β2
+β3
+�
+�
+�
+�
+�
+�
+,
+(28)
+ˆΩ1 =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+− V2
+α1V1
+− α3β2
+α1V1
+α2α3
+α1V1
+− α3β3
+α1V1
+α2
+3
+α1V1
+− V3
+α1V1
+α2β2
+α1V1
+− α2
+2
+α1V1
+α2β3
+α1V1
+−α2α3
+α1V1
+− V 2
+2
+α1V 2
+1
+(α3β1V1−α2β3V3)
+α1V 2
+1
+α3(α2V2−α1V1)
+α1V 2
+1
+−α3β3V2
+α1V 2
+1
+α2
+2V2
+α1V 2
+1
+− V2V3
+α1V 2
+1
+α2β2V2
+α1V 2
+1
+− α2
+2V2
+α1V 2
+1
+−α3β3‘V3
+α1V 2
+1
+α2
+3V3
+α1V 2
+1
+− V 2
+3
+α1V 2
+1
+α2β2V3
+α1V 2
+1
+− α2
+2V3
+α1V 2
+1
+(α3β2V3−α2β1V1)
+α1V 2
+1
+α2(α1V1−α3V3)
+α1V 2
+1
+�
+�
+�
+�
+�
+�
+�
+�
+�
+(29)
+Then the solution of equation (23) can be represented as:
+ˆn1 = ˆΩ1ˆω1,
+(30)
+were
+ˆnT
+1 = (n12, n13, n22, n23, n33);
+ˆωT
+1 = (−( ˙β1 + α1n11), − ˙β2, ˙α2, −β3, ˙α3),
+7
+
+Function
+n11,
+as well as the functions
+αa,
+βa
+are arbitrary functions of
+u0,
+that
+obey the condition (27).
+2.
+α2V1 ̸= 0, ⇒ α1 = 0 ⇒ the minor ˆW −1
+14 and its inverse matrix ˆΩ2 = ˆW −1
+14 have the
+form:
+ˆW14 =
+�
+�
+�
+�
+�
+�
+α2
+α3
+0
+0
+0
+β2
+β3
+0
+0
+0
+0
+0
+α2
+α3
+0
+0
+0
+0
+α2
+α3
+0
+β1
+0
+β2
+β3
+�
+�
+�
+�
+�
+�
+,
+ˆΩ2 =
+�
+�
+�
+�
+�
+�
+�
+�
+β3
+V1
+−α3
+V1
+0
+0
+0
+− β2
+V1
+α2
+V1
+0
+0
+0
+a2
+3β1β2
+α2V 2
+1
+−α2
+3β1
+V 2
+1
+1
+α2
+− α3β3
+α2V1
+a2
+3
+α2V1
+−a3β1β2
+V 2
+1
+α2α3β1
+V 2
+1
+0
+β3
+V1
+− a3
+V1
+a2β1β2
+V1
+−α2
+2β1
+V1
+0
+− β2
+V1
+α2
+V1
+�
+�
+�
+�
+�
+�
+�
+�
+(31)
+Solution of the equation (23) can be represented as:
+ˆn2 = ˆΩˆω2,
+(32)
+were
+ˆnT
+2 = (n12, n13, n22, n23, n33);
+ˆω2 = (− ˙β1, −β1n11, − ˙β2, − ˙β3, ˙α3)
+Function
+n11,
+as well as the functions
+αa,
+βa
+are arbitrary functions of
+u0,
+that
+obey the condition (27).
+3.
+a3V1 ̸= 0, ⇒ a1 = a2 = 0 ⇒ the minor ˆW −1
+16 and its inverse matrix ˆΩ3 = ˆW −1
+16 have the
+form:
+ˆW16 =
+�
+�
+�
+�
+�
+�
+0
+a3
+0
+0
+0
+β2
+β3
+0
+0
+0
+0
+0
+0
+a3
+0
+β1
+0
+β2
+β3
+0
+0
+0
+0
+0
+a3
+�
+�
+�
+�
+�
+�
+,
+ˆΩ3 =
+�
+�
+�
+�
+�
+�
+�
+− β3
+a3β2
+1
+β3
+0
+0
+0
+1
+a3
+0
+0
+0
+0
+β1β3
+a3β2
+2
+− β1
+β2
+2
+− β3
+β2a3
+1
+β2
+0
+0
+0
+1
+a3
+0
+0
+0
+0
+0
+0
+1
+a3
+�
+�
+�
+�
+�
+�
+�
+(33)
+Then the solution of equation (23) can be represented as:
+ˆn3 = ˆΩ3ˆω3,
+(34)
+were
+ˆnT
+3 = (n12, n13, n22, n23, n33);
+ˆωT
+3 = (− ˙β1, −β1n11, − ˙β2, 0, − ˙β3)
+Function
+n11,
+as well as the functions
+α3,
+βa
+are arbitrary functions of
+u0,
+that
+obey the condition (27).
+4.
+a1V3 ̸= 0. ⇒ V1 = V2 = 0,
+otherwise, we get a solution equivalent to the previous
+ones. As
+V3 ̸= 0 ⇒
+α3 = β3 = 0.
+The minor ˆW62 and its inverse matrix ˆΩ4 = ˆW −1
+62 have
+8
+
+the form:
+ˆW26 =
+�
+�
+�
+�
+�
+�
+α1
+α2
+0
+0
+0
+0
+α1
+0
+a2
+0
+0
+β1
+0
+β2
+0
+0
+0
+α1
+0
+α2
+0
+0
+β1
+0
+β2
+�
+�
+�
+�
+�
+�
+,
+ˆΩ4 =
+�
+�
+�
+�
+�
+�
+�
+1
+α1
+− α2β2
+α1V3
+α2
+2
+α1V3
+0
+0
+0
+β2
+V3
+−α2
+V3
+0
+0
+0
+0
+0
+β2
+V3
+−α2
+V3
+0
+− β1
+V3
+α1
+V3
+0
+0
+0
+0
+0
+− β1
+V3
+α1
+V3
+�
+�
+�
+�
+�
+�
+�
+(35)
+Then the solution of equation (23) can be represented as:
+ˆn4 = ˆΩ4ˆω4.
+(36)
+were
+ˆnT
+4 = (n11, n12, n13, n22, n23);
+ˆωT
+4 = (− ˙β1, − ˙β2, ˙α2, 0, 0).
+Function
+n33,
+as well as the functions
+α1,
+α2
+βa
+are arbitrary functions of
+u0,
+that obey the condition (27).
+5.
+Va = 0.
+Let us represent the system of Maxwell equations in the form:
+ˆQIˆnI = ˆωI
+were
+ˆQ =
+�
+�
+�
+�
+�
+�
+�
+�
+α1
+α2
+α3
+0
+0
+0
+0
+α1
+0
+α2
+α3
+0
+0
+0
+α1
+0
+α2
+α3
+β1
+β2
+β3
+0
+0
+0
+0
+β1
+0
+β2
+β3
+0
+0
+0
+β1
+0
+β2
+β3
+�
+�
+�
+�
+�
+�
+�
+�
+,
+(37)
+ˆωI = (ˆωβ, ˆωα);
+ˆωβ = −( ˙β1, ˙β2, ˙β3),
+ˆωα = ( ˙α1, ˙α2, ˙α3)
+ˆnI = (ˆnα, ˆnβ);
+ˆnα = (n11, n12, n13),
+ˆnβ = (n22, n23, n33).
+To provide the classification, it is sufficient to consider the options:
+1)
+a1 ̸= 0,
+2)
+a3 ̸=
+0,
+a1 = a2 = 0.
+a) a1 ̸= 0 ⇒ βa = αaβ1
+α1 .
+ˆWIˆnα = (ˆωβ − ˆQ1ˆnβ) ⇒ ˆnα = ˆW −1
+I (ˆωβ − ˆQ1ˆnβ),
+β1 ˆWIˆnα = α1ˆωα − β1 ˆQ1ˆnβ ⇒ β1ˆωβ − α1ˆωα = 0 ⇒
+�
+�
+�
+α1 ˙α2 + β1 ˙β2 = 0,
+α1 ˙α3 + β1 ˙β3 = 0,
+α1 ˙α1 + β1 ˙β1 = 0.
+⇒
+�
+�
+�
+α1 = e sin ϕ,
+β1 = e cos ϕ,
+e = const,
+α2 = ec2 sin ϕ,
+β1 = ec2 cos ϕ,
+e, c2 = const,
+α3 = ec3 sin ϕ,
+β1 = ec3 cos ϕ,
+e, c3 = const.
+(38)
+9
+
+Here:
+ˆWI =
+�
+�
+α1
+α2
+α3
+0
+α1
+0
+0
+0
+α1
+�
+� , ˆW −1
+I
+=
+�
+�
+1
+α1
+−α2
+α2
+1
+−α3
+α2
+1
+0
+1
+α1
+0
+0
+0
+1
+α1
+�
+� , ˆQI =
+�
+�
+0
+0
+0
+α2
+α3
+0
+0
+α2
+α3,
+�
+�
+α1 = e sin ϕ,
+β1 = e cos ϕ,
+e, ca = const,
+Then matrices ˆWI, ˆW −1
+I , ˆQI and lines ˆωT take the form:
+ˆWI = sin ϕ ˆP,
+ˆW −1
+I
+=
+1
+sin ϕ
+ˆP −1,
+ˆQI = sin ϕ ˆQ.
+ˆP =
+�
+�
+1
+c2
+c3
+0
+1
+0
+0
+0
+1
+�
+� ,
+ˆP −1 =
+�
+�
+1
+−c2
+−c3
+0
+1
+0
+0
+0
+1
+�
+� ,
+ˆQ =
+�
+�
+0
+0
+0
+c2
+c3
+0
+0
+c2
+c3,
+�
+�
+ˆωT
+α = ˆωT
+β = ˙ϕ sin ϕ ˆCT = ˙ϕ sin ϕ(1, c2, c3),
+ˆnα = ˆw−1( ˙ϕ ˆCT − ˆQˆnβ)
+Function
+n22, n23, n33,
+as well as the function
+ϕ
+are arbitrary functions of
+u0.
+b) Va = 0,
+α3 ̸= 0.
+⇒ β1 = β2 = 0.
+The system of Maxwell equations has the form:
+α3n13 = α3n23 = 0,
+α3n33 = − ˙β3,
+β3n33 = ˙α3.
+a3 ˙a3 + β3 ˙β3 = 0 ⇒ a3 = c sin ϕ,
+β3 = cos ϕ
+From here:
+n33 = ˙ϕ,
+n13 = n23 = α1 = α2 = β1 = β2 = 0,
+α3 = c sin ϕ,
+β3 = c cos ϕ.
+Functions
+ϕ,
+n11,
+n12,
+n22 - are arbitrary functions on
+u0,
+c = const.
+5
+Conclusion
+It is known that homogeneous spaces of IV and IX types according to Bianchi classification
+include as special cases the spaces of constant curvature.This causes a special interest to them
+in cosmology. In the Universe with the metric of homogeneous space all physical fields are
+invariant with respect to the group of motions of the space-time. Therefore, exactly such fields
+should be considered in the first place when solving the self-consistent Einstein equations,
+in particular the Einstein-Maxwell equations.
+The final goal of classification of PSS with
+admissible electromagnetic fields is to enumerate all electrovacuum solutions of the Einstein-
+Maxwell equations. In [40], [41] the complete classification of vacuum solutions of the Maxwell
+equations for homogeneous spaces with solvable groups of motions has been carried out. In the
+present paper the same problem is solved for HPSS of IX-type. For the final decision of the
+first stage of the classification problem it remains to consider HPSS V III-type, which will be
+10
+
+done in the next paper. The results obtained will be used in the second stage for integration
+of the corresponding Einstein-Maxwell equations.
+FUNDING: The work is supported by Russian Science Foundation, project number N 23-
+21-00275.
+INSTITUTIONAL REVIEW BOARD STATEMENT: Not applicable.
+INFORMED CONSENT STATEMENT: Not applicable.
+DATA AVAILABILITY STATEMENT: The data that support the findings of this study
+are available within the article.
+CONFLICTS OF INTEREST: The author declares no conflict of interest.
+References
+[1] Stackel. P. Uber die intagration der Hamiltonschen differentialechung mittels separation
+der variablen. Math. Ann. 1897. 49, (145-147 pp.);
+[2] Eisenhart L.P. Separable systems of stackel. Ann.Math. 1934, 35, (284-305 pp).;
+[3] Levi-Civita T. Sulla Integraziome Della Equazione Di Hamilton-Jacobi Per Separazione
+Di Variabili. Math.Ann. 1904 59, (383-397 pp.);
+[4] Jarov-Jrovoy
+M.S.
+Integration
+of
+Hamilton-Jacobi
+equation
+by
+complete
+sep-
+aration
+of
+variables
+method.
+J.Appl.Math.Mech..
+1963,
+27,
+No
+6,
+(173-219
+pp).https://doi.org/10.1016/0021-8928(63)90122-9;
+[5] Carter B. New family of Einstein spaces. Phys.Lett. 1968, A.25, No 9 (399-400pp.),
+doi.org/10.1016/0375-9601(68)90240-5
+[6] Shapovalov V.N., Symmetry and separation of variables in the Hamilton-Jacobi equation.
+Sov. Phys.J.. 1978, 21, 1124-1132pp. doi: 10.1007/BF00894560;
+[7] Shapovalov V.N.,
+Stackel‘s spaces. Sib. Math. J. 1979,
+20,
+(1117-1130pp.),
+doi:
+org/10.1007/BF00971844;
+[8] W.
+Miller.
+Symmetry
+And
+Separation
+Of
+Variables.
+Cambridge
+University
+Press:Cambridge. 1984, (318 p.p.);
+[9] Obukhov V.V. Hamilton-Jacobi equation for a charged test particle in the Stackel space
+of type (2.0). Symmetry, 12, 2020, 12891291. doi: 10.3390/sym12081289.
+[10] Obukhov V.V. Hamilton-Jacobi equation for a charged test particle in the Stackel
+space of type (2.1).Int. J. Geom. Meth. Mod. Phys, 2020, 17, 14, 2050186. doi:
+10.1142/S0219887820501868.
+[11] Obukhov V.V. Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equa-
+tions for a charged test particle in the stackel spaces of type (1.1). Int. J. Geom. Meth.
+Mod. Phys.2021, 18, 03, (2150036); doi:10.1142/S0219887821500365
+11
+
+[12] Odintsov, S.D. Editorial for Special Issue Feature Papers 2020. Symmetry. 2023, 15, 8.
+doi.org/10.3390/sym15010008
+[13] McLenaghan R. G., Rastelli G. and Valero C. Complete separability of the Hamilton-
+Jacobi equation for the charged particle orbits in a Lienard-Wiehert field /em J. Math.
+Phys., /bf2020,61, (122903). doi.org/10.1063/5.0030305.
+[14] Mitsopoulos A., Tsamparlis M., Leon G. A.Paliathanasis. A.Paliathanasis. New conserva-
+tion laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar
+field. Symmetry. 2021, 13(8):1364, doi: 10.3390/sym13081364
+[15] Claudio Dappiaggi, Benito A. Juarez-Aubry, Alessio Marta Ground. State for the Klein-
+Gordon field in anti-de Sitter spacetime with dynamical Wentzell boundary conditions.
+Phys. Rev. D. 2022, 105, 105017 doi.org/10.1103/PhysRevD.105.105017.
+[16] Francisco Astorga, J Felix Salazar and Thomas Zannias On the integrability of the geodesic
+flow on a Friedmann-Robertson-Walker spacetime Physica Scripta, 2018, 93, 8, 93 085205
+doi. 10.1088/1402-4896/aacd44
+[17] Capozziello S., De Laurentis M., Odintsov D. Hamiltonian dynamics and Noether sym-
+metries in extended gravity cosmology. Eur.Phys.J. 2012, C72, 2068 (22 pp.), doi:
+10.1140/epjc/s10052-012-2068-0;
+[18] Salih
+Kibaroglu,
+Oktay
+Cebecioglu.
+Generalized
+cosmological
+constant
+from
+gauging
+Maxwell-conformal
+algebra,
+Phys.Lett.B,
+2020,
+803,
+135295.
+doi.org/10.1016/j.physletb.2020.135295
+[19] Nojiri
+Shin’ichi,
+Odintsov
+Sergei
+D.,
+Faraoni
+Valerio,
+Searching
+for
+dynamical
+black
+holes
+in
+various
+theories
+of
+gravity.
+Phys.Rev.D.
+2021,
+103,
+4,
+044055.
+doi:10.1103/PhysRevD.103.044055
+[20] Epp V. Pervukhina O. The Stormer problem for an aligned rotator. MNRAS, 2018 474,
+(5330-5339) doi.org/10.1093/mnras/stx3102.
+[21] Epp V., Masterova M.A. Effective potential energy for relativistic particles in the field
+of inclined rotating magnetized sphere. Astrophys Space Sci, 2014, 353, (473-483).
+doi.org/10.1007/s10509-014-2066-9.
+[22] Kumaran Y.; Ovgun A. Deflection angle and shadow of the reissner-nordstrom black
+hole with higher-order magnetic correction in einstein-nonlinear-maxwell fields. Symmetry.
+2022, 14, 2054. https://doi.org/10.3390/sym14102054
+[23] Osetrin K.; Osetrin E. Shapovalov wave-like spacetimes. Symmetry 2020, 12, 1372.
+https://doi.org/10.3390/SYM12081372.
+[24] Osetrin E.; Osetrin K.; Filippov A. Plane Gravitational Waves in Spatially-Homogeneous
+Models of type-(3.1) Stackel Spaces. Russian Physics Journal 2019, 62,
+292-301.
+https://doi.org/10.1007/s11182-019-01711-1.
+12
+
+[25] Osetrin K., Osetrin E. and Osetrina E. Geodesic deviation and tidal acceleration in the
+gravitational wave of the Bianchi type IV universe. Eur. Phys. J. Plus. 2022, 137, (856).
+https://doi.org/10.1140/epjp/s13360-022-03061-3
+[26] Osetrin, K.; Osetrin, E.; Osetrina, E. Gravitational wave of the Bianchi VII universe:
+Particle trajectories, geodesic deviation and tidal accelerations. Eur. Phys. J. C 2022,
+82, 1–16. doi.org/10.1140/epjc/s10052-022-10852-6.
+[27] Shapovalov, A.V., Shirokov I.V. Noncommutative integration method for linear partial
+differential equations. functional algebras and dimensional reduction. Theoret. And Math.
+Phys. 1996, 106:1, (1-10). doi.org/10.4213/tmf1093.
+[28] Shapovalov, A.; Breev, A. Harmonic Oscillator Coherent States from the Standpoint of
+Orbit Theory.Symmetry 2023, 15, 282. doi.org/10.3390/sym15020282
+[29] Breev, A.I., Shapovalov, A.V. Non-commutative integration of the Dirac equation in ho-
+mogeneous spaces. Symmetry 2020, 12, 1867.
+[30] Breev, A.I.; Shapovalov, A.V. Yang–Mills gauge fields conserving the symmetry algebra of
+the Dirac equation in a homogeneous space. J. Phys.: Conf. Ser. 2014, 563, 012004.
+[31] Magazev
+A.A.,Boldyreva
+M.N.
+Schrodinger
+equations
+in
+electromagnetic
+fields:
+symmetries
+and
+noncommutative
+integration,
+Symmetry.
+2021,
+13,
+(1527).
+https://doi.org/10.3390/sym13081527
+[32] Magazev A.A. Integrating Klein-Gordon-Fock equations in an extremal electromagnetic
+field on Lie groups. Theor.and Math.Phys., 2012, 173:3, (1654-1667). doi: 10.1007/s11232-
+012-0139-x, arxiv.org/abs/1406.5698;
+[33] Obukhov V.V. Algebra of symmetry operators for Klein-Gordon-Fock Equation. Symme-
+try. 2021, 13, 727 (15p.). https://doi.org/10.3390/sym13040727.
+[34] Odintsov,
+S.D. Editorial for Feature Papers 2021-2022. Symmetry. 2023, 15, 32.
+doi.org/10.3390/sym15010032
+[35] Obukhov V.V. Algebra of the symmetry operators of the Klein-Gordon-Fock equation for
+the case when groups of motions G3 act transitively on null subsurfaces of spacetime.
+Symmetry. 2022, 14, (346). https://doi.org/10.3390/sym14020346
+[36] Obukhov V.V. Algebras of integrals of motion for the Hamilton-Jacobi and Klein-
+Gordon-Fock equations in spacetime with a four-parameter groups of motions in the
+presence of an external electromagnetic field J. Math. Phys. 2022, 63,
+Issue 2.
+https://doi.org/10.1063/5.0080703
+[37] Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C., Herlt, E. Exact Solu-
+tions of Einstein’s Field Equations (2nd ed., Cambridge Monographs on Mathematical
+Physics).2003 Cambridge: Cambridge University Press. doi:10.1017/CBO9780511535185
+[38] Landau L.D., Lifshits E.M. Theoretical physics, Field theory. 7th ed. Moskow.(vol. II):
+Science. Ch. ed. Phys.-Math. lit., 1988. - (512 p). ISBN 5-02-014420-7
+13
+
+[39] Petrov A. Z. Einstein Spaces, Oxford, 1969.
+[40] Obukhov V.V. Maxwell Equations in Homogeneous Spaces for Admissible Electromagnetic
+Fields.Universe. 2022, 8, (245). https://doi.org/10.3390/universe8040245
+[41] Obukhov, V.V. Maxwell Equations in Homogeneous Spaces with Solvable Groups of Mo-
+tions. Symmetry. 2022, 14, (2595).https://doi.org/10.3390/sym14122595
+[42] Stephani H., Kramer D., MacCallum M. A. H., Hoenselaers C., Herlt E. Exact Solu-
+tions of Einstein’s Field Equations Second Edition, 2003, Cambrige university press.
+doi.org/10.1017/CBO9780511535185
+14
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf,len=665
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='11595v1  [math-ph]  27 Jan 2023  Exact solutions of Maxwell equations in homogeneous  spaces with group of motions G3(IX)  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Obukhov  Institute of Scietific Research and Development, Tomsk State Pedagogical University  (TSPU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Tomsk State Pedagogical University, 60 Kievskaya St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Tomsk, 634041, Russia;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Laboratory for Theoretical Cosmology, International Center of Gravity and Cosmos, Tomsk  State University of Control Systems and Radio Electronics (TUSUR), 36, Lenin Avenue, Tomsk,  634050, Russia  Keywords: Maxwell equations, Klein-Gordon-Fock equation, algebra of symmetry operators,  theory of symmetry, linear partial differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Exact solutions of Maxwell equations in homogeneous spaces with group of motions G3(IX)  1  Introduction  All known methods of integration of main differential equations of mathematical physics are  based on complete reduction of these equations to a system of ordinary differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Reduction is carried out using symmetry operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' For the equations of motion of classical  or quantum sample particle in external electromagnetic and gravitational fields the symmetry  operators are integrals of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' It is known that a necessary condition for the existence of  integrals of motion is the existence of spacetime symmetry given by the Killing fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Thus the problem of exact integration is closely related to the study of space-time symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  At present two methods of exact integration of equations of motion are known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' These are  methods of commutative (CIM) and noncommutative (NCIM) integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The first method is  based on the theory of complete separation of variables, and it is applicable in stackel spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Stackel spaces admit complete sets consisting of mutually commuting Killing fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Theory  of Stackel spaces was developed in [1], [2], [3], [4], [5], [6],[7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  A description of the theory  and a detailed bibliography can be found in [8], [9] [10], [13] (see also [12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Solutions of field  equations, which are still used widely in the theory of gravitation, have been constructed on  the basis of Stackel spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' These solutions are often used in the study of various effects in  gravitational fields (see, for example,[14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25],  [26]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The second method (NCI method) is based on the use of noncommutative algebras of  symmetry operators linear in moments and constructed using vector Killing fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The method  was proposed in [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The development of the method and its application to gravity theory can  be found in [28], [29], [30], [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  1  As in stackel spaces in the spaces with a noncommutative group of motions the equations  of motion of a test particle admit the complete reduction to a system of ordinary differential  equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Therefore, we will call space-time manifolds admitting noncommutative groups  Gr, r ≥ 3 as post-Stackel spaces (PSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  By analogy with stackel spaces we will call the PSS non-isotropic if a group Gr (or its  subgroup of rank 3) acts transitive on a non-isotropic hypersurface of spacetime, or isotropic,  if the hypersurface is isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' For non-isotropic post-stackel spaces we will also use the term  ”homogeneous post-stackel space (HPSS)”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The same classification problems can be considered for the PSS as for the stackel spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  For example, in the papers [9] [10], [11] a complete classification is given for the case when  the Hamilton-Jacobi equation for a charged test particle admits the complete separation of  variables in the external electromagnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' A similar classification problem has been solved  for PSS-spaces as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' In [32] PSS-spaces with transitive four-parameter groups of motions  are considered;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' in [33] HPSS-spaces are considered (see also [34]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' in [35] PSS-spaces with  groups acting on isotropic hypersurfaces of transitivity are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' PSS-spaces with four-  parameter groups of motions are considered in [36], provided that these groups have transitive  three-parameter subgroups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Thus, one has found the potentials of all admissible electromag-  netic fields, for which the Hamilton-Jacobi and Klein-Gordon-Fock equations have algebras of  symmetry operators given by groups of motions of post-stackel spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' It was proved, that  the Klein-Gordon-Fock equation admits the algebra of symmetry operators given by groups of  motions of PSS if and only if the Hamilton-Jacobi equations admits the appropriate algebra of  integrals of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Next classification problem is the classification of electrovacuum solutions of the Einstein-  Maxwell equations for the case, when CIM and NCIM methods are applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' During the  century-long history of General relativity, many exact solutions of the vacuum and electrovac-  uum Einstein equations have been found (see, for example,[42] ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Nevertheless, this problem has  not lost its relevance up to now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The main purpose of the classification is not so much to find  new exact solutions, as to list all gravitational and electromagnetic fields, in which equations  of motion of test particles can be exactly integrated or at least reduced to systems of ordinary  differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' This problem divided into two stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  At the first stage all non-equivalent classes of solutions of the vacuum Maxwell equations for  the potentials of admissible electromagnetic fields are found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' At the second stage the obtained  classification is used to classify the corresponding electrovacuum spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Historically, for Stackel  spaces this problem was solved before the problem of the first stage (see the bibliography given  in [9], [10], [11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The present article is devoted to solving the first stage of this classification  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' All non-equivalent solutions of empty Maxwell equations in homogeneous spaces of  type IX according to Bianchi’s classification are found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  2  Admissible electromagnetic fields in homogeneous spaces  There are two definitions of homogeneous spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  According to the first a spacetime  V4  is homogeneous if its subspace  V3,  endowed with the Euclidean space signature, admits  coordinate transformations (forming the group G3(N) of motions of spaces V4), that allow to  connect any two points in  V3  (see [38]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' This definition directly implies that metric of the  2  V4 in the semi-geodesic coordinate system  [ui]  can be represented as follows:  ds2 = −du02 + ηabla  αlb  βduαduβ,  gij = −δ0  i δ0  j + δa  i δb  jea  αeb  βηab(u0),  det|ηab| > 0  ea  α,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (1)  The coordinate indices of the variables of the semi-geodesic coordinate system are denoted  by lower case Latin letters:  i, j, k = 0, 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The coordinate indices of the variables of the  local coordinate system on the hypersurface  V3  are denoted by lower case Greek letters:  α, β, γ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  the time variable is denoted by a 0 index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Group indices and indices of  nonholonomic frame are denoted by  a, b, c = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Summation is performed over repeated  upper and lower indices within the index range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The 1-form  ea  αduα  is invariant under the acting of the group G3(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The vectors of the  frame ea  α define a non-holonomic coordinate system in V3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The dual triplet of vectors  eα  a,  eα  aeb  α = δb  a,  eα  aea  β = δα  β  defines the operators of the group algebra:  ˆYa = eα  a∂a,  [ ˆYa, ˆYb] = Cc  ab ˆYc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (2)  According to another definition, space-time  V4  is homogeneous if it admits a three-parameter  group of motions  G3(N),  whose hypersurface  V3  of transitivity has the Euclidean space  signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The Killing vector fields ξα  a  and their dual vector fields  ξa  α  form another frame  of the space V3 and another representation of the algebra of the group G3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The vector fields  ξα  a  satisfy the Killing equations:  gαβ  ,γ ξγ  a = gαγξβ  a,γ + gβγξα  a,γ,  (3)  and sets the infinitesimal group operators of the algebra G3  ˆXa = ξα  a ∂α,  [ ˆXa, ˆXb] = Cc  ab ˆXc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (4)  Let us consider electromagnetic field with potential Ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' For a charged test particle, moving in  this external electromagnetic field, it has been proved, that the Hamilton-Jacobi equation:  gijPiPj = m,  Pi = pi + Ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (5)  and the Klein-Gordon-Fock equation:  ˆHϕ = (gij ˆPi ˆPj)ϕ = m2ϕ,  ˆPk = ˆpk + Ak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (6)  admit the integrals of motion, which are given by Killing vectors:  ˜Xα = ξi  αpi  (or  ˆ˜Xα = ξi  αˆpi),  if and only if the conditions:  ξα  a ( ˜A),α = Cc  ab ˜A  (7)  are satisfied (see papers [33]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Here  pi = ∂iϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆpk = −ı ˆ∇k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ( ˆ∇k is the covariant deriva-  tive operator corresponding to the partial derivative operator -  ˆ∂i  in the coordinate field  ui),  ϕ  is a scalar function of particle with mass  m;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˜Aa = ξα  a Aα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  3  The electromagnetic field whose potential satisfies condition (7) is called admissible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' All  admissible electromagnetic fields for groups of motion  Gr(N)  (r ≤ 4),  acting transitively  on hypersurfaces of the spacetime, have been found in [33], [35], [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Solutions of the set of equations (7) for HPSS of type IX have the form:  Aα = αa(u0)la  α ⇒ Aa = lα  aAα = αa(u0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (8)  To prove this let’s find the frame vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' We will use the metric tensor of IX-type space by  Bianchi, found in Petrov’s book [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' As it is known, the Bianchi type IX metric contains as  a special case the space of constant positive curvature and therefore is of special interest for  cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ds2 = du12[a11 − (a12 cos 2u3 + a22 sin 2u3)] + 2du1du3((a13 cos u3 − a23 sin u3)+  (9)  +2du1du2[(a13 cos u3 − a23 sin u3) cos u1 + (a12 cos 2u3 − a22 sin 2u3) sin u1]  +du22[a33cos u12 + (a23 cos u3 + a13 sin u3) sin 2u1 + (a12 sin 2u3 + a22 cos 2u3 + a11)sin u12]  2du2du3(a33 cos u1 + (a23 cos u3 + a13 sin u3) sin u1) + du32a33 + edu02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  aab are arbitrary functions on u0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  To obtain the functions  lα  a  , it is sufficient to consider the components  g13, g23  from the system (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The solution has the form:  la  α = δp  αla  p(u1, u3) + δ3  αδa  3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  From the equations:  g13 = a13 cos u3 − a23 sin u3 = η3ala  1,  g23 = a33 cos u1 + (a23 cos u3 + a13 sin u3) sin u1 = η3ala  1  it follows:  la  α =  �  �  cos u3  − sin u3  0  sin u1 sin u3  sin u1 cos u3  cos u1  0  0  1  �  � , lα  a =  �  �  cos u3  sin u3  sin u1  −cos u1 sin u3  sin u1  − sin u3  cos u3  sin u1  −cos u1 cos u3  sin u1  0  0  1  �  � ,  (10)  la  αlα  b = δa  b .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The lower index numbers the lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' One can show that the vector fields (10) satisfy the  equations (1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' (2): We present the components of the vectors ξα  a in the form of a matrix:  ||ξα  a || =  �  �  0  1  0  cos u2  −cos u1 sin u2  sin u1  sin u2  sin u1  − sin u2  −cos u1 cos u2  sin u1  cos u2  sin u1  �  �  The components ˜Aα can be expressed through Aα as follows:  ˜Aa = Zb  aAb,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  4  where  ||Zb  a = ξα  a lb  α|| =  �  �  sin u1 sin u3  sin u1 cos u3  cos u1  (cos u2 cos u3 − sin u2 sin u3 cos u1)  −(cos u2 sin u3 + sin u2 cos u3 cos u1)  sin u1 sin u2  −(sin u2 cos u3 + cos u2 sin u3 cos u1)  (sin u2 sin u3 − cos u2 cos u3 cos u1)  cos u2 sin u1  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  It can be shown by direct calculation that the elements of the matrix Zb  a satisfy the equation:  Zb  a|c = Ca1  caZb  a1,  |a = lα  a∂α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (11)  Therefore, the equation (7) can be reduced to the form:  ξα  a Ab,α = 0 ⇒ Aa = αa(u0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (12)  3  Maxwell’s equations with zero electromagnetic field  sources in a homogeneous spacetime  All exact solutions of vacuum Maxwell equations for solvable groups have been found in the  papers [40], [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' In the present paper the problem is solved for the group G3(IX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  We will use the first definition of homogeneous spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Note, that for the space-time with  the groups of motions G3(I) − G3(V I), G3(IX) both definitions are equivalent  Consider the Maxwell equations with zero electromagnetic field sources in homogeneous  space in the presence of an electromagnetic field invariant with respect to the group Gr:  1  √−g(√−gF ij),j = 0,  (13)  The metric tensor is defined by relations (1), the electromagnetic potential by the relations (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  When i = 0, from the set of equations (13) it follows:  1  √−g(√−ggαβF0β)α = 1  l (llα  aηab ˙αb),α = ηabρa ˙αb = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (14)  Here it is denoted g = − det ||gαβ|| = −(ηl)2,  where  η2 = det ||ηαβ||,  l = det ||la  α||,  ρa =  lα  a,α + l|a/l,  the dots means the time derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Let  i = α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Then from the equation (13)  it follows:  1  η(ηgαβF0β),0 = 1  l (lgνβgαγFβγ),ν ⇒ 1  η(ηηablα  a ˙αb),0 = 1  l (llν  alβ  b ηablα  ˜alγ  ˜b η˜a˜bFβγ),ν ⇒  (15)  (ηηab ˙αb),0 = ηla  α  l (llβ  b lα  ˜a1lγ  ˜b Fβγ)|a1ηa1bη˜a˜b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (16)  Let us find components of Fαβ, using the relations (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Fαβ = (la  β,α − la  β,α)αa = lc  βlγ  c ld  αlν  d(la  γ,ν − la  ν,γ)αa = lb  βla  αlc  γ(lγ  a|b − lγ  b|a)αc = lb  βla  αCc  baαc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (17)  Then  (lF αβ),β = ηabη˜a˜bCd  ˜bbαd((llα  a)|˜a + llα  alγ  ˜a,γ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (18)  5  Structural constants of a group  G3  can be present in the form:  Cc  ab = Cc  12ε12  ˜a˜b + Cc  13ε13  ˜a˜b + Cc  23ε23  ˜a˜b,  εAB  ab = δA  a δB  b − δA  b δB  a .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (19)  Using the notations:  σ1 = Ca  23αa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  σ2 = Ca  31αa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  σ3 = Ca  12αa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  γ1 = σ1η11 + σ2η12 + σ3η13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  γ2 = σ1η12 + σ2η22 + σ3η23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  γ3 = σ1η13 + σ2η23 + σ3η33,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  let us reduce Maxwell’s equations (13) to the form:  η(ηab ˙αb),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='0 = δa  1(γ1(C1  32) − γ2(C1  31 + ρ3) + γ3(C1  21 + ρ2)) + δa  2(γ1(C2  32 + ρ3)+  (20)  γ2C2  13 − γ3(C2  12ρ1)) + δa  3(−γ1(C3  23 + ρ2) + γ2(C3  13 + ρ1) + γ3C3  21),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The order of the equations (20) can be decreased by introducing a new independent functions:  βa = βa = ηηab ˙αb  ⇒  η ˙αa = ηabβb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (21)  Let us consider the Maxwell equations for the group G3(IX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' As in this case  non zero  structural constants are following:  C3  12 = C2  31 = C1  23 = 1,  functions  σa, γ1  have the form:  σ1 = α1,  σ2 = α2,  σ3 = α3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  γ1 = α1η11 + α2η12 + α3η13,  γ2 = α1η12 + α2η22 + α3η23,  γ1 = α1η13 + α2η23 + α3η33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Using these relations, we obtain Maxwell’s equations (14), (20) as a system of linear algebraic  equations on the unknown functions  nab:  nab = ηab  η ⇒ η =  1  det nab  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (22)  ˆW ˆn = ˆω,  (23)  where  ˆW =  �  �  �  �  �  �  �  �  α1  α2  α3  0  0  0  β1  β2  β3  0  0  0  0  α1  0  α2  α3  0  0  β1  0  β2  β3  0  0  0  α1  0  α2  α3  0  0  β1  0  β2  β3  �  �  �  �  �  �  �  �  ,  (24)  ˆnT = (n11, n12, n13, n22, n23, n33);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆωT = (− ˙β1, ˙α1, − ˙β2, ˙α2, − ˙β3, ˙α3),  6  index T means the transposition of a matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Let us find the algebraic complement of the  matrix ˆW :  ˆV =  �  �  �  �  �  �  �  �  β1V 2  1  −α1V 2  1  β2V 2  1  −α2V 2  1  β3V 2  1  −α3V 2  1  β1V1V2  −α1V1V2  β2V1V2  −α2V1V2  β3V1V2  −α3V1V2  β1V1V3  −α1V1V3  β2V1V3  −α2V1V3  β3V1V3  −α3V1V3  β1V 2  2  −α1V 2  2  β2V 2  2  −α2V 2  2  β3V 2  2  −α3V 2  2  β1V2V3  −α1V2V3  β2V2V3  −α2V2V3  β3V2V3  −α3V2V3  β1V 2  3  −α1V 2  3  β2V 2  3  −α2V 2  3  β3V 2  3  −α3V 2  3  �  �  �  �  �  �  �  �  (25)  As ˆW is singular matrix,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ˆV is the annulling matrix for ˆW:  ˆV ˆW = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (26)  Therefore, one of the equations from the system (23) can be replaced by the equation:  δab( ˙αa ˙αb + ˙βa ˙βb) ⇒ δab(αaαb + βaβb) = c2 = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (27)  Depending on the rank of the matrix ˆW, one or more functions nab are independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The  remaining functions nab can be expressed through them and through the functions αa, βa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' For  classification it is necessary to find non-equivalent solutions of the system (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Obviously, this  system are symmetric with respect to the transposition  lα  1 ↔ lα  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Therefore the reference  indices a = 1 and a = 2 can be interchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Taking this observation into account, let us  consider all non-equivalent options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  4  Solutions of Maxwell equations  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  a1V1 ̸= 0 ⇒ the minor ˆW12 and its inverse matrix ˆΩ = ˆW −1  12 have the form:  ˆW12 =  �  �  �  �  �  �  α2  α3  0  0  0  α1  0  α2  α3  0  β1  0  β2  β3  0  0  α1  0  α2  α3  0  β1  0  β2  β3  �  �  �  �  �  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='(28)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='ˆΩ1 =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='− V2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='− α3β2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content='− α3β3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content='− V3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α2β2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content='− α2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α2β3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='−α2α3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='− V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='(α3β1V1−α2β3V3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α3(α2V2−α1V1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='−α3β3V2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='2V2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='− V2V3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α2β2V2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='− α2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='2V2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='−α3β3‘V3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3V3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='− V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α2β2V3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='− α2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='2V3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='(α3β2V3−α2β1V1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α2(α1V1−α3V3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='α1V 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='(29)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Then the solution of equation (23) can be represented as:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='ˆn1 = ˆΩ1ˆω1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (30)  were  ˆnT  1 = (n12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n33);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆωT  1 = (−( ˙β1 + α1n11), − ˙β2, ˙α2, −β3, ˙α3),  7  Function  n11,  as well as the functions  αa,  βa  are arbitrary functions of  u0,  that  obey the condition (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  α2V1 ̸= 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ⇒ α1 = 0 ⇒ the minor ˆW −1  14 and its inverse matrix ˆΩ2 = ˆW −1  14 have the  form:  ˆW14 =  �  �  �  �  �  �  α2  α3  0  0  0  β2  β3  0  0  0  0  0  α2  α3  0  0  0  0  α2  α3  0  β1  0  β2  β3  �  �  �  �  �  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆΩ2 =  �  �  �  �  �  �  �  �  β3  V1  −α3  V1  0  0  0  − β2  V1  α2  V1  0  0  0  a2  3β1β2  α2V 2  1  −α2  3β1  V 2  1  1  α2  − α3β3  α2V1  a2  3  α2V1  −a3β1β2  V 2  1  α2α3β1  V 2  1  0  β3  V1  − a3  V1  a2β1β2  V1  −α2  2β1  V1  0  − β2  V1  α2  V1  �  �  �  �  �  �  �  �  (31)  Solution of the equation (23) can be represented as:  ˆn2 = ˆΩˆω2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (32)  were  ˆnT  2 = (n12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n33);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆω2 = (− ˙β1, −β1n11, − ˙β2, − ˙β3, ˙α3)  Function  n11,  as well as the functions  αa,  βa  are arbitrary functions of  u0,  that  obey the condition (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  a3V1 ̸= 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ⇒ a1 = a2 = 0 ⇒ the minor ˆW −1  16 and its inverse matrix ˆΩ3 = ˆW −1  16 have the  form:  ˆW16 =  �  �  �  �  �  �  0  a3  0  0  0  β2  β3  0  0  0  0  0  0  a3  0  β1  0  β2  β3  0  0  0  0  0  a3  �  �  �  �  �  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆΩ3 =  �  �  �  �  �  �  �  − β3  a3β2  1  β3  0  0  0  1  a3  0  0  0  0  β1β3  a3β2  2  − β1  β2  2  − β3  β2a3  1  β2  0  0  0  1  a3  0  0  0  0  0  0  1  a3  �  �  �  �  �  �  �  (33)  Then the solution of equation (23) can be represented as:  ˆn3 = ˆΩ3ˆω3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (34)  were  ˆnT  3 = (n12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' n33);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆωT  3 = (− ˙β1, −β1n11, − ˙β2, 0, − ˙β3)  Function  n11,  as well as the functions  α3,  βa  are arbitrary functions of  u0,  that  obey the condition (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  a1V3 ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ⇒ V1 = V2 = 0,  otherwise, we get a solution equivalent to the previous  ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' As  V3 ̸= 0 ⇒  α3 = β3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The minor ˆW62 and its inverse matrix ˆΩ4 = ˆW −1  62 have  8  the form:  ˆW26 =  �  �  �  �  �  �  α1  α2  0  0  0  0  α1  0  a2  0  0  β1  0  β2  0  0  0  α1  0  α2  0  0  β1  0  β2  �  �  �  �  �  �  ,  ˆΩ4 =  �  �  �  �  �  �  �  1  α1  − α2β2  α1V3  α2  2  α1V3  0  0  0  β2  V3  −α2  V3  0  0  0  0  0  β2  V3  −α2  V3  0  − β1  V3  α1  V3  0  0  0  0  0  − β1  V3  α1  V3  �  �  �  �  �  �  �  (35)  Then the solution of equation (23) can be represented as:  ˆn4 = ˆΩ4ˆω4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (36)  were  ˆnT  4 = (n11, n12, n13, n22, n23);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆωT  4 = (− ˙β1, − ˙β2, ˙α2, 0, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Function  n33,  as well as the functions  α1,  α2  βa  are arbitrary functions of  u0,  that obey the condition (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Va = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Let us represent the system of Maxwell equations in the form:  ˆQIˆnI = ˆωI  were  ˆQ =  �  �  �  �  �  �  �  �  α1  α2  α3  0  0  0  0  α1  0  α2  α3  0  0  0  α1  0  α2  α3  β1  β2  β3  0  0  0  0  β1  0  β2  β3  0  0  0  β1  0  β2  β3  �  �  �  �  �  �  �  �  ,  (37)  ˆωI = (ˆωβ, ˆωα);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆωβ = −( ˙β1, ˙β2, ˙β3),  ˆωα = ( ˙α1, ˙α2, ˙α3)  ˆnI = (ˆnα, ˆnβ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆnα = (n11, n12, n13),  ˆnβ = (n22, n23, n33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  To provide the classification, it is sufficient to consider the options:  1)  a1 ̸= 0,  2)  a3 ̸=  0,  a1 = a2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  a) a1 ̸= 0 ⇒ βa = αaβ1  α1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆWIˆnα = (ˆωβ − ˆQ1ˆnβ) ⇒ ˆnα = ˆW −1  I (ˆωβ − ˆQ1ˆnβ),  β1 ˆWIˆnα = α1ˆωα − β1 ˆQ1ˆnβ ⇒ β1ˆωβ − α1ˆωα = 0 ⇒  �  �  �  α1 ˙α2 + β1 ˙β2 = 0,  α1 ˙α3 + β1 ˙β3 = 0,  α1 ˙α1 + β1 ˙β1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ⇒  �  �  �  α1 = e sin ϕ,  β1 = e cos ϕ,  e = const,  α2 = ec2 sin ϕ,  β1 = ec2 cos ϕ,  e, c2 = const,  α3 = ec3 sin ϕ,  β1 = ec3 cos ϕ,  e, c3 = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  (38)  9  Here:  ˆWI =  �  �  α1  α2  α3  0  α1  0  0  0  α1  �  � , ˆW −1  I  =  �  �  1  α1  −α2  α2  1  −α3  α2  1  0  1  α1  0  0  0  1  α1  �  � , ˆQI =  �  �  0  0  0  α2  α3  0  0  α2  α3,  �  �  α1 = e sin ϕ,  β1 = e cos ϕ,  e, ca = const,  Then matrices ˆWI, ˆW −1  I , ˆQI and lines ˆωT take the form:  ˆWI = sin ϕ ˆP,  ˆW −1  I  =  1  sin ϕ  ˆP −1,  ˆQI = sin ϕ ˆQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ˆP =  �  �  1  c2  c3  0  1  0  0  0  1  �  � ,  ˆP −1 =  �  �  1  −c2  −c3  0  1  0  0  0  1  �  � ,  ˆQ =  �  �  0  0  0  c2  c3  0  0  c2  c3,  �  �  ˆωT  α = ˆωT  β = ˙ϕ sin ϕ ˆCT = ˙ϕ sin ϕ(1, c2, c3),  ˆnα = ˆw−1( ˙ϕ ˆCT − ˆQˆnβ)  Function  n22, n23, n33,  as well as the function  ϕ  are arbitrary functions of  u0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  b) Va = 0,  α3 ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  ⇒ β1 = β2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The system of Maxwell equations has the form:  α3n13 = α3n23 = 0,  α3n33 = − ˙β3,  β3n33 = ˙α3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  a3 ˙a3 + β3 ˙β3 = 0 ⇒ a3 = c sin ϕ,  β3 = cos ϕ  From here:  n33 = ˙ϕ,  n13 = n23 = α1 = α2 = β1 = β2 = 0,  α3 = c sin ϕ,  β3 = c cos ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Functions  ϕ,  n11,  n12,  n22 - are arbitrary functions on  u0,  c = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  5  Conclusion  It is known that homogeneous spaces of IV and IX types according to Bianchi classification  include as special cases the spaces of constant curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='This causes a special interest to them  in cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' In the Universe with the metric of homogeneous space all physical fields are  invariant with respect to the group of motions of the space-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Therefore, exactly such fields  should be considered in the first place when solving the self-consistent Einstein equations,  in particular the Einstein-Maxwell equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  The final goal of classification of PSS with  admissible electromagnetic fields is to enumerate all electrovacuum solutions of the Einstein-  Maxwell equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' In [40], [41] the complete classification of vacuum solutions of the Maxwell  equations for homogeneous spaces with solvable groups of motions has been carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' In the  present paper the same problem is solved for HPSS of IX-type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' For the final decision of the  first stage of the classification problem it remains to consider HPSS V III-type, which will be  10  done in the next paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The results obtained will be used in the second stage for integration  of the corresponding Einstein-Maxwell equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  FUNDING: The work is supported by Russian Science Foundation, project number N 23-  21-00275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  INSTITUTIONAL REVIEW BOARD STATEMENT: Not applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  INFORMED CONSENT STATEMENT: Not applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  DATA AVAILABILITY STATEMENT: The data that support the findings of this study  are available within the article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  CONFLICTS OF INTEREST: The author declares no conflict of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  References  [1] Stackel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Uber die intagration der Hamiltonschen differentialechung mittels separation  der variablen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 1897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 49, (145-147 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [2] Eisenhart L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Separable systems of stackel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 1934, 35, (284-305 pp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [3] Levi-Civita T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Sulla Integraziome Della Equazione Di Hamilton-Jacobi Per Separazione  Di Variabili.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 1904 59, (383-397 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [4] Jarov-Jrovoy  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Integration  of  Hamilton-Jacobi  equation  by  complete  sep-  aration  of  variables  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='.  1963,  27,  No  6,  (173-219  pp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1016/0021-8928(63)90122-9;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [5] Carter B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' New family of Einstein spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 1968, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='25, No 9 (399-400pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ),  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1016/0375-9601(68)90240-5  [6] Shapovalov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Symmetry and separation of variables in the Hamilton-Jacobi equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='. 1978, 21, 1124-1132pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1007/BF00894560;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [7] Shapovalov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=',  Stackel‘s spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Sib.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 1979,  20,  (1117-1130pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content='  Miller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Symmetry  And  Separation  Of  Variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Cambridge  University  Press:Cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 1984, (318 p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content='  [9] Obukhov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Hamilton-Jacobi equation for a charged test particle in the Stackel space  of type (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content=' Symmetry, 12, 2020, 12891291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content='  [11] Obukhov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content='2021, 18, 03, (2150036);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+page_content='1142/S0219887821500365  11  [12] Odintsov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Editorial for Special Issue Feature Papers 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2023, 15, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym15010008  [13] McLenaghan R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Rastelli G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' and Valero C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Complete separability of the Hamilton-  Jacobi equation for the charged particle orbits in a Lienard-Wiehert field /em J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', /bf2020,61, (122903).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='0030305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [14] Mitsopoulos A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Tsamparlis M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Leon G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Paliathanasis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Paliathanasis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' New conserva-  tion laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2021, 13(8):1364, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym13081364  [15] Claudio Dappiaggi, Benito A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Juarez-Aubry, Alessio Marta Ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' State for the Klein-  Gordon field in anti-de Sitter spacetime with dynamical Wentzell boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2022, 105, 105017 doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='105017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [16] Francisco Astorga, J Felix Salazar and Thomas Zannias On the integrability of the geodesic  flow on a Friedmann-Robertson-Walker spacetime Physica Scripta, 2018, 93, 8, 93 085205  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1088/1402-4896/aacd44  [17] Capozziello S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', De Laurentis M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Odintsov D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Hamiltonian dynamics and Noether sym-  metries in extended gravity cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2012, C72, 2068 (22 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ), doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1140/epjc/s10052-012-2068-0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [18] Salih  Kibaroglu,  Oktay  Cebecioglu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Generalized  cosmological  constant  from  gauging  Maxwell-conformal  algebra,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='B,  2020,  803,  135295.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='135295  [19] Nojiri  Shin’ichi,  Odintsov  Sergei  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=',  Faraoni  Valerio,  Searching  for  dynamical  black  holes  in  various  theories  of  gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  2021,  103,  4,  044055.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='044055  [20] Epp V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Pervukhina O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' The Stormer problem for an aligned rotator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' MNRAS, 2018 474,  (5330-5339) doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1093/mnras/stx3102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [21] Epp V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Masterova M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Effective potential energy for relativistic particles in the field  of inclined rotating magnetized sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Astrophys Space Sci, 2014, 353, (473-483).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1007/s10509-014-2066-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [22] Kumaran Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Ovgun A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Deflection angle and shadow of the reissner-nordstrom black  hole with higher-order magnetic correction in einstein-nonlinear-maxwell fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  2022, 14, 2054.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym14102054  [23] Osetrin K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Osetrin E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Shapovalov wave-like spacetimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Symmetry 2020, 12, 1372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/SYM12081372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [24] Osetrin E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Osetrin K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Filippov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Plane Gravitational Waves in Spatially-Homogeneous  Models of type-(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1) Stackel Spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Russian Physics Journal 2019, 62,  292-301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1007/s11182-019-01711-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  12  [25] Osetrin K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Osetrin E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' and Osetrina E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Geodesic deviation and tidal acceleration in the  gravitational wave of the Bianchi type IV universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Plus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2022, 137, (856).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1140/epjp/s13360-022-03061-3  [26] Osetrin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Osetrin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Osetrina, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Gravitational wave of the Bianchi VII universe:  Particle trajectories, geodesic deviation and tidal accelerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' C 2022,  82, 1–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1140/epjc/s10052-022-10852-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [27] Shapovalov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Shirokov I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Noncommutative integration method for linear partial  differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' functional algebras and dimensional reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Theoret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' And Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 1996, 106:1, (1-10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='4213/tmf1093.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [28] Shapovalov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Breev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Harmonic Oscillator Coherent States from the Standpoint of  Orbit Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Symmetry 2023, 15, 282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym15020282  [29] Breev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Shapovalov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Non-commutative integration of the Dirac equation in ho-  mogeneous spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Symmetry 2020, 12, 1867.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [30] Breev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Shapovalov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Yang–Mills gauge fields conserving the symmetry algebra of  the Dirac equation in a homogeneous space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' : Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2014, 563, 012004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [31] Magazev  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=',Boldyreva  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Schrodinger  equations  in  electromagnetic  fields:  symmetries  and  noncommutative  integration,  Symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  2021,  13,  (1527).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym13081527  [32] Magazev A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Integrating Klein-Gordon-Fock equations in an extremal electromagnetic  field on Lie groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='and Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', 2012, 173:3, (1654-1667).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1007/s11232-  012-0139-x, arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/abs/1406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='5698;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [33] Obukhov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Algebra of symmetry operators for Klein-Gordon-Fock Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Symme-  try.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2021, 13, 727 (15p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym13040727.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [34] Odintsov,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Editorial for Feature Papers 2021-2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2023, 15, 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym15010032  [35] Obukhov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Algebra of the symmetry operators of the Klein-Gordon-Fock equation for  the case when groups of motions G3 act transitively on null subsurfaces of spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  Symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2022, 14, (346).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym14020346  [36] Obukhov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Algebras of integrals of motion for the Hamilton-Jacobi and Klein-  Gordon-Fock equations in spacetime with a four-parameter groups of motions in the  presence of an external electromagnetic field J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2022, 63,  Issue 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='0080703  [37] Stephani, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Kramer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', MacCallum, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Hoenselaers, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Herlt, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Exact Solu-  tions of Einstein’s Field Equations (2nd ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Cambridge Monographs on Mathematical  Physics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='2003 Cambridge: Cambridge University Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='1017/CBO9780511535185  [38] Landau L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Lifshits E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Theoretical physics, Field theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 7th ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Moskow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='(vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' II):  Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='-Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' lit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' - (512 p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' ISBN 5-02-014420-7  13  [39] Petrov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Einstein Spaces, Oxford, 1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='  [40] Obukhov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Maxwell Equations in Homogeneous Spaces for Admissible Electromagnetic  Fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2022, 8, (245).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/universe8040245  [41] Obukhov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Maxwell Equations in Homogeneous Spaces with Solvable Groups of Mo-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' 2022, 14, (2595).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content='3390/sym14122595  [42] Stephani H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Kramer D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', MacCallum M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Hoenselaers C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=', Herlt E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
+page_content=' Exact Solu-  tions of Einstein’s Field Equations Second Edition, 2003, Cambrige university press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NFJT4oBgHgl3EQfoSxe/content/2301.11595v1.pdf'}
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+Draft version January 9, 2023
+Typeset using LATEX twocolumn style in AASTeX631
+Diverse Carbonates in Exoplanet Oceans Promote the Carbon Cycle
+Kaustubh Hakim
+,1 Meng Tian
+,1 Dan J. Bower
+,1 and Kevin Heng
+2, 3, 4
+1University of Bern, Center for Space and Habitability, Gesellschaftsstrasse 6, CH-3012 Bern, Switzerland
+2Ludwig Maximilian University, University Observatory Munich, Scheinerstrasse 1, Munich D-81679, Germany
+3University of Warwick, Department of Physics, Astronomy & Astrophysics Group, Coventry CV4 7AL, United Kingdom
+4University of Bern, ARTORG Center for Biomedical Engineering Research, Murtenstrasse 50, CH-3008, Bern, Switzerland
+ABSTRACT
+Carbonate precipitation in oceans is essential for the carbonate-silicate cycle (inorganic carbon cycle)
+to maintain temperate climates.
+By considering the thermodynamics of carbonate chemistry, we
+demonstrate that the ocean pH decreases by approximately 0.5 for a factor of 10 increase in the
+atmospheric carbon dioxide content. The upper and lower limits of ocean pH are within 1–4 of each
+other, where the upper limit is buffered by carbonate precipitation and defines the ocean pH when
+the carbon cycle operates. If the carbonate compensation depth (CCD) resides above the ocean floor,
+then carbonate precipitation and the carbon cycle cease to operate.
+The CCD is deep (>40 km)
+for high ocean temperature and high atmospheric carbon dioxide content. Key divalent carbonates of
+magnesium, calcium and iron produce an increasingly wider parameter space of deep CCDs, suggesting
+that chemical diversity promotes the carbon cycle. The search for life from exoplanets will benefit by
+including chemically more diverse targets than Earth twins.
+Keywords: Extrasolar rocky planets (511); Carbon dioxide (196); Habitable zone (696); Ocean-
+atmosphere interactions (1150); Geological processes (2288); (Unified Astronomy Thesaurus)
+1. INTRODUCTION
+The carbonate-silicate cycle, also known as the in-
+organic carbon cycle, is a negative climate feedback
+mechanism that stabilises the surface temperature via
+the greenhouse effect of carbon dioxide in response
+to changes in volcanism rates, stellar luminosity, at-
+mospheric composition and opacity, planetary orbital
+movements and spin axis tilt (Berner 2004; Catling
+& Kasting 2017).
+Continental silicate rocks and at-
+mospheric carbon dioxide react with water in a pro-
+cess known as silicate weathering to produce carbonate-
+forming ions that precipitate as carbonates onto the
+ocean floor (Walker et al. 1981).
+The carbon cycle
+is completed when carbonates are transferred into the
+mantle for deep storage or carbon is eventually re-
+leased back into the atmosphere by volcanism (Holland
+1978; Sleep & Zahnle 2001), although the degassing ef-
+Corresponding author: Kaustubh Hakim
+kaustubh.hakim@unibe.ch
+ficiency is debated (Kelemen & Manning 2015; Foley
+2015). Silicate weathering and carbonate precipitation
+are traditionally represented by the net chemical reac-
+tion (Walker et al. 1981),
+CaSiO3 + CO2 → CaCO3 + SiO2,
+(1)
+where wollastonite (CaSiO3), which serves as a proxy for
+silicate rocks, is converted into calcite (CaCO3). Cal-
+cium thus plays a crucial role in silicate weathering and
+carbonate precipitation and is present as Ca2+ cations
+in oceans (Sect. 2).
+The existence of habitable zones assumes that the
+carbon cycle operates on Earth analogues to stabilise
+their atmospheric carbon dioxide content (Kasting et al.
+1993).
+Implicitly, this assumes not only that silicate
+weathering operates, but that ocean floor precipitation
+and deep storage of carbonates also occur. There exists
+a critical ocean depth known as the carbonate compen-
+sation depth (CCD), below which carbonates are unable
+to exist in their solid form because carbonate solubility
+increases with pressure in the ocean (Zeebe & West-
+broek 2003, see also Sect. 2.3, Figure 1). In modern
+arXiv:2301.02652v1  [astro-ph.EP]  6 Jan 2023
+
+ID2
+CCD
+!"#$#
+%&'(
+Ocean	Depth
+%)*+,-
+%&'( ≤ %,/0
+1)*+,- = 13456 = 1
+!78'(,#$#
+Carbonates
+Silicates
+Dissolved	ions
+Figure 1. Model parameters, nDtot where D = Ca, Mg or
+Fe, nSiO2,tot, PCO2, Patm, Poc and T. See Sect. 2 and Table 1
+for a full list of output quantities and description.
+Earth oceans, the CCD is located between 4–5 km, be-
+low the average ocean depth of about 3.8 km (Zeebe
+2012). If the CCD resides at a depth above the ocean
+floor, then carbonates are unable to settle. This leads
+to the disruption of the carbon cycle—at least, as it is
+understood to operate on Earth. Moreover, there are
+currently no theoretical constraints on exoplanet ocean
+chemistry. We investigate the interplay between atmo-
+spheric carbon dioxide content, ocean acidity (pH) and
+carbonate precipitation.
+We then calculate the CCD
+over a broad range of physical conditions.
+2. METHODS
+2.1. Ocean chemistry model
+2.1.1. Ca system
+Ocean chemistry is modelled by considering thermo-
+chemical equilibrium for pure Ca, Mg, or Fe systems.
+The CO2 partial pressure PCO2, ocean–surface temper-
+ature T and local ocean pressure Poc are control pa-
+rameters (Figure 1, Table 1). In the Ca system, there
+are 13 unknowns, the number density n of H+, OH−,
+H2O, HCO−
+3 , CO2−
+3 , CO2(aq), Catot, Ca2+, SiO2,tot,
+SiO2(aq), quartz SiO2(s), wollastonite CaSiO3(s) and
+calcite CaCO3(s). Out of the 13 unknowns, 2 are conti-
+nental silicate weathering products, nCatot and nSiO2,tot,
+that depend on PCO2 and T (Sect.
+2.2).
+There are
+11 remaining unknowns. We solve for 3 mass conserva-
+tion equations (for H, Ca and SiO2), 1 charge balance
+equation, and 7 equations from 7 chemical reactions pro-
+viding relations between equilibrium constants (that de-
+pend on Poc and T), reactants and products.
+Table 1. Parameters and output quantities.
+Symbol
+Description
+Reference
+Parameters for ocean chemistry
+T
+Ocean–Surface temperature
+288 K
+PCO2
+CO2 partial pressure
+0.3 mbar
+Patm
+Atmospheric pressure
+1 bar
+Poc
+Ocean layer pressure
+1 bar
+Parameters for weathering
+nDtot,0
+Ca, Mg or Fe ref. number density
+1 m−3
+β
+Weathering power-law exponent
+0.3
+Te
+e-folding temperature
+13.7 K
+Output quantities
+nX
+Number density of X [m−3]
+pH
+–log10(nH+/n0); n0 = 103 m−3
+These 3 mass-conservation equations, 1 charge balance
+equation and 7 reactions (water dissociation, Henry’s
+law/physical CO2 dissolution, chemical CO2 dissolu-
+tion, bicarbonate ion dissociation, calcite precipitation,
+quartz precipitation and wollastonite precipitation) are
+specified below. Henry’s law gives the amount of CO2
+physically dissolved in ocean water in equilibrium with
+PCO2:
+CO2(g) ⇌ CO2(aq).
+(2)
+The chemical dissolution or dissociation of CO2 in ocean
+water leads to the production of HCO−
+3 and H+ ions and
+thereby increases the ocean acidity (and decreases ocean
+pH = − log10(nH+/n0), where the standard number den-
+sity n0 = 1 m−3) by the following reaction:
+CO2(g) + H2O ⇌ H+ + HCO−
+3 .
+(3)
+To maintain the charge balance in ocean water, the ad-
+dition of Ca2+ to oceans decreases the number density
+of H+ and hence increases the ocean pH. The charge
+balance equation is given by:
+2nCa2+ + nH+ = nHCO−
+3 + 2nCO2−
+3
++ nOH−,
+(4)
+where CO2−
+3
+is produced due to the bicarbonate disso-
+ciation reaction:
+HCO−
+3 ⇌ CO2−
+3
++ H+,
+(5)
+and where OH− is produced due to the water dissocia-
+tion reaction:
+H2O ⇌ H+ + OH−.
+(6)
+
+3
+The mass conservation of H is given by
+nHtot = 2nH2O + nH+ + nHCO−
+3 .
+(7)
+Catot partitions into Ca2+, calcite and wollastonite
+which is accounted for by mass conservation:
+nCatot = nCa2+ + nCal + nWo.
+(8)
+Calcite precipitation occurs when nCa2+ is saturated to
+a certain value determined by the equilibrium constant
+of the calcite precipitation reaction and the abundance
+of nCO2−
+3 :
+Ca2+ + CO2−
+3
+⇌ CaCO3(s).
+(9)
+SiO2,tot partitions into aqueous silica SiO2(aq), quartz
+SiO2(s) and wollastonite CaSiO3(s). The mass conser-
+vation for SiO2 is given by:
+nSiO2,tot = nSiO2(aq) + nQz + nWo.
+(10)
+The quartz precipitation reaction is:
+SiO2(aq) ⇌ SiO2(s).
+(11)
+The reaction of wollastonite precipitation is given by:
+Ca2+ + SiO2(aq) + H2O ⇌ 2H+ + CaSiO3(s).
+(12)
+These equilibrium chemistry calculations are per-
+formed using Reaktoro v2 (Leal 2015), a multi-phase
+(aqueous, gas and solid mineral phases) chemistry soft-
+ware.
+This software implements the extended law of
+mass action including the determination of stable and
+unstable species for a given set of species in the system
+(Leal et al. 2017).
+We use the SUPCRTBL database
+for thermodynamic data (Johnson et al. 1992; Zimmer
+et al. 2016), the Peng-Robinson activity model for gases
+(Peng & Robinson 1976), the HKF activity model for
+water (Helgeson et al. 1981) and the Drummond activ-
+ity model for CO2(aq) (Drummond 1981).
+2.1.2. Mg and Fe systems
+In the Mg system, Ca is replaced by Mg, calcite
+by magnesite MgCO3(s) and wollastonite by enstatite
+Mg2Si2O6(s). This includes replacing equilibrium con-
+stants of all reactions including Mg. Similarly, in the
+Fe system, Ca is replaced by Fe, calcite by siderite
+FeCO3(s) and wollastonite by fayalite Fe2SiO4(s). We
+limit our calculations to Fe2+ although its oxidation has
+inhibited the formation of siderite during Earth’s his-
+tory, particularly since the great oxidation event (Rye
+et al. 1995).
+2.2. Weathering model
+The introduction of carbonate-producing divalent
+cations in oceans is dictated by silicate weathering. Sil-
+icate weathering and therefore the total number density
+of divalent cations D2+ (D = Ca, Mg or Fe) must depend
+on the CO2 partial pressure PCO2 and surface tempera-
+ture T (Walker et al. 1981; Hakim et al. 2021),
+nDtot = fW (PCO2, T) = nDtot,0
+� PCO2
+PCO2,0
+�β
+exp
+�T − T0
+Te
+�
+,
+(13)
+where ‘0’ represents the Earth reference values (Table 1),
+Te = 13.7 K is the e-folding temperature and β = 0.3 is
+the weathering power-law exponent (Walker et al. 1981).
+However, not all added Ca (or Mg, Fe) in oceans re-
+mains in the form of divalent cations, a fraction of it
+precipitates as carbonates on the ocean floor and an-
+other fraction as silicates. For this reason, we perform
+partitioning calculations of Ca (or Mg, Fe) in different
+phases following the ocean chemistry model (Sect. 2.1).
+2.3. CCD model
+Carbonates are deposited onto the ocean floor as part
+of sediments. The transition from calcite-rich to calcite-
+free sediments is gradual. The carbonate compensation
+depth (CCD) for the Earth ocean is normally defined
+as the depth at which the dissolution flux of calcite bal-
+ances the precipitation flux (Zeebe 2012). The depth
+at which the rapid dissolution of calcite-rich sediments
+begins is known as the lysocline, which is a sediment
+property (Zeebe & Westbroek 2003). The lysocline and
+CCD serve as bounds on the transition zone (∼0.5 km)
+between calcite-rich and calcite-free sediments. Other
+definitions for the CCD exist (Berger et al. 1976; Ridg-
+well & Zeebe 2005; Zeebe 2012). The depth of ocean d
+[km] in terms of ocean pressure Poc [bar] at the equator
+is given by (Leroy & Parthiot 1998)
+d =
+1
+9.7803 × 103 + 0.011Poc (97.266Poc − 2.512 × 10−3P 2
+oc
++ 2.28 × 10−7P 3
+oc − 1.8 × 10−11P 4
+oc).
+(14)
+We consider the CCD to be the depth dCCD (equiv-
+alent to the ocean pressure where Poc = PCCD) at
+which 99.9% of near-surface (Poc = Psurf) Ca, Mg or
+Fe-carbonates dissolve,
+nCarb,CCD = 0.001 nCarb,surf.
+(15)
+Our calculations of CCD are performed up to dCCD =
+45 km because of the availability of thermodynamic data
+up to the pressure of 5000 bar (Zimmer et al. 2016). This
+limitation does not affect our conclusions.
+
+4
+2.4. Analytical solution of ocean pH
+Upper limit of ocean pH. For calcite precipitation, all
+reactions in Section 2 need to be satisfied. However, two
+of these reactions can be used to analytically constrain
+ocean pH: Equations 9 and 16 where Equation 16 is a
+combination of Equations 3 and 5,
+CO2(g) + H2O ⇌ 2H+ + CO2−
+3 .
+(16)
+The ocean pH can be written as a function of PCO2,
+nCa2+ and equilibrium constants of Equations 9 and 16
+(Appendix A):
+pH = −1
+2
+�
+log PCO2 + log K9K16 + log nCa2+
+n0
+�
+. (17)
+This equation demonstrates the reason for the slope of
+approximately −0.5 for the upper limit of ocean pH as a
+function of the logarithm (base 10) of PCO2. Because K9
+and K16 are constants at a fixed T and P, pH becomes
+a function of only PCO2 and nCa2+ in Equation 17. As a
+function of PCO2, nCa2+ at the limit of carbonate satura-
+tion varies between ∼0.1 m−3 (at PCO2 = 0.01 µbar) and
+∼6 m−3 (at PCO2 = 0.3 bar). This additional increase
+in nCa2+ of less than two orders of magnitude over seven
+orders of magnitude increase in PCO2, makes the slope
+of ocean pH slightly steeper than −0.5 (see Fig. A1).
+Using nCa2+ from the numerical solution in Equation 17
+results in a semi-analytical solution matching with the
+numerical solution until PCO2 = 0.1 bar, beyond which
+non-ideal effects accounted in the numerical solution ex-
+hibit a small deviation from the analytical equation.
+Lower limit of ocean pH. In the absence of divalent
+cations in ocean, the ocean pH is largely governed by the
+conversion of CO2 to protons (Equation 3). For PCO2 >
+1 µbar, the ocean is acidic, where the number density of
+H+ is larger than that of OH− and the number density
+of HCO−
+3 is larger than CO2−
+3
+(bicarbonate-carbonate-
+water equilibria, Wolf-Gladrow et al. 2007). Therefore,
+the charge balance equation can be approximated as
+nH+ = nHCO−
+3 .
+(18)
+In terms of the equilibrium constant of Equation 3, this
+leads to (Appendix A)
+pH = −1
+2 (log PCO2 + log K3) .
+(19)
+At a fixed T and P, K3 is constant and thus the ocean
+pH exhibits a slope of −0.5 for PCO2 > 1 µbar (Fig. A1).
+For PCO2 < 1 µbar, the analytical solution does not
+hold because the number density of OH− is significant
+enough to make the charge balance approximation in
+Equation 18 invalid.
+The lower limit of ocean pH is
+independent of the Ca, Mg or Fe systems considered.
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+4
+5
+6
+7
+8
+9
+10
+11
+Ocean pH
+(a)
+Carbon Cycle
+No Carbon Cycle
+Modern 
+Earth pH
+Forbidden
+Forbidden
+Ca
+nCa, tot = fW(PCO2)
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+4
+5
+6
+7
+8
+9
+10
+11
+Ocean pH
+(b)
+Carbon Cycle
+No Carbon Cycle
+Modern 
+Earth pH
+Forbidden
+Forbidden
+Mg
+nMg, tot = fW(PCO2)
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+4
+5
+6
+7
+8
+9
+10
+11
+Ocean pH
+(c)
+Carbon Cycle
+No Carbon Cycle
+Modern 
+Earth pH
+Forbidden
+Forbidden
+Fe
+nFe, tot = fW(PCO2)
+Figure 2.
+Sensitivity of ocean pH to PCO2 at T = 288 K for
+pure (a) Ca, (b) Mg, (c) Fe systems. Upper and lower bounds
+of ocean pH are represented by the blue shaded region. Pink
+shaded regions are forbidden.
+
+5
+3. RESULTS AND DISCUSSION
+We consider the ocean pH to be determined by the
+chemical dissolution of atmospheric carbon dioxide in
+a well-mixed ocean, which occurs at the atmosphere–
+ocean interface. The chemical dissolution of CO2 is gov-
+erned by the reaction between water and CO2 to produce
+H+, HCO−
+3 and CO2−
+3
+ions (Sect. 2). As PCO2 increases,
+the ocean becomes more acidic. We consider an atmo-
+spheric surface pressure of 1 bar, but allow the atmo-
+spheric carbon dioxide content to vary via PCO2. Atmo-
+spheric surface pressures up to 100 bar have a negligible
+effect on our results and those between 100–1000 bar
+exhibit a small effect (Fig. A2a).
+For a given value of PCO2, the ocean pH is bounded
+between two limits (Fig. 2a). The ocean pH is restricted
+to a narrow range between 7–11 at PCO2 = 0.01 µbar
+and 4–7 for PCO2 = 0.1 bar. These ocean pH ranges
+are consistent with the inferences for Earth’s history,
+transitioning from an acidic ocean during the Archean
+at high PCO2 to an alkaline ocean at present-day PCO2
+(Halevy & Bachan 2017; Krissansen-Totton et al. 2018).
+The lower limit corresponds to the complete absence of
+divalent cations and thus it is independent of the car-
+bonate system under investigation (Sect. 2). The upper
+limit corresponds to the saturation of calcium cations
+in ocean water such that more weathering does not pro-
+duce further changes in pH and simply produces more
+calcite. This upper limit is buffered by the precipita-
+tion of carbonates and hence it results in one solution
+of ocean pH when the carbon cycle is operational for
+a given carbonate system and PCO2. Both upper and
+lower limits of ocean pH follow a slope of approximately
+–0.5 as a function of PCO2 (see Sect.
+2.4).
+Between
+these two limits, the number density of calcium cations
+is below the threshold to precipitate carbonates onto the
+ocean floor; thus, the carbon cycle is not operational.
+Due to their high condensation temperatures, the
+relative abundances of refractory elements observed in
+the photosphere of stars are expected to be mirrored
+in the rocky exoplanets they host (Bond et al. 2010;
+Thiabaud et al. 2015).
+For example, the calcium-to-
+magnesium ratio of the solar photosphere and Earth are
+0.062 and 0.066, respectively (Lodders 2003; Elser et al.
+2012). The relative abundances of Ca, Mg and Fe, mea-
+sured from the spectra of stars, vary by up to an or-
+der of magnitude. For example, Ca/Mg=0.02–0.2 and
+Ca/Fe=0.04–0.2 in the Hypatia catalogue of more than
+7000 stars (Hinkel et al. 2014). Furthermore, carbonates
+involving Mg and Fe are known to have formed during
+Earth’s history: e.g., magnesite (MgCO3) and siderite
+(FeCO3); these carbonates have dissolution properties
+that differ from those of calcite.
+Siderite could have
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+280
+300
+320
+340
+360
+T [K]
+(a)
+nCa, tot = 100 m
+3
+nCa, tot = 1 m
+3
+Carbon Cycle
+No Carbon Cycle 
+(cations consumed 
+by silicates)
+No Carbon Cycle 
+(too little CO2)
+No Carbon Cycle 
+(too acidic)
+nCa, tot = fW(PCO2, T)
+Ca-CCD
+1
+2
+4
+10
+20
+40
+CCD [km]
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+280
+300
+320
+340
+360
+T [K]
+(b)
+nMg, tot = 100 m
+3
+nMg, tot = 1 m
+3
+Carbon Cycle
+No Carbon Cycle 
+(cations consumed 
+by slicates)
+No Carbon Cycle 
+(too little CO2)
+No Carbon Cycle 
+(too acidic)
+nMg, tot = fW(PCO2, T)
+Mg-CCD
+1
+2
+4
+10
+20
+40
+CCD [km]
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+280
+300
+320
+340
+360
+T [K]
+(c)
+nFe, tot = 100 m
+3
+nFe, tot = 1 m
+3
+Carbon Cycle
+No Carbon Cycle 
+(cations consumed 
+by slicates)
+nFe, tot = fW(PCO2, T)
+Fe-CCD
+1
+2
+4
+10
+20
+40
+CCD [km]
+Figure 3. Carbonate compensation depth (CCD) as a func-
+tion of PCO2 and T (Patm = 1 bar) for (a) Ca, (b) Mg and
+(c) Fe systems.
+Gray contours represent the weathering-
+dependent cation number density as a function of PCO2 and
+T (Eq. 13). Gray disc denotes modern Earth PCO2 and T.
+
+6
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+10
+1
+100
+101
+n [m
+3]
+(a)
+nCa, tot = fW(PCO2)
+Ca Partitioning
+Ca++
+Calcite
+Silicates
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+10
+1
+100
+101
+n [m
+3]
+(b)
+nMg, tot = fW(PCO2)
+Mg Partitioning
+Mg++
+Magnesite
+Silicates
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+10
+1
+100
+101
+n [m
+3]
+(c)
+nFe, tot = fW(PCO2)
+Fe Partitioning
+Fe++
+Siderite
+Silicates
+Figure 4.
+Partitioning of (a) Ca, (b) Mg and (c) Fe in
+aqueous, carbonate and silicate phases as a function of PCO2
+at T = 310 K (Patm = Poc = 1 bar) in pure Ca, Mg and Fe
+systems, respectively.
+played a key role in locking up CO2 in carbonates on
+Earth during the Archean (Rye et al. 1995; Sverjensky
+& Lee 2010). We calculate ocean pH for the pure Mg and
+Fe systems in addition to the Ca system (Fig. 2b,c). The
+upper limit of ocean pH for a given PCO2 varies when
+considering systems with purely Ca, Mg or Fe as the
+source of weathering cations. The upper limit of ocean
+pH for the Mg system is only 0.2 higher than for the Ca
+system, whereas it is more than unity lower for the Fe
+system.
+For PCO2 < 10 µbar, ocean chemistry and hence
+the CCD is sensitive to the addition of aqueous silica
+(SiO2) in the ocean (Fig. 3). Silica is another product
+of silicate weathering, which enables the locking up of
+cations in silicate minerals instead of carbonate minerals
+(Walker et al. 1981; Hakim et al. 2021). For instance,
+for T > 300 K and PCO2 < 0.1 µbar in the Ca sys-
+tem in the presence of aqueous silica, silicates impinge
+on the stability of calcite (Fig. 4a) and prevent carbon-
+ate precipitation at all depths (Fig. 3a).
+In contrast,
+when no silica is present in the ocean for T > 300 K
+and PCO2 < 0.1 µbar, calcite is stable (Fig. B2a) and
+deep CCDs are produced (Fig. B1a), thereby increasing
+the parameter-space where the carbon cycle is stable.
+Similarly, in the Mg and Fe systems, silicates are more
+stable than carbonates for PCO2 < 10 µbar (Fig. 4b,c).
+PCO2 > 10 µbar favours the thermodynamic stability of
+carbonates over silicates.
+Carbon cycle box models of exoplanets often omit self-
+consistent modelling of ocean chemistry and precipita-
+tion of carbonates. Carbonate precipitation is implicitly
+assumed to persist and is not expected to be a bottle-
+neck for carbon cycling.
+Our ocean chemistry model
+can be incorporated directly into carbon cycle box mod-
+els for exoplanets, which can couple via key parameters,
+PCO2, T, and the carbonate chemistry. Thermochemi-
+cal equilibrium calculations of our ocean model can be
+used to determine the carbon fluxes into or out of the
+near-surface reservoirs.
+The carbon cycle box models
+can also be informed of the effect of ocean chemistry
+and ocean depth on the efficiency of carbon degassing
+and recycling.
+Upcoming observations of terrestrial exoplanets from
+the James Webb Space Telescope, Atmospheric Remote-
+sensing Infrared Exoplanet Large-survey and Extremely
+Large Telescopes will put constraints on their atmo-
+spheric composition, for instance, the volume mixing
+ratio of atmospheric carbon dioxide (PCO2/P). Deter-
+mining the partial pressure of carbon dioxide (PCO2)
+requires the atmospheric surface pressure (P) which is
+not easily constrained. Nonetheless, our thermodynamic
+calculations provide strong constraints on ocean chem-
+
+7
+istry in the presence or absence of magnesium, calcium
+or iron carbonates; the relative abundances of these
+carbonate-forming elements in planetary systems can
+be deduced from observations of stellar photospheres.
+Our results suggest that the carbon cycle will oper-
+ate robustly on chemically-diverse terrestrial exoplanets
+exhibiting silicate weathering.
+This implies that the
+search for life from exoplanets with temperate climates
+or biospheres will benefit by broadening the target list
+to planets that are more chemically diverse than Earth.
+We acknowledge financial support from the European
+Research Council via Consolidator Grant (ERC-2017-
+CoG-771620-EXOKLEIN, awarded to K. Heng) and the
+Center for Space and Habitability, University of Bern.
+We thank Allan Leal for the support with Reaktoro.
+DATA AVAILABILITY
+All data generated or analysed during this study are
+included in the published article.
+CODE AVAILABILITY
+OCRA (Ocean Chemistry with Reaktoro And beyond):
+the open-source code developed in this work is hosted
+at https://github.com/kaustubhhakim/ocra. OCRA v1.0
+was used in this study and is also available on Zenodo
+(Hakim 2022).
+Software:
+numpy (Harris et al. 2020), scipy (Vir-
+tanen et al. 2020), pandas (The pandas development
+team 2020), astropy (Astropy Collaboration et al.
+2013, 2022), matplotlib (Hunter 2007), Reaktoro (Leal
+2015)
+APPENDIX
+A. ANALYTICAL SOLUTION OF OCEAN PH AND
+P–T SENSITIVITY
+The analytical solution for the upper limit of ocean
+pH is derived from the relations between the equilibrium
+constants and reactants and products (assuming water
+activity to be unity in diluted solutions) of reactions
+described by Equations 9 and 16,
+K9 =
+n2
+0
+nCa2+nCO2−
+3
+,
+(A1)
+K16 =
+n2
+H+nCO2−
+3
+PCO2n3
+0
+.
+(A2)
+By eliminating the carbonate ion number density from
+these two equations, proton number density is
+nH+
+n0
+=
+�
+PCO2K9K16
+nCa2+
+n0
+�1/2
+(A3)
+Because the pH is given by
+pH = − log(nH+/n0),
+(A4)
+the analytical upper limit of ocean pH is Equation 17.
+The analytical solution for the lower limit of ocean
+pH is derived from the the equilibrium constant of the
+reaction described by Equation 3,
+K3 =
+nH+nHCO−
+3
+PCO2n2
+0
+.
+(A5)
+Then the proton number density is
+nH+
+n0
+= K3PCO2n0
+nHCO−
+3
+(A6)
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+4
+5
+6
+7
+8
+9
+10
+11
+Ocean pH
+Carbon Cycle
+No Carbon Cycle
+Modern 
+Earth pH
+Forbidden
+Ca
+Up (numerical)
+Up (semi-analytical)
+Up (ana., nCa2 + = 1 m
+3)
+Low (numerical)
+Low (analytical)
+Figure A1. Numerical, analytical and semi-analytical so-
+lutions of the upper and lower limits of ocean pH in the Ca
+system.
+Thus, the lower limit of ocean pH is given by Equation
+19.
+The analytical solutions of upper and lower limits of
+ocean pH as a function of PCO2 result in a slope of –0.5
+(Fig. A1). Pressure and temperature have a negligible
+effect on ocean pH (Fig. A2).
+
+8
+100
+101
+102
+103
+P [bar]
+4
+5
+6
+7
+8
+9
+10
+11
+Ocean pH
+(a)
+Carbon Cycle
+No Carbon Cycle
+Modern 
+Earth pH
+Forbidden
+Forbidden
+Ca
+nCa, tot = fW(PCO2)
+280
+300
+320
+340
+360
+T [K]
+4
+5
+6
+7
+8
+9
+10
+11
+Ocean pH
+(b)
+Carbon Cycle
+No Carbon Cycle
+Modern 
+Earth pH
+Forbidden
+Forbidden
+Ca
+nCa, tot = fW(PCO2)
+Figure A2. The sensitivity of ocean pH to (a) P and (b) T
+in the Ca-system.
+B. CCD WITHOUT SILICATE PRECIPITATION
+When no silicates are allowed to precipitate, CCDs for
+the Ca, Mg and Fe systems become deeper for PCO2 <
+1 µbar (Fig. B1). This is reflected in the phase stability
+plots in Fig. B2.
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+280
+300
+320
+340
+360
+T [K]
+(a)
+nCa, tot = 100 m
+3
+nCa, tot = 1 m
+3
+Carbon Cycle
+No Carbon Cycle 
+(too little CO2)
+No Carbon Cycle 
+(too acidic)
+nCa, tot = fW(PCO2, T)
+Ca CCD
+1
+2
+4
+10
+20
+40
+CCD [km]
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+280
+300
+320
+340
+360
+T [K]
+(b)
+nMg, tot = 100 m
+3
+nMg, tot = 1 m
+3
+Carbon Cycle
+No Carbon Cycle 
+(too little CO2)
+No Carbon Cycle 
+(too acidic)
+nMg, tot = fW(PCO2, T)
+Mg CCD
+1
+2
+4
+10
+20
+40
+CCD [km]
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+280
+300
+320
+340
+360
+T [K]
+(c)
+nFe, tot = 100 m
+3
+nFe, tot = 1 m
+3
+Carbon Cycle
+nFe, tot = fW(PCO2, T)
+Fe CCD
+1
+2
+4
+10
+20
+40
+CCD [km]
+Figure B1. Same as Fig. 3 but with no silica nSiO2,tot = 0.
+
+9
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+10
+1
+100
+101
+n [m
+3]
+(a)
+nCa, tot = fW(PCO2)
+Ca Partitioning
+Ca++
+Calcite
+Silicates
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+10
+1
+100
+101
+n [m
+3]
+(b)
+nMg, tot = fW(PCO2)
+Mg Partitioning
+Mg++
+Magnesite
+Silicates
+10
+8
+10
+7
+10
+6
+10
+5
+10
+4
+10
+3
+10
+2
+10
+1
+PCO2 [bar]
+10
+1
+100
+101
+n [m
+3]
+(c)
+nFe, tot = fW(PCO2)
+Fe Partitioning
+Fe++
+Siderite
+Silicates
+Figure B2. Same as Fig. 4 but with no silica nSiO2,tot = 0.
+
+10
+REFERENCES
+Astropy Collaboration, Robitaille, T. P., Tollerud, E. J.,
+et al. 2013, A&A, 558, A33,
+doi: 10.1051/0004-6361/201322068
+Astropy Collaboration, Price-Whelan, A. M., Lim, P. L.,
+et al. 2022, ApJ, 935, 167, doi: 10.3847/1538-4357/ac7c74
+Berger, W. H., Adelseck, C. G., J., & Mayer, L. A. 1976,
+J. Geophys. Res., 81, 2617,
+doi: 10.1029/JC081i015p02617
+Berner, R. A. 2004, The Phanerozoic carbon cycle: CO2
+and O2 (Oxford University Press on Demand)
+Bond, J. C., O’Brien, D. P., & Lauretta, D. S. 2010, ApJ,
+715, 1050, doi: 10.1088/0004-637X/715/2/1050
+Catling, D. C., & Kasting, J. F. 2017, Atmospheric
+Evolution on Inhabited and Lifeless Worlds (Cambridge
+University Press)
+Drummond, S. 1981, PhD thesis, Pennsylvania State
+University
+Elser, S., Meyer, M. R., & Moore, B. 2012, Icarus, 221, 859,
+doi: 10.1016/j.icarus.2012.09.016
+Foley, B. J. 2015, ApJ, 812, 36,
+doi: 10.1088/0004-637X/812/1/36
+Hakim, K. 2022, kaustubhhakim/ocra: OCRA, v1.0,
+Zenodo, doi: 10.5281/zenodo.7380526.
+https://doi.org/10.5281/zenodo.7380526
+Hakim, K., Bower, D. J., Tian, M., et al. 2021, PSJ, 2, 49,
+doi: 10.3847/PSJ/abe1b8
+Halevy, I., & Bachan, A. 2017, Science, 355, 1069,
+doi: 10.1126/science.aal4151
+Harris, C. R., Millman, K. J., van der Walt, S. J., et al.
+2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2
+Helgeson, H. C., Kirkham, D. H., & Flowers, G. C. 1981,
+American Journal of Science, 281, 1249,
+doi: 10.2475/ajs.281.10.1249
+Hinkel, N. R., Timmes, F. X., Young, P. A., Pagano, M. D.,
+& Turnbull, M. C. 2014, AJ, 148, 54,
+doi: 10.1088/0004-6256/148/3/54
+Holland, H. D. 1978, The chemistry of the atmosphere and
+oceans (New York, NY (USA) Wiley-Interscience)
+Hunter, J. D. 2007, Computing in Science & Engineering, 9,
+90, doi: 10.1109/MCSE.2007.55
+Johnson, J. W., Oelkers, E. H., & Helgeson, H. C. 1992,
+Computers and Geosciences, 18, 899,
+doi: 10.1016/0098-3004(92)90029-Q
+Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993,
+Icarus, 101, 108, doi: 10.1006/icar.1993.1010
+Kelemen, P. B., & Manning, C. E. 2015, Proceedings of the
+National Academy of Science, 112, E3997,
+doi: 10.1073/pnas.1507889112
+Krissansen-Totton, J., Arney, G. N., & Catling, D. C. 2018,
+Proceedings of the National Academy of Science, 115,
+4105, doi: 10.1073/pnas.1721296115
+Leal, A. M. M. 2015, Reaktoro: An open-source unified
+framework for modeling chemically reactive systems, 2.0.
+https://reaktoro.org
+Leal, A. M. M., Kulik, D. A., Smith, W. R., & Saar, M. O.
+2017, Pure and Applied Chemistry, 89, 597,
+doi: doi:10.1515/pac-2016-1107
+Leroy, C. C., & Parthiot, F. 1998, Acoustical Society of
+America Journal, 103, 1346, doi: 10.1121/1.421275
+Lodders, K. 2003, ApJ, 591, 1220, doi: 10.1086/375492
+Peng, D.-Y., & Robinson, D. B. 1976, Industrial &
+Engineering Chemistry Fundamentals, 15, 59
+Ridgwell, A., & Zeebe, R. E. 2005, Earth and Planetary
+Science Letters, 234, 299, doi: 10.1016/j.epsl.2005.03.006
+Rye, R., Kuo, P. H., & Holland, H. D. 1995, Nature, 378,
+603, doi: 10.1038/378603a0
+Sleep, N. H., & Zahnle, K. 2001, J. Geophys. Res., 106,
+1373, doi: 10.1029/2000JE001247
+Sverjensky, D., & Lee, N. 2010, Elements, 6, 31,
+doi: 10.2113/gselements.6.1.31
+The pandas development team. 2020, pandas-dev/pandas:
+Pandas, latest, Zenodo, doi: 10.5281/zenodo.3509134.
+https://doi.org/10.5281/zenodo.3509134
+Thiabaud, A., Marboeuf, U., Alibert, Y., Leya, I., &
+Mezger, K. 2015, A&A, 580, A30,
+doi: 10.1051/0004-6361/201525963
+Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020,
+Nature Methods, 17, 261,
+doi: https://doi.org/10.1038/s41592-019-0686-2
+Walker, J. C. G., Hays, P. B., & Kasting, J. F. 1981,
+J. Geophys. Res., 86, 9776,
+doi: 10.1029/JC086iC10p09776
+Wolf-Gladrow, D. A., Zeebe, R. E., Klaas, C., K¨ortzinger,
+A., & Dickson, A. G. 2007, Marine Chemistry, 106, 287,
+doi: https://doi.org/10.1016/j.marchem.2007.01.006
+Zeebe, R. E. 2012, Annual Review of Earth and Planetary
+Sciences, 40, 141,
+doi: 10.1146/annurev-earth-042711-105521
+Zeebe, R. E., & Westbroek, P. 2003, Geochemistry,
+Geophysics, Geosystems, 4, 1104,
+doi: 10.1029/2003GC000538
+Zimmer, K., Zhang, Y., Lu, P., et al. 2016, Computers and
+Geosciences, 90, 97, doi: 10.1016/j.cageo.2016.02.013
+
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+page_content=' 4  1University of Bern,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Center for Space and Habitability,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
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+page_content=' Switzerland  2Ludwig Maximilian University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' University Observatory Munich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Scheinerstrasse 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
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+page_content=' Germany  3University of Warwick,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Astronomy & Astrophysics Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Coventry CV4 7AL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' United Kingdom  4University of Bern,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' ARTORG Center for Biomedical Engineering Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Murtenstrasse 50,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' CH-3008,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Bern,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Switzerland  ABSTRACT  Carbonate precipitation in oceans is essential for the carbonate-silicate cycle (inorganic carbon cycle)  to maintain temperate climates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  By considering the thermodynamics of carbonate chemistry, we  demonstrate that the ocean pH decreases by approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5 for a factor of 10 increase in the  atmospheric carbon dioxide content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The upper and lower limits of ocean pH are within 1–4 of each  other, where the upper limit is buffered by carbonate precipitation and defines the ocean pH when  the carbon cycle operates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' If the carbonate compensation depth (CCD) resides above the ocean floor,  then carbonate precipitation and the carbon cycle cease to operate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The CCD is deep (>40 km)  for high ocean temperature and high atmospheric carbon dioxide content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Key divalent carbonates of  magnesium, calcium and iron produce an increasingly wider parameter space of deep CCDs, suggesting  that chemical diversity promotes the carbon cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The search for life from exoplanets will benefit by  including chemically more diverse targets than Earth twins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Keywords: Extrasolar rocky planets (511);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Carbon dioxide (196);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Habitable zone (696);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Ocean-  atmosphere interactions (1150);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Geological processes (2288);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' (Unified Astronomy Thesaurus)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' INTRODUCTION  The carbonate-silicate cycle, also known as the in-  organic carbon cycle, is a negative climate feedback  mechanism that stabilises the surface temperature via  the greenhouse effect of carbon dioxide in response  to changes in volcanism rates, stellar luminosity, at-  mospheric composition and opacity, planetary orbital  movements and spin axis tilt (Berner 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Catling  & Kasting 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Continental silicate rocks and at-  mospheric carbon dioxide react with water in a pro-  cess known as silicate weathering to produce carbonate-  forming ions that precipitate as carbonates onto the  ocean floor (Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The carbon cycle  is completed when carbonates are transferred into the  mantle for deep storage or carbon is eventually re-  leased back into the atmosphere by volcanism (Holland  1978;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Sleep & Zahnle 2001), although the degassing ef-  Corresponding author: Kaustubh Hakim  kaustubh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='hakim@unibe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='ch  ficiency is debated (Kelemen & Manning 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Foley  2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Silicate weathering and carbonate precipitation  are traditionally represented by the net chemical reac-  tion (Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981),  CaSiO3 + CO2 → CaCO3 + SiO2,  (1)  where wollastonite (CaSiO3), which serves as a proxy for  silicate rocks, is converted into calcite (CaCO3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Cal-  cium thus plays a crucial role in silicate weathering and  carbonate precipitation and is present as Ca2+ cations  in oceans (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The existence of habitable zones assumes that the  carbon cycle operates on Earth analogues to stabilise  their atmospheric carbon dioxide content (Kasting et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Implicitly, this assumes not only that silicate  weathering operates, but that ocean floor precipitation  and deep storage of carbonates also occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' There exists  a critical ocean depth known as the carbonate compen-  sation depth (CCD), below which carbonates are unable  to exist in their solid form because carbonate solubility  increases with pressure in the ocean (Zeebe & West-  broek 2003, see also Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3, Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' In modern  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='02652v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='EP]  6 Jan 2023  ID2  CCD  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' "#$#  %&\'(  Ocean Depth  %)*+,-  %&\'( ≤ %,/0  1)*+,- = 13456 = 1  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content="78'(,#$#  Carbonates  Silicates  Dissolved ions  Figure 1." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Model parameters, nDtot where D = Ca, Mg or  Fe, nSiO2,tot, PCO2, Patm, Poc and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' See Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2 and Table 1  for a full list of output quantities and description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Earth oceans, the CCD is located between 4–5 km, be-  low the average ocean depth of about 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='8 km (Zeebe  2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' If the CCD resides at a depth above the ocean  floor, then carbonates are unable to settle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' This leads  to the disruption of the carbon cycle—at least, as it is  understood to operate on Earth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Moreover, there are  currently no theoretical constraints on exoplanet ocean  chemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' We investigate the interplay between atmo-  spheric carbon dioxide content, ocean acidity (pH) and  carbonate precipitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  We then calculate the CCD  over a broad range of physical conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' METHODS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Ocean chemistry model  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Ca system  Ocean chemistry is modelled by considering thermo-  chemical equilibrium for pure Ca, Mg, or Fe systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The CO2 partial pressure PCO2, ocean–surface temper-  ature T and local ocean pressure Poc are control pa-  rameters (Figure 1, Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' In the Ca system, there  are 13 unknowns, the number density n of H+, OH−,  H2O, HCO−  3 , CO2−  3 , CO2(aq), Catot, Ca2+, SiO2,tot,  SiO2(aq), quartz SiO2(s), wollastonite CaSiO3(s) and  calcite CaCO3(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Out of the 13 unknowns, 2 are conti-  nental silicate weathering products, nCatot and nSiO2,tot,  that depend on PCO2 and T (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  There are  11 remaining unknowns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' We solve for 3 mass conserva-  tion equations (for H, Ca and SiO2), 1 charge balance  equation, and 7 equations from 7 chemical reactions pro-  viding relations between equilibrium constants (that de-  pend on Poc and T), reactants and products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Parameters and output quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Symbol  Description  Reference  Parameters for ocean chemistry  T  Ocean–Surface temperature  288 K  PCO2  CO2 partial pressure  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3 mbar  Patm  Atmospheric pressure  1 bar  Poc  Ocean layer pressure  1 bar  Parameters for weathering  nDtot,0  Ca, Mg or Fe ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' number density  1 m−3  β  Weathering power-law exponent  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3  Te  e-folding temperature  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='7 K  Output quantities  nX  Number density of X [m−3]  pH  –log10(nH+/n0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' n0 = 103 m−3  These 3 mass-conservation equations, 1 charge balance  equation and 7 reactions (water dissociation, Henry’s  law/physical CO2 dissolution, chemical CO2 dissolu-  tion, bicarbonate ion dissociation, calcite precipitation,  quartz precipitation and wollastonite precipitation) are  specified below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Henry’s law gives the amount of CO2  physically dissolved in ocean water in equilibrium with  PCO2:  CO2(g) ⇌ CO2(aq).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (2)  The chemical dissolution or dissociation of CO2 in ocean  water leads to the production of HCO−  3 and H+ ions and  thereby increases the ocean acidity (and decreases ocean  pH = − log10(nH+/n0), where the standard number den-  sity n0 = 1 m−3) by the following reaction:  CO2(g) + H2O ⇌ H+ + HCO−  3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (3)  To maintain the charge balance in ocean water, the ad-  dition of Ca2+ to oceans decreases the number density  of H+ and hence increases the ocean pH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The charge  balance equation is given by:  2nCa2+ + nH+ = nHCO−  3 + 2nCO2−  3  + nOH−,  (4)  where CO2−  3  is produced due to the bicarbonate disso-  ciation reaction:  HCO−  3 ⇌ CO2−  3  + H+,  (5)  and where OH− is produced due to the water dissocia-  tion reaction:  H2O ⇌ H+ + OH−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (6)  3  The mass conservation of H is given by  nHtot = 2nH2O + nH+ + nHCO−  3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (7)  Catot partitions into Ca2+, calcite and wollastonite  which is accounted for by mass conservation:  nCatot = nCa2+ + nCal + nWo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (8)  Calcite precipitation occurs when nCa2+ is saturated to  a certain value determined by the equilibrium constant  of the calcite precipitation reaction and the abundance  of nCO2−  3 :  Ca2+ + CO2−  3  ⇌ CaCO3(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (9)  SiO2,tot partitions into aqueous silica SiO2(aq), quartz  SiO2(s) and wollastonite CaSiO3(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The mass conser-  vation for SiO2 is given by:  nSiO2,tot = nSiO2(aq) + nQz + nWo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (10)  The quartz precipitation reaction is:  SiO2(aq) ⇌ SiO2(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (11)  The reaction of wollastonite precipitation is given by:  Ca2+ + SiO2(aq) + H2O ⇌ 2H+ + CaSiO3(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (12)  These equilibrium chemistry calculations are per-  formed using Reaktoro v2 (Leal 2015), a multi-phase  (aqueous, gas and solid mineral phases) chemistry soft-  ware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  This software implements the extended law of  mass action including the determination of stable and  unstable species for a given set of species in the system  (Leal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  We use the SUPCRTBL database  for thermodynamic data (Johnson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1992;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Zimmer  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2016), the Peng-Robinson activity model for gases  (Peng & Robinson 1976), the HKF activity model for  water (Helgeson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981) and the Drummond activ-  ity model for CO2(aq) (Drummond 1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Mg and Fe systems  In the Mg system, Ca is replaced by Mg, calcite  by magnesite MgCO3(s) and wollastonite by enstatite  Mg2Si2O6(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' This includes replacing equilibrium con-  stants of all reactions including Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Similarly, in the  Fe system, Ca is replaced by Fe, calcite by siderite  FeCO3(s) and wollastonite by fayalite Fe2SiO4(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' We  limit our calculations to Fe2+ although its oxidation has  inhibited the formation of siderite during Earth’s his-  tory, particularly since the great oxidation event (Rye  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Weathering model  The introduction of carbonate-producing divalent  cations in oceans is dictated by silicate weathering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Sil-  icate weathering and therefore the total number density  of divalent cations D2+ (D = Ca, Mg or Fe) must depend  on the CO2 partial pressure PCO2 and surface tempera-  ture T (Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Hakim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2021),  nDtot = fW (PCO2, T) = nDtot,0  � PCO2  PCO2,0  �β  exp  �T − T0  Te  �  ,  (13)  where ‘0’ represents the Earth reference values (Table 1),  Te = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='7 K is the e-folding temperature and β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3 is  the weathering power-law exponent (Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  However, not all added Ca (or Mg, Fe) in oceans re-  mains in the form of divalent cations, a fraction of it  precipitates as carbonates on the ocean floor and an-  other fraction as silicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' For this reason, we perform  partitioning calculations of Ca (or Mg, Fe) in different  phases following the ocean chemistry model (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' CCD model  Carbonates are deposited onto the ocean floor as part  of sediments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The transition from calcite-rich to calcite-  free sediments is gradual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The carbonate compensation  depth (CCD) for the Earth ocean is normally defined  as the depth at which the dissolution flux of calcite bal-  ances the precipitation flux (Zeebe 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The depth  at which the rapid dissolution of calcite-rich sediments  begins is known as the lysocline, which is a sediment  property (Zeebe & Westbroek 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The lysocline and  CCD serve as bounds on the transition zone (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5 km)  between calcite-rich and calcite-free sediments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Other  definitions for the CCD exist (Berger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1976;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Ridg-  well & Zeebe 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Zeebe 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The depth of ocean d  [km] in terms of ocean pressure Poc [bar] at the equator  is given by (Leroy & Parthiot 1998)  d =  1  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='7803 × 103 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='011Poc (97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='266Poc − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='512 × 10−3P 2  oc  + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='28 × 10−7P 3  oc − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='8 × 10−11P 4  oc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (14)  We consider the CCD to be the depth dCCD (equiv-  alent to the ocean pressure where Poc = PCCD) at  which 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='9% of near-surface (Poc = Psurf) Ca, Mg or  Fe-carbonates dissolve,  nCarb,CCD = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='001 nCarb,surf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (15)  Our calculations of CCD are performed up to dCCD =  45 km because of the availability of thermodynamic data  up to the pressure of 5000 bar (Zimmer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' This  limitation does not affect our conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Analytical solution of ocean pH  Upper limit of ocean pH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' For calcite precipitation, all  reactions in Section 2 need to be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' However, two  of these reactions can be used to analytically constrain  ocean pH: Equations 9 and 16 where Equation 16 is a  combination of Equations 3 and 5,  CO2(g) + H2O ⇌ 2H+ + CO2−  3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (16)  The ocean pH can be written as a function of PCO2,  nCa2+ and equilibrium constants of Equations 9 and 16  (Appendix A):  pH = −1  2  �  log PCO2 + log K9K16 + log nCa2+  n0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' (17)  This equation demonstrates the reason for the slope of  approximately −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5 for the upper limit of ocean pH as a  function of the logarithm (base 10) of PCO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Because K9  and K16 are constants at a fixed T and P, pH becomes  a function of only PCO2 and nCa2+ in Equation 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' As a  function of PCO2, nCa2+ at the limit of carbonate satura-  tion varies between ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1 m−3 (at PCO2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='01 µbar) and  ∼6 m−3 (at PCO2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3 bar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' This additional increase  in nCa2+ of less than two orders of magnitude over seven  orders of magnitude increase in PCO2, makes the slope  of ocean pH slightly steeper than −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Using nCa2+ from the numerical solution in Equation 17  results in a semi-analytical solution matching with the  numerical solution until PCO2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1 bar, beyond which  non-ideal effects accounted in the numerical solution ex-  hibit a small deviation from the analytical equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Lower limit of ocean pH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' In the absence of divalent  cations in ocean, the ocean pH is largely governed by the  conversion of CO2 to protons (Equation 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' For PCO2 >  1 µbar, the ocean is acidic, where the number density of  H+ is larger than that of OH− and the number density  of HCO−  3 is larger than CO2−  3  (bicarbonate-carbonate-  water equilibria, Wolf-Gladrow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Therefore,  the charge balance equation can be approximated as  nH+ = nHCO−  3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (18)  In terms of the equilibrium constant of Equation 3, this  leads to (Appendix A)  pH = −1  2 (log PCO2 + log K3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (19)  At a fixed T and P, K3 is constant and thus the ocean  pH exhibits a slope of −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5 for PCO2 > 1 µbar (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  For PCO2 < 1 µbar, the analytical solution does not  hold because the number density of OH− is significant  enough to make the charge balance approximation in  Equation 18 invalid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The lower limit of ocean pH is  independent of the Ca, Mg or Fe systems considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  4  5  6  7  8  9  10  11  Ocean pH  (a)  Carbon Cycle  No Carbon Cycle  Modern  Earth pH  Forbidden  Forbidden  Ca  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  4  5  6  7  8  9  10  11  Ocean pH  (b)  Carbon Cycle  No Carbon Cycle  Modern  Earth pH  Forbidden  Forbidden  Mg  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  4  5  6  7  8  9  10  11  Ocean pH  (c)  Carbon Cycle  No Carbon Cycle  Modern  Earth pH  Forbidden  Forbidden  Fe  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Sensitivity of ocean pH to PCO2 at T = 288 K for  pure (a) Ca, (b) Mg, (c) Fe systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Upper and lower bounds  of ocean pH are represented by the blue shaded region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Pink  shaded regions are forbidden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' RESULTS AND DISCUSSION  We consider the ocean pH to be determined by the  chemical dissolution of atmospheric carbon dioxide in  a well-mixed ocean, which occurs at the atmosphere–  ocean interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The chemical dissolution of CO2 is gov-  erned by the reaction between water and CO2 to produce  H+, HCO−  3 and CO2−  3  ions (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' As PCO2 increases,  the ocean becomes more acidic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' We consider an atmo-  spheric surface pressure of 1 bar, but allow the atmo-  spheric carbon dioxide content to vary via PCO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Atmo-  spheric surface pressures up to 100 bar have a negligible  effect on our results and those between 100–1000 bar  exhibit a small effect (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  For a given value of PCO2, the ocean pH is bounded  between two limits (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The ocean pH is restricted  to a narrow range between 7–11 at PCO2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='01 µbar  and 4–7 for PCO2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1 bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' These ocean pH ranges  are consistent with the inferences for Earth’s history,  transitioning from an acidic ocean during the Archean  at high PCO2 to an alkaline ocean at present-day PCO2  (Halevy & Bachan 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Krissansen-Totton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The lower limit corresponds to the complete absence of  divalent cations and thus it is independent of the car-  bonate system under investigation (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The upper  limit corresponds to the saturation of calcium cations  in ocean water such that more weathering does not pro-  duce further changes in pH and simply produces more  calcite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' This upper limit is buffered by the precipita-  tion of carbonates and hence it results in one solution  of ocean pH when the carbon cycle is operational for  a given carbonate system and PCO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Both upper and  lower limits of ocean pH follow a slope of approximately  –0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5 as a function of PCO2 (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Between  these two limits, the number density of calcium cations  is below the threshold to precipitate carbonates onto the  ocean floor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' thus, the carbon cycle is not operational.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Due to their high condensation temperatures, the  relative abundances of refractory elements observed in  the photosphere of stars are expected to be mirrored  in the rocky exoplanets they host (Bond et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Thiabaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  For example, the calcium-to-  magnesium ratio of the solar photosphere and Earth are  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='062 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='066, respectively (Lodders 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Elser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The relative abundances of Ca, Mg and Fe, mea-  sured from the spectra of stars, vary by up to an or-  der of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' For example, Ca/Mg=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='02–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2 and  Ca/Fe=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='04–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2 in the Hypatia catalogue of more than  7000 stars (Hinkel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Furthermore, carbonates  involving Mg and Fe are known to have formed during  Earth’s history: e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', magnesite (MgCO3) and siderite  (FeCO3);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' these carbonates have dissolution properties  that differ from those of calcite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Siderite could have  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  280  300  320  340  360  T [K]  (a)  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 100 m  3  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 1 m  3  Carbon Cycle  No Carbon Cycle  (cations consumed  by silicates)  No Carbon Cycle  (too little CO2)  No Carbon Cycle  (too acidic)  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' T)  Ca-CCD  1  2  4  10  20  40  CCD [km]  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  280  300  320  340  360  T [K]  (b)  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 100 m  3  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 1 m  3  Carbon Cycle  No Carbon Cycle  (cations consumed  by slicates)  No Carbon Cycle  (too little CO2)  No Carbon Cycle  (too acidic)  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' T)  Mg-CCD  1  2  4  10  20  40  CCD [km]  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  280  300  320  340  360  T [K]  (c)  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 100 m  3  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 1 m  3  Carbon Cycle  No Carbon Cycle  (cations consumed  by slicates)  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' T)  Fe-CCD  1  2  4  10  20  40  CCD [km]  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Carbonate compensation depth (CCD) as a func-  tion of PCO2 and T (Patm = 1 bar) for (a) Ca, (b) Mg and  (c) Fe systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Gray contours represent the weathering-  dependent cation number density as a function of PCO2 and  T (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Gray disc denotes modern Earth PCO2 and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  6  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  10  1  100  101  n [m  3]  (a)  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  Ca Partitioning  Ca++  Calcite  Silicates  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  10  1  100  101  n [m  3]  (b)  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  Mg Partitioning  Mg++  Magnesite  Silicates  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  10  1  100  101  n [m  3]  (c)  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  Fe Partitioning  Fe++  Siderite  Silicates  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Partitioning of (a) Ca, (b) Mg and (c) Fe in  aqueous, carbonate and silicate phases as a function of PCO2  at T = 310 K (Patm = Poc = 1 bar) in pure Ca, Mg and Fe  systems, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  played a key role in locking up CO2 in carbonates on  Earth during the Archean (Rye et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1995;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Sverjensky  & Lee 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' We calculate ocean pH for the pure Mg and  Fe systems in addition to the Ca system (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2b,c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The  upper limit of ocean pH for a given PCO2 varies when  considering systems with purely Ca, Mg or Fe as the  source of weathering cations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The upper limit of ocean  pH for the Mg system is only 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2 higher than for the Ca  system, whereas it is more than unity lower for the Fe  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  For PCO2 < 10 µbar, ocean chemistry and hence  the CCD is sensitive to the addition of aqueous silica  (SiO2) in the ocean (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Silica is another product  of silicate weathering, which enables the locking up of  cations in silicate minerals instead of carbonate minerals  (Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Hakim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' For instance,  for T > 300 K and PCO2 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1 µbar in the Ca sys-  tem in the presence of aqueous silica, silicates impinge  on the stability of calcite (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 4a) and prevent carbon-  ate precipitation at all depths (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 3a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  In contrast,  when no silica is present in the ocean for T > 300 K  and PCO2 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1 µbar, calcite is stable (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' B2a) and  deep CCDs are produced (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' B1a), thereby increasing  the parameter-space where the carbon cycle is stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Similarly, in the Mg and Fe systems, silicates are more  stable than carbonates for PCO2 < 10 µbar (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 4b,c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  PCO2 > 10 µbar favours the thermodynamic stability of  carbonates over silicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Carbon cycle box models of exoplanets often omit self-  consistent modelling of ocean chemistry and precipita-  tion of carbonates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Carbonate precipitation is implicitly  assumed to persist and is not expected to be a bottle-  neck for carbon cycling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Our ocean chemistry model  can be incorporated directly into carbon cycle box mod-  els for exoplanets, which can couple via key parameters,  PCO2, T, and the carbonate chemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Thermochemi-  cal equilibrium calculations of our ocean model can be  used to determine the carbon fluxes into or out of the  near-surface reservoirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The carbon cycle box models  can also be informed of the effect of ocean chemistry  and ocean depth on the efficiency of carbon degassing  and recycling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Upcoming observations of terrestrial exoplanets from  the James Webb Space Telescope, Atmospheric Remote-  sensing Infrared Exoplanet Large-survey and Extremely  Large Telescopes will put constraints on their atmo-  spheric composition, for instance, the volume mixing  ratio of atmospheric carbon dioxide (PCO2/P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Deter-  mining the partial pressure of carbon dioxide (PCO2)  requires the atmospheric surface pressure (P) which is  not easily constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Nonetheless, our thermodynamic  calculations provide strong constraints on ocean chem-  7  istry in the presence or absence of magnesium, calcium  or iron carbonates;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' the relative abundances of these  carbonate-forming elements in planetary systems can  be deduced from observations of stellar photospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Our results suggest that the carbon cycle will oper-  ate robustly on chemically-diverse terrestrial exoplanets  exhibiting silicate weathering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  This implies that the  search for life from exoplanets with temperate climates  or biospheres will benefit by broadening the target list  to planets that are more chemically diverse than Earth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  We acknowledge financial support from the European  Research Council via Consolidator Grant (ERC-2017-  CoG-771620-EXOKLEIN, awarded to K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Heng) and the  Center for Space and Habitability, University of Bern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  We thank Allan Leal for the support with Reaktoro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  DATA AVAILABILITY  All data generated or analysed during this study are  included in the published article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  CODE AVAILABILITY  OCRA (Ocean Chemistry with Reaktoro And beyond):  the open-source code developed in this work is hosted  at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='com/kaustubhhakim/ocra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' OCRA v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='0  was used in this study and is also available on Zenodo  (Hakim 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Software:  numpy (Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2020), scipy (Vir-  tanen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2020), pandas (The pandas development  team 2020), astropy (Astropy Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2013, 2022), matplotlib (Hunter 2007), Reaktoro (Leal  2015)  APPENDIX  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' ANALYTICAL SOLUTION OF OCEAN PH AND  P–T SENSITIVITY  The analytical solution for the upper limit of ocean  pH is derived from the relations between the equilibrium  constants and reactants and products (assuming water  activity to be unity in diluted solutions) of reactions  described by Equations 9 and 16,  K9 =  n2  0  nCa2+nCO2−  3  ,  (A1)  K16 =  n2  H+nCO2−  3  PCO2n3  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (A2)  By eliminating the carbonate ion number density from  these two equations, proton number density is  nH+  n0  =  �  PCO2K9K16  nCa2+  n0  �1/2  (A3)  Because the pH is given by  pH = − log(nH+/n0),  (A4)  the analytical upper limit of ocean pH is Equation 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The analytical solution for the lower limit of ocean  pH is derived from the the equilibrium constant of the  reaction described by Equation 3,  K3 =  nH+nHCO−  3  PCO2n2  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  (A5)  Then the proton number density is  nH+  n0  = K3PCO2n0  nHCO−  3  (A6)  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  4  5  6  7  8  9  10  11  Ocean pH  Carbon Cycle  No Carbon Cycle  Modern  Earth pH  Forbidden  Ca  Up (numerical)  Up (semi-analytical)  Up (ana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', nCa2 + = 1 m  3)  Low (numerical)  Low (analytical)  Figure A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Numerical, analytical and semi-analytical so-  lutions of the upper and lower limits of ocean pH in the Ca  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  Thus, the lower limit of ocean pH is given by Equation  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  The analytical solutions of upper and lower limits of  ocean pH as a function of PCO2 result in a slope of –0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Pressure and temperature have a negligible  effect on ocean pH (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  8  100  101  102  103  P [bar]  4  5  6  7  8  9  10  11  Ocean pH  (a)  Carbon Cycle  No Carbon Cycle  Modern  Earth pH  Forbidden  Forbidden  Ca  nCa, tot = fW(PCO2)  280  300  320  340  360  T [K]  4  5  6  7  8  9  10  11  Ocean pH  (b)  Carbon Cycle  No Carbon Cycle  Modern  Earth pH  Forbidden  Forbidden  Ca  nCa, tot = fW(PCO2)  Figure A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' The sensitivity of ocean pH to (a) P and (b) T  in the Ca-system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' CCD WITHOUT SILICATE PRECIPITATION  When no silicates are allowed to precipitate, CCDs for  the Ca, Mg and Fe systems become deeper for PCO2 <  1 µbar (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' This is reflected in the phase stability  plots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  280  300  320  340  360  T [K]  (a)  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 100 m  3  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 1 m  3  Carbon Cycle  No Carbon Cycle  (too little CO2)  No Carbon Cycle  (too acidic)  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' T)  Ca CCD  1  2  4  10  20  40  CCD [km]  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  280  300  320  340  360  T [K]  (b)  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 100 m  3  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 1 m  3  Carbon Cycle  No Carbon Cycle  (too little CO2)  No Carbon Cycle  (too acidic)  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' T)  Mg CCD  1  2  4  10  20  40  CCD [km]  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  280  300  320  340  360  T [K]  (c)  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 100 m  3  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = 1 m  3  Carbon Cycle  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' T)  Fe CCD  1  2  4  10  20  40  CCD [km]  Figure B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 3 but with no silica nSiO2,tot = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  9  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  10  1  100  101  n [m  3]  (a)  nCa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  Ca Partitioning  Ca++  Calcite  Silicates  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  10  1  100  101  n [m  3]  (b)  nMg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  Mg Partitioning  Mg++  Magnesite  Silicates  10  8  10  7  10  6  10  5  10  4  10  3  10  2  10  1  PCO2 [bar]  10  1  100  101  n [m  3]  (c)  nFe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' tot = fW(PCO2)  Fe Partitioning  Fe++  Siderite  Silicates  Figure B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 4 but with no silica nSiO2,tot = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  10  REFERENCES  Astropy Collaboration, Robitaille, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Tollerud, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2013, A&A, 558, A33,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1051/0004-6361/201322068  Astropy Collaboration, Price-Whelan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Lim, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2022, ApJ, 935, 167, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3847/1538-4357/ac7c74  Berger, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Adelseck, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Mayer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1976,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', 81, 2617,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1029/JC081i015p02617  Berner, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2004, The Phanerozoic carbon cycle: CO2  and O2 (Oxford University Press on Demand)  Bond, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', O’Brien, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Lauretta, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2010, ApJ,  715, 1050, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1088/0004-637X/715/2/1050  Catling, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Kasting, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2017, Atmospheric  Evolution on Inhabited and Lifeless Worlds (Cambridge  University Press)  Drummond, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981, PhD thesis, Pennsylvania State  University  Elser, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Meyer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Moore, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2012, Icarus, 221, 859,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='icarus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='016  Foley, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2015, ApJ, 812, 36,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1088/0004-637X/812/1/36  Hakim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2022, kaustubhhakim/ocra: OCRA, v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='0,  Zenodo, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='7380526.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='7380526  Hakim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Bower, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Tian, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2021, PSJ, 2, 49,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3847/PSJ/abe1b8  Halevy, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Bachan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2017, Science, 355, 1069,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='aal4151  Harris, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Millman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', van der Walt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2020, Nature, 585, 357, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1038/s41586-020-2649-2  Helgeson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Kirkham, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Flowers, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981,  American Journal of Science, 281, 1249,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2475/ajs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='281.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1249  Hinkel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Timmes, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Young, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Pagano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=',  & Turnbull, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2014, AJ, 148, 54,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1088/0004-6256/148/3/54  Holland, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1978, The chemistry of the atmosphere and  oceans (New York, NY (USA) Wiley-Interscience)  Hunter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2007, Computing in Science & Engineering, 9,  90, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1109/MCSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='55  Johnson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Oelkers, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Helgeson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1992,  Computers and Geosciences, 18, 899,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1016/0098-3004(92)90029-Q  Kasting, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Whitmire, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Reynolds, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1993,  Icarus, 101, 108, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1006/icar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1010  Kelemen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Manning, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2015, Proceedings of the  National Academy of Science, 112, E3997,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1073/pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1507889112  Krissansen-Totton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Arney, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Catling, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2018,  Proceedings of the National Academy of Science, 115,  4105, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1073/pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1721296115  Leal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2015, Reaktoro: An open-source unified  framework for modeling chemically reactive systems, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  https://reaktoro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='org  Leal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Kulik, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Smith, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Saar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  2017, Pure and Applied Chemistry, 89, 597,  doi: doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1515/pac-2016-1107  Leroy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Parthiot, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1998, Acoustical Society of  America Journal, 103, 1346, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1121/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='421275  Lodders, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2003, ApJ, 591, 1220, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1086/375492  Peng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Robinson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1976, Industrial &  Engineering Chemistry Fundamentals, 15, 59  Ridgwell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Zeebe, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2005, Earth and Planetary  Science Letters, 234, 299, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='epsl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='006  Rye, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Kuo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Holland, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1995, Nature, 378,  603, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1038/378603a0  Sleep, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Zahnle, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2001, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', 106,  1373, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1029/2000JE001247  Sverjensky, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Lee, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2010, Elements, 6, 31,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2113/gselements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='31  The pandas development team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2020, pandas-dev/pandas:  Pandas, latest, Zenodo, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3509134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='3509134  Thiabaud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Marboeuf, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Alibert, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Leya, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', &  Mezger, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2015, A&A, 580, A30,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1051/0004-6361/201525963  Virtanen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Gommers, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Oliphant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2020,  Nature Methods, 17, 261,  doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1038/s41592-019-0686-2  Walker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Hays, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Kasting, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 1981,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', 86, 9776,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1029/JC086iC10p09776  Wolf-Gladrow, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Zeebe, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Klaas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', K¨ortzinger,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Dickson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2007, Marine Chemistry, 106, 287,  doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='marchem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='006  Zeebe, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2012, Annual Review of Earth and Planetary  Sciences, 40, 141,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1146/annurev-earth-042711-105521  Zeebe, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', & Westbroek, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2003, Geochemistry,  Geophysics, Geosystems, 4, 1104,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='1029/2003GC000538  Zimmer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', Lu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content=' 2016, Computers and  Geosciences, 90, 97, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
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+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE0T4oBgHgl3EQfyAIA/content/2301.02652v1.pdf'}
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+Astronomy & Astrophysics manuscript no. VMS
+©ESO 2023
+January 13, 2023
+Clues on the presence and segregation of very massive stars in
+the Sunburst Lyman-continuum cluster at z=2.37⋆
+U. Meštri´c1,⋆⋆, E. Vanzella1, A. Upadhyaya2, F. Martins3, R. Marques-Chaves2, D. Schaerer2, 4,
+J. Guibert2, A. Zanella5, C. Grillo6, 7, P. Rosati8, F. Calura1, G.B. Caminha9, 10, A. Bolamperti5, 11, 12,
+M. Meneghetti1, P. Bergamini1, 6, A. Mercurio13, 14, M. Nonino15, R. Pascale1
+1 INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy
+2 Geneva Observatory, Department of Astronomy, University of Geneva, Chemin Pegasi 51, CH-1290 Versoix, Switzerland
+3 LUPM, Université de Montpellier, CNRS, Place Eugène Bataillon, F-34095 Montpellier, France
+4 CNRS, IRAP, 14 Avenue E. Belin, 31400 Toulouse, France
+5 INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122, Padova, Italy
+6 Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy
+7 INAF – IASF Milano, via A. Corti 12, I-20133 Milano, Italy
+8 Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, via Saragat 1, I-44122 Ferrara, Italy
+9 Technical University of Munich, TUM School of Natural Sciences, Department of Physics, James-Franck-Str 1, 85748 Garching,
+Germany
+10 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching, Germany
+11 Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy
+12 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching bei München, Germany
+13 Dipartimento di Fisica “E.R. Caianiello”, Università Degli Studi di Salerno, Via Giovanni Paolo II, I–84084 Fisciano (SA), Italy
+14 INAF – INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
+15 INAF – Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, I-34143, Trieste, Italy
+ABSTRACT
+We report on the identification of very massive stars (VMS, mass > 100 M⊙) possibly segregated in the center of the young massive
+star cluster at z=2.37 hosted in the Sunburst lensed galaxy. Such a result is based on two pieces of evidence: (1) the VLT/MUSE
+spectra of several multiple images of the same star cluster show key spectral signatures of VMS, like the Heiiλ1640 broad emission,
+Nivλ1486 emission and Nivλ1720 P-Cygni profile. In particular, Heiiλ1640 is broad (∼ 1610 ± 300 km s−1) with an equivalent width
+of 3Å and shows an asymmetric profile. Such features require an extremely young (∼ 2.5 Myr) stellar population component with
+masses of the stars exceeding 100 M⊙. Assuming a Salpeter IMF and BPASS models for normal massive stars, the observed spectral
+features require ∼400 VMS; (2) the same star cluster is detected at S/N ∼ 100 in the LyC domain (λ < 900Å). The LyC emission
+emerges from a region with a radius at least 2 times smaller than what is observed at 1700Å (independently from magnification)
+and is located in the center of the cluster. In absolute scales, after de-lensing, the effective radii are Reff[LyC] ∼ 4.7 ± 1.5 pc and
+Reff[1700] = 7.8 ± 1.4 pc. The LyC radiation is mainly produced by hot and massive stars, implying that their spatial distribution
+(including VMS) is preferentially more confined in the central parts of the cluster. Approximately 400 VMS hosted by a cluster of
+∼ 107 M⊙ are producing ∼15% of the escaping LyC photons, while the rest is produced from other massive early-type stars.
+Key words. galaxies: high-redshift – galaxies: star formation – galaxies: ISM – galaxies: star clusters: general – gravitational lensing:
+strong – galaxies: individual: Sunburst galaxy.
+1. Introduction
+For many years the existence and occurrence of very massive
+stars (VMS) was mostly associated with the early Universe and
+metal-free environments in the context of the so-called Popula-
+tion III stars (e.g. Abel et al. 2002). VMS are short-lived stars ∼
+2 – 3 Myr (e.g. Yusof et al. 2013) with mass M > 100 M⊙ (Vink
+et al. 2015) and predominantly populate the central regions of
+young massive star clusters (within the core radius rc ∼ 0.1−0.2
+pc, Portegies Zwart et al. 2010). Due to their narrow lifetime,
+⋆ Based on observations collected at the European Southern Observa-
+tory for Astronomical research in the Southern Hemisphere under ESO
+programmes DDT MUSE program ID 107.22SK.001 (PI E. Vanzella),
+X-Shooter program ID 0103.A-0688 (PI E. Vanzella) and DDT MUSE
+program ID 297.A-5012(A) (PI Aghanim).
+⋆⋆ E-mail: uros.mestric@inaf.it
+studies of VMS in Milky Way star clusters is limited only to
+few targets, for example, the Arches cluster (Martins et al. 2008)
+or NGC3603 (Crowther et al. 2010). Individual VMS have been
+investigated in the local Universe, with high spatial resolution,
+thanks to the Hubble Space Telescope (HST, Cignoni et al. 2015;
+Crowther et al. 2016; Calzetti et al. 2015; Smith et al. 2016,
+2020; Brands et al. 2022). Very massive stars with masses above
+100 M⊙ are recognized as objects with significant impact on the
+evolution of early galaxies, influencing their chemical enrich-
+ment and star formation through feedback (e.g. Goswami et al.
+2021). Therefore, extending upper masses beyond 100 M⊙ of the
+current population synthesis models is essential for investigating
+and understanding young massive star clusters and VMS at dif-
+ferent redshifts (Smith et al. 2016; Crowther et al. 2016).
+Article number, page 1 of 10
+arXiv:2301.04672v1  [astro-ph.GA]  11 Jan 2023
+
+A&A proofs: manuscript no. VMS
+Despite some progress, the maximum stellar mass attained
+and the conditions determining the presence of VMS remain
+largely unknown. Recent observations of local star clusters re-
+port initial stellar masses up to ∼ 270 M⊙ (Brands et al. 2022) in
+the star cluster R136, with a cluster age of ∼1.5 Myr (Crowther
+et al. 2016). Furthermore, observations of young stellar clus-
+ters have revealed the presence of peculiar spectroscopic fea-
+tures such as unusually strong broad Heiiλ1640 emission (with
+FWHM > 1000 km s−1), which suggests the presence of VMS
+in these objects (e.g., Wofford et al. 2014; Crowther et al. 2016;
+Senchyna et al. 2021).
+Alongside with the observations, different models are try-
+ing to predict and trace the evolution, through different ages
+and masses, of the various spectroscopic features characteristic
+to VMS (e.g., Köhler et al. 2015; Gräfener 2021). For exam-
+ple, Martins & Palacios (2022) have generated new evolution-
+ary models and synthetic spectra of stars with initial masses in
+the range 150 – 400 M⊙, taking into account the existence of
+stellar winds stronger than typical OB-type stars produce. The
+resulting models predict specific features in the UV and optical
+part of the spectra, which are characteristic signatures of VMS.
+The most robust ultraviolet spectral features associated to VMS
+are Nivλ1486, broad Heiiλ1640 emission, and the Nivλ1720 P-
+Cygni profile (Martins & Palacios 2022). Such lines are expected
+to have equivalent widths spanning the interval 0.1 − 7 Å rest-
+frame. High signal-to-noise spectra with well detected contin-
+uum are therefore required to identify them, as shown, e.g., by
+Crowther et al. (2016) in the R136 stellar cluster in the local
+Universe. At cosmological distance strong gravitational lensing
+is necessary to detect these faint spectral features, allowing us to
+further gain in spatial resolution at tens of parsec scale and depth
+(see also, Vanzella et al. 2016; Johnson et al. 2017; Rigby et al.
+2017, 2018b,a; Vanzella et al. 2017, 2021; Meštri´c et al. 2022;
+Vanzella et al. 2022b).
+In this paper, we present for the first time convincing spec-
+troscopic evidence for the presence of VMS in a stellar cluster
+at cosmological distance (z=2.37, Vanzella et al. 2020a, 2022a).
+The host galaxy is dubbed Sunburst (Rivera-Thorsen et al.
+2019, 2017), and Lyman continuum (LyC) radiation is detected
+from the same clumpy regions which are showing the presence
+of VMS. Those massive stars in the center of the stellar cluster
+are significant producers of LyC radiation and hence are the main
+culprits for creating porous interstellar medium (ISM) enabling
+LyC escape. For purpose of this work, we perform a compre-
+hensive analysis of deep VLT/MUSE, X-Shooter and synthetic
+spectra with aim to confirm presence of VMS. Additionally we
+investigate the existence of the segregation of VMS by modeling
+the morphology of the young massive star cluster (YMC) hosted
+in the Sunburst galaxy.
+The paper is organized as follows. In Section 2 we briefly de-
+scribe the Sunburst galaxy and the available observational data.
+In Section 3 we analyze the spectral signatures of very massive
+stars using MUSE/IFU and X-Shooter observations in combina-
+tion with the latest evolutionary models and synthetic spectra. In
+Section 4 we discuss the morphological properties of the YMC
+(dubbed 5.1) and the possible segregation of the (very) massive
+stars in its central parts. We present our conclusion in Section 5.
+We assume a flat cosmology with ΩM= 0.3, ΩΛ= 0.7 and
+H0 = 70 km s−1 Mpc−1. Within this model, one arcsec at z = 2.37
+corresponds to a projected physical scale of 8200 parsec. All
+magnitudes are given in the AB system.
+Fig. 1. Left: The HST F555W band image, showing the six aperture po-
+sitions where a MUSE 1D spectrum is extracted (red contours). White
+arrows point to the multiple images of the young stellar cluster. Right:
+The MUSE IFU image at ∼ 1800Å of the same region shown on the left
+with the same apertures in red.
+2. The Sunburst lensed galaxy
+The Sunburst is a galaxy at z=2.37, strongly lensed by the
+Planck cluster PSZ1 G311.65-18.48 at z=0.44, initially reported
+by Dahle et al. (2016). The strong gravitational lensing effect
+deflects the light from the background high-z Sunburst galaxy
+into four bright arcs. These bright arcs harbor at least 13 star-
+forming knots, which likely are stellar clusters. There are more
+than 50 multiple images of this system (Pignataro et al. 2021),
+whose physical properties are studied in detail in Vanzella et al.
+(2022a). Among the 13 young stellar clusters, one has been iden-
+tified 12 times (dubbed 5.1) and it is the subject of this work
+(see Figure 1). The source 5.1 shows a multi-peaked Lyα emis-
+sion consistent with an optically thin medium and Lyman con-
+tinuum (LyC) leakage along the line of sight (Rivera-Thorsen
+et al. 2017). Furthermore, the detection of LyC radiation emerg-
+ing from the 12 detected multiple images of the 5.1 young mas-
+sive star cluster is confirmed by HST multi-band observations
+(Rivera-Thorsen et al. 2019). Additional analyses of the 12 LyC
+multiple images of 5.1 have revealed that the star cluster has
+an age younger than 3 Myr and a stellar metallicity of 0.5Z⊙
+(Chisholm et al. 2019), with a physical size of ≃ 10 pc and a
+stellar (and dynamical) mass value of ≃ 107 M⊙ (Vanzella et al.
+2022a).
+The Sunburst was observed with HST, providing multi-
+band photometry in the F275W, F410M, F555W, F606W,
+F814W, F098M, F105W, F140W and F160W filters, under the
+programs 15101 (PI Dahle), 15949 (PI Gladders), and 15377
+(PI Bayliss). Sunburst has also been targeted with ground-
+based high resolution (R ∼ 5000 − 9000) VLT/X-Shooter spec-
+troscopy covering the spectral range 3000-22000Å in three main
+arms, UVB, VIS abd NIR. The observational strategy and the
+data reduction procedures applied to HST imaging and VLT/X-
+Shooter spectroscopy have been presented in Vanzella et al.
+(2020b, 2022a). VLT/MUSE integral field spectroscopy at res-
+olution R = 3000 and covering the spectral range 4800-9400Å
+was obtained during 2016 (1h integration, DDT, PI. Aghanim)
+and 2021 (1h integration, PI, Vanzella) in the wide field mode
+configuration. The final datacube which combines the two hours
+and the data reduction is described in Vanzella et al. (2022a).
+We also presented a first version of the lens model in Pignataro
+et al. (2021) based on the 62 spectroscopically confirmed mul-
+tiple images in the redshift range 1 < z < 3.5 (see also Sharon
+et al. 2022; Diego et al. 2022). A revised lens model will be com-
+puted once the new VLT/MUSE observations (7h integration)
+planned during 2023 will be performed (prog. 110.249D.001,
+PI. Vanzella).
+Article number, page 2 of 10
+
+PSF
+HST F555W
+PSF
+MUSE IFU
+AP1
+AP2
+AP3
+5.1a
+5.1b
+5.1c
+5.1d'
+ 5.1f
+5.1e
+AP4
+AP5
+AP5
+.5.1h
+AP6
+5.1iU. Mestric et al.: Very massive, spatially segregated stars at z=2.4
+Here we focus on the ≃ 3 Myr old, UV-bright and Ly-
+man continuum source with MUV = −18.6 (1700Å magnitude
+and ultraviolet slope β = −1.71 ± 0.01, Fλ ∼ λβ), massive
+(M ∼ 107 M⊙) star cluster 5.1, subjected to large magnification
+values (µ ∼ 10 − 70 over 12 multiple images, Pignataro et al.
+2021; Vanzella et al. 2022a). In the following we perform a new
+analysis focusing on the nature of the ionizing source (Sect. 3)
+and its morphology (Sect. 4).
+3. Spectral signatures of very massive stars in the
+Sunburst star cluster at z=2.37
+We aim to investigate the UV and optical spectroscopic prop-
+erties of the young stellar cluster 5.1. The VLT/MUSE one-
+dimensional spectra are extracted from six apertures enclosing
+nine multiple images of 5.1 (shown in Fig. 1) and subsequently
+combined to produce a continuum-detected high signal-to-noise
+ratio SNR (> 60) weighted-average spectrum (Figure 2). The
+stacked spectrum shown in Figure 2 is equivalent to an inte-
+gration time of (2 × 9) × 302 > 16, 000 hours without lensing
+amplification, adopting the minimum amplification among the 9
+multiple images (µ = 30).
+3.1. Observed VMS features with VLT MUSE and X-Shooter
+The very high SNR MUSE spectrum (Fig. 2) allows us to
+identify several emission and absorption lines. Among them
+we have the nebular emission lines associated to the interstel-
+lar medium of the galaxy, like Oiii]λ1661, 1666, Niii]λ1750,
+[Siiii]λ1883, 1892, and Ciii]λλ1907, 1909. The well detected
+continuum allows us to investigate faint line emissions (of a frac-
+tion of an Å rest-frame equivalent width), and to sample the de-
+tails of the line profiles, otherwise not accessible without lens-
+ing amplification. In particular, faint Nivλ1486 emission, the ev-
+ident P-Cygni profile of the Civλ1550, the prominent broad and
+asymmetric Heiiλ1640 line profile, and the P-Cygni signature of
+Nivλ1720 clearly stand out. All these lines are associated with
+young, hot and (very) massive stars.
+We report detection of Heiiλ1640 emission with measured
+rest frame EW=3.0±0.3Å and FWHM=8.8±1.7Å (∼ 1610±300
+km s−1). The broad shape of the Heiiλ1640 emission line ob-
+served in the Sunburst cluster is asymmetric and resembles a
+typical P-Cygni profile. The blue end of the emission line drops
+steeply, while the red end drops more gradually. The P-Cygni
+profile of Heiiλ1640 line is consistent with that predicted by
+models and synthetic spectra (see, Martins & Palacios 2022).
+Broad Heiiλ1640 emission observed in galaxies is usually re-
+lated to non-nebular origin, commonly associated with Wolf-
+Rayet (WR) stars, (e.g. Schaerer & Stasi´nska 1999; Brinchmann
+et al. 2008; Leitherer et al. 2018; Senchyna et al. 2021), though
+the failure of the synthesis models to reproduce some of the
+strong Heiiλ1640 lines might be related to missing ingredients in
+stellar evolution models (see, e.g., Leitherer et al. 2018). How-
+ever, far-UV spectroscopic investigation of ∼57 individual stars
+located within the R136 star cluster reveals that massive stars
+with M>100 M⊙ have a crucial role in producing the Heiiλ1640
+emission line (Gräfener & Vink 2015; Crowther et al. 2016).
+On the other hand, Martins & Palacios (2022) have shown that
+Heiiλ1640 can be produced in significant amount only when stel-
+lar winds are stronger than in normal O stars. VMS develop
+such strong winds because of their proximity to the Eddington
+limit (Vink et al. 2011; Bestenlehner 2020; Gräfener 2021). At
+the same time, these winds peel off the external layers of the
+stars and expose to the surface the products of hydrogen burn-
+ing through the CNO cycle. This results in a strong nitrogen
+(and helium) enrichment that boosts the strength of Nivλ1486
+and Nivλ1720. This typically happens after ∼1.5 Myr. Both
+mentioned emission lines are detected in the spectrum of the
+Sunburst cluster at SNR > 15 (Figure 2), with EW=0.2Å and
+FWHM=2.9Å for Nivλ1486 and EW=0.15Å and FWHM ∼ 2Å
+for Nivλ1720. The helium enrichment also contributes to the
+strength of Heiiλ1640. The same effects (strong winds combined
+with surface chemical enrichment) happen in normal evolved
+massive stars when they are seen as WR stars. The key difference
+compared to VMS is that helium enrichment takes place only af-
+ter the main sequence (>∼ 4 Myr), while the same process takes
+place at younger ages in VMS. Furthermore, VMS are more lu-
+minous than normal WR stars and hence their contribution to
+integrated light is larger.
+The nebular Hα equivalent width provides constraints on the
+cluster age and hence on whether the Heiiλ1640 line is primar-
+ily due to WR stars or VMS. According to the BPASS mod-
+els and results from Eldridge & Stanway (2012) (their Fig. 3)
+they predict that normal and WR stars produce EWHα < 1Å for
+ages <∼ 3Myr. The X-Shooter spectrum reveals a prominent Hα
+line and no continuum detection, which very conservatively im-
+plies an equivalent width larger than 200Å rest-frame at 1-sigma.
+However, if we assume for Hα the same continuum level ob-
+served at λ ∼ 5000Å rest-frame in the photometric spectral en-
+ergy distribution (SED) by Vanzella et al. (2022a) such a limit in-
+creases to ∼ 840Å. This value would be still a lower limit, even in
+the case of leakage of ionizing photons. After correcting the Hα
+flux for the fraction of escaping LyC photons (Hα/(1− f abs
+esc )), the
+resulting EW increases to EWHα ∼ 1231Å. We adopt f abs
+esc values
+from Rivera-Thorsen et al. (2019), where the corresponding ab-
+solute escape fraction of LyC photons along the line of sight is
+f abs
+esc = 32+2
+−4% . Such a large Hα equivalent width is consistent
+with a star-forming burst younger than ∼ 3 Myr (e.g., Leitherer
+et al. 2014). Furthermore as discussed in Chisholm et al. (2019)
+Nvλ1240 stellar wind profile predominantly depends on the stel-
+lar age while variations due to different metallicity are negligible
+and it is related to the young stellar populations (< 5 Myr). From
+the comparison of the observed Nvλ1240 with the models Figure
+3 and 4 we additionally demonstrate that the age of the cluster is
+< 3 Myr. From our age analysis, we can conclude that properties
+of both Nvλ1240 and Hα fit well with < 3 Myr age of the stel-
+lar cluster which requires other sources than WR stars to explain
+the observed strong Heiiλ1640 EW=3.0±0.3Å. Therefore these
+results strongly suggest that VMS are responsible for the pro-
+duction of the spectral ultraviolet features we observe in such a
+young massive star cluster. Moreover, Wofford et al. (2014) and
+Smith et al. (2016) have argued that the presence of Ovλ1371 in
+integrated light of the clusters was also a key feature of VMS.
+This line is not seen in the Sunburst cluster, see Figure 2. As
+demonstrated by Martins & Palacios (2022), this is not incom-
+patible with the presence of VMS, since Ovλ1371 disappears as
+VMS evolve to lower effective temperature. In their Fig. 4, we
+see that no sign of Ovλ1371 exists after ∼1 Myr. This, together
+with the presence of Nivλ1486, places a rather tight constraint
+on the cluster age.
+3.2. Comparing observations with models
+To investigate the rest-frame UV spectrum of the cluster, we have
+created an integrated VMS model following Martins & Palacios
+Article number, page 3 of 10
+
+A&A proofs: manuscript no. VMS
+Fig. 2. The MUSE IFU spectrum of the 5.1 young massive star cluster extracted from 6 apertures is shown in black (thin line) and the X-Shooter
+long slit spectrum of 5.1l knot is shown in blue (bold line). The key confirmed features indicating the presence of VMS in the stellar cluster
+are marked with shaded light red strips while the dark-orange line shows the best-fit Fλ ∼ λβ, with β = −1.71. The shaded grey strip indicates
+the (absence of) Ovλ1371 line, which usually is an indicator of VMS too. The prominent P-Cygni of Nvλ1240 and strong emission part of the
+Civλ1550 are present and indicate the young age of the stellar cluster (black bold markers). In the bottom, the 1-sigma errors of both spectra are
+shown. Other detected interstellar features and stellar features are marked with dashed red and green lines, respectively.
+(2022) that includes normal mass stars (0.1-100 M⊙) with differ-
+ent VMS (150 M⊙ and 200 M⊙).
+We have used the spectral energy distribution (SEDs) of
+BPASS (Eldridge et al. 2017; Stanway & Eldridge 2018) v2.2.1
+single-star population synthesis model. The model has an up-
+per mass limit of 100 M⊙ with the Salpeter IMF, metallicity of
+Z=0.006 (where 0.02 corresponds to solar metallicity), and in-
+stantaneous star formation history, with a burst of mass 106 M⊙.
+The adopted metallicity of the model is the closest to our mea-
+sured value based on N2 index (Marino et al. 2013), which is
+≃ 0.4Z⊙ and consistent with the estimate provided by Mainali
+et al. (2022) (see also Chisholm et al. 2019).
+We have extrapolated the Salpeter IMF to 225 M⊙ upper
+mass limit within a few mass bins given by Equation 1 from the
+BPASS manual1. Equation 1 gives the number of massive stars
+in the mass range [Ma; Mb].
+N(Ma; Mb) = C × Mα1
+1
+� Mb
+Ma
+Mα2 dM
+(1)
+Here, C is a constant and has a value of 1.23×105 for an arbitrary
+burst mass of 106 M⊙. Also, M1 = 0.5 M⊙ α1 = -1.3, α2 = -
+2.35. The mass bins are selected in a way to add the SEDs of
+appropriate numbers of single VMS stars, which are available
+for discrete sets of VMS with masses including 150 M⊙ and 200
+M⊙. In this manner we compute SEDs including VMS with IMFs
+extending up to 175 and 225 M⊙, respectively, following Martins
+& Palacios (2022).
+1 https://flexiblelearning.auckland.ac.nz/bpass/9.html
+From Figure 2, we can see that the cluster shows signifi-
+cant Nivλ1486 emission. From the VMS models and synthetic
+spectra, Nivλ1486 emission only appears after 1.5 Myr of VMS
+evolution (see, Martins & Palacios 2022) and VMS last approx-
+imately until 2.5 Myr. Based on this, we created the SEDs of in-
+tegrated VMS models at 1.5 Myr, 2 Myr, and 2.5 Myr. We have
+normalized the spectrum of the cluster and the models by fitting
+a UV power law by using the spectral windows provided by Rix
+et al. (2004).
+We have directly compared the cluster spectrum with the two
+VMS models at 3 different ages. The comparison shows that
+VMS are clearly needed to reproduce the observations (see, Fig-
+ures 3, 4, and A.1). However, the Heiiλ1640 and Nivλ1720 lines
+in the models appear stronger than observed even at the age of
+1.5 Myr and with a maximum mass of 175 M⊙. To match the
+observed Heiiλ1640 and Nivλ1720 profiles, we have therefore
+reduced the VMS contribution by decreasing their numbers. We
+find good agreement if we reduce the VMS contribution by a fac-
+tor of 6 in the VMS model, which includes only 150 M⊙ VMS
+at 2.5 Myr (Fig. 3). Alternatively, a similar match is also found
+by reducing the VMS contribution by a factor of 8 in models in-
+cluding also the 200 M⊙ VMS (Fig. 4). In short, the observations
+are compatible with an IMF extending up to ∼ 175 or 225 M⊙,
+but with an IMF slope steeper than Salpeter (α2 < −2.35) for
+M > 100 M⊙.
+Article number, page 4 of 10
+
+Aobs / A
+4000
+4500
+5000
+5500
+6000
+6500
+3.0
+1H13
+IIIS.+IO
+AS:
+{IIIN
+IIIS
+IIIS
+AID
+全13
+sv
+CIV1550
+2.5
+NV1240
+y1486
+ux
+fl
+Normalized
+1.0
+0.5
+0.0
+F
+1100
+1200
+1300
+1400
+1500
+1600
+1700
+1800
+1900
+2000
+Arest / AU. Mestric et al.: Very massive, spatially segregated stars at z=2.4
+3.3. VMS contribution to the LyC budget of the young stellar
+cluster
+After adopting the results from the previous section, we can now
+estimate the number of O-type stars hosted by the same stellar
+cluster and the percentage of LyC photons emitted by VMS only.
+Measurements are performed in the range of ∼730–900Å
+rest-frame (range covered by HST F275W filter in which LyC
+radiation is detected and fesc later on evaluated). First, we cal-
+culate the mean flux from the model which include both normal
+and VMS stars and, secondly, we calculate the mean flux from
+the model including only VMS. The resulting ratio of those two
+models gives us the fraction of the LyC photons produced by
+VMS, which is ∼15%. Since LyC photons are mainly produced
+by O-type and more massive stars, we can see that ∼15% of the
+LyC production is generated only from ∼1% of the stars capable
+of producing LyC photons. It is worth noting that the fraction
+of LyC ionizing radiation produced from VMS in the Sunburst
+5.1 stellar cluster is smaller than the predicted LyC fraction pro-
+duced by the VMS located in R136 stellar cluster, which is 25%
+(Doran et al. 2013). However, we also note that in the case of the
+Sunburst stellar cluster the light coming from the host galaxy
+could slightly decreases the inferred equivalent width of the key
+spectral features discussed above. While such dilution is difficult
+to address with the present ground-based spectroscopic data2, its
+effect implies a possible slightly higher contribution of VMS to
+the LyC radiation.
+4. Spatial segregation of the Lyman continuum
+radiation
+We now address the morphological properties of image 5.1l,
+which is the most magnified among the multiple images of the
+star cluster (µtot ≃ 76, Pignataro et al. 2021). 5.1l is the brightest
+image detected with a large SNR in the F275W (SNR ∼ 90) and
+F555W (SNR ≫100), allowing us to investigate and compare
+the morphology in these two spectral regions: the emitting LyC
+(λ < 900Å, in HST F275W band) and the non-ionizing radiation
+at 1700Å (HST F555W band). We follow two approaches: (1)
+we ran simulations injecting the sources in the F275W band and
+(2) we analyzed the curve of growth of the resulting images.
+Figure 5 shows the F555W image of 5.1l, in which the elon-
+gation is clearly visible in the direction of the tangential stretch
+produced by gravitational lensing. As discussed in Pignataro
+et al. (2021) (see also Vanzella et al. 2022a), the tangential am-
+plification largely dominates along the arc (µtang ≃ 57). We per-
+form here a relative comparison between images, to ensure that
+the the results do not depend on the magnification values.
+As a first step, we compute a realistic model of 5.1l on the
+HST F555W image using Galfit (Peng et al. 2010). The point
+spread function (PSF) has been extracted by combining non-
+saturated stars available in the field of view. While the fit with a
+single component does not produce acceptable residuals (larger
+than 20%), we reproduce quite well the light profile of the ob-
+ject by combining two components: a core with a Gaussian light
+profile and an effective radius (Reff) smaller than 0.5 pixels (in
+practice nearly unresolved) and an extended component with
+Reff = 6 pixels and Sersic index n=1 (similar results are ob-
+tained also with n=0.5). The combination of the two components
+produces an optimal shape which leaves normalized residuals
+smaller than 10% (see Figure 5). It is worth now investigating if
+2 JWST/NIRSpec-IFU and NIRCAM observations on the same YMC
+are planned during 2023, prog. 2555, PI. Rivera-Thorsen
+such a resolved shape (sampled at 1700Å) is recovered if placed
+in the F275W Lyman continuum image. For this check, we in-
+jected mock images of 5.1l into the F275W image on five dif-
+ferent positions around 5.1l, which are not contaminated by the
+flux coming from other sources. Such images are produced from
+the aforementioned two-component Galfit model constructed
+at 1700Å (F555W), but now accounting for the F275W PSF (in
+other words convolved by the F275W PSF) to allow for a proper
+comparison with the LyC 5.1l source (observed in HST F275W
+band). Such images have been added to F275W after rescaling
+each of them to the observed peak value of the LyC 5.1l ob-
+ject. This step has been performed with IRAF (Tody 1986) task
+IMARITH and IMCOPY. Figure 6 shows the results, in which all
+the injected images show a spatially-resolved morphology along
+the tangential magnification. Conversely, the observed LyC im-
+age (of 5.1l) appears nucleated, suggesting that the emitting LyC
+region is smaller than the one at 1700Å.
+To quantify this result, we calculate the curve of growth
+(CoG) of the images shown in Figure 6. The flux is then mea-
+sured in the F275W band in 34 circular apertures. The small-
+est aperture has a radius of 0.1 pixel. Intermediate apertures are
+drawn with increasing radii, with a step of 0.5 pix, up to largest
+one, which has a radius of 34 pixels. As a reference point-like
+source, we constructed the mean CoG from a selected sample of
+twenty non-saturated and non-contaminated stars. The resulting
+CoG is shown in Figure 7, where the y-axis reports the frac-
+tion of the flux enclosed at the corresponding radius in pixels
+(x-axis).
+The same procedure has been applied to the LyC emitting
+source 5.1l, while another CoG has been constructed by averag-
+ing the five CoG of the injected models resembling the morphol-
+ogy at 1700Å. Figure 7 compares all the CoG after normalizing
+them to the saturation value at the largest radius. The first re-
+sult which emerges from this test is the clear deviation of the
+CoG of the observed 5.1l LyC source from the behavior of a
+point-like source (stars). This was not explored before and sug-
+gests that in the most magnified image of the star cluster the
+LyC appears spatially resolved. This is the first evidence of a re-
+solved stellar LyC emission at cosmological distance. Second,
+such barely resolved LyC emission appears more nucleated than
+the one at 1700Å. Consequently, the sources of ionizing radi-
+ation appears located in the central part of the cluster. Indeed,
+from those curves, it emerges that 50% of the flux of the stars is
+enclosed within a radius of ∼1.9 pixel, while for 5.1l it lies within
+∼2.2 pixels. Additionally, we perform the Kolmogorov-Smirnov
+two-sample test (KS-test) to check if the CoGs derived from the
+stars and 5.1l source follow the same distribution (null hypothe-
+sis). For this purpose, we used the statistical function ks_2samp
+from scipy.stats. After comparing the average CoG of the
+stars with cyan and violet CoGs, the KS-test gives p << 0.05. It
+means that the null hypothesis is not satisfied with the LyC pro-
+file of 5.1l and it deviates from the CoG of a point-like source.
+Furthermore, we also find that the half-light size of 5.1l at 1700Å
+is larger than the ionizing region, ∼2.6 pixels compared to the
+∼2.2 pixels. If we correct such radii for the instrumental reso-
+lution (given by the stars) we obtain an effective radius for 5.1l
+at 1700Å ≃ 7.8 ± 1.4 pc after de-lensing3, in agreement with
+Vanzella et al. (2020a), while the LyC image (5.1l) has a smaller
+radius, Reff ≃ 4.7 ± 1.5 pc. We therefore find a LyC emission
+which is more compact than the non-ionizing UV continuum,
+3 Adopting the pixel scale of 0.03′′/pixel, 8200 pc per arcsecond at
+z=2.37 and µtang ≃ 57, Reff = 0.03∗8200∗((2.62−1.92)0.5)/57, adopting
+the same uncertainty on µtang reported by Vanzella et al. (2022a).
+Article number, page 5 of 10
+
+A&A proofs: manuscript no. VMS
+Fig. 3. The MUSE ultraviolet spectra of the young star cluster (blue) is shown in the bottom panel with the X-Shooter spectrum (green). The
+grey-shaded regions show specific UV features closely associated with the presence of the VMS (Nivλ1486, Heiiλ1640, and Nivλ1720) and some
+of them show a P-Cygni profile, characteristic of young and massive stars. Furthermore, the black line shows the single BPASS model including
+only normal stars at 2.5 Myr, while the red line shows the BPASS single-star model augmented by VMS with masses up to 150 M⊙. The upper
+panels show the zoom in VMS characteristic features compared with models and Nvλ1240 P-Cygni line, characteristic due to the presence of very
+young stellar populations.
+which we interpret as a spatial segregation of the most massive
+stars.
+5. Summary and Conclusions
+In this paper, we have presented a detailed spectroscopic and
+morphological analysis of the massive and young stellar cluster
+hosted in the Sunburst lensed galaxy at z=2.37, for which also
+LyC emission was confirmed in the literature. We used results
+from recent stellar evolutions and atmosphere models including
+VMS (Martins & Palacios 2022) to conduct extensive compar-
+isons with high spectral resolution observations performed with
+VLT/MUSE and X-Shooter. The main results of this work can
+be summarized as follows:
+– In the spectroscopic observations, the high signal-to-noise
+MUSE and X-Shooter spectra reveal features of broad (and
+asymmetric) Heiiλ1640 emission with EW ≃ 3Å rest-frame
+and line width of 1610 km s−1, and Nivλ1486 with EW ≃
+0.2Å emission. In addition, the P-Cygni profile of Nivλ1720
+(along with NV and CIV) is also observed. All these features
+suggest the presence of very massive (> 100M⊙) stars. The
+absence of Ovλ1371 provides a lower age limit of 1 Myr. On
+the other hand, the large Hα EW (> 1231Å after correcting
+for the escaping LyC radiation) indicates an age younger than
+∼ 3 Myr. These narrow age constraints strongly favor the
+existence of VMS over WR stars, implying that the strength
+of the Heiiλ1640 emission line is entirely due to VMS.
+– A comparison of the observations with the models reveals
+that the most plausible age of the star cluster is 2.5 Myr, and
+an estimated number of ∼ 370 − 400 VMS for a cluster mass
+of 107 M⊙. The observations are compatible with an IMF
+extending up to ∼ 175 − 225 M⊙, but with a slope which is
+steeper than the Salpeter IMF.
+– The fraction of LyC radiation emerging from the VMS com-
+ponent is not negligible. We estimate that in the 730Å – 900Å
+range (probed by the HST/F275W band) about 360 – 400
+VMS (or roughly 1% of the total population of O-type stars
+in the star cluster) account for 15% of the escaping LyC pho-
+tons, with the rest being produced mostly by the other less
+massive O-type stars.
+– Detailed morphological analysis of the most magnified im-
+age of the star cluster shows that the region emitting LyC
+is not point-like, with a light profile different from the av-
+erage profile of stars present in the same field of view. This
+is the first evidence of a resolved LyC emission at any red-
+shift. Remarkably, the physical scale of the LyC emitting re-
+gion appears also smaller (with a significant K-S probability
+p << 0.05) than the non-ionizing region (1700Å), suggest-
+ing that massive O-type stars responsible for the LyC radi-
+ation, and likely the VMS (significantly contributing to it),
+are segregated in the central part of the star cluster. After de-
+lensing the angular half-light radii, the LyC region appears
+barely resolved with Reff ≃ 4.7 ± 1.5pc, while at 1700Å it
+is Reff ≃ 7.8 ± 1.4 pc. The packaging of such a large num-
+ber of massive O-type stars per parsec cube in the central
+region, ≃ 70 pc−3, is likely a element which allowed to carve
+the ionizing channel and the development of a high-speed
+outflowing gas (Rivera-Thorsen et al. 2017; Vanzella et al.
+2022a; Mainali et al. 2022).
+Acknowledgements. We acknowledge financial support through grants PRIN-
+MIUR 2017WSCC32, 2020SKSTHZ and the INAF GO Grant 2022 “The rev-
+Article number, page 6 of 10
+
+Nv1240A
+NIV1486A
+NIV1720A
+HeI1640A
+1.6
+1.4
+ Sunburst Cluster Mus
+1.5
+1.3 E
+BPASS 100 M。+ 150 M。VMS (39.43) at 2.5 Myr
+1.4
+1.2
+ 0.7 E
+0.7 
+0.4E
+0.61705
+1220
+1492
+1640
+1650
+1240
+1480
+1484
+1488
+1660
+670
+1710
+1715
+1720
+1725
+1730
+Rest Frame Wavelength [A]
+Rest Frame Wavelength [A]
+ Rest Frame Wavelength [A]
+ Rest Frame Wavelength [A]
+2.0E
+ Sunburst Cluster MUSE
+Sunburst Cluster Xshooter
+BPASS 2.5 Myr
+1.8E
+Single BPASSup to 100 Mo + 39.43 number of 150 Mo VMS at 2.5 Myr 
+1.6E
+1.4
+1.2E
+1.0M
+W
+0.8E
+Nor
+0.6
+0.4
+0.2日
+1250
+1300
+1350
+1400
+1450
+1500
+1550
+1600
+1650
+1700
+1750
+Rest Frame Wavelength [A]U. Mestric et al.: Very massive, spatially segregated stars at z=2.4
+Fig. 4. All symbols as in Figure 3 except for the red lines, showing the BPASS single-star model augmented by VMS with masses up to 200 M⊙.
+Fig. 5. The results from Galfit modeling after using a two-component
+fit. From the left, the first panel shows the 5.1l source in the F555W
+band (UV1700Å). The second panel shows the model from Galfit. The
+third panel shows the residual and the fourth panel is the normalized
+residual produced after dividing the residual with the original image.
+The white contour encloses the region used to check the quality of the
+produced model.
+olution is around the corner: JWST will probe globular cluster precursors and
+Population III stellar clusters at cosmic dawn” (PI Vanzella). FC and RP ac-
+knowledge funding from PRIN INAF 1.05.01.85.01.
+References
+Abel, T., Bryan, G. L., & Norman, M. L. 2002, Science, 295, 93
+Bestenlehner, J. M. 2020, MNRAS, 493, 3938
+Brands, S. A., de Koter, A., Bestenlehner, J. M., et al. 2022, A&A, 663, A36
+Brinchmann, J., Kunth, D., & Durret, F. 2008, A&A, 485, 657
+Calzetti, D., Johnson, K. E., Adamo, A., et al. 2015, ApJ, 811, 75
+Chisholm, J., Rigby, J. R., Bayliss, M., et al. 2019, ApJ, 882, 182
+Cignoni, M., Sabbi, E., van der Marel, R. P., et al. 2015, ApJ, 811, 76
+Crowther, P. A., Caballero-Nieves, S. M., Bostroem, K. A., et al. 2016, MNRAS,
+458, 624
+Crowther, P. A., Schnurr, O., Hirschi, R., et al. 2010, MNRAS, 408, 731
+Dahle, H., Aghanim, N., Guennou, L., et al. 2016, A&A, 590, L4
+Diego, J. M., Pascale, M., Kavanagh, B. J., et al. 2022, A&A, 665, A134
+Doran, E. I., Crowther, P. A., de Koter, A., et al. 2013, A&A, 558, A134
+Eldridge, J. J. & Stanway, E. R. 2012, MNRAS, 419, 479
+Eldridge, J. J., Stanway, E. R., Xiao, L., et al. 2017, PASA, 34, e058
+Goswami, S., Slemer, A., Marigo, P., et al. 2021, A&A, 650, A203
+Gräfener, G. 2021, A&A, 647, A13
+Gräfener, G. & Vink, J. S. 2015, A&A, 578, L2
+Fig. 6. The HST F275W image showing 5.1l LyC leaking source in
+its centre; other two multiple images, of the same source, are labeled
+as 5.1i and 5.1h. Around 5.1l, in the region not contaminated by other
+sources, five models are injected (see text for more details), enclosed
+in the white squares. In the bottom right corner, we shown the largest
+(34pix diameter) aperture size used to construct CoGs.
+Johnson, T. L., Rigby, J. R., Sharon, K., et al. 2017, ApJ, 843, L21
+Köhler, K., Langer, N., de Koter, A., et al. 2015, A&A, 573, A71
+Leitherer, C., Byler, N., Lee, J. C., & Levesque, E. M. 2018, ApJ, 865, 55
+Leitherer, C., Ekström, S., Meynet, G., et al. 2014, ApJS, 212, 14
+Mainali, R., Rigby, J. R., Chisholm, J., et al. 2022, ApJ, 940, 160
+Marino, R. A., Rosales-Ortega, F. F., Sánchez, S. F., et al. 2013, A&A, 559, A114
+Article number, page 7 of 10
+
+Nv1240A
+NIV1486A
+HeII1640A
+NIV1720A
+- Sunburst Cluster Xshootel
+1.05
+1260
+1480
+1492
+1496
+1630
+1640
+1650
+1670
+1220
+1484
+1488
+1710
+1715
+1725
+1730
+1230
+Rest Frame Wavelength [A]
+Rest Frame Wavelength [A]
+Rest Frame Wavelength [A]
+Rest Frame Wavelength [A]
+2.0
+Sunburst Cluster MUSE
+1.8E
+Sunburst Cluster Xshooter
+BPASS 2.5 Myr
+1.6E
+1.4
+.2
+1.0
+MA
+0.8
+LLLLLLLLLLLLL
+LJON
+0.6
+0.4E
+0.2E
+一
+0.0
+1250
+1300
+1350
+1400
+1450
+1500
+1550
+1600
+1650
+1700
+1750
+Rest Frame Wavelength [A]5.11
+normalised
+model
+residual
+HST
+F555W
+residual5.1h
+1"
+Model5
+Model
+5.1i
+Model
+5.11
+Model
+ModelA&A proofs: manuscript no. VMS
+Fig. 7. Three curves of growth normalized to 1. The cyan CoG cor-
+responds to the 5.1l LyC leaking source located in the Sunburst arc
+(F275W band). The violet CoG is the PSF-convolved, best-fit model of
+the 5.1l source observed in F555W constructed averaging 5 CoGs (see
+text for more details). The orange growth curve is used for comparison
+and it is constructed averaging 20 single CoGs from randomly selected
+stars. In both cases (cyan and violet) error bars are 1σ. Vertical lines in
+the bottom left part of the figure mark the pixel radii at which 50% of
+the light is enclosed. The colors corresponds to the CoG colors.
+Martins, F., Hillier, D. J., Paumard, T., et al. 2008, A&A, 478, 219
+Martins, F. & Palacios, A. 2022, A&A, 659, A163
+Meštri´c, U., Vanzella, E., Zanella, A., et al. 2022, MNRAS, 516, 3532
+Peng, C. Y., Ho, L. C., Impey, C. D., & Rix, H.-W. 2010, AJ, 139, 2097
+Pignataro, G. V., Bergamini, P., Meneghetti, M., et al. 2021, A&A, 655, A81
+Portegies Zwart, S. F., McMillan, S. L. W., & Gieles, M. 2010, ARA&A, 48, 431
+Rigby, J. R., Bayliss, M. B., Chisholm, J., et al. 2018a, ApJ, 853, 87
+Rigby, J. R., Bayliss, M. B., Sharon, K., et al. 2018b, AJ, 155, 104
+Rigby, J. R., Johnson, T. L., Sharon, K., et al. 2017, ApJ, 843, 79
+Rivera-Thorsen, T. E., Dahle, H., Chisholm, J., et al. 2019, Science, 366, 738
+Rivera-Thorsen, T. E., Dahle, H., Gronke, M., et al. 2017, A&A, 608, L4
+Rix, S. A., Pettini, M., Leitherer, C., et al. 2004, ApJ, 615, 98
+Schaerer, D. & Stasi´nska, G. 1999, A&A, 345, L17
+Senchyna, P., Stark, D. P., Charlot, S., et al. 2021, MNRAS, 503, 6112
+Sharon, K., Mahler, G., Rivera-Thorsen, T. E., et al. 2022, arXiv e-prints,
+arXiv:2209.03417
+Smith, L. J., Bajaj, V., Ryon, J., & Sabbi, E. 2020, ApJ, 896, 84
+Smith, L. J., Crowther, P. A., Calzetti, D., & Sidoli, F. 2016, ApJ, 823, 38
+Stanway, E. R. & Eldridge, J. J. 2018, MNRAS, 479, 75
+Tody, D. 1986, in Proc. SPIE, Vol. 627, Instrumentation in astronomy VI, ed.
+D. L. Crawford, 733
+Vanzella, E., Calura, F., Meneghetti, M., et al. 2017, MNRAS, 467, 4304
+Vanzella, E., Caminha, G. B., Calura, F., et al. 2020a, MNRAS, 491, 1093
+Vanzella, E., Caminha, G. B., Rosati, P., et al. 2021, A&A, 646, A57
+Vanzella, E., Castellano, M., Bergamini, P., et al. 2022a, A&A, 659, A2
+Vanzella, E., Castellano, M., Bergamini, P., et al. 2022b, ApJ, 940, L53
+Vanzella, E., De Barros, S., Cupani, G., et al. 2016, ApJ, 821, L27
+Vanzella, E., Meneghetti, M., Pastorello, A., et al. 2020b, MNRAS, 499, L67
+Vink, J. S., Heger, A., Krumholz, M. R., et al. 2015, Highlights of Astronomy,
+16, 51
+Vink, J. S., Muijres, L. E., Anthonisse, B., et al. 2011, A&A, 531, A132
+Wofford, A., Leitherer, C., Chandar, R., & Bouret, J.-C. 2014, ApJ, 781, 122
+Yusof, N., Hirschi, R., Meynet, G., et al. 2013, MNRAS, 433, 1114
+Article number, page 8 of 10
+
+1.0
+0.8
+iction
+rd
+0.6
+ux
+0.4
+0.2
+observed CoG of 5.1l in F275W
+★
+avg CoG for 5 observed Stars
+0.0
+6AE
+CoG model n=0.5
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+17.5
+Radius
+[pixels]U. Mestric et al.: Very massive, spatially segregated stars at z=2.4
+Appendix A: Initial models
+As described in Section 3.2, we compare the X-Shooter and
+MUSE spectroscopic observations with the BPASS models at
+different ages (1.5 Myr, 2 Myr, and 2.5 Myr). We narrow our
+models to the mentioned age range since the predicted age of the
+cluster is higher than 1.5 Myr (inferred from Nivλ1486 emission
+line) and the lifetime of the VMS is about 2.5 Myr (Martins &
+Palacios 2022). We started with the BPASS which has an upper
+mass limit of 100 M⊙ and added 236.56 stars in the 100 - 175
+M⊙ mass range and 60.30 stars in the mass range 175 – 225 M⊙.
+Resulting models (at different ages) are shown in A.1; all models
+produce significantly strong spectroscopic features characteristic
+of the presence of VMS. To better match models with observa-
+tions, we decreased the numbers of the VMS and the final results
+are presented in Section 3 (Figure. 3 and 4).
+Article number, page 9 of 10
+
+A&A proofs: manuscript no. VMS
+Fig. A.1. The six panels are showing the comparison of the observations (MUSE spectrum, red line) with BPASS models (black line). The left
+column shows three BPASS models with an IMF up to 100 M⊙, ages of 1.5 Myr, 2 Myr, 2.5 Myr and an added number of 236.56 150 M⊙ VMS.
+The right column shows BPASS model with an IMF up to 100 M⊙ at same ages (as shown in previous column) but with added nuber of 236.56
+and 60.30 VMS of 150 M⊙ and 200 M⊙, respectively. In all six panels we can see that the strength of feature characteristic to VMS is higher than
+in observed cluster, see the Section 3 for more details.
+Article number, page 10 of 10
+
diff --git a/BdE3T4oBgHgl3EQftAtl/content/tmp_files/load_file.txt b/BdE3T4oBgHgl3EQftAtl/content/tmp_files/load_file.txt
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+page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS  ©ESO 2023  January 13, 2023  Clues on the presence and segregation of very massive stars in  the Sunburst Lyman-continuum cluster at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='37⋆  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Meštri´c1,⋆⋆, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Vanzella1, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Upadhyaya2, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Martins3, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Marques-Chaves2, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Schaerer2, 4,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Guibert2, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Zanella5, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Grillo6, 7, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Rosati8, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Calura1, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Caminha9, 10, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Bolamperti5, 11, 12,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Meneghetti1, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Bergamini1, 6, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Mercurio13, 14, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Nonino15, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Pascale1  1 INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy  2 Geneva Observatory, Department of Astronomy, University of Geneva, Chemin Pegasi 51, CH-1290 Versoix, Switzerland  3 LUPM, Université de Montpellier, CNRS, Place Eugène Bataillon, F-34095 Montpellier, France  4 CNRS, IRAP, 14 Avenue E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Belin, 31400 Toulouse, France  5 INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122, Padova, Italy  6 Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy  7 INAF – IASF Milano, via A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Corti 12, I-20133 Milano, Italy  8 Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, via Saragat 1, I-44122 Ferrara, Italy  9 Technical University of Munich, TUM School of Natural Sciences, Department of Physics, James-Franck-Str 1, 85748 Garching,  Germany  10 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 1, D-85748 Garching, Germany  11 Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy  12 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching bei München, Germany  13 Dipartimento di Fisica “E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Caianiello”, Università Degli Studi di Salerno, Via Giovanni Paolo II, I–84084 Fisciano (SA), Italy  14 INAF – INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy  15 INAF – Osservatorio Astronomico di Trieste, via G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Tiepolo 11, I-34143, Trieste, Italy  ABSTRACT  We report on the identification of very massive stars (VMS, mass > 100 M⊙) possibly segregated in the center of the young massive  star cluster at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='37 hosted in the Sunburst lensed galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Such a result is based on two pieces of evidence: (1) the VLT/MUSE  spectra of several multiple images of the same star cluster show key spectral signatures of VMS, like the Heiiλ1640 broad emission,  Nivλ1486 emission and Nivλ1720 P-Cygni profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In particular, Heiiλ1640 is broad (∼ 1610 ± 300 km s−1) with an equivalent width  of 3Å and shows an asymmetric profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Such features require an extremely young (∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr) stellar population component with  masses of the stars exceeding 100 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Assuming a Salpeter IMF and BPASS models for normal massive stars, the observed spectral  features require ∼400 VMS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2) the same star cluster is detected at S/N ∼ 100 in the LyC domain (λ < 900Å).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The LyC emission  emerges from a region with a radius at least 2 times smaller than what is observed at 1700Å (independently from magnification)  and is located in the center of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In absolute scales, after de-lensing, the effective radii are Reff[LyC] ∼ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 pc and  Reff[1700] = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The LyC radiation is mainly produced by hot and massive stars, implying that their spatial distribution  (including VMS) is preferentially more confined in the central parts of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Approximately 400 VMS hosted by a cluster of  ∼ 107 M⊙ are producing ∼15% of the escaping LyC photons, while the rest is produced from other massive early-type stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' galaxies: high-redshift – galaxies: star formation – galaxies: ISM – galaxies: star clusters: general – gravitational lensing:  strong – galaxies: individual: Sunburst galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Introduction  For many years the existence and occurrence of very massive  stars (VMS) was mostly associated with the early Universe and  metal-free environments in the context of the so-called Popula-  tion III stars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Abel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS are short-lived stars ∼  2 – 3 Myr (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Yusof et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2013) with mass M > 100 M⊙ (Vink  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015) and predominantly populate the central regions of  young massive star clusters (within the core radius rc ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2  pc, Portegies Zwart et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Due to their narrow lifetime,  ⋆ Based on observations collected at the European Southern Observa-  tory for Astronomical research in the Southern Hemisphere under ESO  programmes DDT MUSE program ID 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='22SK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='001 (PI E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Vanzella),  X-Shooter program ID 0103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='A-0688 (PI E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Vanzella) and DDT MUSE  program ID 297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='A-5012(A) (PI Aghanim).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  ⋆⋆ E-mail: uros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='mestric@inaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='it  studies of VMS in Milky Way star clusters is limited only to  few targets, for example, the Arches cluster (Martins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2008)  or NGC3603 (Crowther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Individual VMS have been  investigated in the local Universe, with high spatial resolution,  thanks to the Hubble Space Telescope (HST, Cignoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Crowther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Calzetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016,  2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Brands et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Very massive stars with masses above  100 M⊙ are recognized as objects with significant impact on the  evolution of early galaxies, influencing their chemical enrich-  ment and star formation through feedback (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Goswami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Therefore, extending upper masses beyond 100 M⊙ of the  current population synthesis models is essential for investigating  and understanding young massive star clusters and VMS at dif-  ferent redshifts (Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Crowther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Article number, page 1 of 10  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='04672v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='GA]  11 Jan 2023  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS  Despite some progress, the maximum stellar mass attained  and the conditions determining the presence of VMS remain  largely unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Recent observations of local star clusters re-  port initial stellar masses up to ∼ 270 M⊙ (Brands et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022) in  the star cluster R136, with a cluster age of ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr (Crowther  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Furthermore, observations of young stellar clus-  ters have revealed the presence of peculiar spectroscopic fea-  tures such as unusually strong broad Heiiλ1640 emission (with  FWHM > 1000 km s−1), which suggests the presence of VMS  in these objects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Wofford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Crowther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Senchyna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Alongside with the observations, different models are try-  ing to predict and trace the evolution, through different ages  and masses, of the various spectroscopic features characteristic  to VMS (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Köhler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Gräfener 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' For exam-  ple, Martins & Palacios (2022) have generated new evolution-  ary models and synthetic spectra of stars with initial masses in  the range 150 – 400 M⊙, taking into account the existence of  stellar winds stronger than typical OB-type stars produce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The  resulting models predict specific features in the UV and optical  part of the spectra, which are characteristic signatures of VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The most robust ultraviolet spectral features associated to VMS  are Nivλ1486, broad Heiiλ1640 emission, and the Nivλ1720 P-  Cygni profile (Martins & Palacios 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Such lines are expected  to have equivalent widths spanning the interval 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1 − 7 Å rest-  frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' High signal-to-noise spectra with well detected contin-  uum are therefore required to identify them, as shown, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', by  Crowther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2016) in the R136 stellar cluster in the local  Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' At cosmological distance strong gravitational lensing  is necessary to detect these faint spectral features, allowing us to  further gain in spatial resolution at tens of parsec scale and depth  (see also, Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Johnson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Rigby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  2017, 2018b,a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Meštri´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  In this paper, we present for the first time convincing spec-  troscopic evidence for the presence of VMS in a stellar cluster  at cosmological distance (z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='37, Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2020a, 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The host galaxy is dubbed Sunburst (Rivera-Thorsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  2019, 2017), and Lyman continuum (LyC) radiation is detected  from the same clumpy regions which are showing the presence  of VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Those massive stars in the center of the stellar cluster  are significant producers of LyC radiation and hence are the main  culprits for creating porous interstellar medium (ISM) enabling  LyC escape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' For purpose of this work, we perform a compre-  hensive analysis of deep VLT/MUSE, X-Shooter and synthetic  spectra with aim to confirm presence of VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Additionally we  investigate the existence of the segregation of VMS by modeling  the morphology of the young massive star cluster (YMC) hosted  in the Sunburst galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In Section 2 we briefly de-  scribe the Sunburst galaxy and the available observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  In Section 3 we analyze the spectral signatures of very massive  stars using MUSE/IFU and X-Shooter observations in combina-  tion with the latest evolutionary models and synthetic spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In  Section 4 we discuss the morphological properties of the YMC  (dubbed 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1) and the possible segregation of the (very) massive  stars in its central parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We present our conclusion in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  We assume a flat cosmology with ΩM= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='3, ΩΛ= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='7 and  H0 = 70 km s−1 Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Within this model, one arcsec at z = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='37  corresponds to a projected physical scale of 8200 parsec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' All  magnitudes are given in the AB system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Left: The HST F555W band image, showing the six aperture po-  sitions where a MUSE 1D spectrum is extracted (red contours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' White  arrows point to the multiple images of the young stellar cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Right:  The MUSE IFU image at ∼ 1800Å of the same region shown on the left  with the same apertures in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The Sunburst lensed galaxy  The Sunburst is a galaxy at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='37, strongly lensed by the  Planck cluster PSZ1 G311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='65-18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='48 at z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='44, initially reported  by Dahle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The strong gravitational lensing effect  deflects the light from the background high-z Sunburst galaxy  into four bright arcs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' These bright arcs harbor at least 13 star-  forming knots, which likely are stellar clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' There are more  than 50 multiple images of this system (Pignataro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021),  whose physical properties are studied in detail in Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  (2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Among the 13 young stellar clusters, one has been iden-  tified 12 times (dubbed 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1) and it is the subject of this work  (see Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The source 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1 shows a multi-peaked Lyα emis-  sion consistent with an optically thin medium and Lyman con-  tinuum (LyC) leakage along the line of sight (Rivera-Thorsen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Furthermore, the detection of LyC radiation emerg-  ing from the 12 detected multiple images of the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1 young mas-  sive star cluster is confirmed by HST multi-band observations  (Rivera-Thorsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Additional analyses of the 12 LyC  multiple images of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1 have revealed that the star cluster has  an age younger than 3 Myr and a stellar metallicity of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5Z⊙  (Chisholm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2019), with a physical size of ≃ 10 pc and a  stellar (and dynamical) mass value of ≃ 107 M⊙ (Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The Sunburst was observed with HST, providing multi-  band photometry in the F275W, F410M, F555W, F606W,  F814W, F098M, F105W, F140W and F160W filters, under the  programs 15101 (PI Dahle), 15949 (PI Gladders), and 15377  (PI Bayliss).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Sunburst has also been targeted with ground-  based high resolution (R ∼ 5000 − 9000) VLT/X-Shooter spec-  troscopy covering the spectral range 3000-22000Å in three main  arms, UVB, VIS abd NIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The observational strategy and the  data reduction procedures applied to HST imaging and VLT/X-  Shooter spectroscopy have been presented in Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  (2020b, 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VLT/MUSE integral field spectroscopy at res-  olution R = 3000 and covering the spectral range 4800-9400Å  was obtained during 2016 (1h integration, DDT, PI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Aghanim)  and 2021 (1h integration, PI, Vanzella) in the wide field mode  configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The final datacube which combines the two hours  and the data reduction is described in Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  We also presented a first version of the lens model in Pignataro  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2021) based on the 62 spectroscopically confirmed mul-  tiple images in the redshift range 1 < z < 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 (see also Sharon  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Diego et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A revised lens model will be com-  puted once the new VLT/MUSE observations (7h integration)  planned during 2023 will be performed (prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='249D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='001,  PI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Vanzella).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Article number, page 2 of 10  PSF  HST F555W  PSF  MUSE IFU  AP1  AP2  AP3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1a  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1b  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1c  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content="1d'  5." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1f  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1e  AP4  AP5  AP5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1h  AP6  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1iU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Mestric et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' : Very massive, spatially segregated stars at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  Here we focus on the ≃ 3 Myr old, UV-bright and Ly-  man continuum source with MUV = −18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='6 (1700Å magnitude  and ultraviolet slope β = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='71 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='01, Fλ ∼ λβ), massive  (M ∼ 107 M⊙) star cluster 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1, subjected to large magnification  values (µ ∼ 10 − 70 over 12 multiple images, Pignataro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In the following we perform a new  analysis focusing on the nature of the ionizing source (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 3)  and its morphology (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Spectral signatures of very massive stars in the  Sunburst star cluster at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='37  We aim to investigate the UV and optical spectroscopic prop-  erties of the young stellar cluster 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The VLT/MUSE one-  dimensional spectra are extracted from six apertures enclosing  nine multiple images of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1 (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 1) and subsequently  combined to produce a continuum-detected high signal-to-noise  ratio SNR (> 60) weighted-average spectrum (Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The  stacked spectrum shown in Figure 2 is equivalent to an inte-  gration time of (2 × 9) × 302 > 16, 000 hours without lensing  amplification, adopting the minimum amplification among the 9  multiple images (µ = 30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Observed VMS features with VLT MUSE and X-Shooter  The very high SNR MUSE spectrum (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2) allows us to  identify several emission and absorption lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Among them  we have the nebular emission lines associated to the interstel-  lar medium of the galaxy, like Oiii]λ1661, 1666, Niii]λ1750,  [Siiii]λ1883, 1892, and Ciii]λλ1907, 1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The well detected  continuum allows us to investigate faint line emissions (of a frac-  tion of an Å rest-frame equivalent width), and to sample the de-  tails of the line profiles, otherwise not accessible without lens-  ing amplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In particular, faint Nivλ1486 emission, the ev-  ident P-Cygni profile of the Civλ1550, the prominent broad and  asymmetric Heiiλ1640 line profile, and the P-Cygni signature of  Nivλ1720 clearly stand out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' All these lines are associated with  young, hot and (very) massive stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  We report detection of Heiiλ1640 emission with measured  rest frame EW=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='3Å and FWHM=8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='7Å (∼ 1610±300  km s−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The broad shape of the Heiiλ1640 emission line ob-  served in the Sunburst cluster is asymmetric and resembles a  typical P-Cygni profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The blue end of the emission line drops  steeply, while the red end drops more gradually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The P-Cygni  profile of Heiiλ1640 line is consistent with that predicted by  models and synthetic spectra (see, Martins & Palacios 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Broad Heiiλ1640 emission observed in galaxies is usually re-  lated to non-nebular origin, commonly associated with Wolf-  Rayet (WR) stars, (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Schaerer & Stasi´nska 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Brinchmann  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Leitherer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Senchyna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021), though  the failure of the synthesis models to reproduce some of the  strong Heiiλ1640 lines might be related to missing ingredients in  stellar evolution models (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Leitherer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' How-  ever, far-UV spectroscopic investigation of ∼57 individual stars  located within the R136 star cluster reveals that massive stars  with M>100 M⊙ have a crucial role in producing the Heiiλ1640  emission line (Gräfener & Vink 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Crowther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  On the other hand, Martins & Palacios (2022) have shown that  Heiiλ1640 can be produced in significant amount only when stel-  lar winds are stronger than in normal O stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS develop  such strong winds because of their proximity to the Eddington  limit (Vink et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Bestenlehner 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Gräfener 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' At  the same time, these winds peel off the external layers of the  stars and expose to the surface the products of hydrogen burn-  ing through the CNO cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' This results in a strong nitrogen  (and helium) enrichment that boosts the strength of Nivλ1486  and Nivλ1720.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' This typically happens after ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Both  mentioned emission lines are detected in the spectrum of the  Sunburst cluster at SNR > 15 (Figure 2), with EW=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2Å and  FWHM=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='9Å for Nivλ1486 and EW=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='15Å and FWHM ∼ 2Å  for Nivλ1720.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The helium enrichment also contributes to the  strength of Heiiλ1640.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The same effects (strong winds combined  with surface chemical enrichment) happen in normal evolved  massive stars when they are seen as WR stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The key difference  compared to VMS is that helium enrichment takes place only af-  ter the main sequence (>∼ 4 Myr), while the same process takes  place at younger ages in VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Furthermore, VMS are more lu-  minous than normal WR stars and hence their contribution to  integrated light is larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The nebular Hα equivalent width provides constraints on the  cluster age and hence on whether the Heiiλ1640 line is primar-  ily due to WR stars or VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' According to the BPASS mod-  els and results from Eldridge & Stanway (2012) (their Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 3)  they predict that normal and WR stars produce EWHα < 1Å for  ages <∼ 3Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The X-Shooter spectrum reveals a prominent Hα  line and no continuum detection, which very conservatively im-  plies an equivalent width larger than 200Å rest-frame at 1-sigma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  However, if we assume for Hα the same continuum level ob-  served at λ ∼ 5000Å rest-frame in the photometric spectral en-  ergy distribution (SED) by Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2022a) such a limit in-  creases to ∼ 840Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' This value would be still a lower limit, even in  the case of leakage of ionizing photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' After correcting the Hα  flux for the fraction of escaping LyC photons (Hα/(1− f abs  esc )), the  resulting EW increases to EWHα ∼ 1231Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We adopt f abs  esc values  from Rivera-Thorsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2019), where the corresponding ab-  solute escape fraction of LyC photons along the line of sight is  f abs  esc = 32+2  −4% .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Such a large Hα equivalent width is consistent  with a star-forming burst younger than ∼ 3 Myr (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Leitherer  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Furthermore as discussed in Chisholm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2019)  Nvλ1240 stellar wind profile predominantly depends on the stel-  lar age while variations due to different metallicity are negligible  and it is related to the young stellar populations (< 5 Myr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' From  the comparison of the observed Nvλ1240 with the models Figure  3 and 4 we additionally demonstrate that the age of the cluster is  < 3 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' From our age analysis, we can conclude that properties  of both Nvλ1240 and Hα fit well with < 3 Myr age of the stel-  lar cluster which requires other sources than WR stars to explain  the observed strong Heiiλ1640 EW=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='3Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Therefore these  results strongly suggest that VMS are responsible for the pro-  duction of the spectral ultraviolet features we observe in such a  young massive star cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Moreover, Wofford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2014) and  Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2016) have argued that the presence of Ovλ1371 in  integrated light of the clusters was also a key feature of VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  This line is not seen in the Sunburst cluster, see Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' As  demonstrated by Martins & Palacios (2022), this is not incom-  patible with the presence of VMS, since Ovλ1371 disappears as  VMS evolve to lower effective temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In their Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 4, we  see that no sign of Ovλ1371 exists after ∼1 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' This, together  with the presence of Nivλ1486, places a rather tight constraint  on the cluster age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Comparing observations with models  To investigate the rest-frame UV spectrum of the cluster, we have  created an integrated VMS model following Martins & Palacios  Article number, page 3 of 10  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The MUSE IFU spectrum of the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1 young massive star cluster extracted from 6 apertures is shown in black (thin line) and the X-Shooter  long slit spectrum of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l knot is shown in blue (bold line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The key confirmed features indicating the presence of VMS in the stellar cluster  are marked with shaded light red strips while the dark-orange line shows the best-fit Fλ ∼ λβ, with β = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The shaded grey strip indicates  the (absence of) Ovλ1371 line, which usually is an indicator of VMS too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The prominent P-Cygni of Nvλ1240 and strong emission part of the  Civλ1550 are present and indicate the young age of the stellar cluster (black bold markers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In the bottom, the 1-sigma errors of both spectra are  shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Other detected interstellar features and stellar features are marked with dashed red and green lines, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  (2022) that includes normal mass stars (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1-100 M⊙) with differ-  ent VMS (150 M⊙ and 200 M⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  We have used the spectral energy distribution (SEDs) of  BPASS (Eldridge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Stanway & Eldridge 2018) v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1  single-star population synthesis model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The model has an up-  per mass limit of 100 M⊙ with the Salpeter IMF, metallicity of  Z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='006 (where 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='02 corresponds to solar metallicity), and in-  stantaneous star formation history, with a burst of mass 106 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The adopted metallicity of the model is the closest to our mea-  sured value based on N2 index (Marino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2013), which is  ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4Z⊙ and consistent with the estimate provided by Mainali  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2022) (see also Chisholm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  We have extrapolated the Salpeter IMF to 225 M⊙ upper  mass limit within a few mass bins given by Equation 1 from the  BPASS manual1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Equation 1 gives the number of massive stars  in the mass range [Ma;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Mb].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  N(Ma;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Mb) = C × Mα1  1  � Mb  Ma  Mα2 dM  (1)  Here, C is a constant and has a value of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='23×105 for an arbitrary  burst mass of 106 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Also, M1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 M⊙ α1 = -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='3, α2 = -  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The mass bins are selected in a way to add the SEDs of  appropriate numbers of single VMS stars, which are available  for discrete sets of VMS with masses including 150 M⊙ and 200  M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In this manner we compute SEDs including VMS with IMFs  extending up to 175 and 225 M⊙, respectively, following Martins  & Palacios (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  1 https://flexiblelearning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='auckland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='nz/bpass/9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='html  From Figure 2, we can see that the cluster shows signifi-  cant Nivλ1486 emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' From the VMS models and synthetic  spectra, Nivλ1486 emission only appears after 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr of VMS  evolution (see, Martins & Palacios 2022) and VMS last approx-  imately until 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Based on this, we created the SEDs of in-  tegrated VMS models at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr, 2 Myr, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We have  normalized the spectrum of the cluster and the models by fitting  a UV power law by using the spectral windows provided by Rix  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  We have directly compared the cluster spectrum with the two  VMS models at 3 different ages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The comparison shows that  VMS are clearly needed to reproduce the observations (see, Fig-  ures 3, 4, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' However, the Heiiλ1640 and Nivλ1720 lines  in the models appear stronger than observed even at the age of  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr and with a maximum mass of 175 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' To match the  observed Heiiλ1640 and Nivλ1720 profiles, we have therefore  reduced the VMS contribution by decreasing their numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We  find good agreement if we reduce the VMS contribution by a fac-  tor of 6 in the VMS model, which includes only 150 M⊙ VMS  at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Alternatively, a similar match is also found  by reducing the VMS contribution by a factor of 8 in models in-  cluding also the 200 M⊙ VMS (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In short, the observations  are compatible with an IMF extending up to ∼ 175 or 225 M⊙,  but with an IMF slope steeper than Salpeter (α2 < −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='35) for  M > 100 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Article number, page 4 of 10  Aobs / A  4000  4500  5000  5500  6000  6500  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  1H13  IIIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='+IO  AS:  {IIIN  IIIS  IIIS  AID  全13  sv  CIV1550  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5  NV1240  y1486  ux  fl  Normalized  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  F  1100  1200  1300  1400  1500  1600  1700  1800  1900  2000  Arest / AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Mestric et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' : Very massive, spatially segregated stars at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS contribution to the LyC budget of the young stellar  cluster  After adopting the results from the previous section, we can now  estimate the number of O-type stars hosted by the same stellar  cluster and the percentage of LyC photons emitted by VMS only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Measurements are performed in the range of ∼730–900Å  rest-frame (range covered by HST F275W filter in which LyC  radiation is detected and fesc later on evaluated).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' First, we cal-  culate the mean flux from the model which include both normal  and VMS stars and, secondly, we calculate the mean flux from  the model including only VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The resulting ratio of those two  models gives us the fraction of the LyC photons produced by  VMS, which is ∼15%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Since LyC photons are mainly produced  by O-type and more massive stars, we can see that ∼15% of the  LyC production is generated only from ∼1% of the stars capable  of producing LyC photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' It is worth noting that the fraction  of LyC ionizing radiation produced from VMS in the Sunburst  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1 stellar cluster is smaller than the predicted LyC fraction pro-  duced by the VMS located in R136 stellar cluster, which is 25%  (Doran et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' However, we also note that in the case of the  Sunburst stellar cluster the light coming from the host galaxy  could slightly decreases the inferred equivalent width of the key  spectral features discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' While such dilution is difficult  to address with the present ground-based spectroscopic data2, its  effect implies a possible slightly higher contribution of VMS to  the LyC radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Spatial segregation of the Lyman continuum  radiation  We now address the morphological properties of image 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l,  which is the most magnified among the multiple images of the  star cluster (µtot ≃ 76, Pignataro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l is the brightest  image detected with a large SNR in the F275W (SNR ∼ 90) and  F555W (SNR ≫100), allowing us to investigate and compare  the morphology in these two spectral regions: the emitting LyC  (λ < 900Å, in HST F275W band) and the non-ionizing radiation  at 1700Å (HST F555W band).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We follow two approaches: (1)  we ran simulations injecting the sources in the F275W band and  (2) we analyzed the curve of growth of the resulting images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Figure 5 shows the F555W image of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l, in which the elon-  gation is clearly visible in the direction of the tangential stretch  produced by gravitational lensing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' As discussed in Pignataro  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2021) (see also Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022a), the tangential am-  plification largely dominates along the arc (µtang ≃ 57).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We per-  form here a relative comparison between images, to ensure that  the the results do not depend on the magnification values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  As a first step, we compute a realistic model of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l on the  HST F555W image using Galfit (Peng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The point  spread function (PSF) has been extracted by combining non-  saturated stars available in the field of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' While the fit with a  single component does not produce acceptable residuals (larger  than 20%), we reproduce quite well the light profile of the ob-  ject by combining two components: a core with a Gaussian light  profile and an effective radius (Reff) smaller than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 pixels (in  practice nearly unresolved) and an extended component with  Reff = 6 pixels and Sersic index n=1 (similar results are ob-  tained also with n=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The combination of the two components  produces an optimal shape which leaves normalized residuals  smaller than 10% (see Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' It is worth now investigating if  2 JWST/NIRSpec-IFU and NIRCAM observations on the same YMC  are planned during 2023, prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2555, PI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Rivera-Thorsen  such a resolved shape (sampled at 1700Å) is recovered if placed  in the F275W Lyman continuum image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' For this check, we in-  jected mock images of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l into the F275W image on five dif-  ferent positions around 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l, which are not contaminated by the  flux coming from other sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Such images are produced from  the aforementioned two-component Galfit model constructed  at 1700Å (F555W), but now accounting for the F275W PSF (in  other words convolved by the F275W PSF) to allow for a proper  comparison with the LyC 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l source (observed in HST F275W  band).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Such images have been added to F275W after rescaling  each of them to the observed peak value of the LyC 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l ob-  ject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' This step has been performed with IRAF (Tody 1986) task  IMARITH and IMCOPY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Figure 6 shows the results, in which all  the injected images show a spatially-resolved morphology along  the tangential magnification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Conversely, the observed LyC im-  age (of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l) appears nucleated, suggesting that the emitting LyC  region is smaller than the one at 1700Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  To quantify this result, we calculate the curve of growth  (CoG) of the images shown in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The flux is then mea-  sured in the F275W band in 34 circular apertures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The small-  est aperture has a radius of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1 pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Intermediate apertures are  drawn with increasing radii, with a step of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 pix, up to largest  one, which has a radius of 34 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' As a reference point-like  source, we constructed the mean CoG from a selected sample of  twenty non-saturated and non-contaminated stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The resulting  CoG is shown in Figure 7, where the y-axis reports the frac-  tion of the flux enclosed at the corresponding radius in pixels  (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The same procedure has been applied to the LyC emitting  source 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l, while another CoG has been constructed by averag-  ing the five CoG of the injected models resembling the morphol-  ogy at 1700Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Figure 7 compares all the CoG after normalizing  them to the saturation value at the largest radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The first re-  sult which emerges from this test is the clear deviation of the  CoG of the observed 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l LyC source from the behavior of a  point-like source (stars).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' This was not explored before and sug-  gests that in the most magnified image of the star cluster the  LyC appears spatially resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' This is the first evidence of a re-  solved stellar LyC emission at cosmological distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Second,  such barely resolved LyC emission appears more nucleated than  the one at 1700Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Consequently, the sources of ionizing radi-  ation appears located in the central part of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Indeed,  from those curves, it emerges that 50% of the flux of the stars is  enclosed within a radius of ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='9 pixel, while for 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l it lies within  ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Additionally, we perform the Kolmogorov-Smirnov  two-sample test (KS-test) to check if the CoGs derived from the  stars and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l source follow the same distribution (null hypothe-  sis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' For this purpose, we used the statistical function ks_2samp  from scipy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='stats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' After comparing the average CoG of the  stars with cyan and violet CoGs, the KS-test gives p << 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' It  means that the null hypothesis is not satisfied with the LyC pro-  file of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l and it deviates from the CoG of a point-like source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Furthermore, we also find that the half-light size of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l at 1700Å  is larger than the ionizing region, ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='6 pixels compared to the  ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' If we correct such radii for the instrumental reso-  lution (given by the stars) we obtain an effective radius for 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l  at 1700Å ≃ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4 pc after de-lensing3, in agreement with  Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2020a), while the LyC image (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l) has a smaller  radius, Reff ≃ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We therefore find a LyC emission  which is more compact than the non-ionizing UV continuum,  3 Adopting the pixel scale of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='03′′/pixel, 8200 pc per arcsecond at  z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='37 and µtang ≃ 57, Reff = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='03∗8200∗((2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='62−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='92)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5)/57, adopting  the same uncertainty on µtang reported by Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' (2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Article number, page 5 of 10  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The MUSE ultraviolet spectra of the young star cluster (blue) is shown in the bottom panel with the X-Shooter spectrum (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The  grey-shaded regions show specific UV features closely associated with the presence of the VMS (Nivλ1486, Heiiλ1640, and Nivλ1720) and some  of them show a P-Cygni profile, characteristic of young and massive stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Furthermore, the black line shows the single BPASS model including  only normal stars at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr, while the red line shows the BPASS single-star model augmented by VMS with masses up to 150 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The upper  panels show the zoom in VMS characteristic features compared with models and Nvλ1240 P-Cygni line, characteristic due to the presence of very  young stellar populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  which we interpret as a spatial segregation of the most massive  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Summary and Conclusions  In this paper, we have presented a detailed spectroscopic and  morphological analysis of the massive and young stellar cluster  hosted in the Sunburst lensed galaxy at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='37, for which also  LyC emission was confirmed in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We used results  from recent stellar evolutions and atmosphere models including  VMS (Martins & Palacios 2022) to conduct extensive compar-  isons with high spectral resolution observations performed with  VLT/MUSE and X-Shooter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The main results of this work can  be summarized as follows:  – In the spectroscopic observations, the high signal-to-noise  MUSE and X-Shooter spectra reveal features of broad (and  asymmetric) Heiiλ1640 emission with EW ≃ 3Å rest-frame  and line width of 1610 km s−1, and Nivλ1486 with EW ≃  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2Å emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In addition, the P-Cygni profile of Nivλ1720  (along with NV and CIV) is also observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' All these features  suggest the presence of very massive (> 100M⊙) stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The  absence of Ovλ1371 provides a lower age limit of 1 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' On  the other hand, the large Hα EW (> 1231Å after correcting  for the escaping LyC radiation) indicates an age younger than  ∼ 3 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' These narrow age constraints strongly favor the  existence of VMS over WR stars, implying that the strength  of the Heiiλ1640 emission line is entirely due to VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  – A comparison of the observations with the models reveals  that the most plausible age of the star cluster is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr, and  an estimated number of ∼ 370 − 400 VMS for a cluster mass  of 107 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The observations are compatible with an IMF  extending up to ∼ 175 − 225 M⊙, but with a slope which is  steeper than the Salpeter IMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  – The fraction of LyC radiation emerging from the VMS com-  ponent is not negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We estimate that in the 730Å – 900Å  range (probed by the HST/F275W band) about 360 – 400  VMS (or roughly 1% of the total population of O-type stars  in the star cluster) account for 15% of the escaping LyC pho-  tons, with the rest being produced mostly by the other less  massive O-type stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  – Detailed morphological analysis of the most magnified im-  age of the star cluster shows that the region emitting LyC  is not point-like, with a light profile different from the av-  erage profile of stars present in the same field of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' This  is the first evidence of a resolved LyC emission at any red-  shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Remarkably, the physical scale of the LyC emitting re-  gion appears also smaller (with a significant K-S probability  p << 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='05) than the non-ionizing region (1700Å), suggest-  ing that massive O-type stars responsible for the LyC radi-  ation, and likely the VMS (significantly contributing to it),  are segregated in the central part of the star cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' After de-  lensing the angular half-light radii, the LyC region appears  barely resolved with Reff ≃ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5pc, while at 1700Å it  is Reff ≃ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The packaging of such a large num-  ber of massive O-type stars per parsec cube in the central  region, ≃ 70 pc−3, is likely a element which allowed to carve  the ionizing channel and the development of a high-speed  outflowing gas (Rivera-Thorsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Vanzella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  2022a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Mainali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We acknowledge financial support through grants PRIN-  MIUR 2017WSCC32, 2020SKSTHZ and the INAF GO Grant 2022 “The rev-  Article number, page 6 of 10  Nv1240A  NIV1486A  NIV1720A  HeI1640A  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  Sunburst Cluster Mus  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='3 E  BPASS 100 M。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='+ 150 M。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='VMS (39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='43) at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='7 E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='61705  1220  1492  1640  1650  1240  1480  1484  1488  1660  670  1710  1715  1720  1725  1730  Rest Frame Wavelength [A]  Rest Frame Wavelength [A]  Rest Frame Wavelength [A]  Rest Frame Wavelength [A]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0E  Sunburst Cluster MUSE  Sunburst Cluster Xshooter  BPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8E  Single BPASSup to 100 Mo + 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='43 number of 150 Mo VMS at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='6E  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2E  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0M  W  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8E  Nor  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2日  1250  1300  1350  1400  1450  1500  1550  1600  1650  1700  1750  Rest Frame Wavelength [A]U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Mestric et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' : Very massive, spatially segregated stars at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' All symbols as in Figure 3 except for the red lines, showing the BPASS single-star model augmented by VMS with masses up to 200 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The results from Galfit modeling after using a two-component  fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' From the left, the first panel shows the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l source in the F555W  band (UV1700Å).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The second panel shows the model from Galfit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The  third panel shows the residual and the fourth panel is the normalized  residual produced after dividing the residual with the original image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The white contour encloses the region used to check the quality of the  produced model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  olution is around the corner: JWST will probe globular cluster precursors and  Population III stellar clusters at cosmic dawn” (PI Vanzella).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' FC and RP ac-  knowledge funding from PRIN INAF 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  References  Abel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bryan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', & Norman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2002, Science, 295, 93  Bestenlehner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2020, MNRAS, 493, 3938  Brands, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', de Koter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bestenlehner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022, A&A, 663, A36  Brinchmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Kunth, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', & Durret, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2008, A&A, 485, 657  Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Johnson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Adamo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015, ApJ, 811, 75  Chisholm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Rigby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bayliss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2019, ApJ, 882, 182  Cignoni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Sabbi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', van der Marel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015, ApJ, 811, 76  Crowther, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Caballero-Nieves, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bostroem, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016, MNRAS,  458, 624  Crowther, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Schnurr, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Hirschi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2010, MNRAS, 408, 731  Dahle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Aghanim, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Guennou, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016, A&A, 590, L4  Diego, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Pascale, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Kavanagh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022, A&A, 665, A134  Doran, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Crowther, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', de Koter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2013, A&A, 558, A134  Eldridge, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' & Stanway, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2012, MNRAS, 419, 479  Eldridge, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Stanway, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Xiao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017, PASA, 34, e058  Goswami, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Slemer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Marigo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021, A&A, 650, A203  Gräfener, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021, A&A, 647, A13  Gräfener, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' & Vink, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015, A&A, 578, L2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The HST F275W image showing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l LyC leaking source in  its centre;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' other two multiple images, of the same source, are labeled  as 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1i and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Around 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l, in the region not contaminated by other  sources, five models are injected (see text for more details), enclosed  in the white squares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In the bottom right corner, we shown the largest  (34pix diameter) aperture size used to construct CoGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Johnson, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Rigby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Sharon, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017, ApJ, 843, L21  Köhler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Langer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', de Koter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015, A&A, 573, A71  Leitherer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Byler, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', & Levesque, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2018, ApJ, 865, 55  Leitherer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Ekström, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Meynet, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2014, ApJS, 212, 14  Mainali, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Rigby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Chisholm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022, ApJ, 940, 160  Marino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Rosales-Ortega, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Sánchez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2013, A&A, 559, A114  Article number, page 7 of 10  Nv1240A  NIV1486A  HeII1640A  NIV1720A  Sunburst Cluster Xshootel  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='05  1260  1480  1492  1496  1630  1640  1650  1670  1220  1484  1488  1710  1715  1725  1730  1230  Rest Frame Wavelength [A]  Rest Frame Wavelength [A]  Rest Frame Wavelength [A]  Rest Frame Wavelength [A]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  Sunburst Cluster MUSE  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8E  Sunburst Cluster Xshooter  BPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='6E  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  MA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8  LLLLLLLLLLLLL  LJON  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2E  一  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  1250  1300  1350  1400  1450  1500  1550  1600  1650  1700  1750  Rest Frame Wavelength [A]5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='11  normalised  model  residual  HST  F555W  residual5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1h  1"  Model5  Model  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1i  Model  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='11  Model  ModelA&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Three curves of growth normalized to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The cyan CoG cor-  responds to the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l LyC leaking source located in the Sunburst arc  (F275W band).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The violet CoG is the PSF-convolved, best-fit model of  the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l source observed in F555W constructed averaging 5 CoGs (see  text for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The orange growth curve is used for comparison  and it is constructed averaging 20 single CoGs from randomly selected  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In both cases (cyan and violet) error bars are 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Vertical lines in  the bottom left part of the figure mark the pixel radii at which 50% of  the light is enclosed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The colors corresponds to the CoG colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Martins, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Hillier, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Paumard, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2008, A&A, 478, 219  Martins, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' & Palacios, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022, A&A, 659, A163  Meštri´c, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Vanzella, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Zanella, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022, MNRAS, 516, 3532  Peng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Ho, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Impey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', & Rix, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2010, AJ, 139, 2097  Pignataro, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bergamini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Meneghetti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021, A&A, 655, A81  Portegies Zwart, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', McMillan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', & Gieles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2010, ARA&A, 48, 431  Rigby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bayliss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Chisholm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2018a, ApJ, 853, 87  Rigby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bayliss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Sharon, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2018b, AJ, 155, 104  Rigby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Johnson, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Sharon, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017, ApJ, 843, 79  Rivera-Thorsen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Dahle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Chisholm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2019, Science, 366, 738  Rivera-Thorsen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Dahle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Gronke, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017, A&A, 608, L4  Rix, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Pettini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Leitherer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2004, ApJ, 615, 98  Schaerer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' & Stasi´nska, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 1999, A&A, 345, L17  Senchyna, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Stark, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Charlot, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021, MNRAS, 503, 6112  Sharon, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Mahler, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Rivera-Thorsen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022, arXiv e-prints,  arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='03417  Smith, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bajaj, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Ryon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', & Sabbi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2020, ApJ, 896, 84  Smith, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Crowther, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', & Sidoli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016, ApJ, 823, 38  Stanway, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' & Eldridge, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2018, MNRAS, 479, 75  Tody, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 1986, in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' SPIE, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 627, Instrumentation in astronomy VI, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Crawford, 733  Vanzella, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Calura, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Meneghetti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2017, MNRAS, 467, 4304  Vanzella, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Caminha, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Calura, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2020a, MNRAS, 491, 1093  Vanzella, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Caminha, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Rosati, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2021, A&A, 646, A57  Vanzella, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Castellano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bergamini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022a, A&A, 659, A2  Vanzella, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Castellano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Bergamini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2022b, ApJ, 940, L53  Vanzella, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', De Barros, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Cupani, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2016, ApJ, 821, L27  Vanzella, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Meneghetti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Pastorello, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2020b, MNRAS, 499, L67  Vink, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Heger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Krumholz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2015, Highlights of Astronomy,  16, 51  Vink, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Muijres, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Anthonisse, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2011, A&A, 531, A132  Wofford, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Leitherer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Chandar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', & Bouret, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2014, ApJ, 781, 122  Yusof, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Hirschi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', Meynet, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 2013, MNRAS, 433, 1114  Article number, page 8 of 10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='8  iction  rd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='6  ux  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2  observed CoG of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1l in F275W  ★  avg CoG for 5 observed Stars  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  6AE  CoG model n=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5  Radius  [pixels]U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' Mestric et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' : Very massive, spatially segregated stars at z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='4  Appendix A: Initial models  As described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='2, we compare the X-Shooter and  MUSE spectroscopic observations with the BPASS models at  different ages (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr, 2 Myr, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We narrow our  models to the mentioned age range since the predicted age of the  cluster is higher than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr (inferred from Nivλ1486 emission  line) and the lifetime of the VMS is about 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr (Martins &  Palacios 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' We started with the BPASS which has an upper  mass limit of 100 M⊙ and added 236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='56 stars in the 100 - 175  M⊙ mass range and 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='30 stars in the mass range 175 – 225 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Resulting models (at different ages) are shown in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' all models  produce significantly strong spectroscopic features characteristic  of the presence of VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' To better match models with observa-  tions, we decreased the numbers of the VMS and the final results  are presented in Section 3 (Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' 3 and 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Article number, page 9 of 10  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' VMS  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The six panels are showing the comparison of the observations (MUSE spectrum, red line) with BPASS models (black line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' The left  column shows three BPASS models with an IMF up to 100 M⊙, ages of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr, 2 Myr, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='5 Myr and an added number of 236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='56 150 M⊙ VMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  The right column shows BPASS model with an IMF up to 100 M⊙ at same ages (as shown in previous column) but with added nuber of 236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='56  and 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='30 VMS of 150 M⊙ and 200 M⊙, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content=' In all six panels we can see that the strength of feature characteristic to VMS is higher than  in observed cluster, see the Section 3 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
+page_content='  Article number, page 10 of 10' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE3T4oBgHgl3EQftAtl/content/2301.04672v1.pdf'}
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+1
+Privacy-Preserving Distributed Energy Resource
+Control with Decentralized Cloud Computing
+Xiang Huo, Graduate Student Member, IEEE, Mingxi Liu, Member, IEEE
+Abstract—The rapidly growing penetration of renewable en-
+ergy resources brings unprecedented challenges to power distri-
+bution networks – management of a large population of grid-
+tied controllable devices encounters control scalability crises and
+potential end-user privacy breaches. Despite the importance,
+research on privacy preservation of distributed energy resource
+(DER) control in a fully scalable manner is lacked. To fill the
+gap, this paper designs a novel decentralized privacy-preserving
+DER control framework that 1) achieves control scalability over
+DER population and heterogeneity; 2) eliminates peer-to-peer
+communications and secures the privacy of all participating
+DERs against various types of adversaries; and 3) enjoys higher
+computation efficiency and accuracy compared to state-of-the-
+art privacy-preserving methods. A strongly coupled optimization
+problem is formulated to control the power consumption and
+output of DERs, including solar photovoltaics and energy storage
+systems, then solved using the projected gradient method. Cloud
+computing and secret sharing are seamlessly integrated into the
+proposed decentralized computing to achieve privacy preserva-
+tion. Simulation results prove the capabilities of the proposed
+approach in DER control applications.
+Index Terms—Decentralized optimization, distributed energy
+resources, privacy preservation, secret sharing
+I. INTRODUCTION
+A. Related Works
+L
+ARGE-scale deployment of distributed energy resources
+(DERs) has proven efficacy in reducing carbon footprint
+and providing grid-edge services such as voltage control, load
+following, and backup power supply [1]. DERs, including
+energy storage systems (ESSs), solar photovoltaic (PV), and
+electric vehicles (EVs), along with other monitoring and
+controllable devices, can offer significant opportunities for
+advancing efficient, reliable, and cost-effective power grids [2],
+[3]. Though integrating DERs into power grids can provide
+multifarious benefits, such as enhanced energy efficiency and
+economic boost, the high penetration of DERs raises surging
+challenges on the scalability of existing control strategies [4].
+To address the aforementioned challenges in large-scale
+DER control problems, distributed and decentralized control
+strategies are drawing increased attention owing to their
+superior scalability. For instance, a distributed coordination
+method based on local droop control and consensus control
+was designed in [5] to deal with the voltage rise problem
+caused by the high penetration of solar PVs. Zhang et al. in [6]
+proposed an asynchronous distributed leader-follower control
+strategy that optimally schedules DERs to lower the voltage
+The authors are with the Department of Electrical and Computer Engineer-
+ing, University of Utah, Salt Lake City, UT 84112 USA (e-mail: xiang.huo,
+mingxi.liu@utah.edu).
+for peak load shaving and long-term energy saving. To reduce
+the communication burden, a distributed low-communication
+algorithm was proposed in [7] to control islanded PV-battery-
+hybrid systems. Though distributed methods can achieve
+scalability, they generically suffer from massive peer-to-peer
+communications. To overcome this issue, Navidi et al. in
+[8] developed a two-layer decentralized DER coordination
+architecture that can scale the solution to large networks, and
+no direct communication is required between local controllers.
+In [9], a decentralized stochastic control strategy was designed
+for radial distribution systems with controllable PVs and ESSs
+to minimize the demand balancing cost. Huo et al. in [10] pro-
+posed a decentralized shrunken primal-multi-dual subgradient
+algorithm with dimension reduction to achieve scalability w.r.t.
+both agent population size and network dimension.
+Despite the superior scalability and communication effi-
+ciency of decentralized methods, their implementation has
+been significantly hampered by the vulnerability to privacy
+breaches. Furthermore, both distributed and decentralized
+strategies rely heavily on mandatory communications which
+can disclose users’ sensitive information and expose system
+vulnerabilities to adversaries. Differential privacy (DP) has re-
+ceived substantial attention in addressing privacy concerns due
+to its rigorous mathematical formulation [11]. DP-based meth-
+ods add persistent randomized perturbations to the datasets,
+constraints, or objective functions for privacy preservation.
+In [12], a DP-based aggregation algorithm is proposed to
+compensate for solar power fluctuations and protect users’
+personal information. Han et al. in [13] developed a distributed
+optimization algorithm based on DP to preserve the privacy
+of the participating agents. Gough et al. in [14] designed an
+innovative DP-compliant algorithm to ensure that the data
+from consumers’ smart meters are protected. Despite the
+success in privacy preservation, DP-based methods inevitably
+suffer from accuracy loss due to the added perturbations.
+In contrast, encryption-based strategies achieve privacy
+preservation with high accuracy by encrypting the original
+data into cyphertexts, and only those holding private keys
+can decrypt the cyphertexts. Lu et al. in [15] proposed an
+efficient and privacy-preserving aggregation scheme for smart
+grid communications, in which the data is encrypted by Paillier
+cryptosystem. In [16], a privacy-preserving and fault-tolerant
+scheme was designed based on homomorphic cryptosystem
+to achieve secure aggregation of metering data. Similarly,
+Cheng et al. in [17] proposed a novel private collaborative
+distributed energy management system based on homomorphic
+encryption to solve the privacy issues in distribution systems
+and microgirds. Despite the high accuracy, the drawback
+arXiv:2301.02198v1  [math.OC]  5 Jan 2023
+
+2
+of encryption-based methods lies in the prevalent comput-
+ing overhead caused by encryption and decryption. Other
+hardware-integrated privacy-preserving methods, e.g., garbled
+circuit [18], [19], are deficient in flexibility and uneconomic
+due to the hardware cost.
+Secret sharing (SS) [20] is a lightweight cryptographic
+method that can securely distribute a secret among a group
+of participants. Each participant will be allocated a share
+of the secret, and only through the collaboration of certain
+participants where the number of participants is greater than a
+threshold can the secret be reconstructed from their shares.
+Adopting SS, Nabil et al. in [21] designed an SS-based
+detection scheme to identify malicious consumers who steal
+electricity, in which system operators only collect masked
+meter readings from the consumers to avoid privacy vio-
+lation. In [22], an SS-based EV charging control protocol
+was developed to achieve privacy-preserving EV charging
+control for overnight valley filling. Compared with encryption-
+based strategies, SS-based methods can preserve privacy while
+avoiding the heavy computational load. Despite the superiority,
+few research studied the integration of SS into DER control
+due to the highly complex distribution network structure, large
+DER population, and lack of theoretical support in privacy
+guarantees. To fill these gaps, this paper designs a novel SS-
+based privacy-preserving algorithm that merits high efficiency,
+security, and accuracy for large-scale DER control problems.
+B. Statement of Contributions
+The contribution of this paper is three-fold: 1) We propose
+a novel decentralized privacy-preserving algorithm that con-
+currently achieves scalability and privacy in large-scale DER
+control. To the best of our knowledge, this is the first paper
+that proposes a decentralized SS-based algorithm for DER
+privacy preservation, in which decentralized solutions, privacy
+guarantees, and rigorous security proofs are provided; 2) The
+proposed method eliminates the frequent peer-to-peer commu-
+nications and secures the privacy of the participating DERs
+against various types of adversaries. The designed framework
+serves as a benchmark for secure and scalable DER control. 3)
+Compared to state-of-the-art approaches, the proposed method
+can achieve lower computational overhead and identically
+accurate solutions as the non-privacy-concerned algorithms.
+The rest of this paper is organized as follows: In Sec-
+tion II, we construct the models of distribution networks,
+PVs, and ESSs, then formulate the DER control problem
+into a constrained optimization problem. Section III derives
+the decentralized solution via the projected gradient method
+and presents the corresponding DER aggregation and control
+strategies. The SS-based privacy-preserving DER control al-
+gorithm and privacy analyses are provided in Section IV. We
+give simulation results and analyses in Section V. Section VI
+concludes this paper.
+II. PROBLEM FORMULATION
+A. Branch Flow Model
+Consider an n-bus radial distribution network where B =
+{0, 1, . . . , n} denotes the set of buses. Let lij denote the line
+segment connecting buses i and j, L = {1, . . . , h} denote
+the set of lines, Cj denote the set of bus j’s child buses, Vj
+denote the voltage magnitude at bus j, Pij and Qij denote
+the active and reactive power flow from bus i to bus j,
+respectively, and rij and xij be the resistance and reactance of
+line lij, respectively. For bus j, let pc
+j and qc
+j denote the active
+and reactive power consumptions, respectively, and pg
+j and qg
+j
+denote its active and reactive power generations, respectively.
+To simplify the network model, a nonlinear DistFlow model
+[23] can be linearized to the LinDistFlow model by omitting
+the higher order terms with negligible error [24]. Therefore,
+this paper adopts the LinDistFlow model, represented as
+Pij −
+�
+u∈Cj
+Pju = pc
+j − pg
+j
+(1a)
+Qij −
+�
+u∈Cj
+Qju = qc
+j − qg
+j
+(1b)
+V 2
+i − V 2
+j = 2(rijPij + xijQij).
+(1c)
+A radial 13-bus distribution network connected with rooftop
+solar PVs and ESSs is shown in Fig. 1 and will be used as an
+example throughout this paper.
+10
+3
+2
+11
+6
+7
+5
+9
+8
+4
+1
+0
+P1, Q1
+<latexit sha1_base64="nPdIyijfg7kH2CtCftJt/5gzaLY=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkoi4mNXdOyBfuAJoTJZNIOnTyYmQglZOlfuPEvunbjQhFx12/wJ5y0XWjbC8MczrmXe+5xY0aFNIyRVlhaXldK6XNja3tnf03
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+P2, Q2
+<latexit sha1_base64="IaoZ/P1zRc4iegI/JD0D2LbqOjw=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkpSxMeu6MZlC/YBTQiTyaQdOnkwMxFKyNK/cONfdO3GhSLirt/gTzhpu9DaC8MczrmXe+5xY0aFNIyxVlhaXldK6XNja3tnf03b2
+WiBKOSRNHLOIdFwnCaEiakpGOjEnKHAZabuD21xvPxAuaBTey2FM7AD1QupTjKSiHP3CciPmiWGgvtQKkOxjxNJ6ljnVM7hQa+Sao5eNijEp+B+YM1CuHY4a349Ho7qjf1lehJOAhBIzJETXNGJp4hLihnJSlYiSIzwAPVIV8EQBUTY6eS+DJ4oxoN+xNULJZywvydSFIjcpurMXYp5LScXad1E+ld2SsM4kSTE0V+wqCMYB4W9CgnWLKhAghzqrxC3EcYakiLakQzPmT/4NWtWKeV64bZrl2A6ZVBAfgGJwCE1yCGrgDdAEGDyBF/AG3rVn7VX70D6nrQVtNrMP/pQ2/gEj/af8</latexit>
+p3, q3
+<latexit sha1_base64="gDgNMRKEQIJW/+4UL0fQMJi6A4=">AC3icbVDLSsNAFJ3UV62vqEtFhbBhZREBXVXdOyBfuANoTJZNIOnUzizEQoUvBjb/ixoVF3PoD7vwGf8J20WtHhjmcM693HuPFzMqlWV9GbmFxaXlfxqYW19Y3PL3N5
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+p2, q2
+<latexit sha1_base64="JCjfzJ1/fuXMTynwfU5OWgRT7cw=">AC3icbVDLSsNAFJ34rPUVdanI0CK4kJIUQd0V3bhswT6gDWEymbRDJ5M4MxFK6FJw46+4cWERt/6AO7/Bn3DSdlFbDwxzOde7r3HixmVyrK+jaXldW19dxGfnNre2fX3
+NtvyCgRmNRxCLR8pAkjHJSV1Qx0oFQaHSNPr32R+84EISN+pwYxcULU5TSgGCktuWah40XMl4NQf2k8dMtncFa514prFq2SNQZcJPaUFCtHo9rP4/Go6pfHT/CSUi4wgxJ2batWDkpEopiRob5TiJjHAfdUlbU45CIp10fMsQnmjFh0Ek9OMKjtXZjhSFMltOV4ZI9eS8l4n/e1EBZdOSnmcKMLxZFCQMKgimAUDfSoIVmygCcKC6l0h7iGBsNLx5XUI9vzJi6RLtnpauaTuMaTJADh6AToENLkAF3IqAMnsALeAMj49l4Nd6Nj0npkjHtOQB/YHz+Ao3dnxc=</latexit>
+p1, q1
+<latexit sha1_base64="QFaEiH12z+13LcqCfvsdkGI/A7o=">AC3icbVDLSsNAFJ3UV62vqEtFhbBhZREBHVXdOyBfuANoTJZNIOnUzizEQoUvBjb/ixoVF3PoD7vwGf8J20VtPTDM4Zx7ufceL2ZUKsv6NnJLyura/n1wsbm1vaOu
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+p6, q6
+<latexit sha1_base64="KwG4fbN+IAWqw0yIdyx7ph0j6fs=">AC3icbVDLSsNAFJ3UV62vqEtFhbBhZRExMeu6MZlC/YBbQiTyaQdOsnEmYlQpeCG3/FjQuLuPUH3PkN/oSTtotaPTDM4Zx7ufceL2ZUKsv6MnILi0vLK/nVwtr6xuaWub3
+TkDwRmNQxZ1y0PCQJoxGpK6oYacWCoNBjpOn1rzO/eU+EpDy6VYOYOCHqRjSgGCktuWax43Hmy0GovzQeumfHcFa504prlqyNQb8S+wpKVX2R7Xvh4NR1TU/Oz7HSUgihRmSsm1bsXJSJBTFjAwLnUSGOE+6pK2phEKiXTS8S1DeKgVHwZc6BcpOFZnO1IUymw5XRki1ZPzXib+57UTFVw4KY3iRJEITwYFCYOKwywY6FNBsGIDTRAWVO8KcQ8JhJWOr6BDsOdP/ksaJ2X7tHxZs0uVKzBHuyBIjgCNjgHFXADqAOMHgEz+AVjIwn48V4M94npTlj2rMLfsH4+AGalZ8g</latexit>
+P4, Q4
+<latexit sha1_base64="NGcTgvPm34Z0bQRxgvkRAHF23E4=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkoixceu6MZlC/YBTQiTyaQdOnkwMxFKyNK/cONfdO3GhSLirt/gTzhpu9DaC8MczrmXe+5xY0aFNIyxVlhaXldK6XNja3tnf03b2
+WiBKOSRNHLOIdFwnCaEiakpGOjEnKHAZabuD21xvPxAuaBTey2FM7AD1QupTjKSiHP3CciPmiWGgvtQKkOxjxNJ6ljnVM7hQa+Sao5eNijEp+B+YM1CuHY4a349Ho7qjf1lehJOAhBIzJETXNGJp4hLihnJSlYiSIzwAPVIV8EQBUTY6eS+DJ4oxoN+xNULJZywvydSFIjcpurMXYp5LScXad1E+ld2SsM4kSTE0V+wqCMYB4W9CgnWLKhAghzqrxC3EcYakiLakQzPmT/4PWecWsVq4bZrl2A6ZVBAfgGJwCE1yCGrgDdAEGDyBF/AG3rVn7VX70D6nrQVtNrMP/pQ2/gEqRagA</latexit>
+P5, Q5
+<latexit sha1_base64="I1WyzaQL94IsEQIjMxbBVPfB/oY=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkoiPndFNy5bsA9oQphMJu3QyYOZiVBClv6FG/+iazcuFBF3/QZ/wknrQteGOZwzr3c48bMyqkYy0wsLi0vJKcbW0tr6xuaVv7
+zRFlHBMGjhiEW+7SBGQ9KQVDLSjlBgctIy+3f5nrgXBo/BeDmJiB6gbUp9iJBXl6BeWGzFPDAL1pVaAZA8jltayzDk/gXO1eq45etmoGOCs8D8BeXq/rD+/XgwrDn6l+VFOAlIKDFDQnRMI5Z2irikmJGsZCWCxAj3UZd0FAxRQISdju/L4JFiPOhHXL1QwjH7dyJFgchtqs7cpZjWcnKe1kmkf2WnNIwTSUI8WeQnDMoI5mFBj3KCJRsogDCnyivEPcQRlirSkgrBnD5FjRPK+Z5bpulqs3YFJFsAcOwTEwSWogjtQAw2AwRN4AW/gXvWXrUP7XPSWtB+Z3bBv9JGPy1pqAI=</latexit>
+P6, Q6
+<latexit sha1_base64="tGy7FfHzImGqZJ+0hCm6mVtXxk=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkoiUnVXdOyBfuAJoTJZNIOnTyYmQglZOlfuPEvunbjQhFx12/wJ5y0XWjthWEO59zLPfe4MaNCGsZYKywtr6yuFdLG5tb2zv67l5
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+P7, Q7
+<latexit sha1_base64="JI1vorLiGfMRP0ugcJWOqAPkm+M=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkoiYnVXdOyBfuAJoTJZNIOnTyYmQglZOlfuPEvunbjQhFx12/wJ5y0XWjthWEO59zLPfe4MaNCGsZYKywtr6yuFdLG5tb2zv67l5L
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+P8, Q8
+<latexit sha1_base64="8wbopYeLFJZVZxEdN6vwTq36xvM=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkoionVXdOyBfuAJoTJZNIOnTyYmQglZOlfuPEvunbjQhFx12/wJ5y0XWjthWEO59zLPfe4MaNCGsZYKywtr6yuFdLG5tb2zv67l5
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+P9, Q9
+<latexit sha1_base64="CiOXOvc/hpLGB3YzgzHfSe57YrA=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkoionZXdOyBfuAJoTJZNIOnTyYmQglZOlfuPEvunbjQhFx12/wJ5y0XWjthWEO59zLPfe4MaNCGsZYKywtr6yuFdLG5tb2zv67l5
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+P10, Q10
+<latexit sha1_base64="JIifQ6gP2q/bqPt/JVjzE8cWt0Y=">ACJXicbVDLSsNAFJ3UV62vqEtFBovgQkoigouim5ctmAf0IQwmUzaoZMHMxOhCz9ETf+Qj/BjQuLCK78AH/CSduFtr0wzOGce7nHjdmVEjD+NIKS8srq2vF9dLG5tb2jr671xR
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+P11, Q11
+<latexit sha1_base64="AhxFdRoafdJMlBFtfVTcJh7VuMA=">ACJXicbVDLSsNAFJ3UV62vqEtFBovgQkoigouim5ctmAf0IQwmUzaoZMHMxOhCz9ETf+Qj/BjQuLCK78AH/CSduFtr0wzOGce7nHjdmVEjD+NIKS8srq2vF9dLG5tb2jr67
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+P12, Q12
+<latexit sha1_base64="46XsXM3IJrv4KoylzA9I+4y9lFw=">ACJXicbVDLSsNAFJ3UV62vqEtFBovgQkpSBVcFN24bME+oAlhMpm0QycPZiZCVn6I278hX6CGxcWEVz5Af6Ek7YLrb0wzOGce7nHjdmVEjD+NQKS8srq2vF9dLG5tb2jr671x
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+p4, q4
+<latexit sha1_base64="PfDf0azKs219i32pWKcsBWEfPAo=">AC3icbVDLSsNAFJ34rPUVdanI0CK4kJIQd0V3bhswT6gDWEymbRDJ5k4MxFK6FJw46+4cWERt/6AO7/Bn3DSdlFbDwxzOde7r3HixmVyrK+jaXldW19dxGfnNre2fX3NtvS
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+p5, q5
+<latexit sha1_base64="pFcmK4pQavogwo5Qgia2L9TsCjY=">AC3icbVDLSsNAFJ3UV62vqEtFhbBhZREFHVXdOyBfuANoTJZNIOnWTizEQoUvBjb/ixoVF3PoD7vwGf8J20WtHhjmcM693HuPFzMqlWV9GbmFxaXlfxqYW19Y3PL3N5pSJ4ITOqYMy5aHpKE0YjUFVWMtGJBUOgx0vT615nfvCdCUh7dqkFMnB1IxpQjJSWXLPY8Tjz5SDUXxoP3bNjOKvcacU1S1bZGgP+JfaUlCr7o9r3w8Go6pqfHZ/jJCSRwgxJ2batWDkpEopiRoaFTiJjHAfdUlb0wiFRDrp+JYhPNSKDwMu9I
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+p7, q7
+<latexit sha1_base64="tnHfbmSvg0HeAm+CKukTGPaJaY=">AC3icbVDLSsNAFJ34rPUVdanI0CK4kJKIUN0V3bhswT6gDWEymbRDJ5k4MxFK6FJw46+4cWERt/6AO7/Bn3DSdlFbDwxzOde7r3HixmVyrK+jaXldW19dxGfnNre2fX3Nt
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+p8, q8
+<latexit sha1_base64="epo4Ir38SV16TbTwKNAhVqXnxk=">AC3icbVDLSsNAFJ34rPUVdanI0CK4kJKIYN0V3bhswT6gDWEymbRDJ5M4MxFK6FJw46+4cWERt/6AO7/Bn3DSdlFbDwxzOde7r3HixmVyrK+jaXldW19dxGfnNre2fX3NtvyCgRmNRxCLR8pAkjHJSV1Qx0oFQaHSNPr32R+84EISN+pwYxcULU5TSgGCktuWah40XMl4NQf2k8dMtncFa514prFq2SNQZcJPaUFCtHo9rP4/Go6pfHT/CSUi4wgxJ2batWDkpEopiRob5TiJjHAfdUlbU45CIp10fMsQnmjFh0Ek9OMKjt
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+p9, q9
+<latexit sha1_base64="Lj1dGxs0OP1UCHefGjQ0m0AFVjs=">AC3icbVDLSsNAFJ34rPUVdanI0CK4kJKIoN0V3bhswT6gDWEymbRDJ5M4MxFK6FJw46+4cWERt/6AO7/Bn3DSdlFbDwxzOde7r3HixmVyrK+jaXldW19dxGfnNre2fX3Nt
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+p10, q10
+<latexit sha1_base64="4Qbrgr2riCekHI8Ziewjbr6x+8w=">ACEXicbVDLSsNAFJ34rPUVdanIYBG6kJKIoO6Kbly2YB/QhjCZTNqhk4czE6GELN268Vdc1IUibt258xv8CSdNF7X1wDCHc+7l3nuciFEhDeNbW1hcWl5ZLawV1zc2t7b1nd2mCGOSQOHL
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+p11, q11
+<latexit sha1_base64="KBzJnFLiRLRwcByMfRML5Asryo=">ACEXicbVDLSsNAFJ34rPUVdanIYBG6kJKIoO6Kbly2YB/QhjCZTNqhk4czE6GELN268Vdc1IUibt258xv8CSdNF7X1wDCHc+7l3nuciFEhDeNbW1hcWl5ZLawV1zc2t7b1nd2mCGOSQO
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+p12, q12
+<latexit sha1_base64="dWxgl5imBz+iP1N8FA6fR6Jc7yY=">ACEXicbVC7SgNBFJ2Nrxhfq5aKDAYhYTdIKhd0MYyAfOAZFlmZyfJkNmHM7NCWLa0tfFXLGKhiK2dnd/gTzibTRETDwxzOde7r3HCRkV0jC+tdzS8srqWn69sLG5tb2j7+41RBxTBo4Y
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+P3, Q3
+<latexit sha1_base64="6EOuKvteBQqnMgvSnp+f414+4jo=">ACH3icbVDLSsNAFJ3UV62vqEtFBovgQkqi4mNXdOyBfuAJoTJZNIOnTyYmQglZOlfuPEvunbjQhFx12/wJ5y0LrTthWEO59zLPfe4MaNCGsZIKywsLi2vFdLa+sbm1v69k5
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+12
+Fig. 1.
+A radial 13-bus distribution network connected with rooftop solar
+PVs and ESSs.
+In this paper, one control objective is to minimize the
+total power loss of the distribution network by controlling the
+dynamics of PVs and ESSs, which is approximated by
+f1(pg
+1, . . . , pg
+n) =
+�
+lij∈L
+rij
+�∥Pij∥2
+2 + ∥Qij∥2
+2
+V 2
+0
+�
+(2)
+where V0 denotes the nominal voltage magnitude, pg
+j, Pij, and
+Qij ∈ RT are augmented vectors of pg
+j, Pij, and Qij across T
+time intervals, respectively. Note that we only consider active
+power loss and assume reactive power flows Qij to be constant
+vectors. Though the reactive power loss is not included here for
+simplicity, it can be added without affecting algorithm design.
+The active power flows are constrained by
+0 ≤ Pij ≤ Pij
+(3)
+where Pij denotes the maximum active power flow limit.
+B. Solar Photovoltaic
+Let V denote the set of in total V solar PVs. During T time
+intervals of a day, the active power injection ˜pν ∈ RT from
+the νth PV inverter should satisfy
+0 ≤ ˜pν ≤ pv
+ν
+(4)
+
+田田3
+where pv
+ν denotes the maximum active power injection and is
+assumed to be known by the forecast. Herein, the curtailment
+cost can be calculated by [25]
+f2(˜pν) = ∥˜pν − pv
+ν∥2
+2.
+(5)
+C. Energy Storage System
+Let S denote the set of E ESSs. The charging/discharging
+power ˆpσ ∈ RT of the σth ESS is constrained by
+− ps
+σ ≤ ˆpσ ≤ ps
+σ
+(6)
+where ps
+σ and ps
+σ denote the maximum discharging and
+charging power, respectively. Let s0
+σ denote the initial state of
+charge (SoC) of the σth ESS and Hσ ≜ [s0
+σ, . . . , s0
+σ]T ∈ RT .
+Aggregate the charging/discharging power across T time in-
+tervals, then the capacity of the σth ESS is constrained by
+pa
+σ ≤ Hσ + Aˆpσ∆T ≤ pa
+σ
+(7)
+where pa
+σ and pa
+σ denote its lower and upper capacity
+bounds, respectively, ∆T denotes the sampling time, and
+the aggregation matrix A is lower triangular consisting of
+ones and zeros, i.e., element Aˆı,ˆȷ = 1 if ˆı ≥ ˆȷ, element
+Aˆı,ˆȷ = 0 if ˆı < ˆȷ, ∀ˆı, ˆȷ = 1, . . . , T. Therefore, the SoCs of
+ESS σ during T time slots are obtained by aggregating the
+charging/discharging power using A.
+Furthermore, the σth ESS’s degradation cost is calculated in
+terms of the smoothness of charging and discharging by [26]
+f3(ˆpσ) = ∥B ˆpσ∥2
+2.
+(8)
+where B calculates discharging/charging differences between
+adjacent times, i.e., Bˆı,ˆı = 1, ∀ˆı = 1, . . . , T, Bˆı,ˆı+1 =
+−1, ∀ˆı = 1, . . . , T − 1, and all other elements are zeros.
+D. Problem Formulation
+The optimization problem is then formulated to minimize
+the summation of total active power loss, PV curtailment cost,
+and ESS degradation cost within the distribution network as
+min
+˜p, ˆp
+δ1f1(pg) +
+V
+�
+ν=1
+δ2f2(˜pν) +
+E
+�
+σ=1
+δ3f3(ˆpσ)
+s.t.
+(1a), (3), (4), (6), (7)
+(P1)
+where
+˜p
+=
+[˜pT
+1 , . . . , ˜pT
+n]T,
+ˆp
+=
+[ˆpT
+1 , . . . , ˆpT
+n]T, pg
+=
+[pg
+1
+T, . . . , pg
+n
+T]T, and δα denotes the cost coefficient asso-
+ciated with the objective function fα(·). Note that the cost
+coefficients are constants that allow flexible adjustments on
+the weights of the global and local objective functions and
+regulate different units.
+III. DECENTRALIZED OPTIMIZATION
+A. Projected Gradient Method
+This paper achieves scalability in solving (P1) via projected
+gradient method (PGM). PGM decomposes a centralized opti-
+mization problem into local optimizations at agents, resulting
+in a paralleled computing structure. Let M = {1, . . . , m}
+denote the set of agents, e.g., buses or DERs, who work
+cooperatively in solving (P1). In this setting, the κth agent
+updates its decision variable xκ using PGM by
+x(ℓ+1)
+κ
+= PXκ[x(ℓ)
+κ − γ(ℓ)
+κ Φκ(x(ℓ))]
+(9)
+where
+ℓ
+denotes
+the
+iteration
+number,
+x(ℓ)
+=
+[x(ℓ)
+1
+T, . . . , x(ℓ)
+m
+T]T
+includes
+all
+decision
+variables,
+i.e.,
+˜pν and ˆpσ in problem (P1), γ(ℓ)
+k
+denotes the step size, Φκ(·)
+denotes the gradient of the Lagrangian w.r.t. x(ℓ)
+κ , and PXκ[·]
+denotes the projection operation onto set Xκ.
+In (P1), the local constraint of the νth PV in (4) and local
+constraints of the σth ESS in (6) and (7) can be represented
+by two feasible sets Pv
+ν and Pe
+σ as
+Pv
+ν ≜ {˜pν| 0 ≤ ˜pν ≤ pv
+ν}
+(10a)
+Pe
+σ ≜ {ˆpσ| − ps
+σ≤ˆpσ≤ps
+σ, pa
+σ≤H+Aˆpσ∆T ≤ pa
+σ}. (10b)
+In what follows, aiming at reducing the number of coupling
+terms, we rewrite the networked constraints in (1a) and (3) to
+a single inequality constraint based on the network topology.
+To this end, we first represent the active power flows in (1a)
+through active power generations of each bus using
+pi = ˜pi − ˆpi − pc
+i
+(11)
+where pi denotes the aggregated active power generation at
+bus i, ˜pi = �Vi
+ν=1 ˜pν and ˆpi = �Ei
+σ=1 ˆpσ denote the aggre-
+gated active power of all PVs and ESSs that are connected at
+bus i, respectively. Vi and Ei denote the total number of PVs
+and ESSs connected at bus i, respectively.
+For the ιth line flow Pι in the distribution network, the
+from-bus is defined by the bus where the flow begins, and the
+to-bus set is defined by the set of buses that the ιth line flow
+travels to till reaching the edge of the distribution network.
+Let Z ∈ Rn×n denote the adjacency matrix of the distribution
+network and Zι denote the ιth row of Z that represents the
+adjacency vector of the ιth line flow. Let Zι(i) denote the ith
+element of Zι, and Zι(i) = 1 if the ιth power flow has bus i
+as a to-bus, e.g., Z9 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]. Then, the
+power flows in the distribution network can be represented by
+Z. Expand Z across T time slots, we have
+˜Z =
+�
+����
+Z1(1)I Z1(2)I · · · Z1(n)I
+...
+...
+...
+Zn(1)I Zn(2)I · · · Zn(n)I
+�
+����
+(12)
+where I∈RT ×T denotes the identity matrix and ˜Z ∈ RnT ×nT .
+In what follows, let ˜P ∈ RnT denote the aggregated active
+power generations defined in (11) from all buses, we have
+˜P =
+�
+��
+p1
+...
+pn
+�
+�� =
+�
+����
+�V1
+ν=1 ˜pν − �E1
+σ=1 ˆpσ − pc
+1
+...
+�Vn
+ν=Vn−1+1 ˜pν − �En
+σ=En−1+1 ˆpσ − pc
+n
+�
+���� .
+(13)
+Furthermore, ˜P can be rewritten compactly as
+˜P =
+n
+�
+i=1
+∆i (˜pi − ˆpi − pc
+i)
+(14)
+
+4
+where ∆i denotes the aggregation matrix whose ith block is
+represented by the identity matrix I, and all other blocks are
+zeros, e.g., ∆1 = [I, 0, . . . , 0]T ∈ RnT ×T . Then, the active
+power flow of the ιth line can be calculated by
+Pι = ˜Zι ˜P .
+(15)
+Consequently, the power flow limit constraint in (3) becomes
+0 ≤ ˜Zι ˜P ≤ Pι.
+(16)
+Therefore, problem (P1) can be written into
+min
+˜p, ˆp
+δ1f1(pg) +
+V
+�
+ν=1
+δ2f2(˜pν) +
+E
+�
+σ=1
+δ3f3(ˆpσ)
+s.t.
+pν ∈ Pv
+ν, ∀ν ∈ V
+pσ ∈ Pe
+σ, ∀σ ∈ S
+0 ≤ ˜Zι ˜P ≤ Pι, ∀ι ∈ L
+(P2)
+The optimization problem in (P2) seeks to find the optimal
+decision variables, i.e., charging and discharging power ˜pσ’s
+of the ESSs and the active power injection ˆpν’s of the PVs. In
+what follows, we focus on solving (P2) through a decentralized
+fashion based on PGM defined in (9). To solve (P2) via PGM,
+we firstly derive its relaxed Lagrangian as
+L(˜p, ˆp, µl, µu) = δ1f1(pg) +
+V
+�
+ν=1
+δ2f2(˜pν) +
+E
+�
+σ=1
+δ3f3(ˆpσ)
++
+L
+�
+ι=1
+µT
+uι( ˜Zι ˜P − Pι)−
+L
+�
+ι=1
+µT
+lι ˜Zι ˜P (17)
+where µl = [µT
+l1, . . . , µT
+lL]T and µu = [µT
+u1, . . . , µT
+uL]T, µlι
+and µuι denote the dual variables associated with lower and
+upper power flow limits of the line ι, respectively.
+Suppose ˜pν and ˆpσ are decision variables of the νth PV and
+σth ESS connected at bus i, respectively. Take the subgradients
+of (17) w.r.t. the primal variables ˜pν and ˆpσ, we have
+∇ ˜pνL(·) = 2δ2(˜pν − pv
+ν) + 2δ1
+V 2
+0
+L
+�
+ι=1
+rι( ˜Zι∆i)T( ˜Zι ˜P )
++
+L
+�
+ι=1
+( ˜Zι∆i)T(µuι − µlι)
+(18a)
+∇ ˆpσL(·) = 2δ3 ˆpσ − 2δ1
+V 2
+0
+L
+�
+ι=1
+rι( ˜Zι∆i)T( ˜Zι ˜P )
+−
+L
+�
+ι=1
+( ˜Zι∆i)T(µuι − µlι).
+(18b)
+Without affecting the efficacy of the algorithm design, we
+assume all power lines have the same resistance ¯r for the
+simplicity of presentation, herein (18) becomes
+∇ ˜pνL(·) = 2δ2(˜pν − pv
+ν) + ¯δ1πi ˜P + ψi(µu − µl)
+(19a)
+∇ ˆpσL(·) = 2δ3 ˆpσ − ¯δ1πi ˜P − ψi(µu − µl)
+(19b)
+where ¯δ1 = 2δ1
+V 2
+0 ¯r, πi = �L
+ι=1( ˜Zι∆i)T ˜Zι, and ψi denotes the
+ith column block of ˜Z.
+The detailed derivation of the Lagrangian subgradients in
+(19) can be found in APPENDIX A.
+Therefore, based on the calculated subgradients in (18), at
+the ℓth iteration, the νth PV and the σth ESS can update their
+decision variables using PGM by
+˜p(ℓ+1)
+ν
+= ΠPvν
+�
+˜p(ℓ)
+ν
+− αv
+ν,ℓ∇ ˜pνL(ℓ) (·)
+�
+(20a)
+ˆp(ℓ+1)
+σ
+= ΠPeσ
+�
+ˆp(ℓ)
+σ − αe
+σ,ℓ∇ ˆpσL(ℓ) (·)
+�
+(20b)
+where αv
+ν,ℓ and αe
+σ,ℓ denote the primal step sizes of the νth PV
+and the σth ESS, respectively, L(ℓ) (·) denotes the calculated
+Lagrangian in (17) at the ℓth iteration. The dual variables can
+be updated similarly using PGM.
+B. DER Aggregation and Control
+In PGM iterations, the ith agent needs to calculate Φi(xℓ)
+in (9) where the decision variables xi’s from all other agents
+are required. As indicated in (19), calculating subgradients
+∇ ˜pνL(·) and ∇ ˆpσL(·) indeed requires the decision variables
+˜P from all the agents. Specifically, the calculation of subgra-
+dients in (19a) and (19b) are coupled through
+C = Cp + Cd = ¯δ1πi ˜P + ψi(µu − µl)
+(21)
+where Cp and Cd denote the coupling terms associated with
+the primal and dual variables, respectively.
+To clearly demonstrate the information exchange needs in
+subgradient calculation, we exemplify the primal update of the
+ˆνth PV connected at bus 2. The ˆνth PV can update its decision
+variable ˜pˆν using the subgradient in (19a) which is
+∇ ˜pˆνL(·) = 2δ2(˜pˆν − pv
+ˆν) +
+2
+�
+ι=1
+�
+¯δ1πι ˜P + µuι + µlι
+�
+(22)
+where π1 ˜P = �n
+i=1 pi and π2 ˜P = p2 + p3. Therefore, the
+ˆνth PV requires the active power generations pi, ∀i = 1, . . . , n
+from all buses to conduct the update in (20a).
+Based on the above observations, two different aggregation
+and control strategies, i.e., Bus-level aggregation and control
+and DER-level aggregation and control, can be applied as
+shown in Fig. 2. In bus-level aggregation and control, the ith
+Each bus aggregates the decision 
+variables                   and 
+DERs exchange decision variables 
+with others to obtain 
+                 and 
+˜pi=
+XVi
+⌫=1 ˜p⌫
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+ˆpi=
+XEi
+�=1 ˆp�
+<latexit sha1_base64="J1PqXdAVQ0WCWiXxcnVQymKUhI=">ACSXicbVDPSxtBFJ6N2qaprWl79DIYCp7CbhG0B0EshR4jGBWycX07mSD82OZeSuEYf+9Xnrf9DLx4s4snZuIf648EwH9/3vpn3vryQwmEc/4laK6tr163Ter97v9H98PHEmdIyPmRGnuWg+NSaD5EgZKfFZaDyiU/zS+/1frpFbdOGH2Mi4KPFcy0mAoGKise5HOAX2aGzlxCxUuX1RVJqjfr2jqSpX51ImZgv2kSrWRQgl05z5VgHMG0n8PvdWLTzS+Kuv24n68LPocJA3okaYGWfd
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+Each individual PV or ESS owns
+decision variable     or     to itself  
+˜p⌫
+<latexit sha1_base64="SM/x7D2mHQVQXsiJ9CAKr6xkWEY=">ACBXicbVC7TsMwFHXKq5RXgBEGiwqJqUpQJWCrYGEsEn1ITRQ5jtadezIdpCqKAsLv8LCAEKs/AMbf4PTZoCWI1k+
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+RjJBHWJriaCcFdPHmZdM8brNxdest67LOKrgCJyAM+C9ACt6ANOgCDR/AMXsGb9WS9WO/Wx7y0YpU9h+APrM8fVh+Zxg=</latexit>
+ˆp�
+<latexit sha1_base64="yRsJzl/IUYDZq3zl9fswdZn4Y=">ACBnicbVDLSsNAFJ3UV62vqEsRBovgqiRSUHdFNy4r2Ac0IUwm03boTCbMTIQSsnLjr7hxoYhbv8Gdf+OkzUJbDwxzOde
+7r0nTBhV2nG+rcrK6tr6RnWztrW9s7tn7x90lUglJh0smJD9ECnCaEw6mpG+okiIeM9MLJTeH3HohUVMT3epoQn6NRTIcUI2kwD72xkhnXihYpKbcfFmS50HmKTriKA/sutNwZoDLxC1JHZRoB/aXFwmchJrzJBSA9dJtJ8hqSlmJK95qSIJwhM0IgNDY8SJ8rPZGTk8NUoEh0KaF2s4U393ZIirYklTyZEeq0WvEP/zBqkeXvoZjZNUkxjPBw1TBrWARSYwopJgzaGICyp2RXiMZIa5NczY
+TgLp68TLrnDbfZuLpr1lvXZRxVcAROwBlwQVogVvQBh2AwSN4Bq/gzXqyXqx362NeWrHKnkPwB9bnDw53mik=</latexit>
+The ith bus performs the primal-
+dual updates for all the DERs
+Each DER performs the primal-
+dual update in Eqs. (22) and (23)
+End iteration if : DERs’ decision variables achieve convergence  
+Aim: Calculate subgradients               and               for the updates in PGM 
+r˜p⌫L(·)
+<latexit sha1_base64="NCdmlfZtlskHCRoWxGd7tDpT0mQ=">ACIHicbVBNS8NAEN34WetX1aOXYBH0UhIpqDfRiwcPFWwVmlIm61dutkNuxOhPwUL/4VLx
+4U0Zv+GjdtDn4NLPt4b4Z58JEcIOe9+HMzM7NLyxWlqrLK6tr67WNzY5RqasTZVQ+iYEwSXrI0cBbtJNIM4FOw6HJ0V+vUd04YreYXjhPViuJV8wCmgpfq1w0BCKCfBchFxLIgVCIy49h+WZLnlpdpngcx4JCyC7yvYBGCvf7tbrX8Cbl/gV+CeqkrFa/9h5EiqYxk0gFGNP1vQR7GWjkVLC8GqSGJUBHcMu6FkqImelkwNzd9cykT
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+rˆp�L(·)
+<latexit sha1_base64="WTcG5eEwOkl6SUea4MtPTARM=">ACIXicbVBNS8NAEN34bf2qevQSLEK9lEQE9SZ68eBwX5AU8pks2XbnbD7kQoIX/Fi3/FiwdF
+vIl/xk3bg7YOLPt4b4Z58JEcIOe9+UsLC4tr6yurZc2Nre2d8q7ew2jUk1ZnSqhdCsEwSXrI4cBWslmkEcCtYMh9eF3nxk2nAlH3CUsE4Mfcl7nAJaqls+DySEArpZMADMglCJyIxi+2VJnlvW8H4MeR7EgAMKIrvNqwGNFB53yxWv5o3LnQf+FTItO65c8gUjSNmUQqwJi27yXYyUAjp4LlpSA1LAE6hD5rWyghZqaTjS/M3SPLRG5Pafsk
+umP290QGsSl8287CqZnVCvI/rZ1i7yTcZmkyCSdLOqlwkXlFnG5EdeMohZAFRz69WlA9BA0YZasiH4syfPg8ZJzT+tXdyfVi6vpnGskQNySKrEJ2fktyQO1InlDyRF/JG3p1n59X5cD4nrQvOdGaf/Cn+wfAO6W5</latexit>
+˜pi=
+XV
+⌫=1 ˜p⌫
+<latexit sha1_base64="sOXuDwMIMEucHRfVxl8qnlY3zU=">ACRHicdVDLSiQxFE05PtXO7N0E2wEV02VCOqiQZyNSwemW6GrLVKptAbzKJbQhPycW78AHfzBW5cKOJWJtX2wueFkM595CTk5eCW4jf9
+HUj+mZ2bn5hcbi0vLKanPtZ8/qylDWpVpoc5oTywRXrAscBDstDSMyF+wkv/xd6ydXzFiu1V8YlWwgybniQ04JBCpr9lPgomAuzbUo7EiGy5XeZ9x1PE5tJTOXqT+FRpwSUHe+ZSeCEuF63n9jr0+a7bidjwe/BkE9BCkznOmrdpoWklmQIqiLX9JC5h4IgBTgXzjbSyrCT0kpyzfoCKSGYHblyCx5uBKfBQm3AU4DH71uGItHXCsFntx+1mvxK61cw3Bs4rsoKmKvDw0rgUHjulFcMoiFEAhBoesmJ6QyhEHpvhBKSj1/+
+DHrb7WSnvf9np3VwOKljHq2jDbSFErSLDtAROkZdRNE1ukMP6DG6ie6jp+j5dXUqmnh+oXcTvfwHsO62FA=</latexit>
+Buses exchange decision variables 
+with others to obtain 
+8i=1 . . . , n
+<latexit sha1_base64="eYA2cw+pfmQ4bl+JGXOd6TBo2Y=">AB/nicbVDLSgMxFL3js9ZXVy5CRbBhZQZKagLoejGZQX7gM5QMpm0Dc0kQ5IRylDwV9y4UMSt3+HOvzFtZ6GtBwKHc+7lnpw4Uwb1/12lpZXVt
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+a65OQ7B/AHzucP2q2VcA=</latexit>
+ˆpi=
+XE
+�=1 ˆp�,
+<latexit sha1_base64="GuE1wgouyMWpJt3pSfGs7Vt7lQo=">ACSHicbVBNaxsxENW6zZeTpm57zEXEFHoZrcY2h4CoaXQYwJxEvA6y6ws2yL6WKTZgBH6eb302Ft/Qy89tJTeonX2kK8Bocd786SZV1ZSOEzTn0n
+ydO19Y3Nre72zrPd570XL0+dqS3jI2akseclOC6F5iMUKPl5ZTmoUvKz8vJzo59dceuE0Se4rPhEwVyLmWCAkSp6Rb4A9Hlp5NQtVbx8FUIhqD8INHe1KnzuxFzBQRZybaRQAt2FzxXgoH0X0J49IHWFd4WvX46SFdFH4KsBX3S1lHR+5FPDasV18gkODfO0gonHiwKJno5rXjFbBLmPNxhBoUdxO/CiLQ15GZ0pmx8WikK/a2w4NyzZSxs9nA3dca8jFtXOPsw8QLXdXINbv5aFZLioY2qdKpsJyhXEYAzIo4K2ULsMAwZt+NIWT3V34ITt8NsuHg4/
+Gwf/ipjWOT7JF98oZk5D05JF/JERkRr6RX+QP+Zt8T34n/5L/N62dpPW8Ineq07kGLPy2Kg=</latexit>
+ˆpi, ˜pi, 8i = 1 . . . , n
+<latexit sha1_base64="ChPanXivTdMBX2Dsthv7AEM2Hyg=">ACLnicbVDLSgMxFM3UV62vqks3wSK4KGVGCupCKIrgsoJ9QGcomUymDc1MhuSOUIZ+kRt/ReCirj1M0wfC217IeRwzr3JucdP
+BNdg2+9WbmV1bX0jv1nY2t7Z3SvuHzS1TBVlDSqFVG2faCZ4zBrAQbB2ohiJfMFa/uBmrLcemdJcxg8wTJgXkV7MQ04JGKpbvHX7BDLXlyLQw8hcWTIadXkZu8BFwJYqoVRECMyvHFcEnTZvFOyK/ak8CJwZqCEZlXvFl/dQNI0YjFQbTuOHYCXkYUcCrYqOCmiWEDkiPdQyMScS0l03WHeETwTYuDAnBjxh/05kJNJjy6YzItDX89qYXKZ1UgvIzHSQosptOPwlRgkHicHQ64YhTE0ABCFTdeMe0TRSi
+YhAsmBGd+5UXQPKs41crlfbVUu57FkUdH6BidIgedoxq6Q3XUQBQ9oRf0gT6tZ+vN+rK+p605azZziP6V9fMLNxmqbQ=</latexit>
+r˜p⌫L(·)
+<latexit sha1_base64="NCdmlfZtlskHCRoWxGd7tDpT0mQ=">ACIHicbVBNS8NAEN34WetX1aOXYBH0UhIpqDfRiwcPFWwVmlIm61dutkNuxOhPwUL/4VLx4U0Z
+v+GjdtDn4NLPt4b4Z58JEcIOe9+HMzM7NLyxWlqrLK6tr67WNzY5RqasTZVQ+iYEwSXrI0cBbtJNIM4FOw6HJ0V+vUd04YreYXjhPViuJV8wCmgpfq1w0BCKCfBchFxLIgVCIy49h+WZLnlpdpngcx4JCyC7yvYBGCvf7tbrX8Cbl/gV+CeqkrFa/9h5EiqYxk0gFGNP1vQR7GWjkVLC8GqSGJUBHcMu6FkqImelkwNzd9cykTtQ2j6J7oT9
+PpFBbArTtrNwan5rBfmf1k1xcNTLuExSZJOFw1S4aJyi7TciGtGUYwtAKq59erSIWigaDOt2hD83yf/BZ2Dht9sHF826yenZRwVsk12yB7xySE5IekRdqEknvySJ7Ji/PgPDmvztu0dcYpZ7bIj3I+vwD93qVW</latexit>
+rˆp�L(·)
+<latexit sha1_base64="WTcG5eEwOkl6SUea4MtPTARM=">ACIXicbVBNS8NAEN34bf2qevQSLEK9lEQE9SZ68eBwX5AU8pks2XbnbD7kQoIX/Fi3/FiwdFvIl/
+xk3bg7YOLPt4b4Z58JEcIOe9+UsLC4tr6yurZc2Nre2d8q7ew2jUk1ZnSqhdCsEwSXrI4cBWslmkEcCtYMh9eF3nxk2nAlH3CUsE4Mfcl7nAJaqls+DySEArpZMADMglCJyIxi+2VJnlvW8H4MeR7EgAMKIrvNqwGNFB53yxWv5o3LnQf+FTItO65c8gUjSNmUQqwJi27yXYyUAjp4LlpSA1LAE6hD5rWyghZqaTjS/M3SPLRG5PafskumP290QGsS
+l8287CqZnVCvI/rZ1i7yTcZmkyCSdLOqlwkXlFnG5EdeMohZAFRz69WlA9BA0YZasiH4syfPg8ZJzT+tXdyfVi6vpnGskQNySKrEJ2fktyQO1InlDyRF/JG3p1n59X5cD4nrQvOdGaf/Cn+wfAO6W5</latexit>
+Individual DER acts an agent to 
+calculate subgradients 
+and               
+r˜p⌫L(·)
+<latexit sha1_base64="NCdmlfZtlskHCRoWxGd7tDpT0mQ=">ACIHicbVBNS8NAEN34WetX1aOXYBH0UhIpqDfRiwcPFWwVmlIm61dutkNuxOhPwUL/4VLx4U0Z
+v+GjdtDn4NLPt4b4Z58JEcIOe9+HMzM7NLyxWlqrLK6tr67WNzY5RqasTZVQ+iYEwSXrI0cBbtJNIM4FOw6HJ0V+vUd04YreYXjhPViuJV8wCmgpfq1w0BCKCfBchFxLIgVCIy49h+WZLnlpdpngcx4JCyC7yvYBGCvf7tbrX8Cbl/gV+CeqkrFa/9h5EiqYxk0gFGNP1vQR7GWjkVLC8GqSGJUBHcMu6FkqImelkwNzd9cykTtQ2j6J7oT9
+PpFBbArTtrNwan5rBfmf1k1xcNTLuExSZJOFw1S4aJyi7TciGtGUYwtAKq59erSIWigaDOt2hD83yf/BZ2Dht9sHF826yenZRwVsk12yB7xySE5IekRdqEknvySJ7Ji/PgPDmvztu0dcYpZ7bIj3I+vwD93qVW</latexit>
+rˆp�L(·)
+<latexit sha1_base64="WTcG5eEwOkl6SUea4MtPTARM=">ACIXicbVBNS8NAEN34bf2qevQSLEK9lEQE9SZ68eBwX5AU8pks2XbnbD7kQoIX/Fi3/FiwdFvIl/
+xk3bg7YOLPt4b4Z58JEcIOe9+UsLC4tr6yurZc2Nre2d8q7ew2jUk1ZnSqhdCsEwSXrI4cBWslmkEcCtYMh9eF3nxk2nAlH3CUsE4Mfcl7nAJaqls+DySEArpZMADMglCJyIxi+2VJnlvW8H4MeR7EgAMKIrvNqwGNFB53yxWv5o3LnQf+FTItO65c8gUjSNmUQqwJi27yXYyUAjp4LlpSA1LAE6hD5rWyghZqaTjS/M3SPLRG5PafskumP290QGsS
+l8287CqZnVCvI/rZ1i7yTcZmkyCSdLOqlwkXlFnG5EdeMohZAFRz69WlA9BA0YZasiH4syfPg8ZJzT+tXdyfVi6vpnGskQNySKrEJ2fktyQO1InlDyRF/JG3p1n59X5cD4nrQvOdGaf/Cn+wfAO6W5</latexit>
+Individual bus acts an agent to 
+calculate subgradients 
+and               
+DER-level aggregation and control
+Bus-level aggregation and control
+Fig. 2.
+Aggregation and control of DERs via bus-level and DER-level
+architectures.
+bus (agent) aggregates the decision variables ˜pi = �Vi
+ν=1 ˜pν
+
+5
+and ˆpi = �Ei
+σ=1 ˆpσ where only aggregated decision variables
+are transmitted and used for the primal updates. In contrast,
+DER-level control strategies require each DER to act as an
+agent and receive all data of others that is demanded for
+updates in (20). However, due to the large number of DERs
+connected to the distribution network, DER-level control can
+suffer from massive data exchange and heavy local computa-
+tion. Therefore, we adopt the bus-level aggregation and control
+scheme which is more computing and communicating effi-
+cient. We will later show that the proposed privacy-preserving
+algorithm can be readily extended to the DER-level control
+(See Remark 1 for details).
+Apart from scalability and efficiency, the inevitable private
+information exposure in both bus-level and DER-level methods
+raises fundamental privacy concerns, e.g., the electrical load
+can reveal sensitive business activities and/or customer’s daily
+routines. To address the privacy concerns, we will develop
+a novel SS-based algorithm to achieve secure information
+exchange in executing (20).
+IV. SS-BASED PRIVACY-PRESERVING DER CONTROL
+A. Real Number to Integer Quantization
+Note that the SS scheme requires modular arithmetic instead
+of real arithmetic. However, decentralized optimization ge-
+netically requires real number calculations, e.g., real decision
+variables and parameters. Therefore, a real number to integer
+transformation is needed to integrate SS into decentralized
+optimization. We adopt the fixed-point number quantization
+[27] to map the real numbers onto the integer space and the
+fixed-point real-number set is defined by
+Qθ,γ,ζ≜
+�
+−θγ, −θγ + θ−ζ, . . . , θγ − 2θ−ζ, θγ − θ−ζ�
+(23)
+where θ ∈ N1+ denotes the basis, γ ∈ N denotes the
+magnitude, and ζ ∈ N denotes the resolution. Therefore, by
+defining a surjective mapping m(·) : R �→ Qθ,γ,ζ, a real
+number can be mapped to the closest point in Qθ,γ,ζ. To limit
+the quantization error, the mapping m(·) needs to satisfy
+|m(ϕ) − ϕ| ≤ θ−ζ, ∀ϕ ∈ [−θγ, θγ]
+(24)
+where the quantization error is restricted by the resolution
+within the range of Qθ,γ,ζ. To map the real-number set onto
+the integer set Z, we simply scale Qθ,γ,ζ by θζ as
+Zθ,γ,ζ = θζQθ,γ,ζ=
+�
+−θγ+ζ, −θγ+ζ+1, . . . , θγ+ζ−1
+�
+(25)
+where Zθ,γ,ζ ⊆ Z denotes the fixed-point set in the integer
+field. Moreover, the SS requires the inputs to be within the
+field E. Therefore, we further map each element in z ∈ Zθ,γ,ζ
+onto E with the modular operation as
+g(z) = z mod e.
+(26)
+Note that z ∈ Zθ,γ,ζ can be any negative integer, and the
+modular operation in (26) will change the sign of a negative
+input, i.e., g(ˆz) = ˆz + e for ˆz < 0. To address the negative
+integer operation, we introduce the partial inverse of g(·) as
+ψ(z) =
+� z − e
+if z ≥ e
+2,
+z
+otherwise.
+(27)
+Therefore, we can readily obtain z = ψ(g(z)), ∀z ∈ E.
+B. SS-based Privacy-Preserving Algorithm
+1) Shamir’s secret sharing scheme: Before introducing the
+privacy-preserving algorithm design, we first briefly intro-
+duce Shamir’s SS scheme [20] which merits an efficient and
+lightweight private information distribution structure. Suppose
+a manager (secret holder) seeks to distribute a secret ω to
+specific agents and mandates the cooperation of at least d
+agents to retrieve the secret. In such needs, Shamir’s SS is
+grounded on the following idea of Lagrange interpolation for
+secret distribution and recovery.
+Theorem 1 (Polynomial interpolation [28]). Let {(ς1, y1), . . . ,
+(ςd, yd)} ⊆ R2 be a set of points whose values of ςı are all
+distinct. Then there exists a unique polynomial Y of degree
+d − 1 that satisfies yı = Y(ςı), ∀ı = 1, . . . , d.
+■
+In SS-based schemes, the manager first constructs a random
+polynomial of degree d − 1 as
+y(z) = ω + a1z + · · · + ad−1zd−1
+(28)
+where ω denotes an integer secret, a1, . . . , ad−1 are random
+coefficients that are uniformly distributed in the field E ≜
+[0, e), and e denotes a prime number that is larger than ω.
+Secondly, the manager calculates the outputs of (28) with
+non-zero integer inputs, e.g., setting τ = 1, . . . , n to retrieve
+(τ, y(τ)) where yΠ
+τ
+= y(τ) mod e. Then, the share yΠ
+τ
+is
+distributed to agent τ. Lastly, at least d agents with shares
+are required to reconstruct the polynomial based on Theorem
+1 and hence recover the secret ω by
+ω =
+d
+�
+τ=1
+yΠ
+τ
+d
+�
+υ=0
+υ̸=τ
+υ
+υ − τ .
+(29)
+2) Proposed privacy-preserving algorithm: We next present
+the proposed two-layer decentralized privacy-preserving al-
+gorithm based on SS in a bus-level aggregation and control
+architecture, to achieve privacy preservation and scalability
+concurrently. In the distribution network layer, all DERs’ deci-
+sion variables are updated in parallel, and only masked data are
+sent from each bus to the servers. In the cloud computing layer,
+the servers calculate the aggregated messages and distribute
+them to the related buses. The computing structure of the
+proposed privacy-preserving algorithm is shown in Fig. 3.
+Cloud Computing
+Distribution 
+Network
+ESS
+Solar 
+PV
+Server
+Secure 
+Data Flow
+Secure 
+Data Flow
+Bus
+Fig. 3. Two-layer privacy-preserving computing structure for DER control in
+distribution networks.
+
+田田Compute20066
+Let C denote the set of clouds and c ≥ 2 denotes the total
+number of clouds. The ith bus generates a random polynomial
+of order d − 1 using (28) to obtain
+y(ℓ)
+i (z) = ω(ℓ)
+i
++ a(ℓ)
+i,1z + · · · + a(ℓ)
+i,d−1zd−1
+(30)
+where 2 ≤ d ≤ c, ω(ℓ)
+i
+denotes the secret of bus i at the ℓth
+iteration, ℓ denotes the iteration number, and a(ℓ)
+i,1, . . . , a(ℓ)
+i,d−1
+denote random coefficients that are uniformly distributed in the
+field E. Note that for a vector secret such as pi, we refer to an
+elementwise calculation of the vector using (30) by default.
+At the ℓth iteration, the uth cloud firstly generates a random
+integer α(ℓ)
+u , then it broadcasts α(ℓ)
+u
+to all the buses. Subse-
+quently, the ith bus can calculate y(ℓ)
+i (α(ℓ)
+u ), ∀u = 1, . . . , c
+using the received inputs based on (30). Finally, the ith bus
+sends y(ℓ)
+i (α(ℓ)
+u ) back to the uth cloud. Note that the coupling
+term πi ˜P in (21) is a linear combination of all pi’s that
+requires the private generation/consumption details from the
+buses. Therefore, a secure computation framework of πi ˜P is
+required to preserve the privacy of buses and DER owners.
+Suppose the clouds are aware of the network topology
+matrix Z which contains no private information of the buses
+or DERs. In order to calculate the aggregated information πi ˜P
+for bus i, the uth cloud firstly multiplies the received outputs
+y1(α(ℓ)
+u ), . . . , yn(α(ℓ)
+u ) utilizing the coefficients of πi to obtain
+{α(ℓ)
+u , πi(1)y(ℓ)
+1 (α(ℓ)
+u ), . . . , πi(n)y(ℓ)
+n (α(ℓ)
+u )}
+(31)
+Then, the uth cloud sums the outputs in (31) to obtain a new
+pair of input and output as
+¯
+Au,i = {α(ℓ)
+u ,
+n
+�
+ˆı=1
+πi(ˆı) y(ℓ)
+ˆı (α(ℓ)
+u )}.
+(32)
+Finally, the uth cloud calculates
+¯
+Au,i, ∀i = 1, . . . , n and
+broadcasts the new input-output share ¯
+Au,i to the ith bus.
+Therefore, after receiving new shares from in total c clouds
+servers, the ith bus now has access to
+˜
+Ai =
+�
+α(ℓ)
+ˆȷ ,
+n
+�
+ˆı=1
+πi(ˆı) y(ℓ)
+ˆı (α(ℓ)
+ˆȷ ), ∀ˆȷ = 1, . . . , c
+�
+.
+(33)
+Note that ˜
+Ai contains in total c shares that can construct a
+new polynomial of the form
+˜y(ℓ)
+i (z) = πi ˜P + ˜a(ℓ)
+i,1z + · · · + ˜a(ℓ)
+i,d−1zd−1
+(34)
+whose constant term is exactly πi ˜P .
+During this information exchange process, each bus only
+sends a single share to each server so that a single cloud server
+is incapable of reconstructing the secret based on the received
+shares, and herein cannot infer agents’ true decision variables.
+The cloud servers only need to calculate aggregated messages
+using outputs of randomized polynomials. The details of the
+proposed method are presented via Algorithm 1.
+Algorithm 1 can achieve privacy preservation while main-
+taining exact solutions as non-privacy PGM-based methods.
+The decision variables will be continuously updated till the
+convergence errors ϵ(ℓ)
+ν
+≜ ∥˜p(ℓ)
+ν − ˜p(ℓ−1)
+ν
+∥2
+2 and ϵ(ℓ)
+σ
+≜ ∥ˆp(ℓ)
+σ −
+ˆp(ℓ−1)
+σ
+∥2
+2 are smaller than the threshold ϵ0. The correctness of
+Algorithm 1 is presented via Theorem 2.
+IEEE 13 bus network
+Decentralized 
+updates
+Cloud
+Aggregation
+y(`)
+3 (↵(`)
+1 )
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+y(`)
+3 (↵(`)
+c )
+<latexit sha1_base64="AT8U+757zt958DYmNWETF
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+Cloud1
+Cloud 2
+Cloud c
+DERs
+DERs
+DERs
+Bus 3
+Bus 2
+Bus 6
+Bus 1
+Bus 4
+Bus 5
+Bus 7
+Bus 9
+Bus 10
+Bus 12
+Bus 11
+Bus 8
+Bus 2
+Bus 1
+Bus 12
+¯
+A(`)
+1,1
+<latexit sha1_base64="OAQemdne2zbAeumZuA9yhroVF64=">ACnicbVDLSsNAFJ3UV42vqEs30SJUkJIQd3VunFZwT6giWEynbRDJw9mJkIZsnbjr7hxoYhbv8Cdf+OkzUJbD1w4nHMv97jJ5RwYVnfWmlpeWV1rbyub2xube8Yu3
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+¯
+A(`)
+1,12
+<latexit sha1_base64="wbvr5FCeuxjCnzM3Uiy/T
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+Bus 0
+Fig. 4. Information exchange structure between the distribution network and
+cloud servers (only the messages sent from bus 3 and cloud 1 are labeled).
+Algorithm 1 Decentralized SS-based privacy-preserving DER
+control strategy
+1: Agents initialize decision variables, tolerance ϵ0, basis θ,
+magnitude γ, resolution ζ, iteration counter ℓ = 0, and
+maximum iteration ℓmax.
+2: while ϵ(ℓ)
+ν(σ) > ϵ0 and ℓ < ℓmax do
+3:
+Each bus performs real number to integer transforma-
+tion using (23)-(26), then obtains the integer secret ω(ℓ)
+i .
+4:
+The uth cloud generates a random integer α(ℓ)
+u , then
+broadcasts α(ℓ)
+u
+to all the buses.
+5:
+The ith bus generates a random polynomial y(ℓ)
+i (z)
+using (30) with ω(ℓ)
+i
+as the constant term, calculates the
+outputs using α(ℓ)
+1 , . . . , α(ℓ)
+c
+to obtain y(ℓ)
+i (α(ℓ)
+1 ), . . . ,
+y(ℓ)
+i (α(ℓ)
+c ), then sends y(ℓ)
+i (α(ℓ)
+u ) to the uth cloud.
+6:
+The uth cloud formulates ¯
+Au,i in (32), then broadcasts
+¯
+Au,i to the ith bus.
+7:
+The ith bus formulates
+˜
+Ai in (33), reconstructs the
+aggregated secrets using c shares to obtain πi ˜P , then
+calculates Cp in (21).
+8:
+The ith bus transforms Cp back to real numbers
+using (27), then decision variables ˜p(ℓ)
+ν
+or ˆp(ℓ)
+σ
+of DERs
+connected at bus i are updated by PGM using (9). The ith
+bus calculates the error ϵ(ℓ)
+ν
+or ϵ(ℓ)
+σ .
+9:
+ℓ = ℓ + 1.
+10: end while
+Theorem 2 (Correctness). Let E denote the domain of the
+input secrets ω1, . . . , ωn, and Cp denote the desired outputs.
+Then, Algorithm 1 satisfies:
+Pr
+�
+∀c ≥ d, Rec
+�
+A, E, Z, ¯δ1, θ, γ, ζ
+�
+= Cp
+�
+= 1
+(35)
+where A = { ˜
+A1, . . . , ˜
+Ac} denotes the set of shares from
+agents, Pr[·] denotes probability, and Rec(·) denotes the secret
+reconstruction operation.
+■
+Theorem 2 states that Algorithm 1 can correctly retrieve
+the aggregated information Cp which would be further used to
+achieve exact primal and dual updates.
+
+Compute田田7
+The detailed proof of Theorem 2 can be found in AP-
+PENDIX B.
+Remark 1 : Though Algorithm 1 is developed based on bus-
+level aggregation and control, it can also be extended to the
+DER-level aggregation and control. In DER-level aggregation
+and control, each DER is required to generate a polynomial in
+(30) and act as an independent agent in secret reconstruction
+using (33). Besides, depending on the practical applications,
+DERs can also be clustered and controlled by the household
+or district where the new clusters act as agents, following the
+similar design of Algorithm 1.
+□
+Remark 2: The multi-server architecture seamlessly integrates
+the SS scheme into DER aggregation and control. Shares
+generated from buses were aggregated and broadcasted to the
+buses by a group of servers for the purpose of secret retrieval.
+The aggregation task is distributed to multiple servers to ensure
+that a single server cannot retrieve any secrets.
+□
+C. Privacy Analysis
+The proposed approach aims at protecting the decision
+variables of the DERs whose disclosure can lead to the leakage
+of customers’ sensitive information. To resolve this issue, Al-
+gorithm 1 achieves privacy preservation against two types of
+adversaries, including honest-but-curious-agent who follows
+the algorithm but may utilize the possessed and received data
+to infer the private information of other agents, and external
+eavesdroppers who wiretap and intercept exchanged messages
+from communication channels.
+Proposition 1: (Secure cloud computing). In Algorithm 1, any
+cloud number less than d − 1 cannot infer any information of
+the aggregated decision variables Cp.
+■
+Proposition 1 presents the security of the proposed al-
+gorithm against corrupted clouds. Based on the polynomial
+interpolation in Theorem 1, at least d clouds are required to
+retrieve any secret through collusion.
+Proposition 1 is proved based on the correctness analysis.
+Please refer to APPENDIX C for the detailed proof.
+Assumption 1. At least one communication link of an indi-
+vidual agent is secure against external eavesdroppers.
+■
+Assumption 1 is essential and generically used in SS-
+based schemes. Given d pairs of shares sent via different
+communication links, i.e., {(ς1, y1), . . . , (ςd, yd)} ⊆ R2, if
+an external eavesdropper wiretap all communication links to
+gain access to the shares, then it can simply deduce the secret
+by Lagrangian interpolation using Theorem 1.
+Theorem 3 (Privacy preservation against adversaries). By
+using Algorithm 1, the following two statements stand:
+1) Algorithm 1 securely computes and updates the deci-
+sion variables between agents in the presence of honest-
+but-curious agents.
+2) External eavesdroppers learn no private information of
+the agents.
+■
+Theorem 3 gives privacy preservation guarantees in the
+presence of honest-but-curious agents and external eavesdrop-
+pers. The privacy preservation of Algorithm 1 can be proved
+from secure multi-party computation (SMC) perspective. Be-
+fore giving detailed privacy analyses and proofs, we first
+introduce some concepts of SMC.
+Definition 1 (Computational indistinguishability [29]). Let
+{Dκ}κ∈N and {Eκ}κ∈N be two distribution ensembles with
+security parameter κ; If for any non-uniform probabilistic
+polynomial-time algorithm G, δ(κ) is negligible, where
+δ(κ) =
+����
+Pr
+x1←Dκ[G(x1) = 1] −
+Pr
+x2←Eκ[G(x2) = 1]
+����
+(36)
+we say that {Dκ}κ∈N and {Eκ}κ∈N are computationally
+indistinguishable, denoted as Dκ
+c≡ Eκ.
+■
+Therefore, Definition 1 states that any polynomial-time
+algorithm cannot distinguish two computationally indistin-
+guishable ensembles because the outputs of those algorithms
+do not significantly differ. In what follows, Definition 2
+presents the standard privacy notion in SMC.
+Definition 2 ([30], [31]). Let Π be an m-party protocol
+for computing the outputs of function F(¯x) where ¯x =
+{x1, . . . , xm} and Fρ(¯x) denotes the ρth output of F(¯x). Let
+M = {M1, . . . , Mm} denote the set of parties. The view
+of the ρth party during the execution of Π is denoted by
+VIEWΠ
+ρ (¯x). We say that Π privately computes F(¯x) if there
+exists a polynomial-time algorithm S, such that for every party
+Mρ in M, we have
+S(ρ, xρ, Fρ(¯x))
+c≡ VIEWΠ
+ρ (¯x).
+(37)
+■
+Definition 2 states that the security of an m-party protocol
+can be evaluated based on computational indistinguishability,
+i.e., the view of the parties can be efficiently simulated based
+solely on their inputs and outputs. In other words, SMC allows
+a group of participants to learn the correct outputs of some
+agreed-upon function applied to their private inputs without
+revealing anything else. The theoretical underpinnings of Def-
+inition 1 and Definition 2 can help prove that Algorithm 1
+securely computes π1 ˜P , . . . , πn ˜P between the agents.
+The detailed proofs of Theorem 3 can be found in AP-
+PENDIX D.
+V. SIMULATION RESULTS
+A simplified single-phase IEEE 13-bus test feeder [32] is
+used to verify the proposed decentralized privacy-preserving
+DER control strategy. In specific, each bus, except the feeder
+head, is assumed to be connected with 2 houses and each house
+is equipped with an ESS and 5 solar panels that can generate
+maximum 2.5 kW solar output. The maximum capacity of all
+residential ESSs are 10 kWh, the initial SoCs of all ESSs are
+uniformly set to be 4 kWh, and the maximum charging and
+discharging rates are ±3 kW, respectively [33]. The forecasted
+solar PV generation is chosen from 01/01/2021 with ∆T = 15
+mins in California from CAISO [34].
+In total c = 4 clouds are responsible for message aggrega-
+tion and distribution. The degree of all polynomials is set to
+be d−1 = 3 and the integer field is chosen as E = [0, 231−1).
+For the fixed-point number quantization, the basis, magnitude,
+and resolution are uniformly set to be θ = 2, γ = 27, and
+ζ = 4, respectively. For the distribution network shown in
+Fig. 1, all 24 houses are assumed to be located in the same
+area with identical solar radiation. The baseline load profiles
+
+8
+00:00
+04:00
+08:00
+12:00
+16:00
+20:00
+24:00
+Time
+0.6
+0.8
+1.0
+1.2
+1.4
+1.6
+Power (kW)
+(a) Heterogeneous baseline loads of 24
+houses
+00:00
+04:00
+08:00
+12:00
+16:00
+20:00
+24:00
+Time
+0.0
+0.5
+1.0
+1.5
+2.0
+Solar PV generations (kW)
+(b) Solar power injection of 24 houses
+00:00
+04:00
+08:00
+12:00
+16:00
+20:00
+24:00
+Time
+−1.00
+−0.75
+−0.50
+−0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+Charging/discharging (kW)
+(c) Charging and discharging power from
+24 ESSs
+00:00
+04:00
+08:00
+12:00
+16:00
+20:00
+24:00
+Time
+0
+5
+10
+15
+20
+25
+Power (kW)
+(d) Power flows of 12 lines in the
+distribution network
+Fig. 5. The optimal solutions of (P2) by controlling DERs in the distribution network.
+of all houses are shown in Fig. 5(a) [34]. The primal and dual
+step sizes are chosen based on experience to be αv
+ν,ℓ = 2.3,
+αe
+σ,ℓ = 1.8, and βµlι,ℓ = 5×10−4, respectively. Note that only
+the lower bound of power flow limits in (16) is active, herein,
+only the results related to µlι are presented.
+Fig. 5(b) and Fig. 5(c) show the active power generations
+and the charging/discharging power from the solar PVs and
+ESSs, respectively. At around 12:00, the solar PVs generate
+the maximum amount of energy, and the ESSs charge at
+peak rates. After 16:00, energy stored in ESSs is extracted to
+supply in-home use and compensate for the power loss in the
+distribution network. The power flows of 12 lines are shown
+in Fig. 5(d) where no inverse flows occur. Moreover, accurate
+primal and dual solutions are achieved without affecting the
+anticipated primal-dual convergence. The iterative solutions
+of the primal and dual variables are shown in Fig. 6.
+Fig.
+0
+20
+40
+60
+80
+100
+Iterations
+0.0
+0.5
+1.0
+1.5
+2.0
+˜pν
+(a) Convergence of solar PVs’ decision
+variables ˜pν
+0
+100
+200
+300
+400
+500
+600
+700
+Iterations
+0.00
+0.01
+0.02
+0.03
+0.04
+0.05
+µlι
+(b) Convergence of the dual variable µlι
+Fig. 6. Convergence of the primal and dual variables
+Fig. 7. Random shares generated by Bus 6 at different iterations
+7 presents normalized shares generated by Bus 6 using the
+random polynomial y(ℓ)
+6 (z) = ω(ℓ)
+6
++ a(ℓ)
+1 z + a2z2 + a(ℓ)
+3 z3
+where the coefficients a(ℓ)
+i , i = 1, 2, 3 are randomized at each
+iteration and different time slots. The privacy preservation of
+Algorithm 1 against external eavesdroppers are guaranteed
+because external eavesdroppers have insufficient information
+in polynomial reconstruction by wiretapping the transmitted
+shares. Without loss of generality, suppose bus 6 is honest-
+but-curious. Fig. 8 shows the existence of a simulator that
+−1
+0
+1
+×1015
+True polynomial y6(z)
+−100
+−75
+−50
+−25
+0
+25
+50
+75
+100
+−1
+0
+1
+×1015
+Simulated polynomial ˜y′
+6(z)
+True constructed polynomial ˜y6(z)
+Fig. 8.
+Polynomials simulated by a simulator to achieve computational
+indistinguishability among agents
+can generate true polynomial y6(z) and simulated polyno-
+mials y′
+i(z) (dashed lines), ∀i = 1, . . . , n, i ̸= 6, such that
+(π6 ˜P )′ = π6 ˜P . Therefore, the computational indistinguisha-
+bility ˜y′
+6(αj)
+c≡ ˜y6(αj), ∀j = 1, . . . , c is satisfied at any
+iteration and any time slot, and herein π1 ˜P , . . . , πn ˜P can
+be securely computed among buses and the ith bus can only
+know the information contained in its own view VIEWi.
+VI. CONCLUSION
+This
+paper
+proposed
+a
+novel
+decentralized
+privacy-
+preserving algorithm with cloud computing architecture for
+DER control in distribution networks. The DER control prob-
+lem was formulated into a constrained optimization problem
+with the objectives of minimizing the line loss, PV curtailment
+cost, and ESS degradation cost. By integrating SS into the
+decentralized PGM, the proposed approach achieved privacy
+preservation for DER owners’ private data, including the
+DERs’ generation, consumption and daily electricity usage.
+The security of the proposed approach was proved rigor-
+ously with privacy guarantees and analyses against honest-but-
+curious agents and external eavesdroppers. Simulation results
+verified the applicability of the proposed approach on the
+modified IEEE 13-bus test feeder with controllable ESSs
+and solar PVs. Moreover, the designed methodology can be
+readily used in general large-scale decentralized optimization
+problems in the context of privacy preservation provisions.
+APPENDIX A
+DERIVATION OF THE PGM UPDATES
+We take the IEEE 13-bus test feeder in Fig. 1 for example
+to illustrate the derivation of subgradients in (18). To prove
+
+0.5
+0.4
+0.3
+0.2
+0.1
+0.0
+00:00
+04:00
+08:00
+104
+12:00
+103
+16:00
+102
+Time
+20:00
+101
+24:009
+(18a), we firstly consider the subgradient of the power loss
+minimization objective, the active power loss is
+f1(pg
+1, . . . , pg
+n) = δ1
+�
+lij∈L
+rij
+�∥Pij∥2
+2
+V 2
+0
+�
+= δ1¯r
+V 2
+0
+�
+ι∈L
+∥Pι∥2
+2
+=
+¯δ1
+2
+�
+ι∈L
+∥Pι∥2
+2.
+(38)
+Take (15) into (38), we have
+f1(pg
+1, . . . , pg
+n) =
+¯δ1
+2
+�
+ι∈L
+∥ ˜Zι ˜P ∥2
+2.
+(39)
+Without loss of generality, assume the νth PV with decision
+variable ˜pν is connected at bus i, we have
+∇ ˜pνL(·) = δ1∇ ˜pνf1(pg
+1, . . . , pg
+n) + δ2∇ ˜pνf2(˜pν)
++
+L
+�
+ι=1
+∇ ˜pνµT
+uι( ˜Zι ˜P −Pι)−
+L
+�
+ι=1
+∇ ˜pνµT
+lι ˜Zι ˜P . (40)
+Substitute (14) and (38) into the first term of (40), we have
+δ1∇ ˜pνf1(·) =
+¯δ1
+2 ∇ ˜pν
+�
+ι∈L
+∥ ˜Zι ˜P ∥2
+2
+= ¯δ1
+�
+ι∈L
+�
+∇ ˜pν ˜Zι
+n
+�
+ˆı=1
+∆ˆı ˜pˆı
+� �
+˜Zι ˜P
+�
+= ¯δ1
+�
+ι∈L
+�
+˜Zι∆i
+�T �
+˜Zι ˜P
+�
+.
+(41)
+Take the subgradient of (5), the second term in (40) becomes
+δ2∇ ˜pνf2(˜pν) = δ2∇ ˜pν∥˜pν − pv
+ν∥2
+2 = 2δ2 (˜pν − pv
+ν) . (42)
+Then, substitute (14) into the third term of (40) on the right
+hand side, we have
+L
+�
+ι=1
+∇ ˜pνµT
+uι( ˜Zι ˜P − Pι) =
+L
+�
+ι=1
+∇ ˜pνµT
+uι ˜Zι(
+n
+�
+ˆı=1
+∆ˆı ˜pˆı)
+=
+L
+�
+ι=1
+( ˜Zι∆i)
+Tµuι.
+(43)
+Similarly, the last term of (40) can be readily obtained as
+−
+L
+�
+ι=1
+∇ ˜pνµT
+lι( ˜Zι ˜P ) = −
+L
+�
+ι=1
+( ˜Zι∆i)
+Tµlι.
+(44)
+Finally, by substituting (41), (42), (43), (44) into (40), (18a)
+is readily proved. Following similar lines, subgradients of the
+primal variable ˆpσ in (18b) can be readily proved.
+APPENDIX B
+PROOF OF THEOREM 2
+Proof: To prove the correctness of Algorithm 1, we show
+that the proposed method has the same primal and dual
+solutions as the non-privacy PGM. Recall that the uth cloud
+multiplies the received n outputs by the elements of πi
+according to (31), it yields
+�
+�
+�
+�
+�
+πi(1)y1(αu) = πi(1)
+�
+ω1 + a1,1αu + · · · + a1,d−1αd−1
+u
+�
+...
+πi(n)yn(αu) = πi(n)
+�
+ωn + an,1αu + · · · + an,d−1αd−1
+u
+�
+(45)
+Then, the aggregated outputs �n
+ˆı=1 πi(ˆı)yˆı(αu) in (31) can be
+obtained by summing the left hand side of (45). Therefore, in
+total c pairs of shares from all clouds as in (32) can be seen
+as the inputs and outputs of a polynomial
+˜y(z) =
+n
+�
+ˆı=1
+πi(ˆı)ωˆı + ˜a1z + · · · + ˜ad−1zd−1
+(46)
+where ˜aˆȷ = �n
+ˆı=1 πi(ˆı)aˆı,ˆȷ, ˆȷ = 1, . . . , d−1 and �n
+ˆı=1 πi(ˆı)ωˆı
+is exactly πi ˜P . Then, the aggregated secret πi ˜P can be
+readily retrieved by using c pairs of shares in (33) since d ≤ c,
+as stated by Theorem 1.
+APPENDIX C
+PROOF OF PROPOSITION 1
+Proof: Under the collusion of d − 1 clouds, they can
+construct the following set of equations
+�
+�
+�
+�
+�
+˜yi(α1) = ˜ω + ˜ai,1α1 + · · · + ˜ai,d−1αd−1
+1
+...
+˜yi(αd−1) = ˜ω + ˜ai,1αd−1 + · · · + ˜ai,d−1αd−1
+d−1
+(47)
+where ˜yi(z) is defined in (34) and ˜ω = πi ˜P . In (47), ˜ai,ı,
+∀ı = 1, . . . , d − 1 and ˜ω are unknown, therefore the d − 1
+clouds can yield in total d − 1 equations yet d unknowns that
+leads to underdetermined solutions.
+APPENDIX D
+PROOF OF THEOREM 3
+Proof: To prove the privacy preservation of Algorithm
+1 against honest-but-curious agents, we aim at verifying
+that whatever an honest-but-curious agent receives can be
+efficiently simulated. That being said, the honest-but-curious
+agent cannot retrieve useful information from others using the
+received data because it cannot distinguish the received data
+from its own. During the ℓth iteration of executing Algorithm
+1, the view of bus i can be described via
+VIEWi = {α1, . . . , αc, θ, γ, ζ, πi ˜P , yi(z), ωi, ¯
+Ai,
+˜yi(αj), ∀j = 1, . . . , c, Cp, Cd}.
+(48)
+Based on Definition 2, we need to prove the existence of a
+polynomial-time algorithm, denoted as simulator S, that can
+simulate VIEWi using the data of agent i, i.e.,
+S(Ξi)
+c≡ VIEWi
+(49)
+where Ξi ≜ {α1, . . . , αc, θ, γ, ζ, πi ˜P , yi(z), ωi, ¯
+Ai, ˜yi(αj),
+∀j = 1, . . . , c, Cp, Cd} denotes the set of data that agent
+i has access to. Manifesting (49) indicates that whatever
+agent i receives can be efficiently reconstructed based on its
+own knowledge Ξi. To this end, the simulator is required to
+generate ˜y′
+i(αj),∀j = 1, . . . , c that satisfy
+˜y′
+i(αj)
+c≡ ˜yi(αj), ∀j = 1, . . . , c.
+(50)
+To achieve this goal, the simulator firstly generates secrets
+w′
+j̸=i ∈ E of other agents such that
+πi ˜P = wi +
+�
+j̸=i
+w′
+j.
+(51)
+
+10
+Then it generates a set of random polynomials as in (30) to
+obtain y′
+j(z), ∀j ̸= i with w′
+j, ∀j ̸= i as the corresponding
+constant terms, i.e.,
+�
+yi(z) = wi + ai,1z + · · · + ai,d−1zd−1
+(52a)
+y′
+j(z) = w′
+j + a′
+i,1z + · · · + a′
+i,d−1zd−1, ∀j ̸= i.
+(52b)
+Consequently, the simulator can use {α1, . . . , αc} as inputs
+for (52) and obtain
+˜
+A′
+i =
+�
+�
+�αˆȷ, yi(αˆȷ) +
+�
+j̸=i
+y′
+j(αˆȷ), ∀, ˆȷ = 1, . . . , c
+�
+�
+� .
+(53)
+By Theorem 1 and Theorem 2, the shares in (53) can be
+used to construct a new polynomial in the form of
+˜y′
+i(x) = (πi ˜P )′ + ˜a′
+i,1z + · · · + ˜a′
+i,d−1zd−1
+(54)
+where (πi ˜P )′ = πi ˜P . Therefore, (50) and (49) hold, by
+Definition 2, Algorithm 1 securely computes π1 ˜P , . . . , πn ˜P
+between the agents.
+In what follows, we prove the privacy preservation of Al-
+gorithm 1 against external eavesdroppers. Under Assumption
+1, assume agent 1 is safe from external eavesdroppers, by
+wiretapping any other agents’ communication channels, an
+external eavesdropper can at most have access to
+Ξe=
+�
+α1,. . ., αc,yi(αu), ¯
+Au,i, ∀i=2,. . ., n,u=1, . . ., c
+�
+.
+(55)
+Since (55) is insufficient to formulate (33), the external eaves-
+dropper is incapable of inferring either yi(z)’s or ˜y′
+i(z)’s,
+i.e., unable to infer agents’ private information pi’s or the
+aggregated message πi ˜P ’s.
+REFERENCES
+[1] J. Campbell, “Ancillary services provided from DER,” Oak Ridge
+National Lab, Oak Ridge, TN, United States, Tech. Rep., 2005.
+[2] J. R. Aguero, E. Takayesu, D. Novosel, and R. Masiello, “Modernizing
+the grid: Challenges and opportunities for a sustainable future,” IEEE
+Power Energy Mag., vol. 15, no. 3, pp. 74–83, 2017.
+[3] I.-K. Song, W.-W. Jung, J.-Y. Kim, S.-Y. Yun, J.-H. Choi, and S.-J.
+Ahn, “Operation schemes of smart distribution networks with distributed
+energy resources for loss reduction and service restoration,” IEEE Trans.
+Smart Grid, vol. 4, no. 1, pp. 367–374, 2012.
+[4] D. K. Molzahn, F. D¨orfler, H. Sandberg, S. H. Low, S. Chakrabarti,
+R. Baldick, and J. Lavaei, “A survey of distributed optimization and
+control algorithms for electric power systems,” IEEE Trans. Smart Grid,
+vol. 8, no. 6, pp. 2941–2962, 2017.
+[5] M. Zeraati, M. E. H. Golshan, and J. M. Guerrero, “Distributed control
+of battery energy storage systems for voltage regulation in distribution
+networks with high PV penetration,” IEEE Trans. Smart Grid, vol. 9,
+no. 4, pp. 3582–3593, 2016.
+[6] Q. Zhang, Y. Guo, Z. Wang, and F. Bu, “Distributed optimal conservation
+voltage reduction in integrated primary-secondary distribution systems,”
+IEEE Trans. Smart Grid, vol. 12, no. 5, pp. 3889–3900, 2021.
+[7] Y. Pan, A. Sangwongwanich, Y. Yang, and F. Blaabjerg, “Distributed
+control of islanded series PV-battery-hybrid systems with low communi-
+cation burden,” IEEE Trans. Power Electron., vol. 36, no. 9, pp. 10 199–
+10 213, 2021.
+[8] T. Navidi, A. El Gamal, and R. Rajagopal, “A two-layer decentralized
+control architecture for DER coordination,” in Proc. IEEE Conf. Decis.
+Control, Miami, FL, USA, Dec. 17-29 2018, pp. 6019–6024.
+[9] W. Lin and E. Bitar, “Decentralized stochastic control of distributed
+energy resources,” IEEE Trans. Power Syst., vol. 33, no. 1, pp. 888–
+900, 2017.
+[10] X. Huo and M. Liu, “Two-facet scalable cooperative optimization of
+multi-agent systems in the networked environment,” IEEE Trans. Control
+Syst. Technol., vol. 30, no. 6, pp. 2317–2332, 2022.
+[11] C. Dwork, F. McSherry, K. Nissim, and A. Smith, “Calibrating noise
+to sensitivity in private data analysis,” in Proc. Theory Cryptogr. Conf.,
+New York, NY, USA, Mar. 4-7 2006, pp. 265–284.
+[12] J. Dong, T. Kuruganti, S. Djouadi, M. Olama, and Y. Xue, “Privacy-
+preserving aggregation of controllable loads to compensate fluctuations
+in solar power,” in Proc. IEEE Electron. Power Grid, Charleston, SC,
+USA, Nov. 12-14 2018, pp. 1–5.
+[13] S. Han, U. Topcu, and G. J. Pappas, “Differentially private distributed
+constrained optimization,” IEEE Trans. Autom. Control, vol. 62, no. 1,
+pp. 50–64, 2016.
+[14] M. B. Gough, S. F. Santos, T. AlSkaif, M. S. Javadi, R. Castro, and
+J. P. Catal˜ao, “Preserving privacy of smart meter data in a smart grid
+environment,” IEEE Trans. Ind. Inform., vol. 18, no. 1, pp. 707–718,
+2021.
+[15] R. Lu, X. Liang, X. Li, X. Lin, and X. Shen, “EPPA: An efficient
+and privacy-preserving aggregation scheme for secure smart grid com-
+munications,” IEEE Trans. Parallel Distrib. Syst., vol. 23, no. 9, pp.
+1621–1631, 2012.
+[16] A. Mohammadali and M. S. Haghighi, “A privacy-preserving homomor-
+phic scheme with multiple dimensions and fault tolerance for metering
+data aggregation in smart grid,” IEEE Trans. Smart Grid, vol. 12, no. 6,
+pp. 5212–5220, 2021.
+[17] Z. Cheng, F. Ye, X. Cao, and M.-Y. Chow, “A homomorphic encryption-
+based private collaborative distributed energy management system,”
+IEEE Trans. Smart Grid, vol. 12, no. 6, pp. 5233–5243, 2021.
+[18] S. Wang, Q. Hu, Y. Sun, and J. Huang, “Privacy preservation in location-
+based services,” IEEE Commun. Mag., vol. 56, no. 3, pp. 134–140, 2018.
+[19] R. Gilad-Bachrach, K. Laine, K. Lauter, P. Rindal, and M. Rosulek,
+“Secure data exchange: A marketplace in the cloud,” in Proc. ACM
+SIGSAC Conf. Cloud Comput. Security Workshop, London, UK, Nov.
+11 2019, pp. 117–128.
+[20] A. Shamir, “How to share a secret,” Commun. ACM, vol. 22, no. 11,
+pp. 612–613, 1979.
+[21] M. Nabil, M. Ismail, M. M. Mahmoud, W. Alasmary, and E. Serpedin,
+“PPETD: Privacy-preserving electricity theft detection scheme with load
+monitoring and billing for AMI networks,” IEEE Access, vol. 7, pp.
+96 334–96 348, 2019.
+[22] X. Huo and M. Liu, “Distributed privacy-preserving electric vehicle
+charging control based on secret sharing,” Electr. Power Syst. Res., vol.
+211, p. 108357, 2022.
+[23] M. Baran and F. F. Wu, “Optimal sizing of capacitors placed on a radial
+distribution system,” IEEE Trans. Power Deliv., vol. 4, no. 1, pp. 735–
+743, 1989.
+[24] M. Farivar, L. Chen, and S. Low, “Equilibrium and dynamics of local
+voltage control in distribution systems,” in Proc. IEEE Conf. Decis.
+Control, Florence, Italy, Dec. 10-13 2013, pp. 4329–4334.
+[25] J. Li, Z. Xu, J. Zhao, and C. Zhang, “Distributed online voltage control
+in active distribution networks considering PV curtailment,” IEEE Trans.
+Ind. Inform., vol. 15, no. 10, pp. 5519–5530, 2019.
+[26] J. Forman, J. Stein, and H. Fathy, “Optimization of dynamic battery
+parameter characterization experiments via differential evolution,” in
+Proc. Am. Control Conf., Washington, DC, USA, Jun. 17-19 2013, pp.
+867–874.
+[27] M. S. Daru and T. Jager, “Encrypted cloud-based control using secret
+sharing with one-time pads,” in Proc. IEEE Conf. Decis. Control, Nice,
+France, Dec. 11-13 2019, pp. 7215–7221.
+[28] J. Humpherys and T. J. Jarvis, Foundations of Applied Mathematics,
+Volume I: Mathematical Analysis.
+Soc. Ind. Appl. Math, 2020.
+[29] O. Goldreich, Foundations of Cryptography: Volume 2, Basic Applica-
+tions.
+Cambridge Univ. Press, 2009.
+[30] D. Evans, V. Kolesnikov, and M. Rosulek, “A pragmatic introduction to
+secure multi-party computation,” Found. Trends Privacy Security, vol. 2,
+no. 2-3, pp. 70–246, 2018.
+[31] O. Goldreich, “Secure multi-party computation,” Manuscript. Prelimi-
+nary Version, vol. 78, p. 110, 1998.
+[32] M. Liu, P. K. Phanivong, Y. Shi, and D. S. Callaway, “Decentralized
+charging control of electric vehicles in residential distribution networks,”
+IEEE Trans. Control Syst. Technol., vol. 27, no. 1, pp. 266–281, 2019.
+[33] National Renewable Energy Laboratory. Residential battery storage.
+[Online].
+Available:
+https://atb.nrel.gov/electricity/2021/residential
+battery storage
+[34] U.S.
+Energy
+Information
+Administration.
+Electric
+power
+annual.
+[Online]. Available: https://www.eia.gov/todayinenergy/detail.php?id=
+49276
+
diff --git a/E9E0T4oBgHgl3EQfQwCg/content/tmp_files/load_file.txt b/E9E0T4oBgHgl3EQfQwCg/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..739c2bfd1dad561a34fec2c1ac9b0423984ac3c8
--- /dev/null
+++ b/E9E0T4oBgHgl3EQfQwCg/content/tmp_files/load_file.txt
@@ -0,0 +1,1213 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf,len=1212
+page_content='1  Privacy-Preserving Distributed Energy Resource  Control with Decentralized Cloud Computing  Xiang Huo, Graduate Student Member, IEEE, Mingxi Liu, Member, IEEE  Abstract—The rapidly growing penetration of renewable en-  ergy resources brings unprecedented challenges to power distri-  bution networks – management of a large population of grid-  tied controllable devices encounters control scalability crises and  potential end-user privacy breaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Despite the importance,  research on privacy preservation of distributed energy resource  (DER) control in a fully scalable manner is lacked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To fill the  gap, this paper designs a novel decentralized privacy-preserving  DER control framework that 1) achieves control scalability over  DER population and heterogeneity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 2) eliminates peer-to-peer  communications and secures the privacy of all participating  DERs against various types of adversaries;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' and 3) enjoys higher  computation efficiency and accuracy compared to state-of-the-  art privacy-preserving methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' A strongly coupled optimization  problem is formulated to control the power consumption and  output of DERs, including solar photovoltaics and energy storage  systems, then solved using the projected gradient method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Cloud  computing and secret sharing are seamlessly integrated into the  proposed decentralized computing to achieve privacy preserva-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Simulation results prove the capabilities of the proposed  approach in DER control applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Index Terms—Decentralized optimization, distributed energy  resources, privacy preservation, secret sharing  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' INTRODUCTION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Related Works  L  ARGE-scale deployment of distributed energy resources  (DERs) has proven efficacy in reducing carbon footprint  and providing grid-edge services such as voltage control, load  following, and backup power supply [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' DERs, including  energy storage systems (ESSs), solar photovoltaic (PV), and  electric vehicles (EVs), along with other monitoring and  controllable devices, can offer significant opportunities for  advancing efficient, reliable, and cost-effective power grids [2],  [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Though integrating DERs into power grids can provide  multifarious benefits, such as enhanced energy efficiency and  economic boost, the high penetration of DERs raises surging  challenges on the scalability of existing control strategies [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  To address the aforementioned challenges in large-scale  DER control problems, distributed and decentralized control  strategies are drawing increased attention owing to their  superior scalability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' For instance, a distributed coordination  method based on local droop control and consensus control  was designed in [5] to deal with the voltage rise problem  caused by the high penetration of solar PVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' in [6]  proposed an asynchronous distributed leader-follower control  strategy that optimally schedules DERs to lower the voltage  The authors are with the Department of Electrical and Computer Engineer-  ing, University of Utah, Salt Lake City, UT 84112 USA (e-mail: xiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='huo,  mingxi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='liu@utah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='edu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  for peak load shaving and long-term energy saving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To reduce  the communication burden, a distributed low-communication  algorithm was proposed in [7] to control islanded PV-battery-  hybrid systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Though distributed methods can achieve  scalability, they generically suffer from massive peer-to-peer  communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To overcome this issue, Navidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' in  [8] developed a two-layer decentralized DER coordination  architecture that can scale the solution to large networks, and  no direct communication is required between local controllers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  In [9], a decentralized stochastic control strategy was designed  for radial distribution systems with controllable PVs and ESSs  to minimize the demand balancing cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Huo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' in [10] pro-  posed a decentralized shrunken primal-multi-dual subgradient  algorithm with dimension reduction to achieve scalability w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  both agent population size and network dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Despite the superior scalability and communication effi-  ciency of decentralized methods, their implementation has  been significantly hampered by the vulnerability to privacy  breaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Furthermore, both distributed and decentralized  strategies rely heavily on mandatory communications which  can disclose users’ sensitive information and expose system  vulnerabilities to adversaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Differential privacy (DP) has re-  ceived substantial attention in addressing privacy concerns due  to its rigorous mathematical formulation [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' DP-based meth-  ods add persistent randomized perturbations to the datasets,  constraints, or objective functions for privacy preservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  In [12], a DP-based aggregation algorithm is proposed to  compensate for solar power fluctuations and protect users’  personal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' in [13] developed a distributed  optimization algorithm based on DP to preserve the privacy  of the participating agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Gough et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' in [14] designed an  innovative DP-compliant algorithm to ensure that the data  from consumers’ smart meters are protected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Despite the  success in privacy preservation, DP-based methods inevitably  suffer from accuracy loss due to the added perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  In contrast, encryption-based strategies achieve privacy  preservation with high accuracy by encrypting the original  data into cyphertexts, and only those holding private keys  can decrypt the cyphertexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' in [15] proposed an  efficient and privacy-preserving aggregation scheme for smart  grid communications, in which the data is encrypted by Paillier  cryptosystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In [16], a privacy-preserving and fault-tolerant  scheme was designed based on homomorphic cryptosystem  to achieve secure aggregation of metering data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Similarly,  Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' in [17] proposed a novel private collaborative  distributed energy management system based on homomorphic  encryption to solve the privacy issues in distribution systems  and microgirds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Despite the high accuracy, the drawback  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='02198v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='OC]  5 Jan 2023  2  of encryption-based methods lies in the prevalent comput-  ing overhead caused by encryption and decryption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Other  hardware-integrated privacy-preserving methods, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', garbled  circuit [18], [19], are deficient in flexibility and uneconomic  due to the hardware cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Secret sharing (SS) [20] is a lightweight cryptographic  method that can securely distribute a secret among a group  of participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Each participant will be allocated a share  of the secret, and only through the collaboration of certain  participants where the number of participants is greater than a  threshold can the secret be reconstructed from their shares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Adopting SS, Nabil et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' in [21] designed an SS-based  detection scheme to identify malicious consumers who steal  electricity, in which system operators only collect masked  meter readings from the consumers to avoid privacy vio-  lation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In [22], an SS-based EV charging control protocol  was developed to achieve privacy-preserving EV charging  control for overnight valley filling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Compared with encryption-  based strategies, SS-based methods can preserve privacy while  avoiding the heavy computational load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Despite the superiority,  few research studied the integration of SS into DER control  due to the highly complex distribution network structure, large  DER population, and lack of theoretical support in privacy  guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To fill these gaps, this paper designs a novel SS-  based privacy-preserving algorithm that merits high efficiency,  security, and accuracy for large-scale DER control problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Statement of Contributions  The contribution of this paper is three-fold: 1) We propose  a novel decentralized privacy-preserving algorithm that con-  currently achieves scalability and privacy in large-scale DER  control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To the best of our knowledge, this is the first paper  that proposes a decentralized SS-based algorithm for DER  privacy preservation, in which decentralized solutions, privacy  guarantees, and rigorous security proofs are provided;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 2) The  proposed method eliminates the frequent peer-to-peer commu-  nications and secures the privacy of the participating DERs  against various types of adversaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The designed framework  serves as a benchmark for secure and scalable DER control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 3)  Compared to state-of-the-art approaches, the proposed method  can achieve lower computational overhead and identically  accurate solutions as the non-privacy-concerned algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  The rest of this paper is organized as follows: In Sec-  tion II, we construct the models of distribution networks,  PVs, and ESSs, then formulate the DER control problem  into a constrained optimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Section III derives  the decentralized solution via the projected gradient method  and presents the corresponding DER aggregation and control  strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The SS-based privacy-preserving DER control al-  gorithm and privacy analyses are provided in Section IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' We  give simulation results and analyses in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Section VI  concludes this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' PROBLEM FORMULATION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Branch Flow Model  Consider an n-bus radial distribution network where B =  {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , n} denotes the set of buses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let lij denote the line  segment connecting buses i and j, L = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , h} denote  the set of lines, Cj denote the set of bus j’s child buses, Vj  denote the voltage magnitude at bus j, Pij and Qij denote  the active and reactive power flow from bus i to bus j,  respectively, and rij and xij be the resistance and reactance of  line lij, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' For bus j, let pc  j and qc  j denote the active  and reactive power consumptions, respectively, and pg  j and qg  j  denote its active and reactive power generations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  To simplify the network model, a nonlinear DistFlow model  [23] can be linearized to the LinDistFlow model by omitting  the higher order terms with negligible error [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore,  this paper adopts the LinDistFlow model, represented as  Pij −  �  u∈Cj  Pju = pc  j − pg  j  (1a)  Qij −  �  u∈Cj  Qju = qc  j − qg  j  (1b)  V 2  i − V 2  j = 2(rijPij + xijQij).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (1c)  A radial 13-bus distribution network connected with rooftop  solar PVs and ESSs is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1 and will be used as an  example throughout this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  10  3  2  11  6  7  5  9  8  4  1  0  P1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  A radial 13-bus distribution network connected with rooftop solar  PVs and ESSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  In this paper, one control objective is to minimize the  total power loss of the distribution network by controlling the  dynamics of PVs and ESSs, which is approximated by  f1(pg  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , pg  n) =  �  lij∈L  rij  �∥Pij∥2  2 + ∥Qij∥2  2  V 2  0  �  (2)  where V0 denotes the nominal voltage magnitude, pg  j, Pij, and  Qij ∈ RT are augmented vectors of pg  j, Pij, and Qij across T  time intervals, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Note that we only consider active  power loss and assume reactive power flows Qij to be constant  vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Though the reactive power loss is not included here for  simplicity, it can be added without affecting algorithm design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  The active power flows are constrained by  0 ≤ Pij ≤ Pij  (3)  where Pij denotes the maximum active power flow limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Solar Photovoltaic  Let V denote the set of in total V solar PVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' During T time  intervals of a day, the active power injection ˜pν ∈ RT from  the νth PV inverter should satisfy  0 ≤ ˜pν ≤ pv  ν  (4)  田田3  where pv  ν denotes the maximum active power injection and is  assumed to be known by the forecast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Herein, the curtailment  cost can be calculated by [25]  f2(˜pν) = ∥˜pν − pv  ν∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (5)  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Energy Storage System  Let S denote the set of E ESSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The charging/discharging  power ˆpσ ∈ RT of the σth ESS is constrained by  − ps  σ ≤ ˆpσ ≤ ps  σ  (6)  where ps  σ and ps  σ denote the maximum discharging and  charging power, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let s0  σ denote the initial state of  charge (SoC) of the σth ESS and Hσ ≜ [s0  σ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , s0  σ]T ∈ RT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Aggregate the charging/discharging power across T time in-  tervals, then the capacity of the σth ESS is constrained by  pa  σ ≤ Hσ + Aˆpσ∆T ≤ pa  σ  (7)  where pa  σ and pa  σ denote its lower and upper capacity  bounds, respectively, ∆T denotes the sampling time, and  the aggregation matrix A is lower triangular consisting of  ones and zeros, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', element Aˆı,ˆȷ = 1 if ˆı ≥ ˆȷ, element  Aˆı,ˆȷ = 0 if ˆı < ˆȷ, ∀ˆı, ˆȷ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, the SoCs of  ESS σ during T time slots are obtained by aggregating the  charging/discharging power using A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Furthermore, the σth ESS’s degradation cost is calculated in  terms of the smoothness of charging and discharging by [26]  f3(ˆpσ) = ∥B ˆpσ∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (8)  where B calculates discharging/charging differences between  adjacent times, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', Bˆı,ˆı = 1, ∀ˆı = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , T, Bˆı,ˆı+1 =  −1, ∀ˆı = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , T − 1, and all other elements are zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Problem Formulation  The optimization problem is then formulated to minimize  the summation of total active power loss, PV curtailment cost,  and ESS degradation cost within the distribution network as  min  ˜p, ˆp  δ1f1(pg) +  V  �  ν=1  δ2f2(˜pν) +  E  �  σ=1  δ3f3(ˆpσ)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (1a), (3), (4), (6), (7)  (P1)  where  ˜p  =  [˜pT  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , ˜pT  n]T,  ˆp  =  [ˆpT  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , ˆpT  n]T, pg  =  [pg  1  T, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , pg  n  T]T, and δα denotes the cost coefficient asso-  ciated with the objective function fα(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Note that the cost  coefficients are constants that allow flexible adjustments on  the weights of the global and local objective functions and  regulate different units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' DECENTRALIZED OPTIMIZATION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Projected Gradient Method  This paper achieves scalability in solving (P1) via projected  gradient method (PGM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' PGM decomposes a centralized opti-  mization problem into local optimizations at agents, resulting  in a paralleled computing structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let M = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , m}  denote the set of agents, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', buses or DERs, who work  cooperatively in solving (P1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In this setting, the κth agent  updates its decision variable xκ using PGM by  x(ℓ+1)  κ  = PXκ[x(ℓ)  κ − γ(ℓ)  κ Φκ(x(ℓ))]  (9)  where  ℓ  denotes  the  iteration  number,  x(ℓ)  =  [x(ℓ)  1  T, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , x(ℓ)  m  T]T  includes  all  decision  variables,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=',  ˜pν and ˆpσ in problem (P1), γ(ℓ)  k  denotes the step size, Φκ(·)  denotes the gradient of the Lagrangian w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' x(ℓ)  κ , and PXκ[·]  denotes the projection operation onto set Xκ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  In (P1), the local constraint of the νth PV in (4) and local  constraints of the σth ESS in (6) and (7) can be represented  by two feasible sets Pv  ν and Pe  σ as  Pv  ν ≜ {˜pν| 0 ≤ ˜pν ≤ pv  ν}  (10a)  Pe  σ ≜ {ˆpσ| − ps  σ≤ˆpσ≤ps  σ, pa  σ≤H+Aˆpσ∆T ≤ pa  σ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' (10b)  In what follows, aiming at reducing the number of coupling  terms, we rewrite the networked constraints in (1a) and (3) to  a single inequality constraint based on the network topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  To this end, we first represent the active power flows in (1a)  through active power generations of each bus using  pi = ˜pi − ˆpi − pc  i  (11)  where pi denotes the aggregated active power generation at  bus i, ˜pi = �Vi  ν=1 ˜pν and ˆpi = �Ei  σ=1 ˆpσ denote the aggre-  gated active power of all PVs and ESSs that are connected at  bus i, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Vi and Ei denote the total number of PVs  and ESSs connected at bus i, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  For the ιth line flow Pι in the distribution network, the  from-bus is defined by the bus where the flow begins, and the  to-bus set is defined by the set of buses that the ιth line flow  travels to till reaching the edge of the distribution network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Let Z ∈ Rn×n denote the adjacency matrix of the distribution  network and Zι denote the ιth row of Z that represents the  adjacency vector of the ιth line flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let Zι(i) denote the ith  element of Zι, and Zι(i) = 1 if the ιth power flow has bus i  as a to-bus, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', Z9 = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Then, the  power flows in the distribution network can be represented by  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Expand Z across T time slots, we have  ˜Z =  �  ����  Z1(1)I Z1(2)I · · · Z1(n)I  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Zn(1)I Zn(2)I · · · Zn(n)I  �  ����  (12)  where I∈RT ×T denotes the identity matrix and ˜Z ∈ RnT ×nT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  In what follows, let ˜P ∈ RnT denote the aggregated active  power generations defined in (11) from all buses, we have  ˜P =  �  ��  p1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  pn  �  �� =  �  ����  �V1  ν=1 ˜pν − �E1  σ=1 ˆpσ − pc  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  �Vn  ν=Vn−1+1 ˜pν − �En  σ=En−1+1 ˆpσ − pc  n  �  ���� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (13)  Furthermore, ˜P can be rewritten compactly as  ˜P =  n  �  i=1  ∆i (˜pi − ˆpi − pc  i)  (14)  4  where ∆i denotes the aggregation matrix whose ith block is  represented by the identity matrix I, and all other blocks are  zeros, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', ∆1 = [I, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , 0]T ∈ RnT ×T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Then, the active  power flow of the ιth line can be calculated by  Pι = ˜Zι ˜P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (15)  Consequently, the power flow limit constraint in (3) becomes  0 ≤ ˜Zι ˜P ≤ Pι.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (16)  Therefore, problem (P1) can be written into  min  ˜p, ˆp  δ1f1(pg) +  V  �  ν=1  δ2f2(˜pν) +  E  �  σ=1  δ3f3(ˆpσ)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  pν ∈ Pv  ν, ∀ν ∈ V  pσ ∈ Pe  σ, ∀σ ∈ S  0 ≤ ˜Zι ˜P ≤ Pι, ∀ι ∈ L  (P2)  The optimization problem in (P2) seeks to find the optimal  decision variables, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', charging and discharging power ˜pσ’s  of the ESSs and the active power injection ˆpν’s of the PVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In  what follows, we focus on solving (P2) through a decentralized  fashion based on PGM defined in (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To solve (P2) via PGM,  we firstly derive its relaxed Lagrangian as  L(˜p, ˆp, µl, µu) = δ1f1(pg) +  V  �  ν=1  δ2f2(˜pν) +  E  �  σ=1  δ3f3(ˆpσ)  +  L  �  ι=1  µT  uι( ˜Zι ˜P − Pι)−  L  �  ι=1  µT  lι ˜Zι ˜P (17)  where µl = [µT  l1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , µT  lL]T and µu = [µT  u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , µT  uL]T, µlι  and µuι denote the dual variables associated with lower and  upper power flow limits of the line ι, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Suppose ˜pν and ˆpσ are decision variables of the νth PV and  σth ESS connected at bus i, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Take the subgradients  of (17) w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' the primal variables ˜pν and ˆpσ, we have  ∇ ˜pνL(·) = 2δ2(˜pν − pv  ν) + 2δ1  V 2  0  L  �  ι=1  rι( ˜Zι∆i)T( ˜Zι ˜P )  +  L  �  ι=1  ( ˜Zι∆i)T(µuι − µlι)  (18a)  ∇ ˆpσL(·) = 2δ3 ˆpσ − 2δ1  V 2  0  L  �  ι=1  rι( ˜Zι∆i)T( ˜Zι ˜P )  −  L  �  ι=1  ( ˜Zι∆i)T(µuι − µlι).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (18b)  Without affecting the efficacy of the algorithm design, we  assume all power lines have the same resistance ¯r for the  simplicity of presentation, herein (18) becomes  ∇ ˜pνL(·) = 2δ2(˜pν − pv  ν) + ¯δ1πi ˜P + ψi(µu − µl)  (19a)  ∇ ˆpσL(·) = 2δ3 ˆpσ − ¯δ1πi ˜P − ψi(µu − µl)  (19b)  where ¯δ1 = 2δ1  V 2  0 ¯r, πi = �L  ι=1( ˜Zι∆i)T ˜Zι, and ψi denotes the  ith column block of ˜Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  The detailed derivation of the Lagrangian subgradients in  (19) can be found in APPENDIX A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Therefore, based on the calculated subgradients in (18), at  the ℓth iteration, the νth PV and the σth ESS can update their  decision variables using PGM by  ˜p(ℓ+1)  ν  = ΠPvν  �  ˜p(ℓ)  ν  − αv  ν,ℓ∇ ˜pνL(ℓ) (·)  �  (20a)  ˆp(ℓ+1)  σ  = ΠPeσ  �  ˆp(ℓ)  σ − αe  σ,ℓ∇ ˆpσL(ℓ) (·)  �  (20b)  where αv  ν,ℓ and αe  σ,ℓ denote the primal step sizes of the νth PV  and the σth ESS, respectively, L(ℓ) (·) denotes the calculated  Lagrangian in (17) at the ℓth iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The dual variables can  be updated similarly using PGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' DER Aggregation and Control  In PGM iterations, the ith agent needs to calculate Φi(xℓ)  in (9) where the decision variables xi’s from all other agents  are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' As indicated in (19), calculating subgradients  ∇ ˜pνL(·) and ∇ ˆpσL(·) indeed requires the decision variables  ˜P from all the agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Specifically, the calculation of subgra-  dients in (19a) and (19b) are coupled through  C = Cp + Cd = ¯δ1πi ˜P + ψi(µu − µl)  (21)  where Cp and Cd denote the coupling terms associated with  the primal and dual variables, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  To clearly demonstrate the information exchange needs in  subgradient calculation, we exemplify the primal update of the  ˆνth PV connected at bus 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The ˆνth PV can update its decision  variable ˜pˆν using the subgradient in (19a) which is  ∇ ˜pˆνL(·) = 2δ2(˜pˆν − pv  ˆν) +  2  �  ι=1  �  ¯δ1πι ˜P + µuι + µlι  �  (22)  where π1 ˜P = �n  i=1 pi and π2 ˜P = p2 + p3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, the  ˆνth PV requires the active power generations pi, ∀i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , n  from all buses to conduct the update in (20a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Based on the above observations, two different aggregation  and control strategies, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', Bus-level aggregation and control  and DER-level aggregation and control, can be applied as  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In bus-level aggregation and control,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' the ith  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Each bus aggregates the decision  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='variables                   ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='and  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='DERs exchange decision variables  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='with others to obtain  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='and  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='˜pi=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='XVi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='⌫=1 ˜p⌫  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content='XEi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='�=1 ˆp�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='<latexit sha1_base64="J1PqXdAVQ0WCWiXxcnVQymKUhI=">ACSXicbVDPSxtBFJ6N2qaprWl79DIYCp7CbhG0B0EshR4jGBWycX07mSD82OZeSuEYf+9Xnrf9DLx4s4snZuIf648EwH9/3vpn3vryQwmEc/4laK6tr163Ter97v9H98PHEmdIyPmRGnuWg+NSaD5EgZKfFZaDyiU/zS+/1frpFbdOGH2Mi4KPFcy0mAoGKise5HOAX2aGzlxCxUuX1RVJqjfr2jqSpX51ImZgv2kSrWRQgl05z5VgHMG0n8PvdWLTzS+Kuv24n68LPocJA3okaYGWfd  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content='Each individual PV or ESS owns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='decision variable     ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='or     ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='to itself  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='˜p⌫  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content='The ith bus performs the primal-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='dual updates for all the DERs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Each DER performs the primal-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='dual update in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' (22) and (23)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='End iteration if : DERs’ decision variables achieve convergence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Aim: Calculate subgradients               ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='and               ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='for the updates in PGM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='r˜p⌫L(·)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content='XV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content='Buses exchange decision variables  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='with others to obtain  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='8i=1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content='and  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content='Individual bus acts an agent to  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='calculate subgradients  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='and  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='DER-level aggregation and control  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Bus-level aggregation and control  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Aggregation and control of DERs via bus-level and DER-level  architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  bus (agent) aggregates the decision variables ˜pi = �Vi  ν=1 ˜pν  5  and ˆpi = �Ei  σ=1 ˆpσ where only aggregated decision variables  are transmitted and used for the primal updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In contrast,  DER-level control strategies require each DER to act as an  agent and receive all data of others that is demanded for  updates in (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' However, due to the large number of DERs  connected to the distribution network, DER-level control can  suffer from massive data exchange and heavy local computa-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, we adopt the bus-level aggregation and control  scheme which is more computing and communicating effi-  cient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' We will later show that the proposed privacy-preserving  algorithm can be readily extended to the DER-level control  (See Remark 1 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Apart from scalability and efficiency, the inevitable private  information exposure in both bus-level and DER-level methods  raises fundamental privacy concerns, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', the electrical load  can reveal sensitive business activities and/or customer’s daily  routines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To address the privacy concerns, we will develop  a novel SS-based algorithm to achieve secure information  exchange in executing (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' SS-BASED PRIVACY-PRESERVING DER CONTROL  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Real Number to Integer Quantization  Note that the SS scheme requires modular arithmetic instead  of real arithmetic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' However, decentralized optimization ge-  netically requires real number calculations, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', real decision  variables and parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, a real number to integer  transformation is needed to integrate SS into decentralized  optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' We adopt the fixed-point number quantization  [27] to map the real numbers onto the integer space and the  fixed-point real-number set is defined by  Qθ,γ,ζ≜  �  −θγ, −θγ + θ−ζ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , θγ − 2θ−ζ, θγ − θ−ζ�  (23)  where θ ∈ N1+ denotes the basis, γ ∈ N denotes the  magnitude, and ζ ∈ N denotes the resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, by  defining a surjective mapping m(·) : R �→ Qθ,γ,ζ, a real  number can be mapped to the closest point in Qθ,γ,ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To limit  the quantization error, the mapping m(·) needs to satisfy  |m(ϕ) − ϕ| ≤ θ−ζ, ∀ϕ ∈ [−θγ, θγ]  (24)  where the quantization error is restricted by the resolution  within the range of Qθ,γ,ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To map the real-number set onto  the integer set Z, we simply scale Qθ,γ,ζ by θζ as  Zθ,γ,ζ = θζQθ,γ,ζ=  �  −θγ+ζ, −θγ+ζ+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , θγ+ζ−1  �  (25)  where Zθ,γ,ζ ⊆ Z denotes the fixed-point set in the integer  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Moreover, the SS requires the inputs to be within the  field E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, we further map each element in z ∈ Zθ,γ,ζ  onto E with the modular operation as  g(z) = z mod e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (26)  Note that z ∈ Zθ,γ,ζ can be any negative integer, and the  modular operation in (26) will change the sign of a negative  input, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', g(ˆz) = ˆz + e for ˆz < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To address the negative  integer operation, we introduce the partial inverse of g(·) as  ψ(z) =  � z − e  if z ≥ e  2,  z  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (27)  Therefore, we can readily obtain z = ψ(g(z)), ∀z ∈ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' SS-based Privacy-Preserving Algorithm  1) Shamir’s secret sharing scheme: Before introducing the  privacy-preserving algorithm design, we first briefly intro-  duce Shamir’s SS scheme [20] which merits an efficient and  lightweight private information distribution structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Suppose  a manager (secret holder) seeks to distribute a secret ω to  specific agents and mandates the cooperation of at least d  agents to retrieve the secret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In such needs, Shamir’s SS is  grounded on the following idea of Lagrange interpolation for  secret distribution and recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Theorem 1 (Polynomial interpolation [28]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let {(ς1, y1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' ,  (ςd, yd)} ⊆ R2 be a set of points whose values of ςı are all  distinct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Then there exists a unique polynomial Y of degree  d − 1 that satisfies yı = Y(ςı), ∀ı = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  ■  In SS-based schemes, the manager first constructs a random  polynomial of degree d − 1 as  y(z) = ω + a1z + · · · + ad−1zd−1  (28)  where ω denotes an integer secret, a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , ad−1 are random  coefficients that are uniformly distributed in the field E ≜  [0, e), and e denotes a prime number that is larger than ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Secondly, the manager calculates the outputs of (28) with  non-zero integer inputs, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', setting τ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , n to retrieve  (τ, y(τ)) where yΠ  τ  = y(τ) mod e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Then, the share yΠ  τ  is  distributed to agent τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Lastly, at least d agents with shares  are required to reconstruct the polynomial based on Theorem  1 and hence recover the secret ω by  ω =  d  �  τ=1  yΠ  τ  d  �  υ=0  υ̸=τ  υ  υ − τ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (29)  2) Proposed privacy-preserving algorithm: We next present  the proposed two-layer decentralized privacy-preserving al-  gorithm based on SS in a bus-level aggregation and control  architecture, to achieve privacy preservation and scalability  concurrently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In the distribution network layer, all DERs’ deci-  sion variables are updated in parallel, and only masked data are  sent from each bus to the servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In the cloud computing layer,  the servers calculate the aggregated messages and distribute  them to the related buses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The computing structure of the  proposed privacy-preserving algorithm is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Cloud Computing  Distribution  Network  ESS  Solar  PV  Server  Secure  Data Flow  Secure  Data Flow  Bus  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Two-layer privacy-preserving computing structure for DER control in  distribution networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  田田Compute20066  Let C denote the set of clouds and c ≥ 2 denotes the total  number of clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The ith bus generates a random polynomial  of order d − 1 using (28) to obtain  y(ℓ)  i (z) = ω(ℓ)  i  + a(ℓ)  i,1z + · · · + a(ℓ)  i,d−1zd−1  (30)  where 2 ≤ d ≤ c, ω(ℓ)  i  denotes the secret of bus i at the ℓth  iteration, ℓ denotes the iteration number, and a(ℓ)  i,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , a(ℓ)  i,d−1  denote random coefficients that are uniformly distributed in the  field E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Note that for a vector secret such as pi, we refer to an  elementwise calculation of the vector using (30) by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  At the ℓth iteration, the uth cloud firstly generates a random  integer α(ℓ)  u , then it broadcasts α(ℓ)  u  to all the buses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Subse-  quently, the ith bus can calculate y(ℓ)  i (α(ℓ)  u ), ∀u = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , c  using the received inputs based on (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Finally, the ith bus  sends y(ℓ)  i (α(ℓ)  u ) back to the uth cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Note that the coupling  term πi ˜P in (21) is a linear combination of all pi’s that  requires the private generation/consumption details from the  buses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, a secure computation framework of πi ˜P is  required to preserve the privacy of buses and DER owners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Suppose the clouds are aware of the network topology  matrix Z which contains no private information of the buses  or DERs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In order to calculate the aggregated information πi ˜P  for bus i, the uth cloud firstly multiplies the received outputs  y1(α(ℓ)  u ), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , yn(α(ℓ)  u ) utilizing the coefficients of πi to obtain  {α(ℓ)  u , πi(1)y(ℓ)  1 (α(ℓ)  u ), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , πi(n)y(ℓ)  n (α(ℓ)  u )}  (31)  Then, the uth cloud sums the outputs in (31) to obtain a new  pair of input and output as  ¯  Au,i = {α(ℓ)  u ,  n  �  ˆı=1  πi(ˆı) y(ℓ)  ˆı (α(ℓ)  u )}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (32)  Finally, the uth cloud calculates  ¯  Au,i, ∀i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , n and  broadcasts the new input-output share ¯  Au,i to the ith bus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Therefore, after receiving new shares from in total c clouds  servers, the ith bus now has access to  ˜  Ai =  �  α(ℓ)  ˆȷ ,  n  �  ˆı=1  πi(ˆı) y(ℓ)  ˆı (α(ℓ)  ˆȷ ), ∀ˆȷ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (33)  Note that ˜  Ai contains in total c shares that can construct a  new polynomial of the form  ˜y(ℓ)  i (z) = πi ˜P + ˜a(ℓ)  i,1z + · · · + ˜a(ℓ)  i,d−1zd−1  (34)  whose constant term is exactly πi ˜P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  During this information exchange process, each bus only  sends a single share to each server so that a single cloud server  is incapable of reconstructing the secret based on the received  shares, and herein cannot infer agents’ true decision variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  The cloud servers only need to calculate aggregated messages  using outputs of randomized polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The details of the  proposed method are presented via Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Algorithm 1 can achieve privacy preservation while main-  taining exact solutions as non-privacy PGM-based methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  The decision variables will be continuously updated till the  convergence errors ϵ(ℓ)  ν  ≜ ∥˜p(ℓ)  ν − ˜p(ℓ−1)  ν  ∥2  2 and ϵ(ℓ)  σ  ≜ ∥ˆp(ℓ)  σ −  ˆp(ℓ−1)  σ  ∥2  2 are smaller than the threshold ϵ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The correctness of  Algorithm 1 is presented via Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='IEEE 13 bus network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Decentralized  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='updates  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Cloud  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='Aggregation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='y(`)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='3 (↵(`)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='1 )  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content=' Information exchange structure between the distribution network and  cloud servers (only the messages sent from bus 3 and cloud 1 are labeled).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Algorithm 1 Decentralized SS-based privacy-preserving DER  control strategy  1: Agents initialize decision variables, tolerance ϵ0, basis θ,  magnitude γ, resolution ζ, iteration counter ℓ = 0, and  maximum iteration ℓmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , α(ℓ)  c  to obtain y(ℓ)  i (α(ℓ)  1 ), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' ,  y(ℓ)  i (α(ℓ)  c ), then sends y(ℓ)  i (α(ℓ)  u ) to the uth cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  6:  The uth cloud formulates ¯  Au,i in (32), then broadcasts  ¯  Au,i to the ith bus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  7:  The ith bus formulates  ˜  Ai in (33), reconstructs the  aggregated secrets using c shares to obtain πi ˜P , then  calculates Cp in (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  8:  The ith bus transforms Cp back to real numbers  using (27), then decision variables ˜p(ℓ)  ν  or ˆp(ℓ)  σ  of DERs  connected at bus i are updated by PGM using (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The ith  bus calculates the error ϵ(ℓ)  ν  or ϵ(ℓ)  σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  9:  ℓ = ℓ + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  10: end while  Theorem 2 (Correctness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let E denote the domain of the  input secrets ω1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , ωn, and Cp denote the desired outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Then, Algorithm 1 satisfies:  Pr  �  ∀c ≥ d, Rec  �  A, E, Z, ¯δ1, θ, γ, ζ  �  = Cp  �  = 1  (35)  where A = { ˜  A1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , ˜  Ac} denotes the set of shares from  agents, Pr[·] denotes probability, and Rec(·) denotes the secret  reconstruction operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  ■  Theorem 2 states that Algorithm 1 can correctly retrieve  the aggregated information Cp which would be further used to  achieve exact primal and dual updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Compute田田7  The detailed proof of Theorem 2 can be found in AP-  PENDIX B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Remark 1 : Though Algorithm 1 is developed based on bus-  level aggregation and control, it can also be extended to the  DER-level aggregation and control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In DER-level aggregation  and control, each DER is required to generate a polynomial in  (30) and act as an independent agent in secret reconstruction  using (33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Besides, depending on the practical applications,  DERs can also be clustered and controlled by the household  or district where the new clusters act as agents, following the  similar design of Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  □  Remark 2: The multi-server architecture seamlessly integrates  the SS scheme into DER aggregation and control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Shares  generated from buses were aggregated and broadcasted to the  buses by a group of servers for the purpose of secret retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  The aggregation task is distributed to multiple servers to ensure  that a single server cannot retrieve any secrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  □  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Privacy Analysis  The proposed approach aims at protecting the decision  variables of the DERs whose disclosure can lead to the leakage  of customers’ sensitive information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To resolve this issue, Al-  gorithm 1 achieves privacy preservation against two types of  adversaries, including honest-but-curious-agent who follows  the algorithm but may utilize the possessed and received data  to infer the private information of other agents, and external  eavesdroppers who wiretap and intercept exchanged messages  from communication channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Proposition 1: (Secure cloud computing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In Algorithm 1, any  cloud number less than d − 1 cannot infer any information of  the aggregated decision variables Cp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  ■  Proposition 1 presents the security of the proposed al-  gorithm against corrupted clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Based on the polynomial  interpolation in Theorem 1, at least d clouds are required to  retrieve any secret through collusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Proposition 1 is proved based on the correctness analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Please refer to APPENDIX C for the detailed proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Assumption 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' At least one communication link of an indi-  vidual agent is secure against external eavesdroppers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  ■  Assumption 1 is essential and generically used in SS-  based schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Given d pairs of shares sent via different  communication links, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', {(ς1, y1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , (ςd, yd)} ⊆ R2, if  an external eavesdropper wiretap all communication links to  gain access to the shares, then it can simply deduce the secret  by Lagrangian interpolation using Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Theorem 3 (Privacy preservation against adversaries).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' By  using Algorithm 1, the following two statements stand:  1) Algorithm 1 securely computes and updates the deci-  sion variables between agents in the presence of honest-  but-curious agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  2) External eavesdroppers learn no private information of  the agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  ■  Theorem 3 gives privacy preservation guarantees in the  presence of honest-but-curious agents and external eavesdrop-  pers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The privacy preservation of Algorithm 1 can be proved  from secure multi-party computation (SMC) perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Be-  fore giving detailed privacy analyses and proofs, we first  introduce some concepts of SMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Definition 1 (Computational indistinguishability [29]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let  {Dκ}κ∈N and {Eκ}κ∈N be two distribution ensembles with  security parameter κ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' If for any non-uniform probabilistic  polynomial-time algorithm G, δ(κ) is negligible, where  δ(κ) =  ����  Pr  x1←Dκ[G(x1) = 1] −  Pr  x2←Eκ[G(x2) = 1]  ����  (36)  we say that {Dκ}κ∈N and {Eκ}κ∈N are computationally  indistinguishable, denoted as Dκ  c≡ Eκ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  ■  Therefore, Definition 1 states that any polynomial-time  algorithm cannot distinguish two computationally indistin-  guishable ensembles because the outputs of those algorithms  do not significantly differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In what follows, Definition 2  presents the standard privacy notion in SMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Definition 2 ([30], [31]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let Π be an m-party protocol  for computing the outputs of function F(¯x) where ¯x =  {x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , xm} and Fρ(¯x) denotes the ρth output of F(¯x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Let  M = {M1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , Mm} denote the set of parties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The view  of the ρth party during the execution of Π is denoted by  VIEWΠ  ρ (¯x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' We say that Π privately computes F(¯x) if there  exists a polynomial-time algorithm S, such that for every party  Mρ in M, we have  S(ρ, xρ, Fρ(¯x))  c≡ VIEWΠ  ρ (¯x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (37)  ■  Definition 2 states that the security of an m-party protocol  can be evaluated based on computational indistinguishability,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', the view of the parties can be efficiently simulated based  solely on their inputs and outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In other words, SMC allows  a group of participants to learn the correct outputs of some  agreed-upon function applied to their private inputs without  revealing anything else.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The theoretical underpinnings of Def-  inition 1 and Definition 2 can help prove that Algorithm 1  securely computes π1 ˜P , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , πn ˜P between the agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  The detailed proofs of Theorem 3 can be found in AP-  PENDIX D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' SIMULATION RESULTS  A simplified single-phase IEEE 13-bus test feeder [32] is  used to verify the proposed decentralized privacy-preserving  DER control strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In specific, each bus, except the feeder  head, is assumed to be connected with 2 houses and each house  is equipped with an ESS and 5 solar panels that can generate  maximum 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='5 kW solar output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The maximum capacity of all  residential ESSs are 10 kWh, the initial SoCs of all ESSs are  uniformly set to be 4 kWh, and the maximum charging and  discharging rates are ±3 kW, respectively [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The forecasted  solar PV generation is chosen from 01/01/2021 with ∆T = 15  mins in California from CAISO [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  In total c = 4 clouds are responsible for message aggrega-  tion and distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The degree of all polynomials is set to  be d−1 = 3 and the integer field is chosen as E = [0, 231−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  For the fixed-point number quantization, the basis, magnitude,  and resolution are uniformly set to be θ = 2, γ = 27, and  ζ = 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' For the distribution network shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1, all 24 houses are assumed to be located in the same  area with identical solar radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The baseline load profiles  8  00:00  04:00  08:00  12:00  16:00  20:00  24:00  Time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='6  Power (kW)  (a) Heterogeneous baseline loads of 24  houses  00:00  04:00  08:00  12:00  16:00  20:00  24:00  Time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='0  Solar PV generations (kW)  (b) Solar power injection of 24 houses  00:00  04:00  08:00  12:00  16:00  20:00  24:00  Time  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='00  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='75  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='50  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='00  Charging/discharging (kW)  (c) Charging and discharging power from  24 ESSs  00:00  04:00  08:00  12:00  16:00  20:00  24:00  Time  0  5  10  15  20  25  Power (kW)  (d) Power flows of 12 lines in the  distribution network  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The optimal solutions of (P2) by controlling DERs in the distribution network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  of all houses are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5(a) [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The primal and dual  step sizes are chosen based on experience to be αv  ν,ℓ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='3,  αe  σ,ℓ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='8, and βµlι,ℓ = 5×10−4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Note that only  the lower bound of power flow limits in (16) is active, herein,  only the results related to µlι are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5(b) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5(c) show the active power generations  and the charging/discharging power from the solar PVs and  ESSs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' At around 12:00, the solar PVs generate  the maximum amount of energy, and the ESSs charge at  peak rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' After 16:00, energy stored in ESSs is extracted to  supply in-home use and compensate for the power loss in the  distribution network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The power flows of 12 lines are shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5(d) where no inverse flows occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Moreover, accurate  primal and dual solutions are achieved without affecting the  anticipated primal-dual convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The iterative solutions  of the primal and dual variables are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  0  20  40  60  80  100  Iterations  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='0  ˜pν  (a) Convergence of solar PVs’ decision  variables ˜pν  0  100  200  300  400  500  600  700  Iterations  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='05  µlι  (b) Convergence of the dual variable µlι  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Convergence of the primal and dual variables  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Random shares generated by Bus 6 at different iterations  7 presents normalized shares generated by Bus 6 using the  random polynomial y(ℓ)  6 (z) = ω(ℓ)  6  + a(ℓ)  1 z + a2z2 + a(ℓ)  3 z3  where the coefficients a(ℓ)  i , i = 1, 2, 3 are randomized at each  iteration and different time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The privacy preservation of  Algorithm 1 against external eavesdroppers are guaranteed  because external eavesdroppers have insufficient information  in polynomial reconstruction by wiretapping the transmitted  shares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Without loss of generality, suppose bus 6 is honest-  but-curious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 8 shows the existence of a simulator that  −1  0  1  ×1015  True polynomial y6(z)  −100  −75  −50  −25  0  25  50  75  100  −1  0  1  ×1015  Simulated polynomial ˜y′  6(z)  True constructed polynomial ˜y6(z)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Polynomials simulated by a simulator to achieve computational  indistinguishability among agents  can generate true polynomial y6(z) and simulated polyno-  mials y′  i(z) (dashed lines), ∀i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , n, i ̸= 6, such that  (π6 ˜P )′ = π6 ˜P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, the computational indistinguisha-  bility ˜y′  6(αj)  c≡ ˜y6(αj), ∀j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , c is satisfied at any  iteration and any time slot, and herein π1 ˜P , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , πn ˜P can  be securely computed among buses and the ith bus can only  know the information contained in its own view VIEWi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' CONCLUSION  This  paper  proposed  a  novel  decentralized  privacy-  preserving algorithm with cloud computing architecture for  DER control in distribution networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' The DER control prob-  lem was formulated into a constrained optimization problem  with the objectives of minimizing the line loss, PV curtailment  cost, and ESS degradation cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' By integrating SS into the  decentralized PGM, the proposed approach achieved privacy  preservation for DER owners’ private data, including the  DERs’ generation, consumption and daily electricity usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  The security of the proposed approach was proved rigor-  ously with privacy guarantees and analyses against honest-but-  curious agents and external eavesdroppers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Simulation results  verified the applicability of the proposed approach on the  modified IEEE 13-bus test feeder with controllable ESSs  and solar PVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Moreover, the designed methodology can be  readily used in general large-scale decentralized optimization  problems in the context of privacy preservation provisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  APPENDIX A  DERIVATION OF THE PGM UPDATES  We take the IEEE 13-bus test feeder in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1 for example  to illustrate the derivation of subgradients in (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To prove  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='0  00:00  04:00  08:00  104  12:00  103  16:00  102  Time  20:00  101  24:009  (18a), we firstly consider the subgradient of the power loss  minimization objective, the active power loss is  f1(pg  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , pg  n) = δ1  �  lij∈L  rij  �∥Pij∥2  2  V 2  0  �  = δ1¯r  V 2  0  �  ι∈L  ∥Pι∥2  2  =  ¯δ1  2  �  ι∈L  ∥Pι∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (38)  Take (15) into (38), we have  f1(pg  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , pg  n) =  ¯δ1  2  �  ι∈L  ∥ ˜Zι ˜P ∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (39)  Without loss of generality, assume the νth PV with decision  variable ˜pν is connected at bus i, we have  ∇ ˜pνL(·) = δ1∇ ˜pνf1(pg  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , pg  n) + δ2∇ ˜pνf2(˜pν)  +  L  �  ι=1  ∇ ˜pνµT  uι( ˜Zι ˜P −Pι)−  L  �  ι=1  ∇ ˜pνµT  lι ˜Zι ˜P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' (40)  Substitute (14) and (38) into the first term of (40), we have  δ1∇ ˜pνf1(·) =  ¯δ1  2 ∇ ˜pν  �  ι∈L  ∥ ˜Zι ˜P ∥2  2  = ¯δ1  �  ι∈L  �  ∇ ˜pν ˜Zι  n  �  ˆı=1  ∆ˆı ˜pˆı  � �  ˜Zι ˜P  �  = ¯δ1  �  ι∈L  �  ˜Zι∆i  �T �  ˜Zι ˜P  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (41)  Take the subgradient of (5), the second term in (40) becomes  δ2∇ ˜pνf2(˜pν) = δ2∇ ˜pν∥˜pν − pv  ν∥2  2 = 2δ2 (˜pν − pv  ν) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' (42)  Then, substitute (14) into the third term of (40) on the right  hand side, we have  L  �  ι=1  ∇ ˜pνµT  uι( ˜Zι ˜P − Pι) =  L  �  ι=1  ∇ ˜pνµT  uι ˜Zι(  n  �  ˆı=1  ∆ˆı ˜pˆı)  =  L  �  ι=1  ( ˜Zι∆i)  Tµuι.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (43)  Similarly, the last term of (40) can be readily obtained as  −  L  �  ι=1  ∇ ˜pνµT  lι( ˜Zι ˜P ) = −  L  �  ι=1  ( ˜Zι∆i)  Tµlι.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (44)  Finally, by substituting (41), (42), (43), (44) into (40), (18a)  is readily proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Following similar lines, subgradients of the  primal variable ˆpσ in (18b) can be readily proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  APPENDIX B  PROOF OF THEOREM 2  Proof: To prove the correctness of Algorithm 1, we show  that the proposed method has the same primal and dual  solutions as the non-privacy PGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Recall that the uth cloud  multiplies the received n outputs by the elements of πi  according to (31), it yields  �  �  �  �  �  πi(1)y1(αu) = πi(1)  �  ω1 + a1,1αu + · · · + a1,d−1αd−1  u  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  πi(n)yn(αu) = πi(n)  �  ωn + an,1αu + · · · + an,d−1αd−1  u  �  (45)  Then, the aggregated outputs �n  ˆı=1 πi(ˆı)yˆı(αu) in (31) can be  obtained by summing the left hand side of (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, in  total c pairs of shares from all clouds as in (32) can be seen  as the inputs and outputs of a polynomial  ˜y(z) =  n  �  ˆı=1  πi(ˆı)ωˆı + ˜a1z + · · · + ˜ad−1zd−1  (46)  where ˜aˆȷ = �n  ˆı=1 πi(ˆı)aˆı,ˆȷ, ˆȷ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , d−1 and �n  ˆı=1 πi(ˆı)ωˆı  is exactly πi ˜P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Then, the aggregated secret πi ˜P can be  readily retrieved by using c pairs of shares in (33) since d ≤ c,  as stated by Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  APPENDIX C  PROOF OF PROPOSITION 1  Proof: Under the collusion of d − 1 clouds, they can  construct the following set of equations  �  �  �  �  �  ˜yi(α1) = ˜ω + ˜ai,1α1 + · · · + ˜ai,d−1αd−1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  ˜yi(αd−1) = ˜ω + ˜ai,1αd−1 + · · · + ˜ai,d−1αd−1  d−1  (47)  where ˜yi(z) is defined in (34) and ˜ω = πi ˜P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' In (47), ˜ai,ı,  ∀ı = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , d − 1 and ˜ω are unknown, therefore the d − 1  clouds can yield in total d − 1 equations yet d unknowns that  leads to underdetermined solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  APPENDIX D  PROOF OF THEOREM 3  Proof: To prove the privacy preservation of Algorithm  1 against honest-but-curious agents, we aim at verifying  that whatever an honest-but-curious agent receives can be  efficiently simulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' That being said, the honest-but-curious  agent cannot retrieve useful information from others using the  received data because it cannot distinguish the received data  from its own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' During the ℓth iteration of executing Algorithm  1, the view of bus i can be described via  VIEWi = {α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , αc, θ, γ, ζ, πi ˜P , yi(z), ωi, ¯  Ai,  ˜yi(αj), ∀j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , c, Cp, Cd}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (48)  Based on Definition 2, we need to prove the existence of a  polynomial-time algorithm, denoted as simulator S, that can  simulate VIEWi using the data of agent i, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=',  S(Ξi)  c≡ VIEWi  (49)  where Ξi ≜ {α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , αc, θ, γ, ζ, πi ˜P , yi(z), ωi, ¯  Ai, ˜yi(αj),  ∀j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , c, Cp, Cd} denotes the set of data that agent  i has access to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Manifesting (49) indicates that whatever  agent i receives can be efficiently reconstructed based on its  own knowledge Ξi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' To this end, the simulator is required to  generate ˜y′  i(αj),∀j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , c that satisfy  ˜y′  i(αj)  c≡ ˜yi(αj), ∀j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (50)  To achieve this goal, the simulator firstly generates secrets  w′  j̸=i ∈ E of other agents such that  πi ˜P = wi +  �  j̸=i  w′  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (51)  10  Then it generates a set of random polynomials as in (30) to  obtain y′  j(z), ∀j ̸= i with w′  j, ∀j ̸= i as the corresponding  constant terms, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=',  �  yi(z) = wi + ai,1z + · · · + ai,d−1zd−1  (52a)  y′  j(z) = w′  j + a′  i,1z + · · · + a′  i,d−1zd−1, ∀j ̸= i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (52b)  Consequently, the simulator can use {α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , αc} as inputs  for (52) and obtain  ˜  A′  i =  �  �  �αˆȷ, yi(αˆȷ) +  �  j̸=i  y′  j(αˆȷ), ∀, ˆȷ = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , c  �  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (53)  By Theorem 1 and Theorem 2, the shares in (53) can be  used to construct a new polynomial in the form of  ˜y′  i(x) = (πi ˜P )′ + ˜a′  i,1z + · · · + ˜a′  i,d−1zd−1  (54)  where (πi ˜P )′ = πi ˜P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Therefore, (50) and (49) hold, by  Definition 2, Algorithm 1 securely computes π1 ˜P , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' , πn ˜P  between the agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  In what follows, we prove the privacy preservation of Al-  gorithm 1 against external eavesdroppers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Under Assumption  1, assume agent 1 is safe from external eavesdroppers, by  wiretapping any other agents’ communication channels, an  external eavesdropper can at most have access to  Ξe=  �  α1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', αc,yi(αu), ¯  Au,i, ∀i=2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', n,u=1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  (55)  Since (55) is insufficient to formulate (33), the external eaves-  dropper is incapable of inferring either yi(z)’s or ˜y′  i(z)’s,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', unable to infer agents’ private information pi’s or the  aggregated message πi ˜P ’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  REFERENCES  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Campbell, “Ancillary services provided from DER,” Oak Ridge  National Lab, Oak Ridge, TN, United States, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Aguero, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Takayesu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Novosel, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Masiello, “Modernizing  the grid: Challenges and opportunities for a sustainable future,” IEEE  Power Energy Mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 74–83, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [3] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Song, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Jung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Yun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Choi, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Ahn, “Operation schemes of smart distribution networks with distributed  energy resources for loss reduction and service restoration,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Smart Grid, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 367–374, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [4] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Molzahn, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' D¨orfler, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Sandberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Low, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Chakrabarti,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Baldick, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Lavaei, “A survey of distributed optimization and  control algorithms for electric power systems,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Smart Grid,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 2941–2962, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Zeraati, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Golshan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Guerrero, “Distributed control  of battery energy storage systems for voltage regulation in distribution  networks with high PV penetration,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Smart Grid, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 9,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 3582–3593, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [6] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Guo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Wang, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Bu, “Distributed optimal conservation  voltage reduction in integrated primary-secondary distribution systems,”  IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Smart Grid, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 3889–3900, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Pan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Sangwongwanich, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Yang, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Blaabjerg, “Distributed  control of islanded series PV-battery-hybrid systems with low communi-  cation burden,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Power Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 36, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 10 199–  10 213, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [8] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Navidi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' El Gamal, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Rajagopal, “A two-layer decentralized  control architecture for DER coordination,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Decis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Control, Miami, FL, USA, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 17-29 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 6019–6024.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [9] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Lin and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Bitar, “Decentralized stochastic control of distributed  energy resources,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Power Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 888–  900, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [10] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Huo and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Liu, “Two-facet scalable cooperative optimization of  multi-agent systems in the networked environment,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Control  Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 30, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 2317–2332, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [11] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Dwork, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' McSherry, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Nissim, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Smith, “Calibrating noise  to sensitivity in private data analysis,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Theory Cryptogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=',  New York, NY, USA, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 4-7 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 265–284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Dong, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Kuruganti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Djouadi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Olama, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Xue, “Privacy-  preserving aggregation of controllable loads to compensate fluctuations  in solar power,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' IEEE Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Power Grid, Charleston, SC,  USA, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 12-14 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Han, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Topcu, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Pappas, “Differentially private distributed  constrained optimization,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Autom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Control, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 62, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 50–64, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Gough, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Santos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' AlSkaif, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Javadi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Castro, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Catal˜ao, “Preserving privacy of smart meter data in a smart grid  environment,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Ind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 707–718,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [15] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Liang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Lin, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Shen, “EPPA: An efficient  and privacy-preserving aggregation scheme for secure smart grid com-  munications,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Parallel Distrib.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  1621–1631, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Mohammadali and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Haghighi, “A privacy-preserving homomor-  phic scheme with multiple dimensions and fault tolerance for metering  data aggregation in smart grid,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Smart Grid, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 6,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5212–5220, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [17] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Cheng, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Ye, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Cao, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Chow, “A homomorphic encryption-  based private collaborative distributed energy management system,”  IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Smart Grid, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5233–5243, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Sun, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Huang, “Privacy preservation in location-  based services,” IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 56, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 134–140, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Gilad-Bachrach, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Laine, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Lauter, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Rindal, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Rosulek,  “Secure data exchange: A marketplace in the cloud,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' ACM  SIGSAC Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Cloud Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Security Workshop, London, UK, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  11 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 117–128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Shamir, “How to share a secret,” Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' ACM, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 11,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 612–613, 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Nabil, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Ismail, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Mahmoud, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Alasmary, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Serpedin,  “PPETD: Privacy-preserving electricity theft detection scheme with load  monitoring and billing for AMI networks,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  96 334–96 348, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [22] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Huo and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Liu, “Distributed privacy-preserving electric vehicle  charging control based on secret sharing,” Electr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Power Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  211, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 108357, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Baran and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Wu, “Optimal sizing of capacitors placed on a radial  distribution system,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Power Deliv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 735–  743, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Farivar, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Chen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Low, “Equilibrium and dynamics of local  voltage control in distribution systems,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Decis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Control, Florence, Italy, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 10-13 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 4329–4334.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [25] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Zhao, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Zhang, “Distributed online voltage control  in active distribution networks considering PV curtailment,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Ind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 5519–5530, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Forman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Stein, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Fathy, “Optimization of dynamic battery  parameter characterization experiments via differential evolution,” in  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Control Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', Washington, DC, USA, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 17-19 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  867–874.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Daru and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Jager, “Encrypted cloud-based control using secret  sharing with one-time pads,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Decis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Control, Nice,  France, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 11-13 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 7215–7221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Humpherys and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Jarvis, Foundations of Applied Mathematics,  Volume I: Mathematical Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Ind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Math, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [29] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Goldreich, Foundations of Cryptography: Volume 2, Basic Applica-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Press, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [30] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Evans, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Kolesnikov, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Rosulek, “A pragmatic introduction to  secure multi-party computation,” Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Trends Privacy Security, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 2,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 2-3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 70–246, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [31] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Goldreich, “Secure multi-party computation,” Manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Prelimi-  nary Version, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 78, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 110, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [32] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Phanivong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Shi, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Callaway, “Decentralized  charging control of electric vehicles in residential distribution networks,”  IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Control Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' 266–281, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [33] National Renewable Energy Laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Residential battery storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Available:  https://atb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='nrel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='gov/electricity/2021/residential  battery storage  [34] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Energy  Information  Administration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  Electric  power  annual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content=' Available: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='eia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
+page_content='gov/todayinenergy/detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E0T4oBgHgl3EQfQwCg/content/2301.02198v1.pdf'}
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+arXiv:2301.04464v1  [math.NT]  8 Jan 2023
+Runs of Consecutive Integers Having the
+Same Number of Divisors
+By Vlad-Titus Sp˘ataru
+Abstract
+Our principal objective is to provide an upper bound for the length ℓN of the
+longest run of consecutive integers smaller than N which have the same number of
+divisors. We prove that ℓN ⩽ exp �C√log N log log N� in an elementary manner.
+1. Introduction
+The equation d(n) = d(n + k) has been studied extensively.
+In 1981, Spiro [Spi81]
+showed that it has infinitely many solutions for k = 5040.
+Subsequently, Heath-Brown
+[HB84] extended Spiro’s work to deal with the case k = 1, and Pinner [Pin97] ultimately
+proved that, in fact, all values of k yield infinitely many solutions.
+As d(n) = d(n+1) infinitely often, one naturally wonders how many consecutive integers
+can there be, having the same number of divisors. Erd˝os and Mirsky [EM52] conjectured
+that there are arbitrarily long such runs of integers. They were not able to provide any
+estimates for the length of such sequences: “A related problem consists in the estimation of
+the longest run of consecutive integers ⩽ x all of which have the same number of divisors.
+This problem seems to be one of exceptional difficulty, and we [Erd˝os & Mirsky] have not
+been able to make any progress with it.”
+Our principal objective is to provide an upper bound for the length of the runs in
+question. We shall obtain the following result, in an elementary manner:
+Theorem 1. Let ℓN denote the length of the longest run of consecutive integers smaller
+than N, having the same number of divisors. Then,
+ℓN ⩽ exp
+Ä
+C
+�
+log N · log log N
+ä
+,
+for an absolute constant C.
+Keywords: divisor counting function, consecutive equidivisible integers.
+2020 Mathematics Subject Classification: Primary: 11A25, 11N37.
+1
+
+2
+VLAD-TITUS SP˘ATARU
+2. The main result
+In proving theorem 1, we will make use of the following lemmas, the first being proven
+in an elementary manner in [Far09] and the second being Mertens’ bound.
+Lemma 1. Let n be a positive integer. Then, lcm(1, 2, . . . , n + 1) ⩾ 2n.
+Lemma 2. There exists an absolute constant C1 such that for any positive integer n ⩾ 2,
+�
+p⩽n
+1
+p ⩽ C1 · log log n,
+the sum being over all prime numbers p not exceeding n.
+Note that it suffices to prove that theorem 1 holds for large enough N. Assume that
+there exist k > 2 consecutive numbers smaller than N, having the same number of divisors.
+Let them be n + 1, n + 2, . . . , n + k and write
+d(n + 1) = d(n + 2) = · · · = d(n + k) = D.
+We will firstly provide an estimate for D, in terms of k. For simplicity, let K = ⌊log2 k⌋.
+As k ⩾ 2K, all residues modulo 2K are among n + 1, n + 2, . . . , n + k. Therefore, for all
+1 ⩽ i ⩽ K − 1, there exists some 1 ⩽ ti ⩽ k such that n + ti ≡ 2i mod 2K. Consequently,
+ν2(n + ti) = i, so (i + 1) divides d(n + ti) = D.
+Hence, D is divisible by lcm(1, 2, . . . , K). Using lemma 1, we infer that
+D ⩾ lcm(1, 2, . . . , K) ⩾ 2K−1.
+Recall that K = ⌊log2 k⌋ ⩾ log2 k − 1, so D ⩾ k/4.
+Next, we will bound ω((n + 1) · · ·(n + k)). Choose 1 ⩽ l ⩽ k arbitrarily. As n + l ⩽ N,
+it follows that νp(n + l) ⩽ logp N ⩽ log2 N for all prime numbers p. Therefore,
+D = d(n + l) =
+�
+p
+(νp(n + l) + 1) ⩽
+�
+p|n+l
+(log2 N + 1) = (log2 N + 1)ω(n+l),
+where p always represents a prime number. Thus, ω(n+l) ⩾ log D/ log(log2 N +1). A prime
+number p can divide at most ⌈k/p⌉ ⩽ k/p + 1 numbers among n + 1, . . . , n + k, so
+ω((n + 1) · · ·(n + k)) ⩾
+k
+�
+i=1
+ω(n + i) −
+�
+p⩽k
+k
+p,
+
+RUNS OF CONSECUTIVE INTEGERS HAVING THE SAME NUMBER OF DIVISORS
+3
+the second sum being taken over all prime numbers p not exceeding k. Using lemma 2 and
+the inequality we have previously deduced for ω(n + l), we may finally infer that
+ω((n + 1) · · ·(n + k)) ⩾
+k · log D
+log(log2 N + 1) − C1k log log k.
+Further, we will write log(log2 N +1) ⩽ C2 log log N, for an absolute constant C2. Recall
+that D ⩾ k/4, so we have
+ω((n + 1) · · ·(n + k)) ⩾ k · log(k/4)
+C2 log log N − C1k log log k.
+(1)
+Write the right-hand side of equation 1 as k · fN(k). Clearly, if ω(a) ⩾ b then a ⩾ b!.
+Using this remark on equation 1, we get (n+1) · · · (n+k) ⩾ ⌈k ·fN(k)⌉!. Moreover, because
+Nk ⩾ (n + 1) · · ·(n + k), by taking logarithms and applying the well-known inequality
+log t! ⩾ t log t − t, we have
+k log N ⩾ log ((n + 1) · · · (n + k)) ⩾ log (⌈k · fN(k)⌉!)
+⩾ k · fN(k) · log(k · fN(k)) − k · fN(k).
+(2)
+Finally, dividing equation 2 by k we obtain
+log N ⩾ fN(k) · log(k · fN(k)) − fN(k).
+(3)
+Define the interval IN = [exp (C1 · C2 · log log N) , ∞). Using standard arguments, one
+may infer that fN is increasing on IN.
+Let us suppose, for the sake of contradiction, that k > exp �C√log N log log N�, where
+C > max(√C2, C1 · C2). Firstly, note that since log N > log log N and C > C1 · C2 then
+exp �C√log N log log N� and k are in IN. Therefore, we have
+fN(k) > fN
+Ä
+exp
+Ä
+C
+�
+log N · log log N
+ää
+= C
+C2
+ 
+log N
+log log N −
+log 4
+C2 log log N − C1 log
+Ä
+C
+�
+log N · log log N
+ä
+.
+(4)
+Viewing equation 4 as a function in N, it is evident that for large enough N (greater than
+some N1) we also have fN(k) > e. In what follows, we will assume that N > N1.
+As fN(k) > e, it follows from equation 3 that log N ⩾ fN(k) · log k. Further, applying
+equation 4 and the estimate for k and isolating the term log N, we get
+C log 4
+C2
+ 
+log N
+log log N + C1C
+�
+log N log log N log
+Ä
+C
+�
+log N log log N
+ä
+⩾
+ÅC2
+C2
+− 1
+ã
+log N.
+Recall that C > √C2, so the latter inequality is absurd for large enough N (greater than some
+N2), as the left-hand side is asymptotically much smaller than log N. Therefore, theorem 1
+holds for N > max(N1, N2) and C > max(√C2, C1 · C2).
+
+4
+VLAD-TITUS SP˘ATARU
+3. Acknowledgments
+The author thanks Alexandru Gica for his proofreading and valuable comments.
+References
+[EM52] P. Erd˝os and L. Mirsky, The distribution of values of the divisor function d(n), Pro-
+ceedings of the London Mathematical Society no. 1 (1952), 257–271.
+[Far09] B. Farhi, An identity involving the least common multiple of binomial coefficients and its
+application, The American Mathematical Monthly 116 no. 9 (2009), 836–839.
+[HB84] D. R. Heath-Brown, The divisor function at consecutive integers, Mathematika 31 no. 1
+(1984), 141–149.
+[Pin97] C. G. Pinner, Repeated values of the divisor function, The Quarterly Journal of Mathe-
+matics 48 no. 4 (1997), 499–502.
+[Spi81] C. A. Spiro, The Frequency with Which an Integral-Valued, Prime-Independent, Mul-
+tiplicative or Additive Function of n Divides a Polynomial Function of n, Ph.D. thesis,
+University of Illinois at Urbana-Champaign, 1981.
+V. T. Sp˘ataru, Bucharest, Romania
+E-mail : vtspataru@gmail.com
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf,len=106
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='04464v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='NT]  8 Jan 2023  Runs of Consecutive Integers Having the  Same Number of Divisors  By Vlad-Titus Sp˘ataru  Abstract  Our principal objective is to provide an upper bound for the length ℓN of the  longest run of consecutive integers smaller than N which have the same number of  divisors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' We prove that ℓN ⩽ exp �C√log N log log N� in an elementary manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Introduction  The equation d(n) = d(n + k) has been studied extensively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  In 1981, Spiro [Spi81]  showed that it has infinitely many solutions for k = 5040.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Subsequently, Heath-Brown  [HB84] extended Spiro’s work to deal with the case k = 1, and Pinner [Pin97] ultimately  proved that, in fact, all values of k yield infinitely many solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  As d(n) = d(n+1) infinitely often, one naturally wonders how many consecutive integers  can there be, having the same number of divisors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Erd˝os and Mirsky [EM52] conjectured  that there are arbitrarily long such runs of integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' They were not able to provide any  estimates for the length of such sequences: “A related problem consists in the estimation of  the longest run of consecutive integers ⩽ x all of which have the same number of divisors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  This problem seems to be one of exceptional difficulty, and we [Erd˝os & Mirsky] have not  been able to make any progress with it.”  Our principal objective is to provide an upper bound for the length of the runs in  question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' We shall obtain the following result, in an elementary manner:  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Let ℓN denote the length of the longest run of consecutive integers smaller  than N, having the same number of divisors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Then,  ℓN ⩽ exp  Ä  C  �  log N · log log N  ä  ,  for an absolute constant C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Keywords: divisor counting function, consecutive equidivisible integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  2020 Mathematics Subject Classification: Primary: 11A25, 11N37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  1  2  VLAD-TITUS SP˘ATARU  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' The main result  In proving theorem 1, we will make use of the following lemmas, the first being proven  in an elementary manner in [Far09] and the second being Mertens’ bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Let n be a positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Then, lcm(1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' , n + 1) ⩾ 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' There exists an absolute constant C1 such that for any positive integer n ⩾ 2,  �  p⩽n  1  p ⩽ C1 · log log n,  the sum being over all prime numbers p not exceeding n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Note that it suffices to prove that theorem 1 holds for large enough N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Assume that  there exist k > 2 consecutive numbers smaller than N, having the same number of divisors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Let them be n + 1, n + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' , n + k and write  d(n + 1) = d(n + 2) = · · · = d(n + k) = D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  We will firstly provide an estimate for D, in terms of k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' For simplicity, let K = ⌊log2 k⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  As k ⩾ 2K, all residues modulo 2K are among n + 1, n + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' , n + k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Therefore, for all  1 ⩽ i ⩽ K − 1, there exists some 1 ⩽ ti ⩽ k such that n + ti ≡ 2i mod 2K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Consequently,  ν2(n + ti) = i, so (i + 1) divides d(n + ti) = D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Hence, D is divisible by lcm(1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' , K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Using lemma 1, we infer that  D ⩾ lcm(1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' , K) ⩾ 2K−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Recall that K = ⌊log2 k⌋ ⩾ log2 k − 1, so D ⩾ k/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Next, we will bound ω((n + 1) · · ·(n + k)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Choose 1 ⩽ l ⩽ k arbitrarily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' As n + l ⩽ N,  it follows that νp(n + l) ⩽ logp N ⩽ log2 N for all prime numbers p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Therefore,  D = d(n + l) =  �  p  (νp(n + l) + 1) ⩽  �  p|n+l  (log2 N + 1) = (log2 N + 1)ω(n+l),  where p always represents a prime number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Thus, ω(n+l) ⩾ log D/ log(log2 N +1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' A prime  number p can divide at most ⌈k/p⌉ ⩽ k/p + 1 numbers among n + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' , n + k, so  ω((n + 1) · · ·(n + k)) ⩾  k  �  i=1  ω(n + i) −  �  p⩽k  k  p,  RUNS OF CONSECUTIVE INTEGERS HAVING THE SAME NUMBER OF DIVISORS  3  the second sum being taken over all prime numbers p not exceeding k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Using lemma 2 and  the inequality we have previously deduced for ω(n + l), we may finally infer that  ω((n + 1) · · ·(n + k)) ⩾  k · log D  log(log2 N + 1) − C1k log log k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Further, we will write log(log2 N +1) ⩽ C2 log log N, for an absolute constant C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Recall  that D ⩾ k/4, so we have  ω((n + 1) · · ·(n + k)) ⩾ k · log(k/4)  C2 log log N − C1k log log k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  (1)  Write the right-hand side of equation 1 as k · fN(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Clearly, if ω(a) ⩾ b then a ⩾ b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='.  Using this remark on equation 1, we get (n+1) · · · (n+k) ⩾ ⌈k ·fN(k)⌉!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='. Moreover, because  Nk ⩾ (n + 1) · · ·(n + k), by taking logarithms and applying the well-known inequality  log t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' ⩾ t log t − t, we have  k log N ⩾ log ((n + 1) · · · (n + k)) ⩾ log (⌈k · fN(k)⌉!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=')  ⩾ k · fN(k) · log(k · fN(k)) − k · fN(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  (2)  Finally, dividing equation 2 by k we obtain  log N ⩾ fN(k) · log(k · fN(k)) − fN(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  (3)  Define the interval IN = [exp (C1 · C2 · log log N) , ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Using standard arguments, one  may infer that fN is increasing on IN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Let us suppose, for the sake of contradiction, that k > exp �C√log N log log N�, where  C > max(√C2, C1 · C2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Firstly, note that since log N > log log N and C > C1 · C2 then  exp �C√log N log log N� and k are in IN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Therefore, we have  fN(k) > fN  Ä  exp  Ä  C  �  log N · log log N  ää  = C  C2  log N  log log N −  log 4  C2 log log N − C1 log  Ä  C  �  log N · log log N  ä  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  (4)  Viewing equation 4 as a function in N, it is evident that for large enough N (greater than  some N1) we also have fN(k) > e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' In what follows, we will assume that N > N1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  As fN(k) > e, it follows from equation 3 that log N ⩾ fN(k) · log k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Further, applying  equation 4 and the estimate for k and isolating the term log N, we get  C log 4  C2  log N  log log N + C1C  �  log N log log N log  Ä  C  �  log N log log N  ä  ⩾  ÅC2  C2  − 1  ã  log N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  Recall that C > √C2, so the latter inequality is absurd for large enough N (greater than some  N2), as the left-hand side is asymptotically much smaller than log N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Therefore, theorem 1  holds for N > max(N1, N2) and C > max(√C2, C1 · C2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  4  VLAD-TITUS SP˘ATARU  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Acknowledgments  The author thanks Alexandru Gica for his proofreading and valuable comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  References  [EM52] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Erd˝os and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Mirsky, The distribution of values of the divisor function d(n), Pro-  ceedings of the London Mathematical Society no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' 1 (1952), 257–271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  [Far09] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Farhi, An identity involving the least common multiple of binomial coefficients and its  application, The American Mathematical Monthly 116 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' 9 (2009), 836–839.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  [HB84] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Heath-Brown, The divisor function at consecutive integers, Mathematika 31 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' 1  (1984), 141–149.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  [Pin97] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Pinner, Repeated values of the divisor function, The Quarterly Journal of Mathe-  matics 48 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' 4 (1997), 499–502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  [Spi81] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Spiro, The Frequency with Which an Integral-Valued, Prime-Independent, Mul-  tiplicative or Additive Function of n Divides a Polynomial Function of n, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' thesis,  University of Illinois at Urbana-Champaign, 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content=' Sp˘ataru, Bucharest, Romania  E-mail : vtspataru@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
+page_content='com' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E3T4oBgHgl3EQfWAol/content/2301.04464v1.pdf'}
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+1 
+ 
+Catalytic action of two-dimensional layered materials (WS2, and MoS2) on hydrogen 
+sorption properties of MgH2 
+Satish Kumar Verma1, Mohammad Abu Shaz1, Thakur Prasad Yadav1,2* 
+1Hydrogen Energy Centre, Department of Physics, Banaras Hindu University, Varanasi-
+221005, India. 
+2Department of Physics, Faculty of Science, University of Allahabad, Prayagraj-211002, 
+India. 
+ 
+Abstract: 
+The present study reports the catalytic action of two-dimensional (2D) layered materials 
+(MoS2 and WS2) for improving the de/re-hydrogenation kinetics of MgH2. The MgH2 
+start desorbing at 277 ºC with a hydrogen storage capacity of 5.95 wt% in the presence of 
+WS2 catalyst whereas onset desorption temperature of MgH2 catalyzed by MoS2 is 330 
+ºC. The MgH2-WS2 absorbed hydrogen ~ 3.72 wt% within 1.3 minutes at 300 ºC under 13 
+atm hydrogen pressure and it desorbed ~5.57 wt% within 20 minutes at 300 ºC under 1 
+atm hydrogen pressure. We have performed 25 cycles of dehydrogenation (under 1 atm 
+hydrogen pressure at 300 ºC) and re-hydrogenation (under 13 atm hydrogen pressure at 
+300 °C) to ensure cyclic stability of catalyzed version of MgH2 where MgH2-WS2 shows 
+better cyclic stability than MgH2-MoS2. MgH2-WS2 also shows the lower reaction 
+activation energy ~117 kJ/mol as compare to other catalyzed and uncatalyzed samples. 
+On the other hand, these catalysts (WS2 and MoS2) do not have any impact on the 
+thermodynamical parameters that is change in enthalpy. 
+ 
+Key words: 2D layered materials, De/re-hydrogenation kinetics, Activation energy, 
+MgH2. 
+*Corresponding author Email: yadavtp@gmail.com 
+ 
+
+2 
+ 
+1. Introduction 
+A crucial and promising area of research for onboard hydrogen applications is the 
+development of safe and efficient hydrogen storage. The solid-state approach is one of 
+the most appropriate, secure, and effective ways to store hydrogen among the several 
+methods that can be used, including gaseous, liquid, and solid-state storage [1,2]. Due to 
+its high hydrogen storage capacity (110 g/L volumetric and 7.6 wt% gravimetric), low 
+cost, light weight, and large abundance (in the form of Mg) in earth crust (8th most) and 
+seawater (3rd most), MgH2 is a leading choice for hydrogen storage in the solid-state 
+mode [3–6]. According to the United States Department of Energy (US DOE) technical 
+targets for hydrogen storage systems [7], MgH2 has certain advantages that make it a 
+viable option. The high dehydrogenation temperature (above 400 ºC), slow kinetics 
+(hydrogen de/re-hydrogenation kinetics 0.4 kg-H2/min), and high thermodynamic 
+properties (high reaction enthalpy 74 kJ/mol) of MgH2 prevent it from being a suitable 
+material for onboard applications even with these advantages [8–10]. In recent years, the 
+creation of suitable catalyst(s), alloys, composite materials with complicated hydrides, 
+and scaffolding have all been used as feasible methods to improve the hydrogen storage 
+performance of MgH2 [11,12]. The use of various types of catalysts and additives to 
+enhance the performance of Mg/MgH2 has been the subject of several studies by various 
+research organizations [13–17]. 
+Another application for the 2D materials is as a catalyst for improving the hydrogen 
+characteristics of MgH2 [18–22]. Due to its enormous surface area, ballistic conduction, 
+thermal conductivity, mechanical stability, and light weight, graphene, which has a 2D 
+planer structure with sp2 carbon atoms arranged in a hexagonal framework, has attracted 
+a lot of attention as a catalyst and as a template material for hydrogen storage application 
+in MgH2 [23,24]. MgH2's de/rehydrogenation kinetics exhibit effective catalytic behavior 
+in the graphene layer, which also inhibits MgH2's agglomeration and grain growth 
+[3,5,25]. Liu et al., for instance, have created MgH2-5% Gr nanosheets [26]. They have 
+demonstrated that graphene nanosheets offer a significant hydrogen diffusion pathway 
+and prevent MgH2 from aggregating. According to Huang et al., [27] report's MgH2 
+nanoparticles supported by graphene exhibit remarkable hydrogen sorption kinetics and 
+
+3 
+ 
+cyclic stability. Due to the strong interaction between graphene and MgH2 nanoparticles 
+and the prevention of nanoparticle agglomeration, the MgH2 nanoparticles demonstrated 
+excellent hydrogen storage performance. Additionally, grapheme prevents the 
+aggregation of nanoparticles during the rehydrogenation of MgH2, according to a 
+theoretical study using molecular dynamics simulation [28]. Rough studies are still 
+required to determine the impact of graphene and other 2D layered materials on MgH2, 
+even though some prior studies have shown the remarkable catalytic/co-catalytic and 
+agglomeration blocking properties of Gr on MgH2. 
+We have examined a comparison between WS2 and MoS2 as a catalyst for enhancing 
+hydrogen sorption properties of MgH2. WS2 and MoS2 are suitable alternatives to 
+graphene for the catalytic action on MgH2 due to their high conductivity (metallic 
+nature), thermal stability, and strong catalytic behavior [29,30]. Tungsten (W) and 
+Molybdenum (Mo) are sandwiched between two Sulphur layers with weak Van der 
+Waals interactions in the family of layered transition-metal dichalcogenides (TMDs) 
+materials that include WS2 and MoS2. The re/de-hydrogenation kinetics, and catalytic 
+behavior of WS2 and MoS2 on MgH2 has been investigated in details. 
+2. Experimental section 
+2.1. Synthesis of a few layered WS2  
+The bulk tungsten sulfide (WS2) (99.80 %) powder was procured from the Alfa Aesar for 
+the present investigation. For the preparation of few layered WS2, WS2 powder was 
+dispersed in de-ionized water and sonicated it for 74 hours using ultrasonicator at 20 kHz 
+frequency. The sonicated sample was then dried at 50 °C under a dynamic vacuum of 
+order 10-2 torr to form the few layered WS2 powder. This preparation method can also be 
+understood by the schematic given in Fig. 1.  
+
+4 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Fig.1: Schematic diagram for the synthesis of a few layers WS2. 
+ 
+2.2. Synthesis of few-layer MoS2 
+The Otto Chemica bulk molybdenum disulfide (MoS2) (99 %) powder was used for the 
+present investigation. MoS2 powder was dispersed in de-ionized water and sonicate it for 
+74 hours using ultrasonicator at 20 kHz frequency to obtain the few-layered MoS2. The 
+sonicated sample was then dried at 50 °C under dynamic vacuum of order 10-2 torr to 
+form the few layered MoS2 powder. Fig. 2, shows the schematic diagram for preparation 
+of few-layered MoS2.    
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+BulkMoS2
+BulkMoS,
+FewlayeredMoS2
+DoublelayeredMoS2
+UltrasonicationofbulkMoS,BulkWS2
+BulkWs,
+FewlayeredwS2
+DoublelayeredWS2
+Ultrasonicationof bulkWS25 
+ 
+ 
+Fig.2: Schematic diagram for the synthesis of a few layers MoS2. 
+ 
+2.3. Synthesis of MgH2 catalyzed by WS2, and MoS2 
+The pure MgH2 was procured from Fujifilm (Japan) (99.9%) for the present investigation. 
+Mechanical ball-milling of MgH2 with graphene at 180 rpm for 24 hours with a ball-to-
+powder ratio of 50:1 (by weight) using a planetary ball-miller (Retsch PM 400) was used 
+to synthesize MgH2 catalyzed by WS2 (MgH2-WS2). To explore the optimum catalyst 
+concentration for hydrogen sorption kinetics of Mg/MgH2, we have synthesized a set of 
+different catalyst concentrations (5, 10, 12 wt%) to catalyze MgH2. For hydrogen 
+sorption in Mg/MgH2, 10 wt% catalysts were found to be optimal (in terms of desorption 
+temperature and hydrogen storage capacity). The ball-miller vials were filled with 5 atm 
+H2 pressure to compensate for the loss of hydrogen from MgH2 during milling. All the 
+loading and unloading of the samples was done inside the N2-filled glove box 
+(MBRAUM MB10 compact) with O2 and H2O levels < 1 ppm. The synthesis of MgH2 
+catalyzed by MoS2 (MgH2-MoS2) was done using the same synthesis route as MgH2-
+WS2. 
+2.4. Characterization techniques 
+The structural characterization of prepared samples was carried out by XRD technique 
+using Empyrean PANalytical X-ray diffractometer equipped with 2D detector with a Cu 
+Kα beam (λ = 1.5415 Å) operated at 40 kV and 40 mA. The microstructural and selected 
+area electron diffraction (SAED) analysis of as-prepared samples was carried out by 
+TEM (Technai-20G2) operating at the accelerating voltage of 200 kV. Perkin Elmer 
+(Spectrum 100) spectrometer in transmission mode with attenuated total reflectance 
+(ATR) sampling mode (wavenumber range 500–4000 cm-1) was used to carry out FTIR 
+spectroscopy. The Raman spectra have been acquired at -60 ºC using Horiba-Jobin-Yvon 
+LABRAM-HR800 spectrometer with diode LASER (532 nm). The desired thickness and 
+surface topography of the prepared samples were examined by using solver next AFM in 
+non-contact mode. The characterized samples then proceed for the hydrogen desorption 
+and absorption using automated two-channel volumetric sieverts type apparatus. The 
+temperature programmed desorption (TPD) was carried out with a heating rate of 5
+ oC-
+
+6 
+ 
+min-1. The activation energy (Ea) study of prepared catalyzed samples has been done by 
+using DSC (Perkin Elmer DSC 8000) with a heating rate of 15 
+oC/min, 18 
+oC/min, 21 
+oC/min, and 24 
+oC/min under nitrogen atmosphere (20 ml/min). 
+ 
+3. Results and discussion 
+3.1. Structural, microstructural, and spectroscopic characterization analysis 
+The structural characteristics of as-prepared samples have been examined using the XRD 
+characterization. Fig. 3(a) shows the XRD pattern of pristine MgH2, which matches well 
+with the tetragonal MgH2 with space group P42/mnm (136) and a=b= 4.516 Å, c = 3.020 
+Å (JCPDS no. 740934). Fig. 3(b) shows the XRD pattern of MoS2, which matches well 
+with the hexagonal structure of MoS2 with space group P63/mmc(194) and a=b= 3.1602 
+Å, c = 12.294 Å (Joint Committee on Powder Diffraction Standards (JCPDS) no. 
+651951). The XRD pattern of as-prepared WS2 is shown in Fig. 3(c), that matches well 
+with the hexagonal structure of WS2 with space group P63/mmc(194) and a=b= 3.1532 
+Å, c = 12.323 Å (JCPDS no. 841398). The usual diffraction pattern of MgH2-MoS2, and 
+MgH2-WS2 are shown in Fig. 3(d-e), respectively, where besides the tetragonal phase of 
+MgH2, some peaks of WS2 and MoS2 are either suppressed or masked by the peaks of 
+MgH2. The diffraction peaks of WS2 and MoS2 are identified and labeled in the Fig. 3(d-
+e), respectively.  
+The different bands position, shapes, and relative intensities of Raman spectra give us 
+essential information about the materials and stacking of layers, i.e., Raman spectroscopy 
+can determine the layer thickness at the atomic level. The Raman spectra of as-prepared 
+WS2, and MoS2 have shown in Fig. 4. In the case of MoS2, the two Raman modes are 
+appeared at ~ 345 cm-1 and ~ 370 cm-1 corresponds to E12g and A1g modes of vibrations 
+(labeled in Fig. 4(b)). The indicated modes of MoS2 have frequency difference of ~ 25 
+cm-1, that means the MoS2 as layered material with few layers of stacking (3-5 layers) 
+[31,32]. The FWHM of A1g mode is ~ 7 cm-1, which can also be referred to stacking a 
+few layers of MoS2 [33]. The Raman shifts at ~316 cm-1 and 384 cm-1 (shown in Fig. 
+4(a)) corresponds to the presence of E12g and A1g modes respectively in WS2 sample. The 
+
+7 
+ 
+intensity ratio of E12g and A1g modes was estimated E12g/A1g i.e. = 1.26, which is higher 
+than the intensity ratio of bulk WS2 (E12g/A1g = 0.47) and lower than the monolayer WS2 
+(E12g/A1g = 2.2) [34,35]. This calculated intensity ratio (E12g/A1g = 1.26) is compatible 
+with the range of 2-3 layers of WS2.  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Fig. 3: XRD patterns of (a) Pristine MgH2, (b) MoS2, (c) WS2, (d) MgH2-MoS2, and (e) 
+MgH2-WS2.  
+ 
+
+o-Parafilm,
+*-MgH2,
+t-Ws2, u -Mos2
+(e)MgH2-Ws
+52
+T
+*
+*
+*
+*
+(d) mgh2-Mos2
+*
+Intensity (wt%)
+(c) WS 2
+(002)
+-(004)
+ (100)
+(101)
+(900)
+(105)
+(110)
+(112)
+-(114)
+(203)
+(116)
+8
+tt
+T
+T
+.1
+1
+T
+(b)Mos.
+(00L)2
+2
+(002)
+U
+C(105)
+(102)
+(103)
+C(110)
+(112)
+c(108)
+(203)
+U
+(a) Pristine
+MgH2
+*
+(200)
+(110)
+(220)
+*(002)
+(310)
+(112)
+(301)
+(202)
+(211)
+*
+8
+8
+*
+*
+￥
+10
+20
+30
+40
+50
+60
+70
+80
+2e(degree8 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Fig. 4: Raman spectra of (a) WS2 and (b) MoS2. 
+ 
+ 
+ 
+The information about stacking layers in 2D layered materials (like WS2 and 
+MoS2) can also be verified by AFM analysis. The surface topography and height profile 
+of prepared MoS2, and WS2 were examined along the blue dotted line as shown in Fig. 
+S1(a-b) (given in supporting information). The layered surface morphology along with 
+height profile (shown in Fig. S1(a-a1)) shown the average thickness of MoS2 is ~1.3 nm, 
+that indicates the presence of ~2 layers of stacking in the MoS2 sample [36,37]. The ~7-8 
+layers of stacking were present in the case of WS2 (shown in Fig. S1(b-b1)) with a 
+monolayer height of ~0.7 nm [38].       
+ 
+ 
+ 
+
+(b) Raman spectra of MoS2
+(370)
+A1g
+(a) Raman spectra of WS2
+(345)
+2g
+Intensity (a.u.)
+(384)
+2g
+A1
+(316)
+175200225250275300325
+350
+375400
+425
+450475500
+Raman shift (cm9 
+ 
+. 
+ 
+3.2 De/Re-hydrogenation kinetics of catalyzed MgH2 
+To identify the optimal percentage of catalyst in MgH2 with optimum temperature range 
+where material performed promptly, we have characterized as-prepared samples for the 
+temperature programmed desorption (TPD) analysis. The TPD curves of MgH2-MoS2 
+have seen in Fig. S2 (given in supporting information). The MgH2-5%MoS2, MgH2-
+10%MoS2, and MgH2-12%MoS2, starts releasing hydrogen at ~ 357 °C, ~ 330 °C, ~ 302 
+°C with ~ 6.41 wt%, ~ 6.00 wt%, ~ 4.88 wt% of hydrogen storage capacity respectively. 
+On the other hand, MgH2-5%WS2, MgH2-10%WS2, and MgH2-12%WS2, starts releasing 
+hydrogen at ~ 339 °C, ~ 277 °C, ~ 258 °C with ~ 6.54 wt%, ~ 5.95 wt%, ~ 5.14 wt% of 
+hydrogen storage capacity respectively (shown in Fig. S3 in supporting information). 
+Based on TPD analysis, the optimum catalyst concentration for catalyzing MgH2 is 10 
+wt% for all catalysts. 
+After getting information about the optimum catalyst for MgH2, we compared the TPD 
+analysis of all optimum catalyzed samples with pristine MgH2, as shown in Fig. 5.  The 
+TPD of pristine MgH2 (shown in Fig. 5(a)) was then carried out to compare hydrogen 
+storage properties with catalyzed samples. The pristine MgH2 has an onset desorption 
+temperature of 376 
+oC with a total release of ~7.45 wt% storage capacity. The onset 
+desorption temperature of MgH2-MoS2 (MgH2-10%MoS2) is ~ 330 
+oC, and it desorbs ~ 
+6.00 wt% hydrogen while the desorption gets completed at 396 
+oC (Fig. 5(b)). In the case 
+of MgH2-WS2 (MgH2-10%WS2), it starts desorbing hydrogen at ~ 277
+ oC with a storage 
+capacity of 5.95 wt% (Fig. 5(c)).  
+
+10 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Fig. 5: Comparative TPD analysis of (a) Pristine MgH2, (b) MgH2-MoS2 and (c) MgH2-
+WS2. 
+ 
+The desorbed samples then proceed for re/de-hydrogenation to check the cyclic stability 
+and reversibility of catalyzed and pristine MgH2. The re-hydrogenation kinetics was 
+carried out at 300 
+oC under 13 atm hydrogen pressures, as shown in Fig. 6. It can be seen, 
+the pristine MgH2 absorbed ~1.16 wt% hydrogen in 1.2 minutes whereas MgH2-MoS2, 
+MgH2-WS2 absorbed 4.60 wt%, 3.72 wt%, hydrogen, respectively, under similar 
+conditions of temperature and pressure.  
+ 
+ 
+ 
+
+0
+Hydrogen desorbed (wt%)
+(a)
+(b)
+(c)
+(a)PristineMgH
+5
+(b) MgH,-Mos,
+6
+(c) MgH,-WS,
+7
+8
+200
+225
+250
+275
+300
+325
+350
+375
+400
+425
+Temperature (C)11 
+ 
+ 
+Fig. 6: Rehydrogenation kinetics curves at 300 °C under 13 atm H2 pressure of (a) b) 
+MgH2-WS2, (c) MgH2-MoS2 and (e) Pristine MgH2. 
+ 
+The rehydrogenated samples were then dehydrogenated at 300 
+oC under 1 atm 
+hydrogen pressure. It can be seen clearly in Fig. 7, that the MgH2-WS2 sample releases 
+5.57 wt% hydrogen within 20 minutes while MgH2-MoS2 and pristine MgH2 releasees 
+2.25 wt%, and 0.23 wt% of hydrogen under similar temperature and pressure conditions, 
+which is 3.32 wt%, and 4.48 wt% more than pristine MgH2, MgH2-MoS2, respectively. 
+Based on the above re/de-hydrogenation kinetics study, it is clearly shown that WS2 
+works as a superior catalyst to MoS2 for catalyzing MgH2. Therefore, in present study 
+WS2 is a prominent catalyst to catalyze MgH2. 
+
+(b)
+5.
+Hydrogen absorbed (wt%)
+(a)
+(c)
+- (a) MgH,-WS
+ (b) MgH,-Mos
+ (c) Pristine MgH,
+0
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+20
+22
+24
+Time (Min.)12 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Fig. 7: Dehydrogenation kinetics curves at 300 °C under 1 atm H2 pressure of (a) MgH2-
+WS2, (b) MgH2-MoS2, and (c) Pristine MgH2. 
+ 
+3.3. Study of kinetics: Estimation of activation energy 
+The DSC was carried out to determine the hydrogen desorption activation energy barrier 
+to convert MgH2 into Mg. The DSC profile of MgH2-MoS2, MgH2-WS2, are shown in 
+Figs. 8-9. In the case of MgH2-WS2, the peak desorption temperature found from DSC is 
+~ 380 
+oC, while the onset desorption temperature found from TPD is ~ 277 
+oC. There is a 
+difference in desorption temperature in TPD (Fig. 5(c)) and DSC (Fig. 9(a)) curves due to 
+the TPD being performed under vacuum with a temperature ramping rate of 5
+ oC/min 
+while DSC was performed under N2 atmosphere with a temperature ramping rate of 15
+ 
+oC/min. For calculating the desorption activation energy, we have performed DSC with a 
+set of the various rate of heating (15, 18, 21, 24 
+oC/min) and plotted the Kissinger curve 
+by using the Kissinger equation[39] as given: 
+
+(a) Pristine MgH,
+- (b) MgH,-MoS,
+Hydrogen desorbed (wt%)
+5
+ (c) MgH,-WS
+(a)
+(b)
+2
+(c)
+0
+0
+5
+10
+15
+20
+25
+30
+35
+40
+45
+50
+55
+60
+Time (min.)13 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+(1) 
+Where β, Tp, and Ea are the heating rate, corresponding peak desorption temperature, and 
+activation energy, respectively. The slope of Kissinger plot (ln(β/Tp
+2) vs. 1000/Tp
+2 plot) 
+(Figs. 8-9) is used to calculate the desorption activation energy. The calculated activation 
+energy for MgH2-MoS2, and MgH2-WS2 is 117.09 kJ/mol (± 1.60 kJ/mol), and 104.00 
+kJ/mol (± 2.74 kJ/mol) respectively. This activation energy indicates that ~104 kJ/mol 
+energy is required to overcome the barrier to convert MgH2 into Mg in the presence of a 
+WS2 catalyst. These calculated activation energies are significantly lower than the 
+activation energy of pristine MgH2 [3,40]. 
+Table 1: Table for plateau pressures at corresponding temperatures, change in enthalpy, 
+and activation energy of MgH2-MoS2, and MgH2-WS2.  
+ 
+ 
+ 
+S.No.  
+Sample 
+name 
+Plateaus 
+pressure 
+          (atm) 
+Temperature 
+(
+ºC) 
+Change 
+in 
+enthalpy 
+ (kJ/mol) 
+Activation 
+energy 
+(kJ/mol) 
+1. 
+MgH2-
+MoS2 
+1.03 
+272.62 
+ 
+  -78.33 
+ 
+117.09 
+2.03 
+292.28 
+3.77 
+313.28 
+2. 
+MgH2-
+WS2 
+1.52 
+281.26 
+ 
+  -77.44 
+ 
+104.66 
+2.92 
+300.60 
+3.45 
+316.29 
+
+14 
+ 
+ 
+ 
+ 
+Fig. 8: (i) DSC profile for desorption of MgH2-MoS2 with the heating rate (a) 15 ºC/min, 
+(b) 18 ºC/min, (c) 21 ºC/min, (d) 24 ºC/min, and (ii) corresponding Kissinger plot for 
+evaluating the desorption activation energy of MgH2-MoS2. 
+ 
+
+DSCprofilefor MgH2-MoS2
+-9.8
+Kissinger plot for MgHb-MoS2
+Linear fit
+(d) 24°C/min
+-9.9
+(a.u.)
+-10.0
+(c)21cC/min
+Heatflow(
+P
+-10.1
+Endo up
+(b) 18 C/min
+Eguation
+y=a+b
+-10.2
+Adj. R-Squ
+0.99937
+Value 
+Standard Er
+-10.3
+In(beta/Tp2) Irtercept
+11.212
+0.30766
+(a) 15 C/min
+In(beta/Tp2) Slope 
+-14.083
+0.20379
+1.4881.4941.5001.5061.5121.5181.5241.530
+250
+275
+300
+325
+350
+375
+400
+425
+450
+1000/T,(K1)
+Temperature (cC)DSCprofileforMgH2-WS2
+Kissinger plot for MgH2-WS2
+-9.8
+(d) 24 C/min
+Linear fit
+-9.9
+Heat flow (a.u.)
+(c) 21 °C/min
+-10.0
+[β/T,
+(b) 18 °C/min
+-10.1
+Endo
+Equation
+=a+
+Adj. R-Sq
+0.9979
+-10.2
+Value
+ Standard
+(a) 15 °C/min
+In(beta/Tp Interce
+9.3313
+0.50735
+In(beta/Tp Slope
+-12.58
+0.33004
+-10.3
+1.520
+1.525
+1.530
+1.535
+1.540
+1.545
+1.550
+1.555
+1000/T(K
+320330340350360370380390400410420430440450
+Temperature (C)15 
+ 
+Fig. 9: (i) DSC profile for desorption of MgH2-WS2 with the heating rate (a) 15 ºC/min, 
+(b) 18 ºC/min, (c) 21 ºC/min, (d) 24 ºC/min, and (ii) corresponding Kissinger plot for 
+evaluating the desorption activation energy of MgH2-WS2. 
+ 
+3.4. Study of thermodynamics 
+After the kinetics and reversibility study, we have proceeded with the thermodynamic 
+analysis of catalyzed MgH2 for comparing the change in enthalpy and entropy of the 
+system using well known Van’t Hoff equation [41]. 
+ 
+ 
+ 
+lnP = (ΔH/RT) - (ΔS/R) 
+ 
+ 
+(2) 
+Where P, ∆H, R, T, and ∆S are the pressure, change in enthalpy, gas constant, absolute 
+temperature, and change in entropy, respectively. The PCI isotherms (Figs. 10(i)-11(i) 
+and Van’t Hoff plots (Figs. 10(ii)-11(ii)) were used for the calculation of change in 
+enthalpy of MgH2-MoS2 and MgH2-WS2, respectively. The calculated change in 
+desorption enthalpy was found to be 78.33 kJ/mol (± 1.40 kJ/mol), and 77.44 kJ/mol (± 
+1.13 kJ/mol), for MgH2-MoS2 and MgH2-WS2 respectively. It is clear from the above 
+estimation of change in enthalpy, that there is no significant enthalpy change in the 
+presence of a catalyst. Thus MoS2, WS2 have not positively impacted the thermodynamic 
+barrier of the MgH2. The plateau pressure at corresponding temperatures, change in 
+enthalpy, and activation energy has been tabulated in Table 1. 
+
+(i) PCl desorption for MgH2-MoS2
+1.4.
+(ii) Vant's Hoff plot for MgH2-MoS2
+6.
+- Linear fit
+1.2
+5.
+1.0
+(atm)
+320°C
+4
+0.8.
+Pressure (
+P
+三 0.6
+3.
+300°C
+0.4
+2
+Equation
+y=a+b*
+0.2-
+Adj. R-Squar0.99936
+280 °C
+Value
+Standard Err
+InP
+Intercept 
+17.3878
+0.298
+0.0
+InP
+Slope
+9.4207
+0.16804
+0
++
+1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88
+0
+1
+2
+3
+4
+5
+1000/T (K
+Hydropgen capacity (wt%)16 
+ 
+Fig. 10: (i) PCI desorption plots for MgH2-MoS2 at different temperatures and (ii) 
+corresponding Van't Hoff plot for calculating the change in enthalpy 
+ 
+Fig. 11: (i) PCI desorption plots for MgH2-WS2 at different temperatures and (ii) 
+corresponding Van't Hoff plot for calculating the change in enthalpy 
+3.5 Cyclic stability of catalyzed MgH2 
+The WS2 (optimum catalyst) plays a significant role in improving the kinetics of MgH2. 
+The cyclic stability is an essential characteristic of the hydride material (MgH2) besides 
+kinetic and thermodynamics, making it a worthy hydrogen storage material. Therefore, it 
+is crucial to look at the cyclic stability of the catalyzed MgH2 samples. We have 
+performed 25 cycles of dehydrogenation (under 1 atm hydrogen pressure at 300 °C) and 
+re-hydrogenation (under 13 atm hydrogen pressure at 300 °C) to ensure cyclic stability of 
+catalyzed MgH2. The cyclic stability curve of MgH2-MoS2 and MgH2-WS2 are shown in 
+Fig. 12. From Fig. 12(a) MgH2-MoS2 shows the ~ 0.42 wt% (from 5.77 wt% to 5.35 
+wt%) degradation in hydrogen storage capacity during rehydrogenation and ~ 0.38 wt% 
+(from 5.69 wt% to 5.31 wt%) in dehydrogenation. The MgH2-WS2 has the loss of 
+hydrogen storage capacity ~ 0.3 wt% (from 5.80 wt% to 5.50 wt%) during re-
+hydrogenation and ~ 0.36 wt% (from 5.76 wt% to 5.40 wt%) during dehydrogenation. 
+Thus, MgH2-WS2 has more substantial cyclic stability than MgH2-MoS2 under similar 
+
+8
+(i) PCI desorption for MgH2-WS2
+1.4
+(ii) Vant's Hoff plot for MgH2-WS2
+1.2
+Linear fit
+6
+(atm)
+1.0
+5
+Pressure
+320 °C
+InP
+0.8
+300°℃
+3
+0.6
+Equation
+y=a+
+Adj. R-Squ0.9995
+2
+280°C
+Value
+Standard E
+0.4 .
+InP
+Intercep
+17.038
+0.23617
+Inp
+Slope
+-9.314
+0.1362
+0.2
+1.68
+1.70
+1.72
+1.74
+1.76
+1.78
+0
+1.80
+1000/T (K-1)
+0
+1
+2
+3
+4
+5
+6
+Hydrogen capacity (wt%)17 
+ 
+temperature and pressure conditions. The comparative study for hydrogen storage 
+properties of different recently used 2D materials as the catalyst for MgH2 is explored in 
+Table 2.  
+ 
+Fig. 12: Cyclic stability of (a) MgH2-MoS2 and (b) MgH2-WS2. 
+ 
+Table 2: Table for different 2D materials as the catalyst for hydrogen storage application. 
+S. 
+No. 
+Material 
+2D- based 
+catalyst 
+Hydrogen 
+storage 
+capacity 
+(wt%) 
+Onset 
+dehydrogen
+ation 
+temperature 
+(ºC) 
+ 
+Activation 
+energy 
+(kJ/mol) 
+Change 
+in 
+enthalpy 
+(kJ/mol) 
+ 
+Ref. 
+1. 
+Mg6C2N 
+C2N 
+6.79 
+-- 
+-- 
+-- 
+[20] 
+2. 
+MgH2-LiAlH4-
+Ti3C2 
+Ti3C2 
+6.50 
+63.0 
+128.4 
+74.3 
+[22] 
+3. 
+MgH2-
+Nb4C3Tx 
+Nb4C3Tx 
+3.50 
+150.6 
+81.2 
+-- 
+[21] 
+4. 
+1T’-MoS2 
+ 
+3.90 
+-- 
+-- 
+-- 
+[42] 
+5. 
+MgH2-Gr 
+Graphene 
+5.80 
+300.0 
+-- 
+-- 
+[43] 
+
+Cyclic stability for MgH,-MoS
+capacity (wt%)
+6
+00300
+=0=0-0:
+5
+-I- Rehydrogenation
+- Dehydrogenation
+4
+3
+Degradation during rehydrogenation=0.42 wt%
+Degradationduring dehydrogenation=0.38 wt%
+Hydrogen :
+2
+1
+0
+6
+8
+10
+16
+18
+222426
+No.of cycleCyclic stability for MgH,-WS
+6
+5.
+ Rehydrogenation
+4.
++- Dehydrogenation
+3
+Degradation during rehydrogenation=0.30 wt%
+Degradation during dehydrogenation=0.36 wt%
+Hydrogen :
+2
+0
+10
+12
+16
+18.20
+222426
+No. of cycle18 
+ 
+6. 
+MgH2-
+TiH2@Gr 
+Graphene 
+6.77 
+204.0 
+88.89 
+74.54 
+[3] 
+MgH2-
+TiO2@Gr 
+Graphene 
+5.98 
+240.0 
+98.00 
+76.87 
+MgH2-Ti@Gr 
+Graphene 
+5.70 
+235.0 
+103.03 
+75.65 
+7. 
+MgH2-Gr 
+Graphene 
+6.14 
+300.0 
+134.95 
+77.90 
+[13] 
+8. 
+MgH2-VS2 
+VS2 
+6.51 
+242.0 
+98.10 
+76.83 
+9. 
+MgH2-WS2 
+WS2 
+5.95 
+277.0 
+104.66 
+77.44 
+Pres
+ent 
+stud
+y 
+10. 
+MgH2-MoS2 
+MoS2 
+6.00 
+330.0 
+117.09 
+78.33 
+Pres
+ent 
+stud
+y 
+ 
+4. Conclusions 
+ 
+ The catalytic effect of MoS2, and WS2 on MgH2 was evaluated and compared. 
+Based on the de/re-hydrogenation study, it is found that WS2 works as an optimum 
+catalyst over MoS2 for MgH2. The MgH2-WS2 has an onset de-hydrogenation ~277 oC 
+with a hydrogen storage capacity of 5.95 wt%. The MgH2-WS2 absorbed hydrogen ~ 3.72 
+wt% within 1.3 minutes at 300 oC under 13 atm hydrogen pressure and it desorbed ~5.57 
+wt% within 20 minutes at 300 oC under 1 atm hydrogen pressure. The MgH2-WS2 shows 
+a minimum degradation of hydrogen storage capacity ~ 0.3 wt% upto 25 cycles which 
+shows a better cyclic stability than cyclic stability of MgH2-MoS2 (~ 0.4 wt% loss in 
+hydrogen storage capacity). MgH2-WS2 also shows the lower reaction activation energy 
+~117 kJ/mol as compare to other catalyzed and uncatalyzed samples. On the other hand, 
+these catalysts (WS2 and MoS2) do not have any impact on the thermodynamical 
+parameters that is change in enthalpy. This study opens a new era to further applications 
+of 2D layered materials for various applications like template materials.  
+
+19 
+ 
+Acknowledgments 
+We gratefully accept funding assistance from the Department of Science and Technology 
+(DST), New Delhi, India. The Council of Scientific and Industrial Research (CSIR), New 
+Delhi, India, has awarded the author (S.K.V.) a CSIR-Senior Research Fellowship 
+(Award No. 09/013(0872)/2019-EMR-I), for which the author is grateful. 
+Conflict of Interest Declaration 
+There are no conflicts of interest among the authors. 
+ 
+ 
+References 
+[1] 
+TP Yadav, A Kumar, SK Verma, NK Mukhopadhyay, High-Entropy Alloys for 
+Solid Hydrogen Storage: Potentials and Prospects, Transactions of the Indian 
+National Academy of Engineering, 7 (2022) 147–156. 
+https://doi.org/10.1007/s41403-021-00316-w.  
+[2] 
+A. Kumar, T.P. Yadav, N. K. Mukhopadhyay, Notable hydrogen storage in Ti–Zr–
+V–Cr–Ni high entropy alloy, International Journal of Hydrogen Energy 47 (2022) 
+22893-22900. https://doi.org/10.1016/j.ijhydene.2022.05.107 
+[3] 
+Verma SK, Bhatnagar A, Shukla V, Soni PK, Pandey AP, Yadav TP, et al. 
+Multiple improvements of hydrogen sorption and their mechanism for MgH2 
+catalyzed through TiH2@Gr. Int J Hydrogen Energy 2020;45:19516–30. 
+https://doi.org/10.1016/j.ijhydene.2020.05.031. 
+[4] 
+SK Pandey, SK Verma, A Bhatnagar, TP Yadav,  Catalytic characteristics of 
+titanium‐(IV)‐isopropoxide (TTIP) on de/re‐hydrogenation of wet ball‐milled 
+MgH2/Mg,  International Journal of Energy Research 46 (12) (2022) 17602-17615. 
+https://doi.org/10.1002/er.8427. 
+[5] 
+Shukla V, Bhatnagar A, Verma SK, Pandey AP, Vishwakarma AK, Srivastava P, 
+et al. Simultaneous improvement of kinetics and thermodynamics based on SrF2 
+and SrF2@Gr additives on hydrogen sorption in MgH2. Mater Adv 2021;2:4277–
+90. https://doi.org/10.1039/D1MA00012H. 
+[6] 
+Srivastava ON, Yadav TP, Shahi RR, Pandey SK, Shaz MA, Bhatnagar A. 
+
+20 
+ 
+Hydrogen energy in India: Storage to application. Proc Indian Natl Sci Acad 
+2015;81:915–37. https://doi.org/10.16943/ptinsa/2015/v81i4/48303. 
+[7] 
+US DoE. Target Explanation Document: Onboard Hydrogen Storage for Light-
+Duty Fuel Cell Vehicles. US Drive 2017:1–29. 
+[8] 
+Bhatnagar A, Pandey SK, Vishwakarma AK, Singh S, Shukla V, Soni PK, et al. 
+Fe3O4 @graphene as a superior catalyst for hydrogen de/absorption from/in MgH 2 
+/Mg. J Mater Chem A 2016;4:14761–72. https://doi.org/10.1039/c6ta05998h. 
+[9] 
+Sadhasivam T, Kim H-T, Jung S, Roh S-H, Park J-H, Jung H-Y. Dimensional 
+effects of nanostructured Mg/MgH2 for hydrogen storage applications: A review. 
+Renew Sustain Energy Rev 2017;72:523–34. 
+https://doi.org/https://doi.org/10.1016/j.rser.2017.01.107. 
+[10] Yartys VA, Lototskyy M V, Akiba E, Albert R, Antonov VE, Ares JR, et al. 
+Magnesium based materials for hydrogen based energy storage: Past, present and 
+future. Int J Hydrogen Energy 2019;44:7809–59. 
+https://doi.org/https://doi.org/10.1016/j.ijhydene.2018.12.212. 
+[11] SK Pandey, A Bhatnagar, SS Mishra, TP Yadav, MA Shaz, ON Srivastava, 
+Curious Catalytic Characteristics of Al–Cu–Fe Quasicrystal for  
+e/Rehydrogenation of MgH2, The Journal of Physical Chemistry C 121 (45) (2017) 
+24936-24944. https://doi.org/10.1021/acs.jpcc.7b07336 
+[12] V Shukla, TP Yadav, Notable catalytic activity of CuO nanoparticles derived from 
+metal‐organic frameworks for improving the hydrogen sorption properties of 
+MgH2, International Journal of Energy Research, 46 (9) (2022) 12804-12819. 
+https://doi.org/10.1002/er.8050. 
+[13] Verma SK, Shaz MA, Yadav TP. Enhanced hydrogen absorption and desorption 
+properties of MgH2 with graphene and vanadium disulfide. Int J Hydrogen Energy 
+2022. https://doi.org/https://doi.org/10.1016/j.ijhydene.2021.12.269. 
+[14] Patelli N, Calizzi M, Migliori A, Morandi V, Pasquini L. Hydrogen Desorption 
+Below 150 °C in MgH2–TiH2 Composite Nanoparticles: Equilibrium and Kinetic 
+Properties. J Phys Chem C 2017;121:11166–77. 
+https://doi.org/10.1021/acs.jpcc.7b03169. 
+[15] Korablov D, Besenbacher F, Jensen TR. Kinetics and thermodynamics of 
+
+21 
+ 
+hydrogenation-dehydrogenation for Mg-25%TM (TM = Ti, Nb or V) composites 
+synthesized by reactive ball milling in hydrogen. Int J Hydrogen Energy 
+2018;43:16804–14. https://doi.org/10.1016/j.ijhydene.2018.05.091. 
+[16] Bhatnagar A, Johnson JK, Shaz MA, Srivastava ON. TiH 2 as a Dynamic Additive 
+for Improving the De/Rehydrogenation Properties of MgH 2 : A Combined 
+Experimental and Theoretical Mechanistic Investigation. J Phys Chem C 
+2018;122:21248–61. https://doi.org/10.1021/acs.jpcc.8b07640. 
+[17] Zhang J, Xia G, Guo Z, Zhou D. Synergetic Effects toward Catalysis and 
+Confinement of Magnesium Hydride on Modified Graphene: A First-Principles 
+Study. J Phys Chem C 2017;121:18401–11. 
+https://doi.org/10.1021/acs.jpcc.7b05848. 
+[18] Singh MK, Bhatnagar A, Pandey SK, Mishra PC, Srivastava ON. Experimental 
+and first principle studies on hydrogen desorption behavior of graphene nanofibre 
+catalyzed MgH2. Int J Hydrogen Energy 2017;42:960–8. 
+https://doi.org/10.1016/J.IJHYDENE.2016.09.210. 
+[19] Liu G, Wang Y, Jiao L, Yuan H. Understanding the role of few-layer graphene 
+nanosheets in enhancing the hydrogen sorption kinetics of magnesium hydride. 
+ACS Appl Mater Interfaces 2014;6:11038–46. https://doi.org/10.1021/am502755s. 
+[20] Varunaa R, Ravindran P. Potential hydrogen storage materials from metal 
+decorated 2D-C2N: An: ab initio study. Phys Chem Chem Phys 2019;21:25311–
+22. https://doi.org/10.1039/c9cp05105h. 
+[21] Liu Y, Gao H, Zhu Y, Li S, Zhang J, Li L. Excellent catalytic activity of a two-
+dimensional Nb4C3Tx (MXene) on hydrogen storage of MgH2. Appl Surf Sci 
+2019;493:431–40. https://doi.org/https://doi.org/10.1016/j.apsusc.2019.07.037. 
+[22] Chen G, Zhang Y, Cheng H, Zhu Y, Li L, Lin H. Effects of two-dimension MXene 
+Ti3C2 on hydrogen storage performances of MgH2-LiAlH4 composite. Chem 
+Phys 2019;522:178–87. 
+https://doi.org/https://doi.org/10.1016/j.chemphys.2019.03.001. 
+[23] Raccichini R, Varzi A, Passerini S, Scrosati B. The role of graphene for 
+electrochemical energy storage. Nat Mater 2015;14:271–9. 
+https://doi.org/10.1038/nmat4170. 
+
+22 
+ 
+[24] Pumera M. Graphene-based nanomaterials for energy storage. Energy Environ Sci 
+2011;4:668–74. https://doi.org/10.1039/C0EE00295J. 
+[25] Singh S, Bhatnagar A, Shukla V, Vishwakarma AK, Soni PK, Verma SK, et al. 
+Ternary transition metal alloy FeCoNi nanoparticles on graphene as new catalyst 
+for hydrogen sorption in MgH2. Int J Hydrogen Energy 2020;45:774–86. 
+https://doi.org/10.1016/j.ijhydene.2019.10.204. 
+[26] Liu G, Wang Y, Xu C, Qiu F, An C, Li L, et al. Excellent catalytic effects of 
+highly crumpled graphene nanosheets on hydrogenation/dehydrogenation of 
+magnesium hydride. Nanoscale 2013;5:1074–81. 
+https://doi.org/10.1039/c2nr33347c. 
+[27] Huang Y, Xia G, Chen J, Zhang B, Li Q, Yu X. One-step uniform growth of 
+magnesium hydride nanoparticles on graphene. Prog Nat Sci Mater Int 
+2017;27:81–7. https://doi.org/https://doi.org/10.1016/j.pnsc.2016.12.015. 
+[28] Liu R, Zhao Y, Chu T. Theoretical exploration of MgH2 and graphene nano-flakes 
+in cyclohexane: proposing a new perspective toward functional hydrogen storage 
+material. Chem Commun 2015;51:2429–32. 
+https://doi.org/10.1039/C4CC09424G. 
+[29] Li W, Huang J, Feng L, Cao L, Feng Y, Wang H, et al. Facile: In situ synthesis of 
+crystalline VOOH-coated VS2 microflowers with superior sodium storage 
+performance. J Mater Chem A 2017;5:20217–27. 
+https://doi.org/10.1039/c7ta05205g. 
+[30] Fang W, Zhao H, Xie Y, Fang J, Xu J, Chen Z. Facile Hydrothermal Synthesis of 
+VS2/Graphene Nanocomposites with Superior High-Rate Capability as Lithium-
+Ion Battery Cathodes. ACS Appl Mater Interfaces 2015;7:13044–52. 
+https://doi.org/10.1021/acsami.5b03124. 
+[31] Ma H, Shen Z, Ben S. Understanding the exfoliation and dispersion of MoS2 
+nanosheets in pure water. J Colloid Interface Sci 2018;517:204–12. 
+https://doi.org/10.1016/j.jcis.2017.11.013. 
+[32] Lu X, Utama MIB, Zhang J, Zhao Y, Xiong Q. Layer-by-layer thinning of MoS2 
+by thermal annealing. Nanoscale 2013;5:8904–8. 
+https://doi.org/10.1039/C3NR03101B. 
+
+23 
+ 
+[33] Chakraborty B, Matte HSSR, Sood AK, Rao CNR. Layer-dependent resonant 
+Raman scattering of a few layer MoS2. J Raman Spectrosc 2013;44:92–6. 
+https://doi.org/https://doi.org/10.1002/jrs.4147. 
+[34] Hazarika SJ, Mohanta D. Inorganic fullerene-type WS2 nanoparticles: processing, 
+characterization and its photocatalytic performance on malachite green. Appl Phys 
+A 2017;123:381. https://doi.org/10.1007/s00339-017-0965-7. 
+[35] Berkdemir A, Gutiérrez HR, Botello-Méndez AR, Perea-López N, Elías AL, Chia 
+C-I, et al. Identification of individual and few layers of WS2 using Raman 
+Spectroscopy. Sci Rep 2013;3:1755. https://doi.org/10.1038/srep01755. 
+[36] Frindt RF. Single Crystals of MoS2 Several Molecular Layers Thick. J Appl Phys 
+1966;37:1928–9. https://doi.org/10.1063/1.1708627. 
+[37] Radisavljevic B, Radenovic A, Brivio J, Giacometti V, Kis A. Single-layer MoS2 
+transistors. Nat Nanotechnol 2011;6:147–50. 
+https://doi.org/10.1038/nnano.2010.279. 
+[38] Ovchinnikov D, Allain A, Huang Y-S, Dumcenco D, Kis A. Electrical Transport 
+Properties of Single-Layer WS2. ACS Nano 2014;8:8174–81. 
+https://doi.org/10.1021/nn502362b. 
+[39] Kissinger HE. Reaction Kinetics in Differential Thermal Analysis. Anal Chem 
+1957;29:1702–6. https://doi.org/10.1021/ac60131a045. 
+[40] Wu Z, Fang J, Liu N, Wu J, Kong L. The Improvement in Hydrogen Storage 
+Performance of MgH2 Enabled by Multilayer Ti3C2. Micromachines  2021;12. 
+https://doi.org/10.3390/mi12101190. 
+[41] Lima EC, Hosseini-Bandegharaei A, Moreno-Piraján JC, Anastopoulos I. A 
+critical review of the estimation of the thermodynamic parameters on adsorption 
+equilibria. Wrong use of equilibrium constant in the Van’t Hoof equation for 
+calculation of thermodynamic parameters of adsorption. J Mol Liq 2019;273:425–
+34. https://doi.org/https://doi.org/10.1016/j.molliq.2018.10.048. 
+[42] Chen J, Cao J, Zhou J, Zhang Y, Li M, Wang W, et al. Mechanism of highly 
+enhanced hydrogen storage by two-dimensional 1T′ MoS2. Phys Chem Chem 
+Phys 2020;22:430–6. https://doi.org/10.1039/c9cp04402g. 
+[43] Singh MK, Bhatnagar A, Pandey SK, Mishra PC, Srivastava ON. Experimental 
+
+24 
+ 
+and first principle studies on hydrogen desorption behavior of graphene nanofibre 
+catalyzed MgH 2. Int J Hydrogen Energy 2017;42:960–8. 
+https://doi.org/10.1016/j.ijhydene.2016.09.210. 
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf,len=823
+page_content='1  Catalytic action of two-dimensional layered materials (WS2, and MoS2) on hydrogen sorption properties of MgH2 Satish Kumar Verma1, Mohammad Abu Shaz1, Thakur Prasad Yadav1,2* 1Hydrogen Energy Centre, Department of Physics, Banaras Hindu University, Varanasi- 221005, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 2Department of Physics, Faculty of Science, University of Allahabad, Prayagraj-211002, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Abstract: The present study reports the catalytic action of two-dimensional (2D) layered materials (MoS2 and WS2) for improving the de/re-hydrogenation kinetics of MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The MgH2 start desorbing at 277 ºC with a hydrogen storage capacity of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='95 wt% in the presence of WS2 catalyst whereas onset desorption temperature of MgH2 catalyzed by MoS2 is 330 ºC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The MgH2-WS2 absorbed hydrogen ~ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='72 wt% within 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3 minutes at 300 ºC under 13 atm hydrogen pressure and it desorbed ~5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='57 wt% within 20 minutes at 300 ºC under 1 atm hydrogen pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' We have performed 25 cycles of dehydrogenation (under 1 atm hydrogen pressure at 300 ºC) and re-hydrogenation (under 13 atm hydrogen pressure at 300 °C) to ensure cyclic stability of catalyzed version of MgH2 where MgH2-WS2 shows better cyclic stability than MgH2-MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' MgH2-WS2 also shows the lower reaction activation energy ~117 kJ/mol as compare to other catalyzed and uncatalyzed samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' On the other hand, these catalysts (WS2 and MoS2) do not have any impact on the thermodynamical parameters that is change in enthalpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Key words: 2D layered materials, De/re-hydrogenation kinetics, Activation energy, MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' *Corresponding author Email: yadavtp@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='com  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Introduction A crucial and promising area of research for onboard hydrogen applications is the development of safe and efficient hydrogen storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The solid-state approach is one of the most appropriate, secure, and effective ways to store hydrogen among the several methods that can be used, including gaseous, liquid, and solid-state storage [1,2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Due to its high hydrogen storage capacity (110 g/L volumetric and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='6 wt% gravimetric), low cost, light weight, and large abundance (in the form of Mg) in earth crust (8th most) and seawater (3rd most), MgH2 is a leading choice for hydrogen storage in the solid-state mode [3–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' According to the United States Department of Energy (US DOE) technical targets for hydrogen storage systems [7], MgH2 has certain advantages that make it a viable option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The high dehydrogenation temperature (above 400 ºC), slow kinetics (hydrogen de/re-hydrogenation kinetics 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4 kg-H2/min), and high thermodynamic properties (high reaction enthalpy 74 kJ/mol) of MgH2 prevent it from being a suitable material for onboard applications even with these advantages [8–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' In recent years, the creation of suitable catalyst(s), alloys, composite materials with complicated hydrides, and scaffolding have all been used as feasible methods to improve the hydrogen storage performance of MgH2 [11,12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  The use of various types of catalysts and additives to enhance the performance of Mg/MgH2 has been the subject of several studies by various research organizations [13–17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Another application for the 2D materials is as a catalyst for improving the hydrogen characteristics of MgH2 [18–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Due to its enormous surface area, ballistic conduction, thermal conductivity, mechanical stability, and light weight, graphene, which has a 2D planer structure with sp2 carbon atoms arranged in a hexagonal framework, has attracted a lot of attention as a catalyst and as a template material for hydrogen storage application in MgH2 [23,24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=" MgH2's de/rehydrogenation kinetics exhibit effective catalytic behavior in the graphene layer, which also inhibits MgH2's agglomeration and grain growth [3,5,25]." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=', for instance, have created MgH2-5% Gr nanosheets [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' They have demonstrated that graphene nanosheets offer a significant hydrogen diffusion pathway and prevent MgH2 from aggregating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' According to Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=", [27] report's MgH2 nanoparticles supported by graphene exhibit remarkable hydrogen sorption kinetics and  3  cyclic stability." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Due to the strong interaction between graphene and MgH2 nanoparticles and the prevention of nanoparticle agglomeration, the MgH2 nanoparticles demonstrated excellent hydrogen storage performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Additionally, grapheme prevents the aggregation of nanoparticles during the rehydrogenation of MgH2, according to a theoretical study using molecular dynamics simulation [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Rough studies are still required to determine the impact of graphene and other 2D layered materials on MgH2, even though some prior studies have shown the remarkable catalytic/co-catalytic and agglomeration blocking properties of Gr on MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' We have examined a comparison between WS2 and MoS2 as a catalyst for enhancing hydrogen sorption properties of MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' WS2 and MoS2 are suitable alternatives to graphene for the catalytic action on MgH2 due to their high conductivity (metallic nature), thermal stability, and strong catalytic behavior [29,30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Tungsten (W) and Molybdenum (Mo) are sandwiched between two Sulphur layers with weak Van der Waals interactions in the family of layered transition-metal dichalcogenides (TMDs) materials that include WS2 and MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The re/de-hydrogenation kinetics, and catalytic behavior of WS2 and MoS2 on MgH2 has been investigated in details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Experimental section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Synthesis of a few layered WS2 The bulk tungsten sulfide (WS2) (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='80 %) powder was procured from the Alfa Aesar for the present investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  For the preparation of few layered WS2, WS2 powder was dispersed in de-ionized water and sonicated it for 74 hours using ultrasonicator at 20 kHz frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The sonicated sample was then dried at 50 °C under a dynamic vacuum of order 10-2 torr to form the few layered WS2 powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' This preparation method can also be understood by the schematic given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1: Schematic diagram for the synthesis of a few layers WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Synthesis of few-layer MoS2 The Otto Chemica bulk molybdenum disulfide (MoS2) (99 %) powder was used for the present investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' MoS2 powder was dispersed in de-ionized water and sonicate it for 74 hours using ultrasonicator at 20 kHz frequency to obtain the few-layered MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The sonicated sample was then dried at 50 °C under dynamic vacuum of order 10-2 torr to form the few layered MoS2 powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 2, shows the schematic diagram for preparation of few-layered MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  BulkMoS2  BulkMoS,  FewlayeredMoS2  DoublelayeredMoS2  UltrasonicationofbulkMoS,BulkWS2  BulkWs,  FewlayeredwS2  DoublelayeredWS2  Ultrasonicationof bulkWS25  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2: Schematic diagram for the synthesis of a few layers MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Synthesis of MgH2 catalyzed by WS2, and MoS2 The pure MgH2 was procured from Fujifilm (Japan) (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='9%) for the present investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Mechanical ball-milling of MgH2 with graphene at 180 rpm for 24 hours with a ball-to- powder ratio of 50:1 (by weight) using a planetary ball-miller (Retsch PM 400) was used to synthesize MgH2 catalyzed by WS2 (MgH2-WS2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' To explore the optimum catalyst concentration for hydrogen sorption kinetics of Mg/MgH2, we have synthesized a set of different catalyst concentrations (5, 10, 12 wt%) to catalyze MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' For hydrogen sorption in Mg/MgH2, 10 wt% catalysts were found to be optimal (in terms of desorption temperature and hydrogen storage capacity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The ball-miller vials were filled with 5 atm H2 pressure to compensate for the loss of hydrogen from MgH2 during milling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' All the loading and unloading of the samples was done inside the N2-filled glove box (MBRAUM MB10 compact) with O2 and H2O levels < 1 ppm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The synthesis of MgH2 catalyzed by MoS2 (MgH2-MoS2) was done using the same synthesis route as MgH2- WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Characterization techniques The structural characterization of prepared samples was carried out by XRD technique using Empyrean PANalytical X-ray diffractometer equipped with 2D detector with a Cu Kα beam (λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5415 Å) operated at 40 kV and 40 mA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The microstructural and selected area electron diffraction (SAED) analysis of as-prepared samples was carried out by TEM (Technai-20G2) operating at the accelerating voltage of 200 kV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Perkin Elmer (Spectrum 100) spectrometer in transmission mode with attenuated total reflectance (ATR) sampling mode (wavenumber range 500–4000 cm-1) was used to carry out FTIR spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The Raman spectra have been acquired at -60 ºC using Horiba-Jobin-Yvon LABRAM-HR800 spectrometer with diode LASER (532 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The desired thickness and surface topography of the prepared samples were examined by using solver next AFM in non-contact mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The characterized samples then proceed for the hydrogen desorption and absorption using automated two-channel volumetric sieverts type apparatus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The temperature programmed desorption (TPD) was carried out with a heating rate of 5 oC-  6  min-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The activation energy (Ea) study of prepared catalyzed samples has been done by using DSC (Perkin Elmer DSC 8000) with a heating rate of 15 oC/min, 18 oC/min, 21 oC/min, and 24 oC/min under nitrogen atmosphere (20 ml/min).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Results and discussion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Structural, microstructural, and spectroscopic characterization analysis The structural characteristics of as-prepared samples have been examined using the XRD characterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 3(a) shows the XRD pattern of pristine MgH2, which matches well with the tetragonal MgH2 with space group P42/mnm (136) and a=b= 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='516 Å, c = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='020 Å (JCPDS no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 740934).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 3(b) shows the XRD pattern of MoS2, which matches well with the hexagonal structure of MoS2 with space group P63/mmc(194) and a=b= 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1602 Å, c = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='294 Å (Joint Committee on Powder Diffraction Standards (JCPDS) no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 651951).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The XRD pattern of as-prepared WS2 is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 3(c), that matches well with the hexagonal structure of WS2 with space group P63/mmc(194) and a=b= 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1532 Å, c = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='323 Å (JCPDS no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 841398).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The usual diffraction pattern of MgH2-MoS2, and MgH2-WS2 are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 3(d-e), respectively, where besides the tetragonal phase of MgH2, some peaks of WS2 and MoS2 are either suppressed or masked by the peaks of MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The diffraction peaks of WS2 and MoS2 are identified and labeled in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 3(d- e), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The different bands position, shapes, and relative intensities of Raman spectra give us essential information about the materials and stacking of layers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=', Raman spectroscopy can determine the layer thickness at the atomic level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The Raman spectra of as-prepared WS2, and MoS2 have shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  In the case of MoS2, the two Raman modes are appeared at ~ 345 cm-1 and ~ 370 cm-1 corresponds to E12g and A1g modes of vibrations (labeled in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 4(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The indicated modes of MoS2 have frequency difference of ~ 25 cm-1, that means the MoS2 as layered material with few layers of stacking (3-5 layers) [31,32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The FWHM of A1g mode is ~ 7 cm-1, which can also be referred to stacking a few layers of MoS2 [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The Raman shifts at ~316 cm-1 and 384 cm-1 (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 4(a)) corresponds to the presence of E12g and A1g modes respectively in WS2 sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The  7  intensity ratio of E12g and A1g modes was estimated E12g/A1g i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='26, which is higher than the intensity ratio of bulk WS2 (E12g/A1g = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='47) and lower than the monolayer WS2 (E12g/A1g = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2) [34,35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' This calculated intensity ratio (E12g/A1g = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='26) is compatible with the range of 2-3 layers of WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 3: XRD patterns of (a) Pristine MgH2, (b) MoS2, (c) WS2, (d) MgH2-MoS2, and (e) MgH2-WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  o Parafilm, MgH2,  t Ws2, u Mos2  (e)MgH2 Ws  52  T (d) mgh2 Mos2 Intensity (wt%)  (c) WS 2  (002) (004)  (100)  (101)  (900)  (105)  (110)  (112) (114)  (203)  (116)  8  tt  T  T  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1  1  T  (b)Mos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  (00L)2  2  (002)  U  C(105)  (102)  (103)  C(110)  (112)  c(108)  (203)  U  (a) Pristine  MgH2 (200)  (110)  (220) (002)  (310)  (112)  (301)  (202)  (211) 8  8 ￥  10  20  30  40  50  60  70  80  2e(degree8  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 4: Raman spectra of (a) WS2 and (b) MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  The information about stacking layers in 2D layered materials (like WS2 and MoS2) can also be verified by AFM analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The surface topography and height profile of prepared MoS2, and WS2 were examined along the blue dotted line as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' S1(a-b) (given in supporting information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The layered surface morphology along with height profile (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' S1(a-a1)) shown the average thickness of MoS2 is ~1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3 nm, that indicates the presence of ~2 layers of stacking in the MoS2 sample [36,37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The ~7-8 layers of stacking were present in the case of WS2 (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' S1(b-b1)) with a monolayer height of ~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='7 nm [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  (b) Raman spectra of MoS2 (370) A1g (a) Raman spectra of WS2 (345) 2g Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=') (384) 2g A1 (316) 175200225250275300325 350 375400 425 450475500 Raman shift (cm9  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2 De/Re-hydrogenation kinetics of catalyzed MgH2 To identify the optimal percentage of catalyst in MgH2 with optimum temperature range where material performed promptly, we have characterized as-prepared samples for the temperature programmed desorption (TPD) analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The TPD curves of MgH2-MoS2 have seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' S2 (given in supporting information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The MgH2-5%MoS2, MgH2- 10%MoS2, and MgH2-12%MoS2, starts releasing hydrogen at ~ 357 °C, ~ 330 °C, ~ 302 °C with ~ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='41 wt%, ~ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='00 wt%, ~ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='88 wt% of hydrogen storage capacity respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' On the other hand, MgH2-5%WS2, MgH2-10%WS2, and MgH2-12%WS2, starts releasing hydrogen at ~ 339 °C, ~ 277 °C, ~ 258 °C with ~ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='54 wt%, ~ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='95 wt%, ~ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='14 wt% of hydrogen storage capacity respectively (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' S3 in supporting information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Based on TPD analysis, the optimum catalyst concentration for catalyzing MgH2 is 10 wt% for all catalysts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' After getting information about the optimum catalyst for MgH2, we compared the TPD analysis of all optimum catalyzed samples with pristine MgH2, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The TPD of pristine MgH2 (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 5(a)) was then carried out to compare hydrogen storage properties with catalyzed samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The pristine MgH2 has an onset desorption temperature of 376 oC with a total release of ~7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='45 wt% storage capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The onset desorption temperature of MgH2-MoS2 (MgH2-10%MoS2) is ~ 330 oC, and it desorbs ~ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='00 wt% hydrogen while the desorption gets completed at 396 oC (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 5(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  In the case of MgH2-WS2 (MgH2-10%WS2), it starts desorbing hydrogen at ~ 277 oC with a storage capacity of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='95 wt% (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 5(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  10  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 5: Comparative TPD analysis of (a) Pristine MgH2, (b) MgH2-MoS2 and (c) MgH2- WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  The desorbed samples then proceed for re/de-hydrogenation to check the cyclic stability and reversibility of catalyzed and pristine MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The re-hydrogenation kinetics was carried out at 300 oC under 13 atm hydrogen pressures, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' It can be seen, the pristine MgH2 absorbed ~1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='16 wt% hydrogen in 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2 minutes whereas MgH2-MoS2, MgH2-WS2 absorbed 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='60 wt%, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='72 wt%, hydrogen, respectively, under similar conditions of temperature and pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  0  Hydrogen desorbed (wt%)  (a)  (b)  (c)  (a)PristineMgH  5  (b) MgH, Mos,  6  (c) MgH, WS,  7  8  200  225  250  275  300  325  350  375  400  425  Temperature (C)11  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 6: Rehydrogenation kinetics curves at 300 °C under 13 atm H2 pressure of (a) b) MgH2-WS2, (c) MgH2-MoS2 and (e) Pristine MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  The rehydrogenated samples were then dehydrogenated at 300 oC under 1 atm hydrogen pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' It can be seen clearly in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 7, that the MgH2-WS2 sample releases 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='57 wt% hydrogen within 20 minutes while MgH2-MoS2 and pristine MgH2 releasees 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='25 wt%, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='23 wt% of hydrogen under similar temperature and pressure conditions, which is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='32 wt%, and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='48 wt% more than pristine MgH2, MgH2-MoS2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Based on the above re/de-hydrogenation kinetics study, it is clearly shown that WS2 works as a superior catalyst to MoS2 for catalyzing MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Therefore, in present study WS2 is a prominent catalyst to catalyze MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  (b)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Hydrogen absorbed (wt%)  (a)  (c) (a) MgH, WS  (b) MgH, Mos  (c) Pristine MgH,  0  0  2  4  6  8  10  12  14  16  18  20  22  24  Time (Min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' )12  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 7: Dehydrogenation kinetics curves at 300 °C under 1 atm H2 pressure of (a) MgH2- WS2, (b) MgH2-MoS2, and (c) Pristine MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Study of kinetics: Estimation of activation energy The DSC was carried out to determine the hydrogen desorption activation energy barrier to convert MgH2 into Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The DSC profile of MgH2-MoS2, MgH2-WS2, are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 8-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' In the case of MgH2-WS2, the peak desorption temperature found from DSC is ~ 380 oC, while the onset desorption temperature found from TPD is ~ 277 oC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' There is a difference in desorption temperature in TPD (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 5(c)) and DSC (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 9(a)) curves due to the TPD being performed under vacuum with a temperature ramping rate of 5 oC/min while DSC was performed under N2 atmosphere with a temperature ramping rate of 15  oC/min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' For calculating the desorption activation energy, we have performed DSC with a set of the various rate of heating (15, 18, 21, 24 oC/min) and plotted the Kissinger curve by using the Kissinger equation[39] as given:  (a) Pristine MgH, (b) MgH, MoS,  Hydrogen desorbed (wt%)  5  (c) MgH, WS  (a)  (b)  2  (c)  0  0  5  10  15  20  25  30  35  40  45  50  55  60  Time (min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' )13  (1) Where β, Tp, and Ea are the heating rate, corresponding peak desorption temperature, and activation energy, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The slope of Kissinger plot (ln(β/Tp 2) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 1000/Tp 2 plot) (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 8-9) is used to calculate the desorption activation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The calculated activation energy for MgH2-MoS2, and MgH2-WS2 is 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='09 kJ/mol (± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='60 kJ/mol), and 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='00 kJ/mol (± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='74 kJ/mol) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' This activation energy indicates that ~104 kJ/mol energy is required to overcome the barrier to convert MgH2 into Mg in the presence of a WS2 catalyst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' These calculated activation energies are significantly lower than the activation energy of pristine MgH2 [3,40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Table 1: Table for plateau pressures at corresponding temperatures, change in enthalpy, and activation energy of MgH2-MoS2, and MgH2-WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Sample  name  Plateaus  pressure  (atm)  Temperature  (  ºC)  Change  in  enthalpy  (kJ/mol)  Activation  energy  (kJ/mol)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 MoS2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='03  272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='62  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='33  117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='03  292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='28  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='77  313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='28  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 WS2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='52  281.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='26  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='44  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='66  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='92  300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='60  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='45  316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='29  14  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 8: (i) DSC profile for desorption of MgH2-MoS2 with the heating rate (a) 15 ºC/min, (b) 18 ºC/min, (c) 21 ºC/min, (d) 24 ºC/min, and (ii) corresponding Kissinger plot for evaluating the desorption activation energy of MgH2-MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  DSCprofilefor MgH2 MoS2 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='8  Kissinger plot for MgHb MoS2  Linear fit  (d) 24°C/min 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='9  (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=') 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  (c)21cC/min  Heatflow(  P 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1  Endo up  (b) 18 C/min  Eguation  y=a+b 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2  Adj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' R Squ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='99937  Value  Standard Er 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3  In(beta/Tp2) Irtercept  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='212  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='30766  (a) 15 C/min  In(beta/Tp2) Slope 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='083  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='20379  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4881.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4941.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='530  250  275  300  325  350  375  400  425  450  1000/T,(K1)  Temperature (cC)DSCprofileforMgH2 WS2  Kissinger plot for MgH2 WS2 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='8  (d) 24 C/min  Linear fit 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='9  Heat flow (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=')  (c) 21 °C/min 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  [β/T,  (b) 18 °C/min 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1  Endo  Equation  =a+  Adj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' R Sq  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='9979 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2  Value  Standard  (a) 15 °C/min  In(beta/Tp Interce  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3313  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='50735  In(beta/Tp Slope 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='58  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='33004 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='520  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='525  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='530  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='535  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='540  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='545  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='550  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='555  1000/T(K  320330340350360370380390400410420430440450  Temperature (C)15  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 9: (i) DSC profile for desorption of MgH2-WS2 with the heating rate (a) 15 ºC/min, (b) 18 ºC/min, (c) 21 ºC/min, (d) 24 ºC/min, and (ii) corresponding Kissinger plot for evaluating the desorption activation energy of MgH2-WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Study of thermodynamics After the kinetics and reversibility study, we have proceeded with the thermodynamic analysis of catalyzed MgH2 for comparing the change in enthalpy and entropy of the system using well known Van’t Hoff equation [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  lnP = (ΔH/RT) (ΔS/R)  (2) Where P, ∆H, R, T, and ∆S are the pressure, change in enthalpy, gas constant, absolute temperature, and change in entropy, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The PCI isotherms (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 10(i)-11(i) and Van’t Hoff plots (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 10(ii)-11(ii)) were used for the calculation of change in enthalpy of MgH2-MoS2 and MgH2-WS2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The calculated change in desorption enthalpy was found to be 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='33 kJ/mol (± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='40 kJ/mol), and 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='44 kJ/mol (± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='13 kJ/mol), for MgH2-MoS2 and MgH2-WS2 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' It is clear from the above estimation of change in enthalpy, that there is no significant enthalpy change in the presence of a catalyst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Thus MoS2, WS2 have not positively impacted the thermodynamic barrier of the MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The plateau pressure at corresponding temperatures, change in enthalpy, and activation energy has been tabulated in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  (i) PCl desorption for MgH2-MoS2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=" (ii) Vant's Hoff plot for MgH2-MoS2 6." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' - Linear fit 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0 (atm) 320°C 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Pressure ( P 三 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 300°C 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4 2 Equation y=a+b* 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2- Adj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' R-Squar0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='99936 280 °C Value Standard Err InP Intercept 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3878 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='298 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0 InP Slope 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4207 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='16804 0 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='70 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='72 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='74 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='76 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='78 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='80 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='82 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='84 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='86 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='88 0 1 2 3 4 5 1000/T (K Hydropgen capacity (wt%)16  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=" 10: (i) PCI desorption plots for MgH2-MoS2 at different temperatures and (ii) corresponding Van't Hoff plot for calculating the change in enthalpy  Fig." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=" 11: (i) PCI desorption plots for MgH2-WS2 at different temperatures and (ii) corresponding Van't Hoff plot for calculating the change in enthalpy 3." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5 Cyclic stability of catalyzed MgH2 The WS2 (optimum catalyst) plays a significant role in improving the kinetics of MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The cyclic stability is an essential characteristic of the hydride material (MgH2) besides kinetic and thermodynamics, making it a worthy hydrogen storage material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Therefore, it is crucial to look at the cyclic stability of the catalyzed MgH2 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' We have performed 25 cycles of dehydrogenation (under 1 atm hydrogen pressure at 300 °C) and re-hydrogenation (under 13 atm hydrogen pressure at 300 °C) to ensure cyclic stability of catalyzed MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The cyclic stability curve of MgH2-MoS2 and MgH2-WS2 are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 12(a) MgH2-MoS2 shows the ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='42 wt% (from 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='77 wt% to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='35 wt%) degradation in hydrogen storage capacity during rehydrogenation and ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='38 wt% (from 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='69 wt% to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='31 wt%) in dehydrogenation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The MgH2-WS2 has the loss of hydrogen storage capacity ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3 wt% (from 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='80 wt% to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='50 wt%) during re- hydrogenation and ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='36 wt% (from 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='76 wt% to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='40 wt%) during dehydrogenation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Thus, MgH2-WS2 has more substantial cyclic stability than MgH2-MoS2 under similar  8 (i) PCI desorption for MgH2-WS2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content="4 (ii) Vant's Hoff plot for MgH2-WS2 1." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2 Linear fit 6 (atm) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0 5 Pressure 320 °C InP 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='8 300°℃ 3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='6 Equation y=a+ Adj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' R-Squ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='9995 2 280°C Value Standard E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' InP Intercep 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='038 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='23617 Inp Slope -9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='314 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1362 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='68 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='70 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='72 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='74 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='76 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='78 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='80 1000/T (K-1) 0 1 2 3 4 5 6 Hydrogen capacity (wt%)17  temperature and pressure conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The comparative study for hydrogen storage properties of different recently used 2D materials as the catalyst for MgH2 is explored in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 12: Cyclic stability of (a) MgH2-MoS2 and (b) MgH2-WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Table 2: Table for different 2D materials as the catalyst for hydrogen storage application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Material 2D- based catalyst Hydrogen storage capacity (wt%) Onset dehydrogen ation temperature (ºC)  Activation  energy  (kJ/mol)  Change  in  enthalpy  (kJ/mol)  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  Mg6C2N  C2N  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='79 [20]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 LiAlH4 Ti3C2  Ti3C2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='50  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3  [22]  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 Nb4C3Tx  Nb4C3Tx  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='50  150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='6  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2 [21]  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  1T’ MoS2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='90 [42]  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 Gr  Graphene  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='80  300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0 [43]  Cyclic stability for MgH,-MoS capacity (wt%) 6 00300 =0=0-0: 5 -I- Rehydrogenation - Dehydrogenation 4 3 Degradation during rehydrogenation=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='42 wt% Degradationduring dehydrogenation=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='38 wt% Hydrogen : 2 1 0 6 8 10 16 18 222426 No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='of cycleCyclic stability for MgH,-WS 6 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Rehydrogenation 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' +- Dehydrogenation 3 Degradation during rehydrogenation=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='30 wt% Degradation during dehydrogenation=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='36 wt% Hydrogen : 2 0 10 12 16 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='20 222426 No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' of cycle18  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 TiH2@Gr  Graphene  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='77  204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='89  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='54  [3]  MgH2 TiO2@Gr  Graphene  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='98  240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='00  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='87  MgH2 Ti@Gr  Graphene  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='70  235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='03  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='65  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 Gr  Graphene  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='14  300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='95  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='90  [13]  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 VS2  VS2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='51  242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='10  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='83  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 WS2  WS2  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='95  277.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='66  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='44  Pres  ent  stud  y  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  MgH2 MoS2  MoS2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='00  330.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='0  117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='09  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='33  Pres  ent  stud  y  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Conclusions  The catalytic effect of MoS2, and WS2 on MgH2 was evaluated and compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Based on the de/re-hydrogenation study, it is found that WS2 works as an optimum catalyst over MoS2 for MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The MgH2-WS2 has an onset de-hydrogenation ~277 oC with a hydrogen storage capacity of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='95 wt%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The MgH2-WS2 absorbed hydrogen ~ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='72 wt% within 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3 minutes at 300 oC under 13 atm hydrogen pressure and it desorbed ~5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='57 wt% within 20 minutes at 300 oC under 1 atm hydrogen pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The MgH2-WS2 shows a minimum degradation of hydrogen storage capacity ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3 wt% upto 25 cycles which shows a better cyclic stability than cyclic stability of MgH2-MoS2 (~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4 wt% loss in hydrogen storage capacity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' MgH2-WS2 also shows the lower reaction activation energy ~117 kJ/mol as compare to other catalyzed and uncatalyzed samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' On the other hand, these catalysts (WS2 and MoS2) do not have any impact on the thermodynamical parameters that is change in enthalpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' This study opens a new era to further applications of 2D layered materials for various applications like template materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  19  Acknowledgments We gratefully accept funding assistance from the Department of Science and Technology (DST), New Delhi, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The Council of Scientific and Industrial Research (CSIR), New Delhi, India, has awarded the author (S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=') a CSIR-Senior Research Fellowship (Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' 09/013(0872)/2019-EMR-I), for which the author is grateful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Conflict of Interest Declaration There are no conflicts of interest among the authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  References [1] TP Yadav, A Kumar, SK Verma, NK Mukhopadhyay, High-Entropy Alloys for Solid Hydrogen Storage: Potentials and Prospects, Transactions of the Indian National Academy of Engineering, 7 (2022) 147–156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1007/s41403-021-00316-w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Kumar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Yadav, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Mukhopadhyay, Notable hydrogen storage in Ti–Zr– V–Cr–Ni high entropy alloy, International Journal of Hydrogen Energy 47 (2022) 22893-22900.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='107 [3] Verma SK, Bhatnagar A, Shukla V, Soni PK, Pandey AP, Yadav TP, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Multiple improvements of hydrogen sorption and their mechanism for MgH2 catalyzed through TiH2@Gr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Int J Hydrogen Energy 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='45:19516–30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='031.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [4] SK Pandey, SK Verma, A Bhatnagar, TP Yadav,  Catalytic characteristics of titanium‐(IV)‐isopropoxide (TTIP) on de/re‐hydrogenation of wet ball‐milled MgH2/Mg,  International Journal of Energy Research 46 (12) (2022) 17602-17615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1002/er.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='8427.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [5] Shukla V, Bhatnagar A, Verma SK, Pandey AP, Vishwakarma AK, Srivastava P, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Simultaneous improvement of kinetics and thermodynamics based on SrF2 and SrF2@Gr additives on hydrogen sorption in MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Mater Adv 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2:4277– 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/D1MA00012H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [6] Srivastava ON, Yadav TP, Shahi RR, Pandey SK, Shaz MA, Bhatnagar A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  20  Hydrogen energy in India: Storage to application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Proc Indian Natl Sci Acad 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='81:915–37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='16943/ptinsa/2015/v81i4/48303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [7] US DoE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Target Explanation Document: Onboard Hydrogen Storage for Light- Duty Fuel Cell Vehicles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' US Drive 2017:1–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [8] Bhatnagar A, Pandey SK, Vishwakarma AK, Singh S, Shukla V, Soni PK, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Fe3O4 @graphene as a superior catalyst for hydrogen de/absorption from/in MgH 2 /Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Mater Chem A 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4:14761–72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/c6ta05998h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [9] Sadhasivam T, Kim H-T, Jung S, Roh S-H, Park J-H, Jung H-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Dimensional effects of nanostructured Mg/MgH2 for hydrogen storage applications: A review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Renew Sustain Energy Rev 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='72:523–34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='rser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [10] Yartys VA, Lototskyy M V, Akiba E, Albert R, Antonov VE, Ares JR, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Magnesium based materials for hydrogen based energy storage: Past, present and future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Int J Hydrogen Energy 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='44:7809–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content='  [11] SK Pandey, A Bhatnagar, SS Mishra, TP Yadav, MA Shaz, ON Srivastava, Curious Catalytic Characteristics of Al–Cu–Fe Quasicrystal for e/Rehydrogenation of MgH2, The Journal of Physical Chemistry C 121 (45) (2017) 24936-24944.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content='7b07336 [12] V Shukla, TP Yadav, Notable catalytic activity of CuO nanoparticles derived from metal‐organic frameworks for improving the hydrogen sorption properties of MgH2, International Journal of Energy Research, 46 (9) (2022) 12804-12819.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content='8050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [13] Verma SK, Shaz MA, Yadav TP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Enhanced hydrogen absorption and desorption properties of MgH2 with graphene and vanadium disulfide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Int J Hydrogen Energy 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content='ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='269.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [14] Patelli N, Calizzi M, Migliori A, Morandi V, Pasquini L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Hydrogen Desorption Below 150 °C in MgH2–TiH2 Composite Nanoparticles: Equilibrium and Kinetic Properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Phys Chem C 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='121:11166–77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content='7b03169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [15] Korablov D, Besenbacher F, Jensen TR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Kinetics and thermodynamics of  21  hydrogenation-dehydrogenation for Mg-25%TM (TM = Ti, Nb or V) composites synthesized by reactive ball milling in hydrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Int J Hydrogen Energy 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='43:16804–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content='ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='091.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [16] Bhatnagar A, Johnson JK, Shaz MA, Srivastava ON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' TiH 2 as a Dynamic Additive for Improving the De/Rehydrogenation Properties of MgH 2 : A Combined Experimental and Theoretical Mechanistic Investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Phys Chem C 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='122:21248–61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content=' [17] Zhang J, Xia G, Guo Z, Zhou D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Synergetic Effects toward Catalysis and Confinement of Magnesium Hydride on Modified Graphene: A First-Principles Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Phys Chem C 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='121:18401–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content=' [18] Singh MK, Bhatnagar A, Pandey SK, Mishra PC, Srivastava ON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Experimental and first principle studies on hydrogen desorption behavior of graphene nanofibre catalyzed MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Int J Hydrogen Energy 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='42:960–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='IJHYDENE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [19] Liu G, Wang Y, Jiao L, Yuan H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Understanding the role of few-layer graphene nanosheets in enhancing the hydrogen sorption kinetics of magnesium hydride.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' ACS Appl Mater Interfaces 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='6:11038–46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1021/am502755s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [20] Varunaa R, Ravindran P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Potential hydrogen storage materials from metal decorated 2D-C2N: An: ab initio study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Phys Chem Chem Phys 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='21:25311– 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/c9cp05105h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  [21] Liu Y, Gao H, Zhu Y, Li S, Zhang J, Li L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Excellent catalytic activity of a two- dimensional Nb4C3Tx (MXene) on hydrogen storage of MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Appl Surf Sci 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='493:431–40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='apsusc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [22] Chen G, Zhang Y, Cheng H, Zhu Y, Li L, Lin H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Effects of two-dimension MXene Ti3C2 on hydrogen storage performances of MgH2-LiAlH4 composite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Chem Phys 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='522:178–87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
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+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='chemphys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [23] Raccichini R, Varzi A, Passerini S, Scrosati B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The role of graphene for electrochemical energy storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Nat Mater 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='14:271–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1038/nmat4170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  22  [24] Pumera M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Graphene-based nanomaterials for energy storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Energy Environ Sci 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4:668–74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/C0EE00295J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [25] Singh S, Bhatnagar A, Shukla V, Vishwakarma AK, Soni PK, Verma SK, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Ternary transition metal alloy FeCoNi nanoparticles on graphene as new catalyst for hydrogen sorption in MgH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Int J Hydrogen Energy 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='45:774–86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [26] Liu G, Wang Y, Xu C, Qiu F, An C, Li L, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Excellent catalytic effects of highly crumpled graphene nanosheets on hydrogenation/dehydrogenation of magnesium hydride.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Nanoscale 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5:1074–81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/c2nr33347c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [27] Huang Y, Xia G, Chen J, Zhang B, Li Q, Yu X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' One-step uniform growth of magnesium hydride nanoparticles on graphene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Prog Nat Sci Mater Int 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='27:81–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='pnsc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [28] Liu R, Zhao Y, Chu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Theoretical exploration of MgH2 and graphene nano-flakes in cyclohexane: proposing a new perspective toward functional hydrogen storage material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Chem Commun 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='51:2429–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/C4CC09424G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [29] Li W, Huang J, Feng L, Cao L, Feng Y, Wang H, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Facile: In situ synthesis of crystalline VOOH-coated VS2 microflowers with superior sodium storage performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Mater Chem A 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5:20217–27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/c7ta05205g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  [30] Fang W, Zhao H, Xie Y, Fang J, Xu J, Chen Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Facile Hydrothermal Synthesis of VS2/Graphene Nanocomposites with Superior High-Rate Capability as Lithium- Ion Battery Cathodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' ACS Appl Mater Interfaces 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='7:13044–52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1021/acsami.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5b03124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [31] Ma H, Shen Z, Ben S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Understanding the exfoliation and dispersion of MoS2 nanosheets in pure water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Colloid Interface Sci 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='517:204–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='jcis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [32] Lu X, Utama MIB, Zhang J, Zhao Y, Xiong Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Layer-by-layer thinning of MoS2 by thermal annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Nanoscale 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='5:8904–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/C3NR03101B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  23  [33] Chakraborty B, Matte HSSR, Sood AK, Rao CNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Layer-dependent resonant Raman scattering of a few layer MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Raman Spectrosc 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='44:92–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1002/jrs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='4147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [34] Hazarika SJ, Mohanta D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Inorganic fullerene-type WS2 nanoparticles: processing, characterization and its photocatalytic performance on malachite green.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Appl Phys A 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='123:381.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1007/s00339-017-0965-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [35] Berkdemir A, Gutiérrez HR, Botello-Méndez AR, Perea-López N, Elías AL, Chia C-I, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Identification of individual and few layers of WS2 using Raman Spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Sci Rep 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3:1755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1038/srep01755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [36] Frindt RF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Single Crystals of MoS2 Several Molecular Layers Thick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Appl Phys 1966;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='37:1928–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1708627.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [37] Radisavljevic B, Radenovic A, Brivio J, Giacometti V, Kis A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Single-layer MoS2 transistors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Nat Nanotechnol 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='6:147–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1038/nnano.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='279.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [38] Ovchinnikov D, Allain A, Huang Y-S, Dumcenco D, Kis A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Electrical Transport Properties of Single-Layer WS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' ACS Nano 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='8:8174–81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1021/nn502362b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [39] Kissinger HE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Reaction Kinetics in Differential Thermal Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Anal Chem 1957;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='29:1702–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1021/ac60131a045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [40] Wu Z, Fang J, Liu N, Wu J, Kong L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' The Improvement in Hydrogen Storage Performance of MgH2 Enabled by Multilayer Ti3C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Micromachines  2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='3390/mi12101190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='  [41] Lima EC, Hosseini-Bandegharaei A, Moreno-Piraján JC, Anastopoulos I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' A critical review of the estimation of the thermodynamic parameters on adsorption equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Wrong use of equilibrium constant in the Van’t Hoof equation for calculation of thermodynamic parameters of adsorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' J Mol Liq 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='273:425– 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='molliq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [42] Chen J, Cao J, Zhou J, Zhang Y, Li M, Wang W, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Mechanism of highly enhanced hydrogen storage by two-dimensional 1T′ MoS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Phys Chem Chem Phys 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='22:430–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1039/c9cp04402g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' [43] Singh MK, Bhatnagar A, Pandey SK, Mishra PC, Srivastava ON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Experimental  24  and first principle studies on hydrogen desorption behavior of graphene nanofibre catalyzed MgH 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' Int J Hydrogen Energy 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='42:960–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='ijhydene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
+page_content='210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GNE1T4oBgHgl3EQfFANy/content/2301.02897v1.pdf'}
diff --git a/GtE5T4oBgHgl3EQfWA9Z/content/tmp_files/2301.05555v1.pdf.txt b/GtE5T4oBgHgl3EQfWA9Z/content/tmp_files/2301.05555v1.pdf.txt
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+Magnetic phase diagram of the breathing-kagome antiferromagnet Nd3BWO9
+D. Flavi´an,1, ∗ J. Nagl,1 S. Hayashida,1, 2 M. Yan,1 O. Zaharko,3
+T. Fennell,3 D. Khalyavin,4 Z. Yan,1 S. Gvasaliya,1 and A. Zheludev1, †
+1Laboratory for Solid State Physics, ETH Z¨urich, 8093 Z¨urich, Switzerland
+2Max-Planck-Institut f¨ur Festk¨orperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany
+3Laboratory for Neutron Scattering and Imaging,
+Paul Scherrer Institut, 5232 Villigen, Switzerland
+4ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
+(Dated: January 16, 2023)
+The highly-frustrated rare-earth based magnet Nd3BWO9 is a promising candidate in the search
+for proximate spin liquid physics. We present a thorough investigation on single crystals of this ma-
+terial using bulk and microscopic techniques. Magnetization data reveal a fractional magnetization
+plateau for three different investigated field directions. The magnetic phase diagram is mapped out
+from calorimetric data and exhibits several domes of magnetic order below 0.3 K. Propagation vec-
+tors for all ordered phases are presented. The results suggest complex ordering in this material, and
+unveil the existence of a commensuration transition of the propagation vector at zero magnetic field.
+A scenario where interplane exchange interactions are essential to a magnetic model of Nd3BWO9
+is discussed.
+I.
+INTRODUCTION
+Strongly frustrated quantum antiferromagnets (AFM)
+are known to realize a panoply of magnetic states due
+to the delicate equilibrium between the magnetic in-
+teractions.
+In the presence of magnetic fields, the
+large ground state degeneracy is lifted in subtle and
+diverse ways, which leads to extremely rich phase di-
+agrams. Realization of spin-density waves [1], magne-
+tization plateaus [2, 3] commensurate-incommensurate
+transitions [4], and even more exotic order like spin
+nematicity [5, 6] is not rare, particularly in quasi-low-
+dimensional systems.
+The archetypal model in 2D frustrated magnetism is
+the kagome lattice Heisenberg S = 1/2 AFM (KHAF).
+The impossibility of satisfying all magnetic interactions
+in this lattice results in a macroscopic degeneracy of the
+ground state already at a classical level [7]. Turning to
+S = 1/2 spins promotes the quantum fluctuations on the
+ground state giving rise to highly non-trivial phases [8].
+Arguably, the most intriguing state is the hypothesized
+Quantum Spin Liquid (QSL) [9] ground state. The pre-
+diction of fractionalization of quasiparticles in a 2D sys-
+tem triggered extensive effort from both theory and ex-
+perimental perspectives [10, 11]. Nevertheless, the QSL
+phase remains elusive [12] as it constitutes a very frag-
+ile state. One of the main causes of the instability of
+the QSL states is the presence of terms in the Hamilto-
+nian that lift the ground state degeneracy [13, 14]. The
+many different ways to lift this degeneracy have led to
+a flurry of new magnetic structures [15–18]. However,
+occasionally deviations from a putative KHAF tend to
+stabilize QSL phases. In particular, the so called breath-
+ing anisotropy has been predicted to favor a resonance
+∗ daniefla@ethz.ch
+† zhelud@ethz.ch; http://www.neutron.ethz.ch/
+valence bond solid ground state for a wide range of cou-
+pling parameters [19, 20].
+In
+this
+context,
+the
+recently
+discovered
+family
+R3BWO9 of rare-earth antiferromagnets is an optimal
+platform for the search of spin-liquid candidates [21].
+Here R is a trivalent rare-earth element and the large
+difference in size of the constituent atoms prevents anti-
+site chemical disorder. All of the members of the family
+realize a breathing kagome lattice in their basal plane
+and show no sign of magnetic ordering down to 2 K.
+The strong spin-orbit coupling in combination with crys-
+tal electric field effects opens the possibility of realizing
+effective Jeff = 1/2 magnetic moments.
+Among all compounds in the family, the most promis-
+ing is Nd3BWO9. A large Weiss temperature [21] has
+been reported and the total angular momentum of Nd3+
+(J = 9/2) makes it a Kramers-doublet system. No mag-
+netic long-range order has been found in previous studies
+down to 1.8 K. However, little is known so far about its
+magnetism. In this study we report on the low tempera-
+ture properties of single crystals of Nd3BWO9. We found
+static magnetic long-range order below 0.3 K. The ob-
+served magnetism suggests a three dimensional network
+of exchange interactions. Nonetheless, due to the highly
+frustrated interaction a complex phase diagram is real-
+ized.
+The paper is structured as follows. First, a summary
+of the various methods used is provided. Then, we out-
+line the main results of the experiments. Subsequently,
+a detailed discussion of the main outcome is provided,
+including a thorough description of the magnetic struc-
+ture and a detailed picture of the magnetic phase dia-
+gram under applied fields. Finally, the main conclusions
+are drawn and further steps in the search of QSL physics
+are examined.
+arXiv:2301.05555v1  [cond-mat.str-el]  13 Jan 2023
+
+(b)
+(e)
+2 mm
+a
+b
+c
+2.66 Å
+2.57 Å
+2.25 Å
+2.49 Å
+2.38 Å
+2.36 Å
+Nd
+2.55 Å
+2.42 Å
+c
+WO6
+B
+NdO8
+a
+b*a*
+b
+c
+(a)
+(d)
+Nd
+a
+b
+c
+l = 16.44 Å
+(c)
+3.95 Å
+4.92 Å
+4.25 Å
+FIG. 1.
+Crystal structure and superexchange topology in
+Nd3BWO9. (a) Schematic structure reflecting the purported
+kagome interaction in the crystallographic ab plane.
+Only
+atoms with 0 ≤ z ≤ 0.5 are shown here. There is an addi-
+tional kagome plane displaced by half lattice parameter along
+the c crystallographic direction. (b) The shortest superex-
+change Nd-O-Nd bond links neodymium atoms in different
+kagome planes, forming isolated spin tubes along the c axis
+arranged in a triangular lattice. The kagome bonds are shown
+for reference along with bond distances. (c) A typical single
+crystal sample of Nd3BWO9. (d) A single spin tube is unfrus-
+trated. However, further-neighbor interactions frustrate the
+system. An arrow indicates the size of the magnetic supercell
+at zero field. (e) The environment of neodymium has very
+low symmetry, resulting in a C1 point group for the magnetic
+ion. Nd-O distances are indicated.
+II.
+METHODS
+Nd3BWO9 crystallizes in a hexagonal structure, with
+space group P63 (No. 173), where the magnetism stems
+from the effective magnetic moment of the Nd3+ ions.
+Single crystal samples were grown by spontaneous crys-
+tallization using a flux method as described in [22]. Pur-
+ple transparent single crystals with well defined facets
+were obtained [Fig. 1(c)].
+Typical masses range from
+a few micrograms to 40 mg and different samples were
+used in this study, depending on the technique.
+The
+chemical structure of the different single-crystal samples
+used in this study was validated using single-crystal X-
+ray diffraction on a Bruker APEX-II instrument, and was
+found to be in agreement with previous reports [21]. The
+structure is schematically depicted in Fig. 1, where the
+kagome-lattice bonds can be readily identified. Powder
+samples of Nd3BWO9, as well as of the non-magnetic
+La3BWO9, were synthesized by a solid state reaction.
+The correct chemical structure and the quality of the
+powders was checked with powder X-ray diffraction in
+a Rigaku MiniFlex diffractometer.
+Boron-11 enriched
+samples (both powder and single crystals) were also pre-
+pared for their use in neutron scattering experiments.
+Measurements of heat capacity, magnetocaloric effect
+(MCE), magnetization and magnetic torque were carried
+out using a 3He-4He dilution refrigerator insert for the
+Quantum Design Physical Property Measurement Sys-
+tem (PPMS). A sample of mass 0.131 mg was used for
+both heat capacity and MCE measurements. Heat ca-
+pacity data were collected using a standard relaxation
+method from Quantum Design for temperatures 100 mK
+< T < 4 K in applied fields of 0 T < µ0H < 3 T. The
+magnetic field was applied along the crystallographic a∗,
+and c directions. In zero field, data were collected from
+100 mK to 300 K. Heat capacity data of La3BWO9 were
+measured down to 2 K and extrapolated to lower tem-
+peratures from an empirical fit to a T 3-power law. MCE
+data were measured using the same puck as for heat ca-
+pacity. The change of temperature of the sample was
+recorded as the magnetic field was swept up and down
+at a constant rate. In order to avoid self heating of the
+puck, the field change rate was optimized and a value of
+0.5 mT/s was selected. In the terminology of MCE mea-
+surements, our experiment was conducted under equilib-
+rium conditions.
+Magnetization was measured using an in house made
+Faraday-balance capacitive magnetometer [23] at 120
+mK and 2 K and magnetic fields applied along three ori-
+entations: a∗, and b, and c. Additional measurements
+of magnetization carried out in the MPMS system at 2
+K were used to calibrate the low temperature data and
+obtain absolute units (not shown here). Using the same
+setup, magnetic torque was measured up to 3 T and
+for temperature from 120 mK to 600 mK. The torque
+data correspond to the deflection of a small cantilever
+on which the sample is mounted.
+The magnetic field
+sweeping rate was also optimized to minimize heating
+due to eddy currents.
+Magnetic susceptibility was measured using the Quan-
+tum Design Magnetic Property Measurement System
+(MPMS) SQUID Magnetometer.
+The temperature
+range from 1.8 K to 300 K was probed using a small po-
+larizing field applied along three crystal directions: a∗,
+and b, and c. The probing field was µ0H = 0.1 T, where
+µ0 denotes the permeability of vacuum.
+Inelastic neutron scattering on powder samples of
+Nd3BWO9 was measured to investigate the crystal elec-
+tric field induced scheme of total angular momentum
+states. The instrument of choice was the thermal neu-
+tron triple-axis-spectrometer EIGER at PSI. 11.1 g of
+Nd3 11BWO9 was sealed in an aluminum can and in-
+stalled in a standard 4He orange cryostat. A final wave-
+length of kf= 2.66 ˚A−1 (λ = 2.36 ˚A) was chosen, us-
+ing a pyrolytic graphite filter to eliminate higher-order
+neutrons without further collimation. Data were mea-
+sured at constant scattering angle, 2θ. The background
+was investigated to select the optimal value for the scat-
+tering angle, sufficiently far from the direct beam and
+low enough to have good counting and small decay in
+the signals due to magnetic structure factors. A value
+of 2θ = 10◦ was chosen, and the incident energy was
+scanned at three different temperatures: 1.5 K, 100 K
+and 300 K.
+Neutron single crystal diffraction was used to investi-
+2
+
+J0
+100
+200
+300
+T (K)
+0
+50
+100
+150
+200
+-1 (mol T μB )
+H || a*
+θCW = -3.76 K
+μ0H = 0.1 T
+H || b
+H || c
+-1
+FIG. 2.
+Inverse magnetic susceptibility on single crystals.
+Data show measurements for three field orientations. A small
+probing field of 0.1 T was used for all measurements. The
+black solid line represents a Curie-Weiss model with the av-
+erage Weiss temperature and effective moment parameters,
+given in Table. I.
+gate the magnetic structures in the ordered phases. A
+single crystal sample of 18 mg in mass of Nd3 11BWO9
+and 5.5×1.4×0.8 mm3 was studied using two different
+instruments. Measurements with H ∥ a∗ were carried
+out at the Thermal Single Crystal Diffractometer ZE-
+BRA at the Swiss Spallation Neutron Source, SINQ,
+in the Paul Scherrer Institut (PSI, Switzerland).
+The
+diffractometer was used in conjunction with a 3He-4He
+dilution refrigerator and a 6-T magnet.
+The crystal
+was aligned with its a∗ axis vertical, the same direc-
+tion as the applied magnetic field. Neutron wavelengths
+of λ = 2.314 ˚A and 1.383 ˚A were selected, provided by
+the PG(200) and Ge(220) monochromators. Additional
+measurements with H ∥ c were carried out in the time-
+of-flight diffractometer WISH at the ISIS facility in the
+Rutherford Appleton Laboratory, in the United King-
+dom. The sample was mounted with its c axis vertical
+and parallel to the magnetic field. A 3He-4He dilution
+refrigerator and a 10-T magnet were used to access the
+ordered states in Nd3BWO9.
+III.
+EXPERIMENTAL RESULTS
+A.
+Magnetic susceptibility
+Figure 2 shows inverse susceptibility measurements for
+probing fields applied along the crystallographic direc-
+tions a∗b, and c.
+Down to the lowest accessible tem-
+perature of 1.8 K, these data show no sign of magnetic
+ordering.
+A fit of the experimental data to a Curie-Weiss model
+is shown overlaid on the experimental results. A good
+TABLE I. Fitting parameters from the Curie-Weiss model for
+data shown in Fig.
+2.
+200 K ≤ T ≤ 300 K 20 K ≤ T ≤ 60 K
+θW (K)
+µeff (µB)
+θW (K) µeff (µB)
+H ∥ a∗
+-54.3
+3.76
+-3.78
+2.94
+H ∥ b
+-54.7
+3.79
+-3.82
+2.90
+H ∥ c
+-59.2
+3.77
+-3.68
+2.91
+agreement is found for data above 130 K, with a large,
+negative Weiss temperature. The resulting Weiss tem-
+peratures, θW are given in Table. I, as well as the cor-
+responding effective magnetic moments extracted from
+the Curie constants as C = NAµ0µ2
+eff/(3kB). The ob-
+tained effective magnetic moments are close to the value
+expected for a free Nd3+ ion: µeff = gJ
+�
+J(J + 1)µB =
+3.6µB. Importantly, the susceptibility data show little
+dependence on the direction of the magnetic field, which
+suggests that, the resulting magnetic anisotropy remains
+quite small.
+Our results are consistent with those re-
+ported in Ref.[21] on polycrystal samples.
+Below 130 K a clear deviation from the high temper-
+ature fit is observed.
+This is roughly consistent with
+the existence of a crystal electric field (CEF) level at
+15.9 meV (see below), signaling the total depletion of
+the population of the first excited state. A Curie-Weiss
+analysis is heavily affected by the partial population of
+excited multiplets and lead to an overestimation of ex-
+change parameters and exchange couplings. Therefore,
+an additional fit to a Curie-Weiss law for a tempera-
+ture range far enough from the CEF resonance has been
+performed.
+The results are also summarized in Table
+I. Temperatures in the range between 20 K and 60 K
+were considered for this fit. The resulting Weiss temper-
+atures are much reduced compared to the high temper-
+ature fit. However, they still reflect a predominant an-
+tiferromagnetic interaction in Nd3BWO9. The effective
+magnetic moments are also reduced with respect to their
+high temperature value, yielding an average moment of
+µeff = 2.92µB.
+B.
+CEF level scheme
+The inelastic neutron scattering spectra are shown in
+Fig. 3.
+Large intensity at zero energy transfer corre-
+sponds to quasielastic scattering. Three resonances are
+identified at 15.9, 32.8, and 43.7 meV, which we ascribe
+to CEF induced levels due to their temperature depen-
+dence. Importantly, no resonance is found below 15.9
+meV. Since the total angular momentum J = 9/2 of the
+free Nd3+ is expected to be fully split into five Kramers
+doublets, this suggests that the low temperature physics
+of Nd3BWO9 can indeed be described in terms of the
+lowest laying doublet, giving rise to an effective two-level
+system well below ∆ = 15.9 meV ≈ 180 K.
+3
+
+0
+10
+20
+30
+40
+0
+0
+0
+ħω (meV)
+T = 1.5 K
+T = 100 K
+T = 300 K
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+Ef = 14.7 meV
+2θ = 10°
+Intensity (arb. units)
+FIG. 3. Inelastic neutron scattering intensity at a constant
+scattering angle for three different temperatures. The final
+energy of Ef= 14.7 meV was fixed and incident energy var-
+ied, fixing a 10 degree scattering angle. CEF resonances are
+indicated by black arrows. An offset of 0.25 and 0.50 units
+was added for visibility, a dashed line indicates the reference
+zero for those data sets.
+C.
+Specific heat
+Specific heat as a function of temperature and mag-
+netic field is used to unveil the magnetic phase diagram
+of Nd3BWO9 at ultra-low temperatures. Data obtained
+at zero field are shown in Fig. 4. Nd3BWO9 shows an up-
+turn in specific heat below 4 K with two clearly distinct
+features [Fig. 4(a)]. Around 1 K, a hump in specific heat
+suggests the onset of short-range magnetic correlations
+[24]. At TN = 300 mK we found a sharp lambda anomaly
+representing the transition into magnetic long range or-
+der.
+Below TN the specific heat signal remains large
+down to the lowest accessible temperatures in our setup,
+likely due to nuclear specific heat from the rare-earth
+ions. In order to understand exactly the nature of the
+magnetic specific heat, we have examined the different
+contributions and subtracted them from the measured
+total specific heat.
+To estimate the phononic contribution, we synthesized
+the non-magnetic isostructural material La3BWO9 and
+measured its specific heat in the same range of temper-
+atures.
+This is shown in Fig. 4(a) and represents the
+lattice contribution, CL, in Fig. 4(b).
+An accurate estimation of the nuclear contribution to
+specific heat is usually much more complicated, as a
+1
+10
+100
+T (K)
+0
+10
+20
+30
+40
+50
+Cp (J mol-1 K-1)
+Nd3BWO9
+Nd3BWO9
+TN
+La3BWO9
+0.1
+0.4
+1
+4
+10
+T (K)
+Rln(2)
+0
+10
+20
+Cp/T (J mol-1 K-2)
+CL
+CN
+Ctot
+Cmag
+0
+1
+2
+3
+4
+T (K)
+0
+2
+4
+6
+8
+Smag (J mol-1
+NdK-1)
+(a) μ0H = 0 T
+(b)
+(c)
+TN
+FIG. 4.
+(a) Total specific heat at zero magnetic field for
+Nd3BWO9 and the nonmagnetic isostructural compound
+La3BWO9.
+Nd3BWO9 shows a substantial magnetic con-
+tribution to specific heat below 3 K. (b) Total specific heat
+(open circles) and magnetic specific heat (filled circles) after
+subtraction of lattice and nuclear degrees of freedom. Lat-
+tice (CL) and nuclear (CN) contribution are estimated as
+discussed in the text. A lambda anomaly can be found at
+TN = 0.30 K, signaling the onset of long-range magnetic or-
+der. (c) The magnetic entropy per Nd3+ ion saturates above
+3 K. A dashed line represents the expected value for a two-
+level system at infinite temperature.
+variety of effects has to be considered.
+These include
+dipole and quadrupolar splitting, or hyperfine coupling
+between nuclei and electrons (which can be quite signif-
+icant in magnetically ordered materials).
+Neodymium
+has two isotopes with nonzero dipolar and quadrupolar
+momenta, out of its 7 stable isotopes. Following the rea-
+soning in Ref. [25], the effect of quadrupolar splitting is
+assumed to be small compared to that of hyperfine cou-
+pling, and we neglect it here. In a magnetized phase,
+local fields are expected to be sizable and therefore hy-
+perfine coupling may significantly contribute to specific
+heat. The contribution from dipole field splitting from a
+single isotopic species is given by
+4
+
+Cp/T (J/molK-2)
+(a) H || a*
+0
+0.5
+1
+1.5
+T (K)
+0
+20
+40
+60
+80
+Cp/T (J/molK-2)
+0 T
+0.85 T
+0.55 T
+1.2 T
+0
+10
+20
+30
+40
+50
+60
+70
+0 T
+0.85 T
+0.975 T
+(b) H || c
+FIG. 5. Typical temperature scans of specific heat for differ-
+ent fixed values of magnetic field applied along (a) H ∥ c and
+(b) H ∥ a∗. An offset of 15 J/mol/K2 has been added for
+visibility. Solid filled triangles show features associated with
+the phase transitions discussed in the main text.
+CH,i =
+NAkB
+α2
+i
+4I2
+i
+�
+�
+1
+sinh2 �
+αi
+2Ii
+� −
+(2Ii + 1)2
+sinh2 �
+(2Ii+1)αi
+2Ii
+�
+�
+�
+(1)
+where αi = AH(µNd
+Hyp/gJ)Ii/kBT, and Ii is the nuclear
+spin, gJ = 8/11 (Land´e factor for Nd), NA is the Avo-
+gadro constant, and kB the Boltzmann constant. AHyp
+represents the strength of the hyperfine coupling and
+here we made a second approximation. We assume all
+the nuclei couple equally to the electron density and the
+value of AHyp is approximated as that of Nd metal [26].
+µNd
+Hyp denotes the static dipole moment of the Nd3+ ions.
+This is precisely the origin of the local field and for its
+value we chose the averaged effective magnetic moment
+from the magnetic susceptibility data at low tempera-
+tures µNd
+Hyp = 2.914µB. Finally, the different species are
+summed, weighted by their isotopical abundance to ob-
+tain the temperature dependence of nuclear specific heat.
+This model with no free parameters is in excellent
+agreement with the lowest temperature data, as shown in
+Fig. 4(b). Having modeled the nuclear specific heat, the
+magnetic specific heat can be extracted by subtraction.
+The magnetic specific heat was subsequently integrated
+to obtain the temperature dependence of magnetic en-
+Cp/T (J/mol K-2)
+150 mK
+250 mK
+350 mK
+500 mK
+800 mK
+0
+0.5
+1
+1.5
+2
+2.5
+3
+0H (T)
+0
+20
+40
+60
+Cp/T (J/mol K-2)
+(a) H || a*
+0
+20
+40
+60
+80
+150 mK
+250 mK
+350 mK
+500 mK
+800 mK
+(b) H || c
+*
+FIG. 6. Typical field scans of specific heat measured at con-
+stant temperature in Nd3BWO9 for (a) H ∥ c and (b) H ∥ a∗.
+An offset of 10 or 15 J/mol/K2 is added for visibility be-
+tween the scans for (a) and (b), respectively.
+Solid filled
+triangles show features associated with the phase transitions
+discussed in the main text. Black arrows signal the existence
+of broad double-hump features, described in the text.
+An
+asterisk shows a feature above the saturation transition.
+tropy, depicted in Fig. 4(c). The high temperature trend
+of this quantity approaches the value of R ln(2), the ex-
+pected value of a two-level system.
+In a magnetic field, a simple estimation of the contri-
+bution of the nuclear spin due to Zeeman splitting could
+not account for the effects observed here. Low tempera-
+ture data in Fig. 5 show that the effect of nuclear specific
+heat is of the same order of magnitude up to 1.2 T and it
+is not strongly field dependent. This suggests that also
+in a field the main contribution comes from hyperfine
+coupling. However, a quantitative determination of this
+effect under magnetic fields becomes paramount.
+The evolution of the specific heat of Nd3BWO9 under
+magnetic fields is shown in Fig. 6 for fields along two
+different crystallographic directions. The total heat ca-
+pacity is displayed here, without subtraction of lattice
+or nuclear degrees of freedom. Typical-field scans show
+a number of anomalies that are consistent with the exis-
+tence of three different phases with static magnetic order
+at low temperatures.
+Up to three distinct features can be observed for
+H ∥ a∗ at the lowest temperature, at 0.45, 0.62 and 1.05
+T and are marked with triangles in Fig. 6(a).These fea-
+5
+
+tures are rather spread in fields, specially at saturation.
+However, the existence of thermodynamic transitions has
+been confirmed by neutron diffraction (as discussed be-
+low). The two lower field anomalies move apart as the
+temperature is increased. The two higher field anoma-
+lies merge at 0.25 K, denoting the highest temperature
+of the ordered phase. Though the specific heat anoma-
+lies in Fig. 6(a) are too broad for a precise estimation
+of the upper critical field, this quantity can be deduced
+from magnetocaloric effect measurements (see below).
+For fields orthogonal to the hexagonal plane (H ∥ c)
+at the lowest temperature one finds two anomalies at 0.5
+T, 0.8 T and a sharper one at 0.95 T. [Fig. 6(b)] Notably,
+in this configuration the different anomalies appear nar-
+rower than for H ∥ a∗, especially at the saturation field.
+The first two anomalies move apart as the temperature
+is increased, while the higher field anomaly barely shifts
+in position up to 0.2 K. The low field anomaly shifts to-
+wards zero field and disappears as TN is reached. The
+two high-field anomalies merge at T = 0.2 K. From the
+high field anomaly we extract an estimate of the satura-
+tion field of µ0Hc = 0.975(3) T. Interestingly, an extra
+feature can be identified above saturation (asterisk in
+Fig. 6(a)).
+This feature shifts to higher fields as the
+temperature is increased and decreases rapidly in mag-
+nitude. Above 0.2 K it is hardly identifiable.
+Finally, double-hump features can be observed above
+0.3 K for both magnetic field configurations. These are
+significant up to the highest measured temperatures and
+particularly prominent around the saturation field (black
+arrows in Fig. 6).
+For H ∥ c the amplitude of these
+modulations is larger than in H ∥ a∗. Such features are
+often associated with a low-dimensional crossover from
+the zero field disordered phase to the fully polarized state
+without the occurrence of a phase transition [27–30].
+D.
+Magnetocaloric effect
+Magnetocaloric
+effect
+(MCE)
+measurements
+in
+Nd3BWO9 provide key information on the nature of the
+various phase transitions found with other techniques
+[31–33].
+Representative temperature profiles are sum-
+marized in Fig.
+7. Several crossings can be observed
+for both configurations.
+The observed anomalies are
+too broad to assign exactly a transition point.
+Due
+to the proximity of the thermodynamic transitions
+in the phase diagram, features corresponding to both
+transitions merge and overlap.
+In our measurements
+the field is swept slow enough as to ensure equilibrium
+conditions.
+Data measured with H ∥ a∗ show mostly symmetric
+features around the crossing points.
+Particularly, this
+suggests that the measured phase transitions are of sec-
+ond order. In contrast, the low temperature profiles for
+H ∥ c show two distinct behaviors. At 0.6 T one finds a
+roughly symmetric feature, suggesting again a second or-
+der phase transition. This is different at 0.975 T, where
+a very asymmetric feature appears, pointing to a first
+0
+μ
+μ
+1
+2
+0H (T)
+0.1
+0.2
+0.3
+0.5 mT/s
+0.5 mT/s
+0.4
+0.5
+0.6
+0.7
+T (K)
+0
+1
+2
+0H (T)
+(b) H || c
+(a) H || a*
+FIG. 7. Plots of the magnetocaloric effect in Nd3BWO9 for
+different base temperatures and fields applied along (a) H ∥
+a∗ and (b) H ∥ c. For all the scans, red (blue) color represents
+data measured while driving the magnetic field up (down).
+A ramping rate of 0.5 mT/s was used throughout all the
+measurements.
+Small prominent features (specially at low
+fields) are spurious and the result of an unstable platform.
+order or discontinuous transition.
+Finally, the absence of anomalies above the saturation
+field for H ∥ c must be noted. The features observed in
+the fully polarized phase in Fig. 6(b) leave no trace in
+the MCE data in the same configuration.
+The MCE technique is based on the change of entropy
+in a magnetic system as it is driven through a phase
+transition, crossover, level crossing, etc. Consequently,
+one can retrieve the change in entropy in a system from
+the change in temperature against magnetic field [31].
+Under equilibrium conditions, we obtain the entropy as
+∆S = S(H) − S0 = −
+�
+κT − Tbath
+T
+dt
+(2)
+where κ is the thermal conductivity of the thermal
+link in the calorimeter, T is the sample temperature, and
+Tbath is the thermal bath temperature. Integration of the
+data in Fig. 7 gives rise to the entropy maps displayed in
+Fig. 8. The data above 0.2 K are a good picture of the
+entropy stored in the magnetic subsystem. However, for
+temperatures below 0.15 K imperfect equilibrium condi-
+tions prevent a reliable estimation of entropy. A strong
+accumulation of entropy is observed above the saturation
+transitions for both field configurations. The position of
+the peaks in entropy match the estimated position of the
+critical fields from specific heat. For H ∥ a∗, the maxima
+in entropy at different temperatures were used to obtain
+an accurate estimate of the upper critical field.
+A fit
+to the data provides Hc,a∗ = 1.187(13) T. This value is
+consistent with the various probes used in this study.
+6
+
+0
+0.5
+1
+1.5
+2
+0
+0.2
+0.4
+0.6
+0.8
+T (K)
+μ0H (T)
+0
+0.2
+0.4
+0.6
+0.8
+T (K)
+(a) H || a*
+A
+B
+S (J molNd K-1)
+-1
+0
+1
+2
+3
+(b) H || c
+A
+C
+FIG. 8. Entropy maps in false color for two magnetic field
+orientations. In false color plots, the change in entropy ex-
+tracted from magnetocaloric data from Fig. 7. Filled circles
+(diamonds) denote phase anomalies associated with phase
+transitions from specific heat field (temperature) scans for
+(a) H ∥ a∗ and (b) H ∥ c.
+In (a) red squares show the
+maxima of entropy at the measured temperatures. A white
+dashed line is a power law fit to the data showing the best
+estimate for the upper critical field.
+E.
+Magnetization
+The evolution of magnetization under a magnetic field
+provides insight on the type of order in Nd3BWO9.
+Strikingly, a fractional magnetization plateau is observed
+for all measured configurations, as displayed in Fig. 9.
+The value of magnetization is consistent with a fractional
+m=1/3 plateau and spans a range of fields of 0.2-0.3 T.
+In addition, the zero field phase shows zero magnetiza-
+tion for all applied fields, which indicates the realization
+of a gapped phase at T = 0. Magnetization data for in-
+equivalent directions in the hexagonal plane show very
+similar behavior, but differ from the results perpendicu-
+lar to the plane.
+For H ∥ a∗ and H ∥ b the zero magnetization phase
+extends up to 0.4 T. Above 0.5 T the system transitions
+into the factional magnetization plateau state up to a
+0
+0.5
+1
+1.5
+2
+0H (T)
+0
+0.5
+1
+1.5
+2
+2.5
+M ( B/Nd3+)
+0
+2
+4
+6
+8
+10
+12
+Ms,c/3
+(a.u.)
+H || a*
+H || b
+H || c
+T = 120 mK
+Magnetometer
+H||c
+(0,2,0), 55 mK
+H||a*
+(0,0,2), 130 mK
+Ms,a*/3
+Ms,b/3
+FIG. 9. Magnetization per Nd3+ ion measured at 120 mK
+in Nd3BWO9 for magnetic fields along the crystallographic
+directions a∗, b, and c from bulk measurements (left axis).
+Magnetization extracted from neutron diffraction intensity
+of nuclear reflections is superimposed to the corresponding
+bulk data. Plotted is the rescaled square root of the static,
+magnetic structure factor S∞
+z,z(q) (right axis). The measured
+reflections (Q) are indicated in the figure. Two of the data
+sets have been offset vertically by 0.5 and 1.0 units to improve
+visibility (a dashed line indicates their respective zero). The
+magnetization value at 1/3 of saturation is indicated for each
+individual data set by an arrow next to the plateau state.
+marked limit at 1 T. The transition into the fully satu-
+rated phase is gradual between 1 T and 1.3 T.
+In contrast, much sharper features are found when
+fields H ∥ c are applied. A non-magnetizable phase ap-
+pears up to 0.5 T, above which the system jumps rapidly
+into the plateau state at 0.65 T. The plateau terminates
+in a first-order jump to saturation around 1 T. Notably,
+despite the presence of a first-order transition, our mea-
+surements did not show signatures of hysteresis across
+the saturation transition for H ∥ c.
+Saturation fields extracted from magnetization data
+are consistent with those found in the specific heat
+data. The values for saturation magnetization show little
+anisotropy, finding 1.34(6) µB, 1.31(3) µB, and 1.35(4)
+µB per magnetic ion for configurations a∗, b, and c re-
+spectively. It suggests a nearly isotropic g-tensor in the
+material.
+F.
+Magnetic torque
+Magnetic torque is arguably the most sensitive tech-
+nique to magnetic phase transitions.
+Raw data are
+presented as the change in the measured capacitance
+7
+
+-0.2
+-0.15
+-0.1
+-0.05
+0
+-0.5
+0
+0.5
+-0.4
+-0.2
+0
+0.2
+C (fF)
+-2
+-1
+0
+1
+dC/dH (fF/T)
+0
+1
+2
+0
+0.2
+0.4
+0.6
+0
+1
+2
+0H (T)
+-0.5
+0
+0.5
+1
+1.5
+2
+2.5
+175 mK
+200 mK
+225 mK
+250 mK
+275 mK
+300 mK
+350 mK
+400 mK
+500 mK
+600 mK
+(a) H || a*
+(b) H || a*
+(c) H || b
+(d) H || b
+(e) H || c
+(f) H || c
+FIG. 10. Magnetic torque (∆C) and its field derivative mea-
+sured at constant temperatures against magnetic field, for
+three field orientations: (a,b) a∗, (c,d) b, and (d,e) c. For all
+data sets, a reference value of capacitance at zero field has
+been chosen and subtracted. Black arrows indicate features
+that may be identified with phase transitions.
+∆C = C(H) − C(H = 0 T) as a function of magnetic
+field for each temperature (Fig. 10). The torque data
+show strong differences between the measurements in the
+basal plane and perpendicular to it, but the obtained re-
+sults are very similar for both measurements within the
+plane. The raw data show some structure, but not sharp
+features as is customary in such measurements. Phase
+transitions are best captured in the first derivative of the
+raw data 10.
+Field derivative data show features that correspond
+with transitions observed in the other techniques re-
+ported in this study. Direct comparison with the other
+data sets is necessary to pinpoint what anomalies repre-
+sent real phase transitions. These features are indicated
+with arrows in the field derivative data [Fig. 10(b), 10(d),
+and 10(f)]. For H ∥ a∗ two distinct anomalies can be ob-
+served in the scan at 175 mK, at 0.68 T and at 0.99 T.
+These correspond to the lower and upper boundaries of
+the plateau phase. Data for H ∥ b show three anomalies
+at 0.68 T, 1.02 T and 1.28 T. The lower fields correspond
+again to the boundaries of the plateau phase. Notably,
+these two anomalies come together as the temperature is
+increased and disappear above 300 mK. The higher field
+anomaly, which is broader and less sharp, corresponds
+to the crossover into the fully saturated state. Finally,
+fields applied along the c direction reveal a completely
+different structure. Three anomalies can be identified at
+0.48 T, 0.71 T, and 0.95 T. The associated transitions in
+this case are the boundaries of the plateau for the high
+field features and the transition from the low field phase
+to paramagnet for the low field anomaly. The low field
+features, though weak, fade away as the transition tem-
+perature is overcome. The high field anomaly remains up
+to the highest temperatures representing the crossover of
+the system into the fully polarized pseudospin.
+G.
+Neutron diffraction
+We resorted to single-crystal neutron diffraction to in-
+vestigate the magnetic structures realized in the low field
+and the plateau phases. Figure 11 summarizes the re-
+sults obtained from the different instruments. The field
+dependence of the order parameter is depicted for both
+field configurations, which is in perfect agreement with
+our thermodynamic measurement data.
+Zero field data from both experiments unveil a com-
+mensurate phase with propagation vector Q = (0, 0,1/3).
+Fig.
+11(a) and Fig.
+11(b) show that magnetic reflec-
+tion (1,1,-1/3) is present throughout phase A for both
+field orientations.
+The phase is consistent with fully
+commensurate order, which leads to the appearance of a
+magnetic supercell, as is shown in Fig. 1(d). Integrated
+intensity of reflection (1,1,-1/3) drops at the intermedi-
+ate transition field, above which a different type of or-
+der is found depending on the direction of the magnetic
+field. For phase B (H ∥ a∗) we found magnetic reflec-
+tions (0,1/2,1/2) and (1/2,0,1/2). These reflections van-
+ish at fields slightly below saturation. Finally, phase C
+(H ∥ c) has been found to realize order with propaga-
+tion vector (1/3,1/3,1/3). Magnetic reflection (1/3,1/3,-
+1/3), which is inequivalent to the former, has also been
+found. Fig. 11(b) shows an abrupt drop in the intensity
+of reflection (1/3,1/3,1/3), consistent with a first order
+transition to saturation.
+An external magnetic field induces a ferromagnetic
+component in every lattice site that gives rise to the
+bulk magnetization. This produces extra scattering pro-
+portional to the square of the induced magnetic mo-
+mentum at the position of each nuclear peak . Fig. 9
+shows the uniform magnetization density extracted from
+two nuclear reflections: (020) for H ∥ a∗ and (200) for
+H ∥ c. We selected reflections where nuclear contribu-
+tion is minimal while a measurable magnetic intensity
+can be observed. The zero-field integrated intensity is
+subtracted from the data in a field to obtain the cor-
+8
+
+0
+2
+4
+6
+0.1
+0
+0.5
+1
+1.5
+0H (T)
+0
+5
+10
+Integrated Intensity (arb. units)
+0.2
+0.3
+0.1
+0.3
+0.1
+0.4
+T (K)
+0
+1
+2
+3
+4
+5
+Int.(arb. units)
+0.2
+0.4
+T (K)
+0.36
+0.35
+0.34
+0.33
+0.32
+(1,1,-l) (r.l.u.)
+Q = (1, 1, -1/3)
+Q = (0, 1/2, 1/2)
+Q = (1, 1, -1/3)
+Q = (1/3, 1/3, 1/3)
+T = 120 mK
+A
+B
+C
+A
+(a)
+(b)
+μ0H || a*
+ZEBRA
+ZEBRA
+T = 55 mK
+μ0H || c
+WISH
+(d)
+µ0H = 0 T
+0.1
+1.0
+Int.
+(a. u.)
+(c)
+Q = (1, 1,-⅓-δ)
+µ0H = 0 T
+FIG. 11. Results from single crystal magnetic neutron diffrac-
+tion. (a,b) Field dependence of the integrated neutron inten-
+sity at the magnetic propagation vectors for: (a) H ∥ a∗
+(ZEBRA, PSI) and (b) H ∥ c (WISH, ISIS). Note that in (a)
+the intensity of the (0,1/2,1/2) reflection has been rescaled by
+×0.1. In (b) the limits of the ordered phases are highlighted
+and shown with arrows. (c) Evolution of the integrated in-
+tensity of the reflection (1,1,-1/3) with temperature at zero
+magnetic field. (d) Incommensuration of the propagation vec-
+tor at zero field against temperature, shown as a shift in the
+peak position of the (1,1,l) reflection.
+responding magnetic scattering. Longitudinal magneti-
+zation is then plotted as the square root of mangetic
+intensity. The agreement with bulk measurements is re-
+markable and further highlights the existence of magne-
+tization plateaus regardless of field orientation.
+Finally, zero field neutron diffraction reveals an incom-
+mensurate state between the low temperature ordered
+phase and the paramagnetic phase.
+The onset of in-
+commensurate magnetic order appears around 0.34 K at
+the wavevector Q = (0, 0, 1/3 + δ).
+Temperature de-
+pendence of the intensity around the (1,1,l) reflection
+in Fig. 11(d), where the peak position is superimposed,
+shows this incommensuration.
+Reduction of the tem-
+perature leads to a change in the incommensurate prop-
+agation vector roughly linearly with temperature.
+At
+0.26 K the propagation vector locks into the commensu-
+rate Q = (0, 0, 1/3), as observed for the low temperature
+structure. The robustness of this evolution to commen-
+suration has been verified for several additional magnetic
+reflections.
+IV.
+DISCUSSION
+The purported breathing kagome structure is shown in
+Fig. 1. Unequal Nd-Nd distances and Nd-O-Nd angles
+result in inequivalent exchange parameters for neighbor-
+ing corner-sharing triangles [21]. This is represented by
+the exchange constants J△ and J▽, respectively. How-
+ever, a crystallographic analysis cannot rule out the ex-
+istence of interaction between adjacent kagome planes.
+Due to the short distances between kagome planes, the
+topology of the exchange interaction in Nd3BWO9 is
+likely three dimensional. In fact, the shortest superex-
+change Nd-O-Nd pathway (nearest neighbors, J1) links
+rare-earth ions belonging to different kagome planes [Fig.
+1(b)]. These couplings are arranged into isolated twisted
+3-legged spin tubes, one-dimensional structures that ex-
+tend perpendicular to the kagome planes [see Fig. 1(c)].
+Noteworthy, the resulting structure considering only
+nearest neighbor coupling is bipartite.
+A single tube
+would show no frustration, highlighting the relevance
+of further neighbor interactions.
+A three-dimensional
+structure with several exchange parameters may have
+to be regarded, as opposed to the originally suggested
+kagome structure. Yet, the onset of static magnetic or-
+der is extremely suppressed by the strong magnetic frus-
+tration f = −θW /TN ≈ 12.6, confirmed from magnetic
+susceptibility.
+Six magnetic rare-earth Nd3+ ions occupy general
+Wyckoff positions in the unit cell. The reduced point
+symmetry around the Nd3+ ions [Fig.
+1(e)] fully lifts
+the degeneracy of the total angular momentum levels (J
+= 9/2) into five Kramers doublets. The strong CEF iso-
+lates a single Kramers doublet with a large gap to excited
+multiplets. The obtained zero-field entropy is consistent
+with a value of S = R ln(2).
+These two observations
+show that Nd3BWO9 can be described as an effective
+spin S = 1/2 system below 100 K. However, the low
+symmetry precludes attempts to identify unequivocally
+a CEF-Hamiltonian and to extract the eigenstates of the
+lowest energy multiplet.
+Both magnetization and susceptibility suggest very lit-
+tle magneto-crystalline anisotropy. Susceptibility mea-
+surements suggest no preferential direction in the high
+temperature paramagnetic state.
+In addition, low-
+temperature magnetization in the fully saturated pseu-
+dospin phase shows no increase up to the highest probed
+fields. The increase of magnetization may be a rough
+estimator of the eigenstate admixing due to anisotropies
+(via Van-Vleck terms). No appreciable change in mag-
+netization is observed up to 2 T, indicating the total
+magnetization in the restricted pseudospin subspace is
+likely to be an approximately good quantum number. It
+9
+
+is, thus, likely that the low energy physics in Nd3BWO9
+can be described in terms of a highly symmetric spin
+Hamiltonian. A small axial anisotropy may be needed
+to account for the sharp features found for H ∥ c.
+To map out the phase diagram in the low tempera-
+ture regime for Nd3BWO9 we use specific heat measure-
+ments. Using a combination of all outlined techniques,we
+identify several regions of magnetic order.
+As shown
+in Fig. 12, the system reveals complex behaviour, with
+two different domes of long-range order observed for each
+configuration.
+A low field phase (A) extends roughly up to 0.6 T
+for both studied orientations. This phase possesses com-
+mensurate order with propagation vector Q =(0,0,1/3).
+Magnetization measurements show that this phase is
+hardly magnetizable, suggesting a gapped state in this
+field range. Although further analysis is needed to un-
+derstand the magnetic structures of the different phases
+in detail, a series of general remarks can be deduced
+from the data. For phase A, the presence of reflections
+(0,0,±2/3) forbids the existence of a collinear structure
+with spins parallel to c. Thus, a coplanar structure in
+the ab plane is likely realized.
+By increasing the magnetic field the system transitions
+into a field-induced ordered phase. A field H ∥ a∗ leads
+to the fractional m = 1/3 plateau phase B, characterized
+by a propagation vector Q =(0,1/2,1/2). The additional
+presence of wavevectors (1/2,0,1/2) and equivalent sug-
+gests a multi-Q structure or the presence of domains in
+the B phase.
+Strikingly, the order realized in the plateau is com-
+pletely different when fields are applied in the basal ab
+plane or perpendicular to it. In a field H ∥ c, phase C
+is found with propagation vector Q =(1/3,1/3,1/3). In
+contrast, saturation H ∥ c occurs through a sharp first
+order phase transition. Magnetocaloric effect supports
+this claim. A tricritical termination point appears where
+first and second order transition lines converge as shown
+in Fig. 12(b), at 0.20 K and 0.975 T. The presence of
+magnetic reflections (1/3,1/3,-1/3) and equivalent also
+indicates a complex spin texture, with either a multi-Q
+structure or the presence of domains.While here domains
+may be consistent with the observed first order transition
+to saturation, it is not possible at this stage to exclude
+either possibility.
+The existence of a tricritical point only for one ori-
+entation may be related to the large spin-lattice inter-
+action stemming from strong spin-orbit coupling. The
+transition to saturation for H ∥ c can be prematurely
+precipitated via an ’order by distortion’ [34] mechanism.
+A gain in magnetic energy compensates a small loss in
+elastic energy, leading to a first order transition to sat-
+uration. Though our neutron diffraction data show no
+evident change in the space group or lattice parameters
+in the high field phase, a detailed study would be neces-
+sary to discard this possibility.
+Phases A and B appear to merge below 100 mK at
+0.56 T. A first order phase transition is speculated be-
+tween A and B, with a termination bicritical point where
+0
+0.2
+0.4
+0.6
+0.8
+T (K)
+0
+5
+10
+15
+Cp/T (J mol-1K-2)
+(b) µ0H || c
+(a) µ0H || a*
+A
+A
+C
+B
+0
+0.5 ?
+(0,0,⅓)
+(0,0,⅓)
+(0,½,½)
+(⅓,⅓,⅓)
+1
+μ0H (T)
+0
+0.2
+0.4
+0.6
+FPP
+20
+25
+30
+FPP
+1.5
+2
+FIG. 12. Magnetic phase diagram of Nd3BWO9 in a mag-
+netic field applied along the principal directions: (a) a∗ and
+(b) c. The background depicts false color maps of Cp(H, T),
+with a shared color scale. Symbols: white circles and dia-
+monds represent transitions obtained from field and tempera-
+ture scans of specific heat, respectively. Green squares repre-
+sent the phase boundaries extracted from neutron diffraction
+data in Fig. 11. Upward-facing blue triangles show transi-
+tions extracted from bulk magnetization, downward facing
+pink triangles transitions from magnetic torque. A red dia-
+mond denotes the estimated position of the tricritical point
+for H ∥ c. An orange star shows the upper critical field es-
+timated in Fig. 8. Solid and dashed lines are a guide to the
+eye, representing second and first order transitions, respec-
+tively. The different phases are labeled as: A, B, C and Fully
+Polarized Pseudospin (FPP). The ordered phases show their
+corresponding magnetic propagation vector, as discussed in
+the text.
+all phase boundaries meet. Neutron diffraction data in
+Fig. 11(a) indicate the phases will likely merge slightly
+below 120 mK. Interestingly, between A and C the phase
+boundaries seem to develop smoothly down to the lowest
+measured temperatures and converge at T = 0. Neutron
+data at 55 mK show the phases are still separated by
+paramagnetism at this temperature Fig. 11(b). A highly
+non-trivial order-to-order quantum phase transition may
+take place between A and C at zero temperature (indi-
+cated with a question mark). Precise measurements in
+10
+
+the vicinity of these phase transitions would provide im-
+portant insight on their nature. However, the strong sig-
+nal from nuclear degrees of freedom and the extremely
+low temperatures involved prevent further investigation.
+The double hump features in specific above the transi-
+tion temperature represent a crossover from the low field
+disordered phase to the high field polarized phase. Such
+features can be understood in terms of models of hard-
+core bosons and are usually associated with quantum
+critical behaviour in one dimensional magnets [35, 36].
+They can be observed in several quasi-1D antiferromag-
+nets [27, 28], and therefore suggest the relevance of one-
+dimensional correlations for the physics of Nd3BWO9.
+These modulations are accentuated when the field is
+applied along the direction of the spin tubes (H ∥ c).
+Notably, despite the first-order nature of the transition
+these modulations are still present and seem to be most
+prominent around the tricritical termination point.
+Plateaux in the magnetically ordered sector are a hall-
+mark of frustrated magnets. The existence of magneti-
+zation plateaus (and particularly at 1/3 of saturation)
+has been predicted for both kagome antiferromagnets
+[37, 38], as well as for a model of isolated spin tubes with
+a weak triangular rung interaction (see Fig. 1(c)) [39–41].
+The presence of magnetization plateaux independent of
+the orientation of the applied magnetic field suggests an
+stabilizing interplay between frustration mechanisms.
+Finally,
+we comment on the origin of the ob-
+served incommensurate-commensurate (IC-C) transi-
+tion.
+Dipolar interactions are not uncommon in the
+study of rare-earth based magnets due to their large
+magnetic moments (µ(Nd3+) = 3.6µB) [42]. Their sta-
+bilizing role on incommensurate structures at temper-
+atures above commensurate order has been argued in
+several systems with hexagonal structure [43–45]. The
+realization of a IC-C transition at zero field opens the
+question to the importance of dipolar coupling for the
+low temperature properties of Nd3BWO9.
+We conclude the discussion by comparing Nd3BWO9
+to its isostructural compounds. To this point, only two
+other systems in the R3BWO9 family have been studied
+at low temperatures. NMR spectra reveal an inconm-
+mensurate magnetic structure in Sm3BWO9[46], while a
+dynamical state has been proposed for Pr3BWO9 at tem-
+peratures as low as 90 mK [47]. These two systems have
+been analyzed in terms of 2D Hamiltonians based on
+the existence of the kagome planes. However, our work
+highlights the presence of three-dimensional couplings
+and the potential dominance of the one-dimensional spin
+tubes. The discussion outlined here is inevitably rele-
+vant for investigations on other members of the family
+of R3BWO9.
+V.
+CONCLUSION
+We have presented a comprehensive study of the low
+temperature physics of the highly frustrated quantum
+antiferromagnet Nd3BWO9. Calorimetric and neutron
+scattering data support the realization of strongly in-
+teracting effective spin-1/2 moments below 100 K. Our
+measurements reveal a complex magnetic phase diagram
+below 300 mK, featuring magnetization plateaux for all
+field orientations. The ordering brings about important
+insight about the relevant magnetic interactions. Differ-
+ent magnetic structures are realized in the plateau states,
+depending on the direction of the magnetic field. Even
+though the phase diagram is considerably anisotropic, it
+can be described in terms of an effective S = 1/2 pseu-
+dospin.
+The experimental framework provided here is key for
+future studies on Nd3BWO9 and in the remaining mem-
+bers of the R3BWO9.
+The presence of the spin-tube
+structures perpendicular to the kagome planes is indi-
+cates that the magnetic properties of these highly frus-
+trated systems cannot be understood in terms of kagome-
+lattice physics. Further work is needed to fathom the
+effective dimensionality of the magnetic lattice.
+VI.
+ACKNOWLEDGEMENTS
+This work is supported by a MINT grant of the Swiss
+National Science Foundation.
+[1] L. Facheris, K. Y. Povarov, S. D. Nabi, D. G. Mazzone,
+J. Lass, B. Roessli, E. Ressouche, Z. Yan, S. Gvasaliya,
+and A. Zheludev, Phys. Rev. Lett. 129, 087201 (2022).
+[2] A. I. Smirnov, H. Yashiro, S. Kimura, M. Hagiwara,
+Y. Narumi, K. Kindo, A. Kikkawa, K. Katsumata, A. Y.
+Shapiro,
+and a. L. N. Demianets, Phys. Rev. B 75,
+134412 (2007).
+[3] F. Levy, I. Sheikin, C. Berthier, M. Horvati´c, M. Taki-
+gawa, H. Kageyama, T. Waki, and Y. Ueda, EPL (Eu-
+rophysics Letters) 81, 67004 (2008).
+[4] N. Wada, K. Ubukoshi, and K. Hirakawa, J. Phys. Soc.
+Jpn. 51, 2833 (1982).
+[5] M. Mourigal, M. Enderle, B. F˚ak, R. K. Kremer, J. M.
+Law, A. Schneidewind, A. Hiess, and A. Prokofiev, Phys.
+Rev. Lett. 109, 027203 (2012).
+[6] V. K. Bhartiya, K. Y. Povarov, D. Blosser, S. Bet-
+tler, Z. Yan, S. Gvasaliya, S. Raymond, E. Ressouche,
+K. Beauvois, J. Xu, et al., Phys. Rev. Research 1, 033078
+(2019).
+[7] E. Kermarrec,
+R. Kumar,
+G. Bernard,
+R. Henaff,
+P. Mendels, F. Bert, P. L. Paulose, B. K. Hazra,
+and
+B. Koteswararao, Phys. Rev. Lett. 127, 157202 (2021).
+[8] P. W. Anderson, Mater. Res. Bull. 8, 153 (1973).
+[9] Y. Zhou, K. Kanoda,
+and T.-K. Ng, Rev. Mod. Phys.
+89, 025003 (2017).
+[10] L. Savary and L. Balents, Rep. Prog. Phys. 80, 016502
+(2016).
+11
+
+[11] J. R. Chamorro, T. M. McQueen,
+and T. T. Tran,
+Chem. Rev. 121, 2898 (2020).
+[12] C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera,
+M. R. Norman, and T. Senthil, Science 367 (2020).
+[13] B.
+Bernu,
+C.
+Lhuillier,
+E.
+Kermarrec,
+F.
+Bert,
+P. Mendels, R. H. Colman, and A. S. Wills, Phys. Rev.
+B 87, 155107 (2013).
+[14] H. K. Yoshida, J. Phys. Soc. Jpn. 91, 101003 (2022).
+[15] M. D. LeBlanc, M. L. Plumer, J. P. Whitehead,
+and
+B. W. Southern, Phys. Rev. B 88, 094406 (2013).
+[16] H. Yoshida,
+N. Noguchi,
+Y. Matsushita,
+Y. Ishii,
+Y.
+Ihara,
+M.
+Oda,
+H.
+Okabe,
+S.
+Yamashita,
+Y. Nakazawa, A. Takata, et al., J. Phys. Soc. Jpn. 86,
+033704 (2017).
+[17] R. Okuma,
+D. Nakamura,
+T. Okubo,
+A. Miyake,
+A. Matsuo, K. Kindo, M. Tokunaga, N. Kawashima,
+S. Takeyama, and Z. Hiroi, Nat. Comm. 10, 1 (2019).
+[18] H. O. Jeschke, H. Nakano, and T. Sakai, Phys. Rev. B
+99, 140410(R) (2019).
+[19] M. Iqbal, D. Poilblanc,
+and N. Schuch, Phys. Rev. B
+101, 155141 (2020).
+[20] S. Jahromi, R. Orus, D. Poilblanc, and F. Mila, SciPost
+Phys. 9, 092 (2020).
+[21] M. Ashtar, J. Guo, Z. Wan, Y. Wang, G. Gong, Y. Liu,
+Y. Su, and Z. Tian, Inor. Chem. 59, 5368 (2020).
+[22] A. Majchrowski, E. Michalski, and A. Brenier, J. Cryst.
+Growth 247, 467 (2003).
+[23] D. Blosser, L. Facheris,
+and A. Zheludev, Rev. of Sci.
+Instr. 91, 073905 (2020).
+[24] S. E. Dutton, M. Kumar, M. Mourigal, Z. G. Soos, J.-
+J. Wen, C. L. Broholm, N. H. Andersen, Q. Huang,
+M. Zbiri, R. Toft-Petersen, and R. J. Cava, Phys. Rev.
+Lett. 108, 187206 (2012).
+[25] K. Kimura, S. Nakatsuji, J. J. Wen, C. Broholm, M. B.
+Stone, E. Nishibori,
+and H. Sawa, Nat. Comm. 4, 1
+(2013).
+[26] B. Bleaney, J. Appl. Phys. 34, 1024 (1963).
+[27] C. R¨uegg, K. Kiefer, B. Thielemann, D. F. McMor-
+row, V. Zapf, B. Normand, M. B. Zvonarev, P. Bouil-
+lot, C. Kollath, T. Giamarchi, S. Capponi, D. Poilblanc,
+D. Biner,
+and K. W. Kr¨amer, Phys. Rev. Lett. 101,
+247202 (2008).
+[28] D. Blosser, V. K. Bhartiya, D. J. Voneshen, and A. Zhe-
+ludev, Phys. Rev. Lett. 121, 247201 (2018).
+[29] S. Hayashida, D. Blosser, K. Y. Povarov, Z. Yan,
+S. Gvasaliya, A. N. Ponomaryov, S. A. Zvyagin,
+and
+A. Zheludev, Phys. Rev. B 100, 134427 (2019).
+[30] D. Flavi´an, S. Hayashida, L. Huberich, D. Blosser, K. Y.
+Povarov, Z. Yan, S. Gvasaliya, and A. Zheludev, Phys.
+Rev. B 101, 224408 (2020).
+[31] V. Zapf, M. Jaime, and C. D. Batista, Rev. Mod. Phys.
+86, 563 (2014).
+[32] Y. Kohama, C. Marcenat, T. Klein, and M. Jaime, Rev.
+Sci. Instrum. 81, 104902 (2010).
+[33] Y. Kohama, J. Phys. Soc. Jpn. 91, 101004 (2022).
+[34] O. Tchernyshyov, R. Moessner, and S. L. Sondhi, Phys.
+Rev. Lett. 88, 067203 (2002).
+[35] V. E. Korepin and N. A. Slavnov, Commun. Math. Phys.
+129, 103 (1990).
+[36] S. Sachdev, T. Senthil,
+and R. Shankar, Phys. Rev. B
+50, 258 (1994).
+[37] T. Sakai and H. Nakano, Phys. Rev. B 83, 100405(R)
+(2011).
+[38] S. Capponi, O. Derzhko, A. Honecker, A. M. L¨auchli,
+and J. Richter, Phys. Rev. B 88, 144416 (2013).
+[39] J.-B. Fouet, A. L¨auchli, S. Pilgram, R. M. Noack, and
+F. Mila, Phys. Rev. B 73, 014409 (2006).
+[40] K. Yonaga and N. Shibata, J. Phys. Soc. Jpn. 84, 094706
+(2015).
+[41] T. Sakai, M. Sato, K. Okunishi, K. Okamoto,
+and
+C. Itoi, in J. Phys., Vol. 400 (IOP Publishing, 2012).
+[42] S. E. Palmer and J. T. Chalker, Phys. Rev. B 62, 488
+(2000).
+[43] H. Shiba and N. Suzuki, J. Phys. Soc. Jpn. 51, 3488
+(1982).
+[44] N. Suzuki, J. Phys. Soc. Jpn. 52, 3199 (1983).
+[45] R. S. Gekht and V. I. Ponomarev, Phase Transitions 20,
+27 (1990).
+[46] K.-Y. Zeng, F.-Y. Song, L.-S. Ling, W. Tong, S.-L. Li,
+Z.-M. Tian, L. Ma, and L. Pi, Chinese Phys. Lett. 39,
+107501 (2022).
+[47] K. Y. Zeng, F. Y. Song, Z. M. Tian, Q. Chen, S. Wang,
+B. Liu, S. Li, L. S. Ling, W. Tong, L. Ma, et al., Phys.
+Rev. B 104, 155150 (2021).
+12
+
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+page_content=' Yan,1 O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zaharko,3  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Fennell,3 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Khalyavin,4 Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yan,1 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Gvasaliya,1 and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zheludev1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' †  1Laboratory for Solid State Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' ETH Z¨urich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 8093 Z¨urich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Switzerland  2Max-Planck-Institut f¨ur Festk¨orperforschung,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Heisenbergstraße 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 70569 Stuttgart,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Germany  3Laboratory for Neutron Scattering and Imaging,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Paul Scherrer Institut,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 5232 Villigen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Switzerland  4ISIS Facility,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rutherford Appleton Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Chilton,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Didcot,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Oxon OX11 0QX,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' United Kingdom  (Dated: January 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 2023)  The highly-frustrated rare-earth based magnet Nd3BWO9 is a promising candidate in the search  for proximate spin liquid physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' We present a thorough investigation on single crystals of this ma-  terial using bulk and microscopic techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Magnetization data reveal a fractional magnetization  plateau for three different investigated field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The magnetic phase diagram is mapped out  from calorimetric data and exhibits several domes of magnetic order below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Propagation vec-  tors for all ordered phases are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The results suggest complex ordering in this material, and  unveil the existence of a commensuration transition of the propagation vector at zero magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  A scenario where interplane exchange interactions are essential to a magnetic model of Nd3BWO9  is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  INTRODUCTION  Strongly frustrated quantum antiferromagnets (AFM)  are known to realize a panoply of magnetic states due  to the delicate equilibrium between the magnetic in-  teractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  In the presence of magnetic fields, the  large ground state degeneracy is lifted in subtle and  diverse ways, which leads to extremely rich phase di-  agrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Realization of spin-density waves [1], magne-  tization plateaus [2, 3] commensurate-incommensurate  transitions [4], and even more exotic order like spin  nematicity [5, 6] is not rare, particularly in quasi-low-  dimensional systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The archetypal model in 2D frustrated magnetism is  the kagome lattice Heisenberg S = 1/2 AFM (KHAF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The impossibility of satisfying all magnetic interactions  in this lattice results in a macroscopic degeneracy of the  ground state already at a classical level [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Turning to  S = 1/2 spins promotes the quantum fluctuations on the  ground state giving rise to highly non-trivial phases [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Arguably, the most intriguing state is the hypothesized  Quantum Spin Liquid (QSL) [9] ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The pre-  diction of fractionalization of quasiparticles in a 2D sys-  tem triggered extensive effort from both theory and ex-  perimental perspectives [10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nevertheless, the QSL  phase remains elusive [12] as it constitutes a very frag-  ile state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' One of the main causes of the instability of  the QSL states is the presence of terms in the Hamilto-  nian that lift the ground state degeneracy [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The  many different ways to lift this degeneracy have led to  a flurry of new magnetic structures [15–18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However,  occasionally deviations from a putative KHAF tend to  stabilize QSL phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In particular, the so called breath-  ing anisotropy has been predicted to favor a resonance  ∗ daniefla@ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='ch  † zhelud@ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='ch;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='neutron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='ch/  valence bond solid ground state for a wide range of cou-  pling parameters [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  In  this  context,  the  recently  discovered  family  R3BWO9 of rare-earth antiferromagnets is an optimal  platform for the search of spin-liquid candidates [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Here R is a trivalent rare-earth element and the large  difference in size of the constituent atoms prevents anti-  site chemical disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' All of the members of the family  realize a breathing kagome lattice in their basal plane  and show no sign of magnetic ordering down to 2 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The strong spin-orbit coupling in combination with crys-  tal electric field effects opens the possibility of realizing  effective Jeff = 1/2 magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Among all compounds in the family, the most promis-  ing is Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A large Weiss temperature [21] has  been reported and the total angular momentum of Nd3+  (J = 9/2) makes it a Kramers-doublet system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' No mag-  netic long-range order has been found in previous studies  down to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However, little is known so far about its  magnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In this study we report on the low tempera-  ture properties of single crystals of Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' We found  static magnetic long-range order below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The ob-  served magnetism suggests a three dimensional network  of exchange interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nonetheless, due to the highly  frustrated interaction a complex phase diagram is real-  ized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The paper is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' First, a summary  of the various methods used is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Then, we out-  line the main results of the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Subsequently,  a detailed discussion of the main outcome is provided,  including a thorough description of the magnetic struc-  ture and a detailed picture of the magnetic phase dia-  gram under applied fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Finally, the main conclusions  are drawn and further steps in the search of QSL physics  are examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='05555v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='str-el]  13 Jan 2023  (b)  (e)  2 mm  a  b  c  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='66 Å  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='57 Å  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='25 Å  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='49 Å  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='38 Å  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='36 Å  Nd  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='55 Å  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='42 Å  c  WO6  B  NdO8  a  b*a*  b  c  (a)  (d)  Nd  a  b  c  l = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='44 Å  (c)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='95 Å  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='92 Å  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='25 Å  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Crystal structure and superexchange topology in  Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (a) Schematic structure reflecting the purported  kagome interaction in the crystallographic ab plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Only  atoms with 0 ≤ z ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 are shown here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' There is an addi-  tional kagome plane displaced by half lattice parameter along  the c crystallographic direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (b) The shortest superex-  change Nd-O-Nd bond links neodymium atoms in different  kagome planes, forming isolated spin tubes along the c axis  arranged in a triangular lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The kagome bonds are shown  for reference along with bond distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (c) A typical single  crystal sample of Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (d) A single spin tube is unfrus-  trated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However, further-neighbor interactions frustrate the  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' An arrow indicates the size of the magnetic supercell  at zero field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (e) The environment of neodymium has very  low symmetry, resulting in a C1 point group for the magnetic  ion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nd-O distances are indicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  METHODS  Nd3BWO9 crystallizes in a hexagonal structure, with  space group P63 (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 173), where the magnetism stems  from the effective magnetic moment of the Nd3+ ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Single crystal samples were grown by spontaneous crys-  tallization using a flux method as described in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Pur-  ple transparent single crystals with well defined facets  were obtained [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 1(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Typical masses range from  a few micrograms to 40 mg and different samples were  used in this study, depending on the technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The  chemical structure of the different single-crystal samples  used in this study was validated using single-crystal X-  ray diffraction on a Bruker APEX-II instrument, and was  found to be in agreement with previous reports [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The  structure is schematically depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 1, where the  kagome-lattice bonds can be readily identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Powder  samples of Nd3BWO9, as well as of the non-magnetic  La3BWO9, were synthesized by a solid state reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The correct chemical structure and the quality of the  powders was checked with powder X-ray diffraction in  a Rigaku MiniFlex diffractometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Boron-11 enriched  samples (both powder and single crystals) were also pre-  pared for their use in neutron scattering experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Measurements of heat capacity, magnetocaloric effect  (MCE), magnetization and magnetic torque were carried  out using a 3He-4He dilution refrigerator insert for the  Quantum Design Physical Property Measurement Sys-  tem (PPMS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A sample of mass 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='131 mg was used for  both heat capacity and MCE measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Heat ca-  pacity data were collected using a standard relaxation  method from Quantum Design for temperatures 100 mK  < T < 4 K in applied fields of 0 T < µ0H < 3 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The  magnetic field was applied along the crystallographic a∗,  and c directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In zero field, data were collected from  100 mK to 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Heat capacity data of La3BWO9 were  measured down to 2 K and extrapolated to lower tem-  peratures from an empirical fit to a T 3-power law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' MCE  data were measured using the same puck as for heat ca-  pacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The change of temperature of the sample was  recorded as the magnetic field was swept up and down  at a constant rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In order to avoid self heating of the  puck, the field change rate was optimized and a value of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 mT/s was selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In the terminology of MCE mea-  surements, our experiment was conducted under equilib-  rium conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Magnetization was measured using an in house made  Faraday-balance capacitive magnetometer [23] at 120  mK and 2 K and magnetic fields applied along three ori-  entations: a∗, and b, and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Additional measurements  of magnetization carried out in the MPMS system at 2  K were used to calibrate the low temperature data and  obtain absolute units (not shown here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Using the same  setup, magnetic torque was measured up to 3 T and  for temperature from 120 mK to 600 mK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The torque  data correspond to the deflection of a small cantilever  on which the sample is mounted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The magnetic field  sweeping rate was also optimized to minimize heating  due to eddy currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Magnetic susceptibility was measured using the Quan-  tum Design Magnetic Property Measurement System  (MPMS) SQUID Magnetometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The temperature  range from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8 K to 300 K was probed using a small po-  larizing field applied along three crystal directions: a∗,  and b, and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The probing field was µ0H = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1 T, where  µ0 denotes the permeability of vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Inelastic neutron scattering on powder samples of  Nd3BWO9 was measured to investigate the crystal elec-  tric field induced scheme of total angular momentum  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The instrument of choice was the thermal neu-  tron triple-axis-spectrometer EIGER at PSI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1 g of  Nd3 11BWO9 was sealed in an aluminum can and in-  stalled in a standard 4He orange cryostat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A final wave-  length of kf= 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='66 ˚A−1 (λ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='36 ˚A) was chosen, us-  ing a pyrolytic graphite filter to eliminate higher-order  neutrons without further collimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Data were mea-  sured at constant scattering angle, 2θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The background  was investigated to select the optimal value for the scat-  tering angle, sufficiently far from the direct beam and  low enough to have good counting and small decay in  the signals due to magnetic structure factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A value  of 2θ = 10◦ was chosen, and the incident energy was  scanned at three different temperatures: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 K, 100 K  and 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Neutron single crystal diffraction was used to investi-  2  J0  100  200  300  T (K)  0  50  100  150  200  1 (mol T μB )  H || a*  θCW = -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='76 K  μ0H = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1 T  H || b  H || c  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Inverse magnetic susceptibility on single crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Data show measurements for three field orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A small  probing field of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1 T was used for all measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The  black solid line represents a Curie-Weiss model with the av-  erage Weiss temperature and effective moment parameters,  given in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  gate the magnetic structures in the ordered phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A  single crystal sample of 18 mg in mass of Nd3 11BWO9  and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5×1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4×0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8 mm3 was studied using two different  instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Measurements with H ∥ a∗ were carried  out at the Thermal Single Crystal Diffractometer ZE-  BRA at the Swiss Spallation Neutron Source, SINQ,  in the Paul Scherrer Institut (PSI, Switzerland).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The  diffractometer was used in conjunction with a 3He-4He  dilution refrigerator and a 6-T magnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The crystal  was aligned with its a∗ axis vertical, the same direc-  tion as the applied magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Neutron wavelengths  of λ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='314 ˚A and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='383 ˚A were selected, provided by  the PG(200) and Ge(220) monochromators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Additional  measurements with H ∥ c were carried out in the time-  of-flight diffractometer WISH at the ISIS facility in the  Rutherford Appleton Laboratory, in the United King-  dom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The sample was mounted with its c axis vertical  and parallel to the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A 3He-4He dilution  refrigerator and a 10-T magnet were used to access the  ordered states in Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  EXPERIMENTAL RESULTS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Magnetic susceptibility  Figure 2 shows inverse susceptibility measurements for  probing fields applied along the crystallographic direc-  tions a∗b, and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Down to the lowest accessible tem-  perature of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8 K, these data show no sign of magnetic  ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  A fit of the experimental data to a Curie-Weiss model  is shown overlaid on the experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A good  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Fitting parameters from the Curie-Weiss model for  data shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  200 K ≤ T ≤ 300 K 20 K ≤ T ≤ 60 K  θW (K)  µeff (µB)  θW (K) µeff (µB)  H ∥ a∗  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='76  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='78  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='94  H ∥ b  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='7  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='79  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='82  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='90  H ∥ c  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='77  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='68  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='91  agreement is found for data above 130 K, with a large,  negative Weiss temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The resulting Weiss tem-  peratures, θW are given in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' I, as well as the cor-  responding effective magnetic moments extracted from  the Curie constants as C = NAµ0µ2  eff/(3kB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The ob-  tained effective magnetic moments are close to the value  expected for a free Nd3+ ion: µeff = gJ  �  J(J + 1)µB =  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6µB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Importantly, the susceptibility data show little  dependence on the direction of the magnetic field, which  suggests that, the resulting magnetic anisotropy remains  quite small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Our results are consistent with those re-  ported in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' [21] on polycrystal samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Below 130 K a clear deviation from the high temper-  ature fit is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  This is roughly consistent with  the existence of a crystal electric field (CEF) level at  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='9 meV (see below), signaling the total depletion of  the population of the first excited state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A Curie-Weiss  analysis is heavily affected by the partial population of  excited multiplets and lead to an overestimation of ex-  change parameters and exchange couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Therefore,  an additional fit to a Curie-Weiss law for a tempera-  ture range far enough from the CEF resonance has been  performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The results are also summarized in Table  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Temperatures in the range between 20 K and 60 K  were considered for this fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The resulting Weiss temper-  atures are much reduced compared to the high temper-  ature fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However, they still reflect a predominant an-  tiferromagnetic interaction in Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The effective  magnetic moments are also reduced with respect to their  high temperature value, yielding an average moment of  µeff = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='92µB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  CEF level scheme  The inelastic neutron scattering spectra are shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Large intensity at zero energy transfer corre-  sponds to quasielastic scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Three resonances are  identified at 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='9, 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8, and 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='7 meV, which we ascribe  to CEF induced levels due to their temperature depen-  dence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Importantly, no resonance is found below 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='9  meV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Since the total angular momentum J = 9/2 of the  free Nd3+ is expected to be fully split into five Kramers  doublets, this suggests that the low temperature physics  of Nd3BWO9 can indeed be described in terms of the  lowest laying doublet, giving rise to an effective two-level  system well below ∆ = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='9 meV ≈ 180 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  3  0  10  20  30  40  0  0  0  ħω (meV)  T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 K  T = 100 K  T = 300 K  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='9  1  Ef = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='7 meV  2θ = 10°  Intensity (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' units)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Inelastic neutron scattering intensity at a constant  scattering angle for three different temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The final  energy of Ef= 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='7 meV was fixed and incident energy var-  ied, fixing a 10 degree scattering angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' CEF resonances are  indicated by black arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' An offset of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='25 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='50 units  was added for visibility, a dashed line indicates the reference  zero for those data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Specific heat  Specific heat as a function of temperature and mag-  netic field is used to unveil the magnetic phase diagram  of Nd3BWO9 at ultra-low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Data obtained  at zero field are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nd3BWO9 shows an up-  turn in specific heat below 4 K with two clearly distinct  features [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 4(a)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Around 1 K, a hump in specific heat  suggests the onset of short-range magnetic correlations  [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' At TN = 300 mK we found a sharp lambda anomaly  representing the transition into magnetic long range or-  der.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Below TN the specific heat signal remains large  down to the lowest accessible temperatures in our setup,  likely due to nuclear specific heat from the rare-earth  ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In order to understand exactly the nature of the  magnetic specific heat, we have examined the different  contributions and subtracted them from the measured  total specific heat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  To estimate the phononic contribution, we synthesized  the non-magnetic isostructural material La3BWO9 and  measured its specific heat in the same range of temper-  atures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  This is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 4(a) and represents the  lattice contribution, CL, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 4(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  An accurate estimation of the nuclear contribution to  specific heat is usually much more complicated, as a  1  10  100  T (K)  0  10  20  30  40  50  Cp (J mol-1 K-1)  Nd3BWO9  Nd3BWO9  TN  La3BWO9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  1  4  10  T (K)  Rln(2)  0  10  20  Cp/T (J mol-1 K-2)  CL  CN  Ctot  Cmag  0  1  2  3  4  T (K)  0  2  4  6  8  Smag (J mol-1  NdK-1)  (a) μ0H = 0 T  (b)  (c)  TN  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  (a) Total specific heat at zero magnetic field for  Nd3BWO9 and the nonmagnetic isostructural compound  La3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Nd3BWO9 shows a substantial magnetic con-  tribution to specific heat below 3 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (b) Total specific heat  (open circles) and magnetic specific heat (filled circles) after  subtraction of lattice and nuclear degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lat-  tice (CL) and nuclear (CN) contribution are estimated as  discussed in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A lambda anomaly can be found at  TN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='30 K, signaling the onset of long-range magnetic or-  der.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (c) The magnetic entropy per Nd3+ ion saturates above  3 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A dashed line represents the expected value for a two-  level system at infinite temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  variety of effects has to be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  These include  dipole and quadrupolar splitting, or hyperfine coupling  between nuclei and electrons (which can be quite signif-  icant in magnetically ordered materials).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Neodymium  has two isotopes with nonzero dipolar and quadrupolar  momenta, out of its 7 stable isotopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Following the rea-  soning in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' [25], the effect of quadrupolar splitting is  assumed to be small compared to that of hyperfine cou-  pling, and we neglect it here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In a magnetized phase,  local fields are expected to be sizable and therefore hy-  perfine coupling may significantly contribute to specific  heat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The contribution from dipole field splitting from a  single isotopic species is given by  4  Cp/T (J/molK-2)  (a) H || a*  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  T (K)  0  20  40  60  80  Cp/T (J/molK-2)  0 T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='85 T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='55 T  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2 T  0  10  20  30  40  50  60  70  0 T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='85 T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='975 T  (b) H || c  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Typical temperature scans of specific heat for differ-  ent fixed values of magnetic field applied along (a) H ∥ c and  (b) H ∥ a∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' An offset of 15 J/mol/K2 has been added for  visibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Solid filled triangles show features associated with  the phase transitions discussed in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  CH,i =  NAkB  α2  i  4I2  i  �  �  1  sinh2 �  αi  2Ii  � −  (2Ii + 1)2  sinh2 �  (2Ii+1)αi  2Ii  �  �  �  (1)  where αi = AH(µNd  Hyp/gJ)Ii/kBT, and Ii is the nuclear  spin, gJ = 8/11 (Land´e factor for Nd), NA is the Avo-  gadro constant, and kB the Boltzmann constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' AHyp  represents the strength of the hyperfine coupling and  here we made a second approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' We assume all  the nuclei couple equally to the electron density and the  value of AHyp is approximated as that of Nd metal [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  µNd  Hyp denotes the static dipole moment of the Nd3+ ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  This is precisely the origin of the local field and for its  value we chose the averaged effective magnetic moment  from the magnetic susceptibility data at low tempera-  tures µNd  Hyp = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='914µB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Finally, the different species are  summed, weighted by their isotopical abundance to ob-  tain the temperature dependence of nuclear specific heat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  This model with no free parameters is in excellent  agreement with the lowest temperature data, as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 4(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Having modeled the nuclear specific heat, the  magnetic specific heat can be extracted by subtraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The magnetic specific heat was subsequently integrated  to obtain the temperature dependence of magnetic en-  Cp/T (J/mol K-2)  150 mK  250 mK  350 mK  500 mK  800 mK  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  3  0H (T)  0  20  40  60  Cp/T (J/mol K-2)  (a) H || a*  0  20  40  60  80  150 mK  250 mK  350 mK  500 mK  800 mK  (b) H || c FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Typical field scans of specific heat measured at con-  stant temperature in Nd3BWO9 for (a) H ∥ c and (b) H ∥ a∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  An offset of 10 or 15 J/mol/K2 is added for visibility be-  tween the scans for (a) and (b), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Solid filled  triangles show features associated with the phase transitions  discussed in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Black arrows signal the existence  of broad double-hump features, described in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  An  asterisk shows a feature above the saturation transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  tropy, depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 4(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The high temperature trend  of this quantity approaches the value of R ln(2), the ex-  pected value of a two-level system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  In a magnetic field, a simple estimation of the contri-  bution of the nuclear spin due to Zeeman splitting could  not account for the effects observed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Low tempera-  ture data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 5 show that the effect of nuclear specific  heat is of the same order of magnitude up to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2 T and it  is not strongly field dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' This suggests that also  in a field the main contribution comes from hyperfine  coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However, a quantitative determination of this  effect under magnetic fields becomes paramount.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The evolution of the specific heat of Nd3BWO9 under  magnetic fields is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 6 for fields along two  different crystallographic directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The total heat ca-  pacity is displayed here, without subtraction of lattice  or nuclear degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Typical-field scans show  a number of anomalies that are consistent with the exis-  tence of three different phases with static magnetic order  at low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Up to three distinct features can be observed for  H ∥ a∗ at the lowest temperature, at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='45, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='62 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='05  T and are marked with triangles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 6(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='These fea-  5  tures are rather spread in fields, specially at saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  However, the existence of thermodynamic transitions has  been confirmed by neutron diffraction (as discussed be-  low).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The two lower field anomalies move apart as the  temperature is increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The two higher field anoma-  lies merge at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='25 K, denoting the highest temperature  of the ordered phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Though the specific heat anoma-  lies in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 6(a) are too broad for a precise estimation  of the upper critical field, this quantity can be deduced  from magnetocaloric effect measurements (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  For fields orthogonal to the hexagonal plane (H ∥ c)  at the lowest temperature one finds two anomalies at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  T, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8 T and a sharper one at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='95 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 6(b)] Notably,  in this configuration the different anomalies appear nar-  rower than for H ∥ a∗, especially at the saturation field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The first two anomalies move apart as the temperature  is increased, while the higher field anomaly barely shifts  in position up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The low field anomaly shifts to-  wards zero field and disappears as TN is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The  two high-field anomalies merge at T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' From the  high field anomaly we extract an estimate of the satura-  tion field of µ0Hc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='975(3) T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Interestingly, an extra  feature can be identified above saturation (asterisk in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 6(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  This feature shifts to higher fields as the  temperature is increased and decreases rapidly in mag-  nitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2 K it is hardly identifiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Finally, double-hump features can be observed above  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3 K for both magnetic field configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' These are  significant up to the highest measured temperatures and  particularly prominent around the saturation field (black  arrows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  For H ∥ c the amplitude of these  modulations is larger than in H ∥ a∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Such features are  often associated with a low-dimensional crossover from  the zero field disordered phase to the fully polarized state  without the occurrence of a phase transition [27–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Magnetocaloric effect  Magnetocaloric  effect  (MCE)  measurements  in  Nd3BWO9 provide key information on the nature of the  various phase transitions found with other techniques  [31–33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Representative temperature profiles are sum-  marized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Several crossings can be observed  for both configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The observed anomalies are  too broad to assign exactly a transition point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Due  to the proximity of the thermodynamic transitions  in the phase diagram, features corresponding to both  transitions merge and overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  In our measurements  the field is swept slow enough as to ensure equilibrium  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Data measured with H ∥ a∗ show mostly symmetric  features around the crossing points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Particularly, this  suggests that the measured phase transitions are of sec-  ond order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In contrast, the low temperature profiles for  H ∥ c show two distinct behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' At 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6 T one finds a  roughly symmetric feature, suggesting again a second or-  der phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' This is different at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='975 T, where  a very asymmetric feature appears, pointing to a first  0  μ  μ  1  2  0H (T)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 mT/s  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 mT/s  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='7  T (K)  0  1  2  0H (T)  (b) H || c  (a) H || a*  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Plots of the magnetocaloric effect in Nd3BWO9 for  different base temperatures and fields applied along (a) H ∥  a∗ and (b) H ∥ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' For all the scans, red (blue) color represents  data measured while driving the magnetic field up (down).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  A ramping rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 mT/s was used throughout all the  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Small prominent features (specially at low  fields) are spurious and the result of an unstable platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  order or discontinuous transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Finally, the absence of anomalies above the saturation  field for H ∥ c must be noted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The features observed in  the fully polarized phase in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 6(b) leave no trace in  the MCE data in the same configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The MCE technique is based on the change of entropy  in a magnetic system as it is driven through a phase  transition, crossover, level crossing, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Consequently,  one can retrieve the change in entropy in a system from  the change in temperature against magnetic field [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Under equilibrium conditions, we obtain the entropy as  ∆S = S(H) − S0 = −  �  κT − Tbath  T  dt  (2)  where κ is the thermal conductivity of the thermal  link in the calorimeter, T is the sample temperature, and  Tbath is the thermal bath temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Integration of the  data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 7 gives rise to the entropy maps displayed in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The data above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2 K are a good picture of the  entropy stored in the magnetic subsystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However, for  temperatures below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='15 K imperfect equilibrium condi-  tions prevent a reliable estimation of entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A strong  accumulation of entropy is observed above the saturation  transitions for both field configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The position of  the peaks in entropy match the estimated position of the  critical fields from specific heat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' For H ∥ a∗, the maxima  in entropy at different temperatures were used to obtain  an accurate estimate of the upper critical field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  A fit  to the data provides Hc,a∗ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='187(13) T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' This value is  consistent with the various probes used in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  6  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8  T (K)  μ0H (T)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8  T (K)  (a) H || a*  A  B  S (J molNd K-1)  1  0  1  2  3  (b) H || c  A  C  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Entropy maps in false color for two magnetic field  orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In false color plots, the change in entropy ex-  tracted from magnetocaloric data from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Filled circles  (diamonds) denote phase anomalies associated with phase  transitions from specific heat field (temperature) scans for  (a) H ∥ a∗ and (b) H ∥ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  In (a) red squares show the  maxima of entropy at the measured temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A white  dashed line is a power law fit to the data showing the best  estimate for the upper critical field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Magnetization  The evolution of magnetization under a magnetic field  provides insight on the type of order in Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Strikingly, a fractional magnetization plateau is observed  for all measured configurations, as displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The value of magnetization is consistent with a fractional  m=1/3 plateau and spans a range of fields of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  In addition, the zero field phase shows zero magnetiza-  tion for all applied fields, which indicates the realization  of a gapped phase at T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Magnetization data for in-  equivalent directions in the hexagonal plane show very  similar behavior, but differ from the results perpendicu-  lar to the plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  For H ∥ a∗ and H ∥ b the zero magnetization phase  extends up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 T the system transitions  into the factional magnetization plateau state up to a  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  2  0H (T)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  M ( B/Nd3+)  0  2  4  6  8  10  12  Ms,c/3  (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=')  H || a*  H || b  H || c  T = 120 mK  Magnetometer  H||c  (0,2,0), 55 mK  H||a*  (0,0,2), 130 mK  Ms,a*/3  Ms,b/3  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Magnetization per Nd3+ ion measured at 120 mK  in Nd3BWO9 for magnetic fields along the crystallographic  directions a∗, b, and c from bulk measurements (left axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Magnetization extracted from neutron diffraction intensity  of nuclear reflections is superimposed to the corresponding  bulk data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Plotted is the rescaled square root of the static,  magnetic structure factor S∞  z,z(q) (right axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The measured  reflections (Q) are indicated in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Two of the data  sets have been offset vertically by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='0 units to improve  visibility (a dashed line indicates their respective zero).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The  magnetization value at 1/3 of saturation is indicated for each  individual data set by an arrow next to the plateau state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  marked limit at 1 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The transition into the fully satu-  rated phase is gradual between 1 T and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  In contrast, much sharper features are found when  fields H ∥ c are applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A non-magnetizable phase ap-  pears up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 T, above which the system jumps rapidly  into the plateau state at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='65 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The plateau terminates  in a first-order jump to saturation around 1 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Notably,  despite the presence of a first-order transition, our mea-  surements did not show signatures of hysteresis across  the saturation transition for H ∥ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Saturation fields extracted from magnetization data  are consistent with those found in the specific heat  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The values for saturation magnetization show little  anisotropy, finding 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='34(6) µB, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='31(3) µB, and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='35(4)  µB per magnetic ion for configurations a∗, b, and c re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' It suggests a nearly isotropic g-tensor in the  material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Magnetic torque  Magnetic torque is arguably the most sensitive tech-  nique to magnetic phase transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Raw data are  presented as the change in the measured capacitance  7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  C (fF)  2  1  0  1  dC/dH (fF/T)  0  1  2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6  0  1  2  0H (T)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  175 mK  200 mK  225 mK  250 mK  275 mK  300 mK  350 mK  400 mK  500 mK  600 mK  (a) H || a*  (b) H || a*  (c) H || b  (d) H || b  (e) H || c  (f) H || c  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Magnetic torque (∆C) and its field derivative mea-  sured at constant temperatures against magnetic field, for  three field orientations: (a,b) a∗, (c,d) b, and (d,e) c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' For all  data sets, a reference value of capacitance at zero field has  been chosen and subtracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Black arrows indicate features  that may be identified with phase transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  ∆C = C(H) − C(H = 0 T) as a function of magnetic  field for each temperature (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The torque data  show strong differences between the measurements in the  basal plane and perpendicular to it, but the obtained re-  sults are very similar for both measurements within the  plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The raw data show some structure, but not sharp  features as is customary in such measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phase  transitions are best captured in the first derivative of the  raw data 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Field derivative data show features that correspond  with transitions observed in the other techniques re-  ported in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Direct comparison with the other  data sets is necessary to pinpoint what anomalies repre-  sent real phase transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' These features are indicated  with arrows in the field derivative data [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 10(b), 10(d),  and 10(f)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' For H ∥ a∗ two distinct anomalies can be ob-  served in the scan at 175 mK, at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='68 T and at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='99 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  These correspond to the lower and upper boundaries of  the plateau phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Data for H ∥ b show three anomalies  at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='68 T, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='02 T and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='28 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The lower fields correspond  again to the boundaries of the plateau phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Notably,  these two anomalies come together as the temperature is  increased and disappear above 300 mK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The higher field  anomaly, which is broader and less sharp, corresponds  to the crossover into the fully saturated state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Finally,  fields applied along the c direction reveal a completely  different structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Three anomalies can be identified at  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='48 T, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='71 T, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='95 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The associated transitions in  this case are the boundaries of the plateau for the high  field features and the transition from the low field phase  to paramagnet for the low field anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The low field  features, though weak, fade away as the transition tem-  perature is overcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The high field anomaly remains up  to the highest temperatures representing the crossover of  the system into the fully polarized pseudospin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Neutron diffraction  We resorted to single-crystal neutron diffraction to in-  vestigate the magnetic structures realized in the low field  and the plateau phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Figure 11 summarizes the re-  sults obtained from the different instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The field  dependence of the order parameter is depicted for both  field configurations, which is in perfect agreement with  our thermodynamic measurement data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Zero field data from both experiments unveil a com-  mensurate phase with propagation vector Q = (0, 0,1/3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  11(a) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  11(b) show that magnetic reflec-  tion (1,1,-1/3) is present throughout phase A for both  field orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The phase is consistent with fully  commensurate order, which leads to the appearance of a  magnetic supercell, as is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 1(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Integrated  intensity of reflection (1,1,-1/3) drops at the intermedi-  ate transition field, above which a different type of or-  der is found depending on the direction of the magnetic  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' For phase B (H ∥ a∗) we found magnetic reflec-  tions (0,1/2,1/2) and (1/2,0,1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' These reflections van-  ish at fields slightly below saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Finally, phase C  (H ∥ c) has been found to realize order with propaga-  tion vector (1/3,1/3,1/3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Magnetic reflection (1/3,1/3,-  1/3), which is inequivalent to the former, has also been  found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 11(b) shows an abrupt drop in the intensity  of reflection (1/3,1/3,1/3), consistent with a first order  transition to saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  An external magnetic field induces a ferromagnetic  component in every lattice site that gives rise to the  bulk magnetization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' This produces extra scattering pro-  portional to the square of the induced magnetic mo-  mentum at the position of each nuclear peak .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 9  shows the uniform magnetization density extracted from  two nuclear reflections: (020) for H ∥ a∗ and (200) for  H ∥ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' We selected reflections where nuclear contribu-  tion is minimal while a measurable magnetic intensity  can be observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The zero-field integrated intensity is  subtracted from the data in a field to obtain the cor-  8  0  2  4  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  0H (T)  0  5  10  Integrated Intensity (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' units)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  T (K)  0  1  2  3  4  5  Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='(arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' units)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  T (K)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='32  (1,1,-l) (r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=')  Q = (1, 1, -1/3)  Q = (0, 1/2, 1/2)  Q = (1, 1, -1/3)  Q = (1/3, 1/3, 1/3)  T = 120 mK  A  B  C  A  (a)  (b)  μ0H || a*  ZEBRA  ZEBRA  T = 55 mK  μ0H || c  WISH  (d)  µ0H = 0 T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='0  Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=')  (c)  Q = (1, 1,-⅓-δ)  µ0H = 0 T  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Results from single crystal magnetic neutron diffrac-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (a,b) Field dependence of the integrated neutron inten-  sity at the magnetic propagation vectors for: (a) H ∥ a∗  (ZEBRA, PSI) and (b) H ∥ c (WISH, ISIS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Note that in (a)  the intensity of the (0,1/2,1/2) reflection has been rescaled by  ×0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In (b) the limits of the ordered phases are highlighted  and shown with arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (c) Evolution of the integrated in-  tensity of the reflection (1,1,-1/3) with temperature at zero  magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' (d) Incommensuration of the propagation vec-  tor at zero field against temperature, shown as a shift in the  peak position of the (1,1,l) reflection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  responding magnetic scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Longitudinal magneti-  zation is then plotted as the square root of mangetic  intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The agreement with bulk measurements is re-  markable and further highlights the existence of magne-  tization plateaus regardless of field orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Finally, zero field neutron diffraction reveals an incom-  mensurate state between the low temperature ordered  phase and the paramagnetic phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The onset of in-  commensurate magnetic order appears around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='34 K at  the wavevector Q = (0, 0, 1/3 + δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Temperature de-  pendence of the intensity around the (1,1,l) reflection  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 11(d), where the peak position is superimposed,  shows this incommensuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Reduction of the tem-  perature leads to a change in the incommensurate prop-  agation vector roughly linearly with temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  At  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='26 K the propagation vector locks into the commensu-  rate Q = (0, 0, 1/3), as observed for the low temperature  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The robustness of this evolution to commen-  suration has been verified for several additional magnetic  reflections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  DISCUSSION  The purported breathing kagome structure is shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Unequal Nd-Nd distances and Nd-O-Nd angles  result in inequivalent exchange parameters for neighbor-  ing corner-sharing triangles [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' This is represented by  the exchange constants J△ and J▽, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' How-  ever, a crystallographic analysis cannot rule out the ex-  istence of interaction between adjacent kagome planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Due to the short distances between kagome planes, the  topology of the exchange interaction in Nd3BWO9 is  likely three dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In fact, the shortest superex-  change Nd-O-Nd pathway (nearest neighbors, J1) links  rare-earth ions belonging to different kagome planes [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  1(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' These couplings are arranged into isolated twisted  3-legged spin tubes, one-dimensional structures that ex-  tend perpendicular to the kagome planes [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 1(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Noteworthy, the resulting structure considering only  nearest neighbor coupling is bipartite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  A single tube  would show no frustration, highlighting the relevance  of further neighbor interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  A three-dimensional  structure with several exchange parameters may have  to be regarded, as opposed to the originally suggested  kagome structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yet, the onset of static magnetic or-  der is extremely suppressed by the strong magnetic frus-  tration f = −θW /TN ≈ 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6, confirmed from magnetic  susceptibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Six magnetic rare-earth Nd3+ ions occupy general  Wyckoff positions in the unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The reduced point  symmetry around the Nd3+ ions [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  1(e)] fully lifts  the degeneracy of the total angular momentum levels (J  = 9/2) into five Kramers doublets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The strong CEF iso-  lates a single Kramers doublet with a large gap to excited  multiplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The obtained zero-field entropy is consistent  with a value of S = R ln(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  These two observations  show that Nd3BWO9 can be described as an effective  spin S = 1/2 system below 100 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However, the low  symmetry precludes attempts to identify unequivocally  a CEF-Hamiltonian and to extract the eigenstates of the  lowest energy multiplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Both magnetization and susceptibility suggest very lit-  tle magneto-crystalline anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Susceptibility mea-  surements suggest no preferential direction in the high  temperature paramagnetic state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  In addition, low-  temperature magnetization in the fully saturated pseu-  dospin phase shows no increase up to the highest probed  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The increase of magnetization may be a rough  estimator of the eigenstate admixing due to anisotropies  (via Van-Vleck terms).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' No appreciable change in mag-  netization is observed up to 2 T, indicating the total  magnetization in the restricted pseudospin subspace is  likely to be an approximately good quantum number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' It  9  is, thus, likely that the low energy physics in Nd3BWO9  can be described in terms of a highly symmetric spin  Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A small axial anisotropy may be needed  to account for the sharp features found for H ∥ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  To map out the phase diagram in the low tempera-  ture regime for Nd3BWO9 we use specific heat measure-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Using a combination of all outlined techniques,we  identify several regions of magnetic order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  As shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 12, the system reveals complex behaviour, with  two different domes of long-range order observed for each  configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  A low field phase (A) extends roughly up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6 T  for both studied orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' This phase possesses com-  mensurate order with propagation vector Q =(0,0,1/3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Magnetization measurements show that this phase is  hardly magnetizable, suggesting a gapped state in this  field range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Although further analysis is needed to un-  derstand the magnetic structures of the different phases  in detail, a series of general remarks can be deduced  from the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' For phase A, the presence of reflections  (0,0,±2/3) forbids the existence of a collinear structure  with spins parallel to c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Thus, a coplanar structure in  the ab plane is likely realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  By increasing the magnetic field the system transitions  into a field-induced ordered phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A field H ∥ a∗ leads  to the fractional m = 1/3 plateau phase B, characterized  by a propagation vector Q =(0,1/2,1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The additional  presence of wavevectors (1/2,0,1/2) and equivalent sug-  gests a multi-Q structure or the presence of domains in  the B phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Strikingly, the order realized in the plateau is com-  pletely different when fields are applied in the basal ab  plane or perpendicular to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In a field H ∥ c, phase C  is found with propagation vector Q =(1/3,1/3,1/3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' In  contrast, saturation H ∥ c occurs through a sharp first  order phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Magnetocaloric effect supports  this claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A tricritical termination point appears where  first and second order transition lines converge as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 12(b), at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='20 K and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='975 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The presence of  magnetic reflections (1/3,1/3,-1/3) and equivalent also  indicates a complex spin texture, with either a multi-Q  structure or the presence of domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='While here domains  may be consistent with the observed first order transition  to saturation, it is not possible at this stage to exclude  either possibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The existence of a tricritical point only for one ori-  entation may be related to the large spin-lattice inter-  action stemming from strong spin-orbit coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The  transition to saturation for H ∥ c can be prematurely  precipitated via an ’order by distortion’ [34] mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  A gain in magnetic energy compensates a small loss in  elastic energy, leading to a first order transition to sat-  uration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Though our neutron diffraction data show no  evident change in the space group or lattice parameters  in the high field phase, a detailed study would be neces-  sary to discard this possibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Phases A and B appear to merge below 100 mK at  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='56 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A first order phase transition is speculated be-  tween A and B, with a termination bicritical point where  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='8  T (K)  0  5  10  15  Cp/T (J mol-1K-2)  (b) µ0H || c  (a) µ0H || a*  A  A  C  B  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  (0,0,⅓)  (0,0,⅓)  (0,½,½)  (⅓,⅓,⅓)  1  μ0H (T)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6  FPP  20  25  30  FPP  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='5  2  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Magnetic phase diagram of Nd3BWO9 in a mag-  netic field applied along the principal directions: (a) a∗ and  (b) c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The background depicts false color maps of Cp(H, T),  with a shared color scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Symbols: white circles and dia-  monds represent transitions obtained from field and tempera-  ture scans of specific heat, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Green squares repre-  sent the phase boundaries extracted from neutron diffraction  data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Upward-facing blue triangles show transi-  tions extracted from bulk magnetization, downward facing  pink triangles transitions from magnetic torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A red dia-  mond denotes the estimated position of the tricritical point  for H ∥ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' An orange star shows the upper critical field es-  timated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Solid and dashed lines are a guide to the  eye, representing second and first order transitions, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The different phases are labeled as: A, B, C and Fully  Polarized Pseudospin (FPP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The ordered phases show their  corresponding magnetic propagation vector, as discussed in  the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  all phase boundaries meet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Neutron diffraction data in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 11(a) indicate the phases will likely merge slightly  below 120 mK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Interestingly, between A and C the phase  boundaries seem to develop smoothly down to the lowest  measured temperatures and converge at T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Neutron  data at 55 mK show the phases are still separated by  paramagnetism at this temperature Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 11(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A highly  non-trivial order-to-order quantum phase transition may  take place between A and C at zero temperature (indi-  cated with a question mark).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Precise measurements in  10  the vicinity of these phase transitions would provide im-  portant insight on their nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However, the strong sig-  nal from nuclear degrees of freedom and the extremely  low temperatures involved prevent further investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The double hump features in specific above the transi-  tion temperature represent a crossover from the low field  disordered phase to the high field polarized phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Such  features can be understood in terms of models of hard-  core bosons and are usually associated with quantum  critical behaviour in one dimensional magnets [35, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  They can be observed in several quasi-1D antiferromag-  nets [27, 28], and therefore suggest the relevance of one-  dimensional correlations for the physics of Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  These modulations are accentuated when the field is  applied along the direction of the spin tubes (H ∥ c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Notably, despite the first-order nature of the transition  these modulations are still present and seem to be most  prominent around the tricritical termination point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Plateaux in the magnetically ordered sector are a hall-  mark of frustrated magnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The existence of magneti-  zation plateaus (and particularly at 1/3 of saturation)  has been predicted for both kagome antiferromagnets  [37, 38], as well as for a model of isolated spin tubes with  a weak triangular rung interaction (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 1(c)) [39–41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The presence of magnetization plateaux independent of  the orientation of the applied magnetic field suggests an  stabilizing interplay between frustration mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Finally,  we comment on the origin of the ob-  served incommensurate-commensurate (IC-C) transi-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Dipolar interactions are not uncommon in the  study of rare-earth based magnets due to their large  magnetic moments (µ(Nd3+) = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='6µB) [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Their sta-  bilizing role on incommensurate structures at temper-  atures above commensurate order has been argued in  several systems with hexagonal structure [43–45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The  realization of a IC-C transition at zero field opens the  question to the importance of dipolar coupling for the  low temperature properties of Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  We conclude the discussion by comparing Nd3BWO9  to its isostructural compounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' To this point, only two  other systems in the R3BWO9 family have been studied  at low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' NMR spectra reveal an inconm-  mensurate magnetic structure in Sm3BWO9[46], while a  dynamical state has been proposed for Pr3BWO9 at tem-  peratures as low as 90 mK [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' These two systems have  been analyzed in terms of 2D Hamiltonians based on  the existence of the kagome planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' However, our work  highlights the presence of three-dimensional couplings  and the potential dominance of the one-dimensional spin  tubes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The discussion outlined here is inevitably rele-  vant for investigations on other members of the family  of R3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  CONCLUSION  We have presented a comprehensive study of the low  temperature physics of the highly frustrated quantum  antiferromagnet Nd3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Calorimetric and neutron  scattering data support the realization of strongly in-  teracting effective spin-1/2 moments below 100 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Our  measurements reveal a complex magnetic phase diagram  below 300 mK, featuring magnetization plateaux for all  field orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' The ordering brings about important  insight about the relevant magnetic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Differ-  ent magnetic structures are realized in the plateau states,  depending on the direction of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Even  though the phase diagram is considerably anisotropic, it  can be described in terms of an effective S = 1/2 pseu-  dospin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The experimental framework provided here is key for  future studies on Nd3BWO9 and in the remaining mem-  bers of the R3BWO9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  The presence of the spin-tube  structures perpendicular to the kagome planes is indi-  cates that the magnetic properties of these highly frus-  trated systems cannot be understood in terms of kagome-  lattice physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Further work is needed to fathom the  effective dimensionality of the magnetic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  This work is supported by a MINT grant of the Swiss  National Science Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [1] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Facheris, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Povarov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nabi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mazzone,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lass, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Roessli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ressouche, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Gvasaliya,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zheludev, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 129, 087201 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Smirnov, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yashiro, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kimura, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Hagiwara,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Narumi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kindo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kikkawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Katsumata, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Shapiro,  and a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Demianets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 75,  134412 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [3] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Levy, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Sheikin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Berthier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Horvati´c, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Taki-  gawa, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kageyama, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Waki, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ueda, EPL (Eu-  rophysics Letters) 81, 67004 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [4] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Wada, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ubukoshi, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Hirakawa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 51, 2833 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mourigal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Enderle, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' F˚ak, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kremer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Law, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Schneidewind, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Hiess, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Prokofiev, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 109, 027203 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [6] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Bhartiya, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Povarov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Blosser, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Bet-  tler, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Gvasaliya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Raymond, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ressouche,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Beauvois, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Xu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Research 1, 033078  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [7] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kermarrec,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kumar,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Bernard,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Henaff,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mendels, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Bert, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Paulose, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Hazra,  and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Koteswararao, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 127, 157202 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [8] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Anderson, Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 8, 153 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zhou, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kanoda,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ng, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  89, 025003 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Savary and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Balents, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
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+page_content=' 80, 016502  (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  11  [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Chamorro, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' McQueen,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Tran,  Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 121, 2898 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [12] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Broholm, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Cava, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kivelson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nocera,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Norman, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Senthil, Science 367 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [13] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Bernu,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Lhuillier,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Kermarrec,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Bert,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mendels, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Colman, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Wills, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  B 87, 155107 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [14] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yoshida, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 91, 101003 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' LeBlanc, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Plumer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Whitehead,  and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Southern, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 88, 094406 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yoshida,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Noguchi,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Matsushita,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ishii,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Ihara,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Oda,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Okabe,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Yamashita,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nakazawa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Takata, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 86,  033704 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Okuma,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nakamura,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Okubo,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Miyake,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Matsuo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kindo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Tokunaga, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kawashima,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Takeyama, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Hiroi, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 10, 1 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [18] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jeschke, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nakano, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Sakai, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B  99, 140410(R) (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Iqbal, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Poilblanc,  and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Schuch, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B  101, 155141 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jahromi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Orus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Poilblanc, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mila, SciPost  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 9, 092 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ashtar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Guo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Wan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Gong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Liu,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Su, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Tian, Inor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 59, 5368 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Majchrowski, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Michalski, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Brenier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Cryst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Growth 247, 467 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [23] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Blosser, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Facheris,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zheludev, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' of Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Instr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 91, 073905 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Dutton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kumar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mourigal, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Soos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='-  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Wen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Broholm, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Andersen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Huang,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zbiri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Toft-Petersen, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Cava, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 108, 187206 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [25] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kimura, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nakatsuji, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Wen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Broholm, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Stone, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nishibori,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Sawa, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 4, 1  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [26] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Bleaney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 34, 1024 (1963).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [27] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' R¨uegg, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kiefer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Thielemann, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' McMor-  row, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zapf, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Normand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zvonarev, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Bouil-  lot, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kollath, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Giamarchi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Capponi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Poilblanc,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Biner,  and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kr¨amer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 101,  247202 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [28] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Blosser, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Bhartiya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Voneshen, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zhe-  ludev, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 121, 247201 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [29] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Hayashida, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Blosser, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Povarov, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yan,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Gvasaliya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ponomaryov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zvyagin,  and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zheludev, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 100, 134427 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [30] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Flavi´an, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Hayashida, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Huberich, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Blosser, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Povarov, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Gvasaliya, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zheludev, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 101, 224408 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [31] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zapf, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jaime, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Batista, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  86, 563 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [32] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kohama, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Marcenat, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Klein, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jaime, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 81, 104902 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [33] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Kohama, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 91, 101004 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [34] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Tchernyshyov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Moessner, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Sondhi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 88, 067203 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [35] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Korepin and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Slavnov, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  129, 103 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Sachdev, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Senthil,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Shankar, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B  50, 258 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [37] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Sakai and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Nakano, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 83, 100405(R)  (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Capponi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Derzhko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Honecker, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' L¨auchli,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Richter, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 88, 144416 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [39] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Fouet, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' L¨auchli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Pilgram, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Noack, and  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Mila, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 73, 014409 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [40] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Yonaga and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Shibata, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 84, 094706  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [41] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Sakai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Sato, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Okunishi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Okamoto,  and  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Itoi, in J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=', Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 400 (IOP Publishing, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [42] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Palmer and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Chalker, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 62, 488  (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [43] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Shiba and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Suzuki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 51, 3488  (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [44] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Suzuki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 52, 3199 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [45] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Gekht and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ponomarev, Phase Transitions 20,  27 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [46] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zeng, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Song, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ling, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Tong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Li,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Tian, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ma, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Pi, Chinese Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' 39,  107501 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  [47] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Zeng, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Song, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Tian, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Wang,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ling, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Tong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' Ma, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content=' B 104, 155150 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
+page_content='  12' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE5T4oBgHgl3EQfWA9Z/content/2301.05555v1.pdf'}
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+Disintegration of Long-Period Comet C/2021 A1 (Leonard)
+David Jewitt1, Yoonyoung Kim2, Michael Mattiazzo3, Max Mutchler4, Jing Li1
+and Jessica Agarwal2
+1Department of Earth, Planetary and Space Sciences, UCLA
+2Institute for Geophysics and Extraterrestrial Physics, TU Braunschweig, D-38106
+Braunschweig, Germany
+3Swan Hill Observatory, Australia
+4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218
+jewitt@ucla.edu
+Received
+;
+accepted
+Revised 2022 January 16
+arXiv:2301.08673v1  [astro-ph.EP]  20 Jan 2023
+
+– 2 –
+ABSTRACT
+We present imaging observations of the disintegrating long-period comet
+C/2021 A1 (Leonard). High resolution observations with Hubble Space Tele-
+scope show no evidence for surviving fragments, and place a 3σ upper limit to
+their possible radius ∼60 m (albedo 0.1 assumed). In contrast, wide field ob-
+servations from the Swan Hill Observatory, Australia, show an extensive debris
+cloud, the cross-section and estimated mass of which are consistent with com-
+plete disintegration of the nucleus near mid- December 2021 (at about 0.8 au).
+Two methods give the pre-disruption nucleus radius, rn = 0.6 ± 0.2 km. Tidal,
+collisional, sublimation and pressure-confined explosion models provide implau-
+sible explanations of the disintegration. However, rotational instability driven
+by outgassing torques has a very short timescale (∼0.1 year) given the orbit and
+size of the C/2021 A1 nucleus, and offers the most plausible mechanism for the
+disruption. Initial rotational breakup is accelerated by the exposure and strong
+sublimation of previously buried volatiles, leading to catastrophic destruction of
+the nucleus.
+Subject headings: comets: general—comets: individual C/2021 A1
+
+– 3 –
+1.
+INTRODUCTION
+Comet C/2021 A1 (Leonard), hereafter “A1”, was discovered on UT 2021 January 3 as
+a diffuse V ∼ 19 magnitude object inbound to the Sun at heliocentric distance rH = 5 au
+(Leonard 2021). A1 is a long-period comet, with heliocentric osculating semimajor axis a
+= -6124 au, eccentricity e = 1.0001 and inclination i = 132.6◦, reaching perihelion (at rH
+= 0.615 au) on UT 2022 January 03.3, about a year after discovery. Although presently
+following a weakly hyperbolic orbit, the pre-entry orbital elements (corrected for planetary
+perturbations to 1900 January 1, when the heliocentric distance was 137 au) are those of a
+bound object, a = 2020 au, e = 0.999696 and i = 132.7◦. A1 is thus not a dynamically new
+comet, having passed through the planetary system ∼ 105 years ago.
+Comet A1 attained naked eye visibility in late 2021 and then displayed spectacular
+gas and dust tails. However, images and commentary recorded in public on-line archives1
+indicate that A1 became photometrically unstable in 2021 December and 2022 January.
+Measurements of the OH production rate from the Nancay radio telescope were steady near
+QOH = 2.6×1028 s−1 between UT 2021 December 9 and 12, but jumped by a factor of ∼8
+to QOH = 22×1028 s−1 on December 15, even as the heliocentric distance barely decreased
+from 0.80 au to 0.74 au (Crovisier et al. 2021). The morphology also changed, becoming
+more diffuse and with “the tail being more prominent than the head” on UT 2022 January
+222 at rH ∼ 0.74 au outbound. Based on these early observational reports we requested
+Director’s Discretionary Time on the Hubble Space Telescope (HST), with the science
+objective being to study the presumed breakup of this long-period comet at the highest
+angular resolution. Independently, coauthor Mattiazzo also obtained wide-field imaging
+data using a private telescope at the Swan Hill Observatory in Australia. The wide-field and
+1e.g. https://britastro.org/cometobs/2021a1/thumbnails.html
+2https://groups.io/g/comets-ml/message/30541
+
+– 4 –
+HST data are highly complementary, with the former providing sensitivity to low surface
+brightness debris over a wide angle and the latter providing ultra-high resolution and very
+deep imaging of the near-nucleus region.
+While the phenomenon of cometary breakup has been known for over a century, very
+few physical observations of disintegrating comets are to be found in the refereed literature.
+In this paper, we present the observations and consider possible causes of the breakup of
+comet A1.
+2.
+OBSERVATIONS
+2.1.
+Hubble Space Telescope
+The 2.4 m diameter Hubble Space Telescope was used to observe disintegrating A1
+under program GO 16929. We used the WFC3 camera, which houses two 2015×4096 pixel
+charge coupled devices separated by a 1.2′′ wide gap. The 0.04′′ pixel−1 image scale gives a
+full-frame 162′′×162′′ field of view. HST images were taken using the F350 LP filter in order
+to maximize throughput. This filter has an effective central wavelength λc = 6230˚A when
+observing a Sun-like (G2V) source and a FWHM ∆λ = 4758˚A. We secured four images
+each of 450 s duration in each of the first three orbits and five frames of 285 s, with a
+sub-frame readout, in the fourth. The first three orbits were obtained in 2022 April with
+spacings of one and four days, with the intention being to measure the sky-plane motions
+of fragments produced by the break-up of A1. The fourth orbit was scheduled on UT 2022
+June 7 to coincide with the passage of the Earth through the projected orbit plane of the
+comet. Observations from this vantage point provide a model-free measure of the thickness
+of the dust distribution perpendicular to the plane. Unfortunately, the images from the
+fourth orbit suffered from extreme field star contamination, as a result of the low (-6◦)
+
+– 5 –
+galactic latitude of the comet, and were not useful.
+2.2.
+Swan Hill Observatory
+Wide-field observations were taken by co-author Michael Mattiazzo using a 0.28 m
+diameter, f/2.2 wide-field telescope at the Swan Hill Observatory (observatory code Q38),
+located in Victoria, Australia. A 4655×3522 pixel CMOS imaging device (Panasonic model
+QHY163M) provided an image scale of 1.27′′ pixel−1, and a field of view approximately
+1.6◦×1.2◦. Each pixel of the 0.28 m telescope subtends a solid angle equal to 103 HST
+pixels. Ten images each of 30 s duration were obtained, during which time the comet moved
+relative to field stars by about 2.7′′, which is small compared to the 5.1′′ full width at half
+maximum of point source objects in the data. The wide field image shows evidence for loss
+of sensitivity due to vignetting, especially near the corners of the device. We removed this
+by fitting a cubic spline surface to the image, using the median signal within 50×50 pixel
+boxes (after checking that the procedure did not self-subtract the comet).
+No filter was employed in order to maximize the throughput of the system. The
+quantum efficiency of the detector peaks near a central wavelength 5500˚A, and has a
+FWHM estimated at ∼4000˚A. The central wavelength is close to that of Johnson V (see
+the discussion in Bessel 1990), but the response is so broad that it captures the same light
+as the Johnson B, V and R filters (or, equivalently, the Sloan g and r filters) combined.
+The large bandwidth and lack of a standard filter together limit the accuracy with which
+the measured magnitudes can be related to, for example, the V band magnitudes. We
+calibrated the data using measurements of field stars on the Sloan filter system, provided
+by the Skymapper southern survey (Wolf et al. 2018). For this purpose we extracted
+measurements using circular apertures of projected radius 12.7′′, with sky subtraction from
+the median signal within a concentric annulus having inner and outer radii 19.1′′ and 38.1′′,
+
+– 6 –
+respectively. In order to minimize the color term in our photometry, we selected stars with
+optical color g-r ∼0.4 to 0.5, so as to approximately match the color of the Sun (given as g-r
+= 0.45±0.02 by Holmberg et al. 2006). We further selected these stars to lie within ∼1′ of
+the comet in order to minimize spatial variations in the photometry caused by imperfect
+flatness of the data.
+The geometrical circumstances of observation are given in Table 1.
+3.
+RESULTS
+3.1.
+High Resolution Data
+We combined the four images from each orbit in order to reject cosmic rays, suppress
+trailed field objects, and reach a fainter limiting magnitude. The composite from UT 2022
+April 5 is shown in Figure 1; composites from April 6 and 10 look the same. The predicted
+location of the nucleus is indicated in the Figure. The JPL Horizons ephemeris for April
+5 gives 3σ positional uncertainties of ±1.3′′ in right ascension and ±1.0′′ in declination,
+both of which are negligible compared to the 160′′ field of view of WFC3. We searched
+for the principal nucleus and discrete fragments in the data by comparing image subsets
+to identify correlated motion, but found none. Instead, the images show evidence for
+diffuse light scattered from cometary dust, evident in Figure 1 as a region of slightly higher
+surface brightness in the south east quadrant of the image (marked by a dashed white
+line in the right-hand panel of the figure). Although it at first resembles a flat-field defect
+or a smudge of internally scattered light, two lines of evidence show that this region of
+diffuse brightness is neither. First, the enhanced region is fixed with respect to the daily
+predicted ephemeris position of A1. Second, the enhanced region moves on the detector as
+the telescope orientation angle changes. The enhancement appears at the same position in
+
+– 7 –
+image composites from all three dates in April, whereas scattered light from bright stars
+outside the WFC3 field of view would vary as the background stars are completely different
+from day to day. A flat-field defect would not rotate as the telescope orientation changes.
+We conclude that the diffuse light is sunlight scattered from cometary debris released from
+the now invisible nucleus of A1.
+The on-line WFC3 Exposure Time Calculator3 gives a 3σ limit for detection of point
+source objects at V = 26.7, in each of our orbits. This limiting magnitude is consistent
+with the measured sky noise in the data. Corrected to absolute magnitude using phase
+coefficient β = 0.04 magnitude degree−1, we find H ≥ 22.81. For a nominal albedo, pV =
+0.1, this corresponds to a 3σ limit to the fragment radius, r ≤ 60 m.
+3.2.
+Wide Field Data
+The composite wide field image is shown in Figure 2. A low surface brightness dust
+structure extends over at least 0.4◦ (2×106 km in the plane of the sky), with a position
+angle 120◦±2◦ and no indication of a brightness peak at the expected location of the
+nucleus. The latter was determined from the JPL Horizons ephemeris for the mid-time of
+the image, and is marked in the figure. Overall, the morphology is similar to that of C/2010
+X1 (Elenin), a long period comet which disintegrated when inbound near rH = 0.6 AU (Li
+and Jewitt 2015), and C/2019 J2 (Palomar), which disintegrated pre-perihelion near rH
+= 1.9 au (Jewitt and Luu 2019). Comparison with Figure 1 shows that the HST, which
+was pointed at the expected location of the nucleus, indeed recorded diffuse light from the
+western tip of this dust structure.
+We estimated the total light from the dust as follows. First, we rotated the image to
+3https://etc.stsci.edu/etc/input/wfc3uvis/imaging/
+
+– 8 –
+bring the long axis of the dust tail to the horizontal (upper panel in Figure 3). Next, we
+manually replaced field stars with the average of surrounding pixels. The median signal from
+the comet was then computed within a rectangular box, “A” in the lower panel of Figure
+3) 1105′′ long by 380′′ tall, and the background sky estimated from equal-sized photometry
+boxes contiguous with the comet box but displaced above and below it (“B” and “C” in
+Figure 3). Figure 3 shows that the tail extends beyond the left edge of the photometry box
+“A” but the increased uncertainty imposed by the sky rendered measurements of this very
+faint material impractical. The light from the tail was calculated from fT = fA−(fB+fC)/2,
+where fx is the flux in box “x”. Then, applying the calibration obtained from field stars,
+we find VT = 10.9±0.5, where the quoted error is our best estimate of the uncertainty
+resulting from non-flatness of the data, the transformation from the wide response of the
+camera and the effective V magnitude. With assumed phase function 0.02±0.02 magnitude
+degree−1 and the geometry given in Table 1, the corresponding absolute magnitude is H =
+7.6±0.6, where the larger uncertainty is introduced by the phase correction. The scattering
+cross-section needed to give this absolute magnitude is C = 1.4+1.0
+−0.8 × 1010 m2, assuming
+geometric albedo pV = 0.1 (appropriate for cometary dust; Zubko et al. 2017).
+Figure 4 shows the averaged surface brightness profile from the March 31 image,
+measured parallel to the long axis of region A in Figure 3. Most of the scatter in the
+surface brightness profile is statistical noise in the data, but larger oscillations (for example
+at ∼480′′ and 750′′) result from spatial background variations caused by the digital removal
+of field stars. In this plot, the peak of 1000 units corresponds to a surface brightness Σ =
+24.4 magnitudes arcsec−1, about 5% of the surface brightness of the night sky. The surface
+brightness shows a steep increase, reaching a maximum at about 100′′ from the ephemeris
+nucleus location, followed by a steady decline at larger projected angles. This profile shape
+is indicative of a suddenly terminated dust mass release, with the peak of the profile giving
+the distance traveled by the largest, slowest particles.
+
+– 9 –
+4.
+DISCUSSION
+4.1.
+Radius and Mass of the Nucleus
+We use the effective spherical nucleus radius of A1 ¯r = 0.6±0.2 km from Jewitt (2022).
+This estimate is based on independent measurements of QH2O(1), the gas production rate
+at 1 au, and of α1, the non-gravitational acceleration at 1 au. Comet A1 has QH2O(1) =
+1.9×1028 s−1 (only pre-perihelion observations are used because post-perihelion rates are
+clearly affected by the breakup) and α1 = 1.3×10−6 m s−2, provided by JPL Horizons. A
+substantially smaller nucleus would have a surface area insufficient to supply the QH2O(1),
+while a substantially larger nucleus would have too much mass to be accelerated at α1
+given the known gas production rate. Using ¯r and nominal nucleus density ρn = 500 kg
+m−3 (Groussin et al. 2019), we estimate the nucleus mass Mn = (4.5+6.5
+−3.2) × 1011 kg. The
+largest surviving fragments, with radii <60 m, individually contain < 10−3 of the mass of
+the primary.
+4.2.
+Time of Disruption
+Syndynes (the loci of particles having one size, released with zero initial relative
+velocity over a range of times; Finson & Probstein (1968)) are curved and do not match
+the linear shape of the debris cloud in A1. Instead, the morphology more resembles a
+set of synchrones as shown in Figure 5. Synchrones trace the loci of particles in the sky
+plane having a range of sizes (hence, radiation pressure accelerations) but released from the
+nucleus simultaneously. The position angle of the debris trail in A1 is most compatible with
+ejection 110±10 days before the image was taken, i.e. on UT 2021 December 11±10. This is
+about a month before reports of distinct morphological change appeared but coincides with
+a dramatic increase in the OH production rate from 4.4×1028 s−1 on UT 2021 December
+
+– 10 –
+19 to 14×1028 s−1 on UT 2021 December 21, in unpublished SOHO/SWAN data (personal
+communication M. Combi). It is also close to a reported OH outburst on UT 2021 December
+15 (Crovisier et al. 2021). While we lack continuous coverage of the gas production from
+A1, it is likely that the sublimation rate became highly unstable as a result of the breakup
+of the nucleus when close to perihelion.
+We assume that the disintegration began on UT 2021 December 11±10. To reach the
+far end of the measured debris cloud (an angular distance ∼1500′′, corresponding to linear
+distance L = 2.2 × 106 km) under the action of radiation pressure requires an average
+acceleration 2L/∆T 2, where ∆T = 111 days (9.6×106 s) is the interval between the time
+of disintegration and the Swan Hill image from UT 2022 March 31. In units of the solar
+gravitational acceleration at the average rH = 1.3 au heliocentric distance in this period,
+β =
+2Lr2
+H
+g⊙(1)∆T 2
+(1)
+where g⊙(1) = 0.006 m s−2 is the solar gravity at 1 au and rH is expressed in au.
+Substituting, we obtain β = 0.01. With β ∼ 1/aµm, where aµm is the particle radius
+expressed in microns (c.f. Bohren & Huffman (1983)), we infer that the particles at the far
+end of the tail in the March 31 image had aµm ∼ 75 µm. All particles in the visible debris
+cloud on UT 2022 March 31 must be larger, while smaller particles were presumably ejected
+but have been swept by radiation pressure beyond the visible extent of the tail. Particles
+near the peak of the surface brightness profile (angular distance ∼100′′, corresponding to
+L = 1.4 × 105 km) have β ∼ 10−3 by Equation 1 and, therefore, radii ∼1 mm.
+
+– 11 –
+4.3.
+Mass of the Optical Debris
+How does the mass of the debris compare with the mass of the nucleus prior to its
+disappearance? To answer this question, we treat the debris as consisting of a distribution
+of spherical particles with radii between a and a+da written as n(a)da. Then, the combined
+mass of the particles between minimum radius a1 and maximum radius a2 is
+Md =
+� a2
+a1
+4
+3πρa3n(a)da
+(2)
+while their combined cross-section is
+C =
+� a2
+a1
+πa2n(a)da
+(3)
+It is useful to represent the size distribution as a power law
+n(a)da = Γa−γda
+(4)
+where γ is the differential size distribution index and Γ is a normalizing constant.
+Substituting equation 4 into equations 2 and 3 and eliminating Γ, we obtain
+Md = 4
+3ρC
+� a2
+a1 a3−γda
+� a2
+a1 a2−γda
+(5)
+The minimum particle radius is selected as a1 = 75 µm, since all smaller particles
+would have been swept out of the image field in the time since ejection. The maximum
+radius, a2 = 60 m, is set by the non-detection of larger bodies in our deep HST imaging
+data. With these values for a1 and a2, we plot Equation 5 as a function of γ in the range 2.5
+≤ γ ≤ 4.0 (Figure 6). The particle mass required to account for the measured cross-section,
+
+– 12 –
+C, is seen to vary by orders of magnitude for modest changes in the index, γ, with smaller
+values (flatter distributions) hiding a larger fraction of the total mass in big bodies.
+Also plotted in the figure is the nucleus mass, Mn = (4.5+6.5
+−3.2) × 1011 kg, computed from
+the effective radius, rn = 0.6±0.2 km, (Section 4.1), and density, ρn = 500 kg m−3, with the
+mass uncertainty marked as a horizontal yellow band. The red point marks the intersection
+of the two curves where Md = Mn and shows that, for index γ = 3.5±0.1, the debris mass
+and nucleus mass are equal. The upper limit to the size distribution could be substantially
+smaller than the 0.6 km limit set by the Hubble data, in which case a smaller value of
+the index would be needed for the mass of the debris to equal the mass of the nucleus.
+A relevant comparison can be made with the size distribution of the Kreutz sungrazing
+comets, which are themselves produced by the fragmentation of a precursor body. The
+Kreutz objects have γ = 3.2 in the 5 m to 35 m radius range (Knight et al. 2010), plotted
+as a blue square in Figure 6. The uncertainty on γ for the Kreutz objects is not stated;
+we have plotted a nominal ±0.1 error bar for reference and note reasonable agreement
+with the index deduced for A1 within the uncertainties. Perhaps less relevant are radar
+measurements of the debris size distributions in six meteoroid streams, most associated
+with decaying comets. These are plotted for comparison using green triangular symbols
+(Blaauw et al. (2011)). The formal meteoroid stream index uncertainties are comparable to
+the size of the symbols in the figure. The measured indices span the range γ = 3.2 to 3.7,
+encompassing the values found for A1 and the Kreutz comets.
+We conclude that the optical cross-section presented by the debris in 2022 March is
+consistent with the complete disintegration of the original ∼0.6 km scale nucleus into a
+power law distribution (index γ = 3.5±0.1) of particle sizes. We emphasize that we possess
+no independent evidence that the debris mass and original nucleus mass are equal, although
+a consideration of the particle properties using more detailed considerations (section 4.4)
+
+– 13 –
+supports this result. It should also be noted that 60 m is an upper limit to the size of
+the largest post-disruption “particles” and our result would be changed if a2 ≪ 60 m, as
+it would if the size distribution of particles is not well represented by a single power law
+across the full range of sizes. It is also not obvious that the density of the particles should
+necessarily be the same as the bulk density of the nucleus, as we have assumed. These and
+other physically plausible possibilities lie beyond the observational constraints obtained
+from the data.
+4.4.
+Monte Carlo Simulation
+We next used a Monte Carlo simulation as developed by Ishiguro et al. (2007) (see
+also Kim et al. (2017)) to model the cometary debris in more detail. The model is
+under-constrained and cannot provide unique solutions for the particle properties. It
+is nevertheless valuable in allowing us to test the deductions made based on order of
+magnitude considerations, and also to more fully explore the range of plausible solutions.
+We particularly examined the effect of the particle size distribution index and the minimum
+and maximum particles sizes in the distribution.
+Figure 7 shows the data with results of simulations for γ = 3.3, 3.4 and 3.5 and size
+parameter in the range 7 × 10−4 ≤ β ≤ 0.07, with ejection on 2021 December 11. The
+upper limit to β (lower limit to particle radius) is set by the field of view, with smaller
+particles have already been pushed out of the field by radiation pressure. We obtain a ≥
+14 µm, different by a factor of five from the limit a ≥ 75 µm estimated by the order of
+magnitude procedure, above. The lower limit to β (upper limit to the particle size of ∼1.4
+mm) is determined from the location of the surface brightness peak in Figure 7. This is very
+small compared to the 60 m upper limit to the radius of the largest possible fragment, set
+by non-detection in the HST images. However, this difference is understandable since, for
+
+– 14 –
+commonly measured cometary size distributions, the scattering cross-section is dominated
+by the smallest particles; large particles contribute little to the cross-section and thus are
+poorly constrained by scattered light observations. In order to fit the data, we assumed
+that the particle ejection speed varies with size parameter as V = V0β1/2, with V0 = 550
+m s−1 being the gas thermal speed. Unlike the particle trails of weakly active comets and
+asteroids, a high ejection speed is required in order to fit the large width of the debris cloud
+in A1.
+As is evident in Figure 7, the plotted models do not perfectly reproduce the measured
+surface brightness profile, with larger γ models being 25% to 30% brighter than the data at
+large distances from the nucleus and smaller γ models being too sharply peaked compared
+to the measurements. If they are real, these differences could result from physical effects not
+included in the model. For example, we have ignored dust released before disintegration,
+reasoning that the dramatic outbursts and brightening starting in mid-December would
+swamp any signal from older material. As another example, large aggregate grains in the
+tail might break up into smaller particles which would be quickly swept from the field of
+view by radiation pressure, perhaps explaining the lower brightness of the tail ≳1000′′ from
+the nucleus. On the other hand, the differences between the models and the measured
+profile are certainly affected by systematic uncertainties intrinsic to the wide field data,
+particularly by imperfect flatness of the data and by the presence of scattered light from
+bright background sources. Rather than over-interpret the data, we conclude from the
+Monte Carlo simulation only that γ ∼ 3.4 ± 0.1 provides a broad match to the profile, while
+much steeper and much less steep distributions do not. The range of allowable indices
+deduced from Monte Carlo models is consistent with γ = 3.5 ± 0.1 as inferred from the
+debris mass in Section 4.3 (c.f. Figure 6).
+Lastly, we used the Monte Carlo model to test the possibility that the debris observed
+
+– 15 –
+in 2022 March could be long-lived material released before perihelion, in the form of a
+so-called “neck-line” structure (e.g. Pansecchi and Fulle 1990). We find that material
+ejected in the period 2021 November 15 to December 15 would produce a tail structure
+in March having position angle (113◦) distinctly different from that measured (120◦) or
+calculated from the impulsive ejection model (119◦). In addition, neck-line structures in
+other comets are most prominent when observed from near the projected orbital plane,
+whereas our observations were taken ∼20◦ from the orbital plane of C/2021 A1 (c.f. Table
+1). The combination of the unfavorable observing geometry, the failure to reproduce the
+measured position angle of the dust in 2022 March, and the obvious importance of the
+outbursts reported in 2021 December together show that pre-perihelion dust is a negligible
+contributor to the post-perihelion appearance.
+4.5.
+Disintegration Mechanism
+The preceding discussion shows that a ∼0.6 km scale nucleus disintegrated into
+fragments, the largest of which were no more than about 10% of the radius of the original
+body. What process could lead to such a dramatic outcome?
+Tidal Breakup: The 0.615 au perihelion distance of A1 far exceeds the Roche radius
+of the Sun (∼10−2 au), negating the possibility of a tidal breakup. Comet A1 did pass
+within a distance rV = 0.029 au from Venus on UT 2021 December 18 (Zhang et al. 2021)
+but this is still ∼300 times the Roche radius (∼10−4 au) of the planet. To within a numerical
+multiplier, the differential of the gravitational force on opposite sides of the nucleus is
+∆F ∼ (GMV ρnr3
+n/r2
+V )(rn/rV ) giving an order of magnitude tidal stress S ∼ ∆F/r2
+n or
+S ∼ GMV ρnr2
+n
+r3
+V
+,
+(6)
+
+– 16 –
+where G = 6.67 × 10−11 N kg−2 m2 is the gravitational constant, MV = 5 × 1024 kg is
+the mass of Venus and the other quantities are already defined. Substituting ρn = 500 kg
+m−3, rn = 600 m, and rV = 0.029 au, we estimate S ∼ 10−6 N m−2 at closest approach,
+which is orders of magnitude smaller even than the cohesive strengths of fine, unconfined
+powders (S ≳ 100 N m−2) measured in the laboratory (Garcia-Trinanes et al. 2019). The
+disintegration of A1 is very unlikely to be a consequence of tidally induced stresses.
+Equilibrium Sublimation: The rate of loss of surface material is drn/dt ∼ −fs/ρ,
+where fs ∼ 2 × 10−4 kg m−2 s−1, at 1 au. Substitution gives drn/dt ∼ -3 cm day−1. At this
+rate, the timescale for eroding the whole nucleus would be |rn/(drn/dt)| ∼ 40 years, which
+is very large compared to the ∼1 year spent by A1 in the vicinity of the Sun. In any case,
+sublimation would produce steady erosion of the comet not a catastrophic disintegration
+like that observed. Equilibrium sublimation cannot account for the sudden disintegration
+of A1.
+Collisional Disruption: Collisional disruption timescales for 0.6 km scale objects,
+even in the dense parts of the asteroid belt, are measured in hundreds of millions of years
+(Bottke et al. 2005). Comet A1 arrived from a high inclination orbit and disintegrated ∼0.5
+au from the ecliptic plane where there are no known objects with which to collide. We
+confidently dismiss the possibility that A1 was collisionally disrupted.
+Internal Pressure: Could internal pressure build-up from sublimated gases cause
+the nucleus to explode (Samarasinha 2001)? The core temperature of the nucleus of A1
+is comparable to the Oort cloud equilibrium temperature of just a few degrees above
+absolute zero. Heat transport from the surface to the interior by conduction is controlled
+by the thermal diffusivity, which is proportional to the conductivity and which, in turn,
+is strongly affected by the particulate nature and porosity of the cometary material.
+Laboratory measurements of porous, dielectric powders yield conductivities ∼ 102 to 103
+
+– 17 –
+times smaller than the solid material (Henke et al. 2012). The expected high porosities
+and low thermal diffusivities of cometary material lead to small thermal skin depths that
+make deep conduction impossible. Heat applied for a time τ will conduct over a distance
+d ∼ (κτ)1/2, where κ is the diffusivity. For example, with κ = 10−8 to 10−9 m2 s−1, even in
+the year between discovery at rH = 5 au and perihelion at 0.6 au, conducted heat travelled
+into the nucleus by a characteristic distance only d ∼ 0.2 m to 0.5 m. This distance is so
+small compared to the nucleus radius that it is difficult to see how subsurface gas produced
+by surface heating could have any relevance to the complete disintegration of the nucleus.
+Rotational Instability: The remaining possibility for nucleus break-up is also the
+most plausible. The timescale for changing the spin angular momentum of a spherical
+nucleus through outgassing torques is (Jewitt 2021)
+τs =
+�16π2
+15
+� � ρnr4
+n
+kTVthP
+� � 1
+˙M
+�
+,
+(7)
+where P is the instantaneous spin-period and kT is the dimensionless moment arm, equal
+to the fraction of the outflow momentum that exerts a torque on the nucleus. The median
+values in a sample of short-period comet nuclei with perihelia in the range 1 ≤ q ≤ 2 au
+are kT = 0.007 and P = 15 hours (5×104 s) (Jewitt 2021). We substitute
+˙M = 800 kg
+s−1, equal to the sublimation rate at 1 au as measured by Combi’s Lyman-α data, on the
+understanding that this sets a lower bound to the mass loss rate at smaller distances and
+therefore sets an upper limit to τs. With ρn = 500 kg m−3, rn = 600 m, and Vth = 500
+m s−1, substitution into Equation 7 gives τs < 5 × 106 s (0.16 year, or 2 months), which
+compares to the 6 weeks (0.12 year) spent by A1 with rH < 1 au. While this is not proof
+that A1 disintegrated through a rotational instability, given the nominal nucleus parameters
+and measured mass loss rate, rotational instability does offer a plausible mechanism for
+nucleus disintegration.
+
+– 18 –
+Rotational breakup is expected to launch fragments with a velocity dispersion
+comparable to the tangential speed of the nucleus due to its rotation. For a strengthless
+nucleus, this equals the gravitational escape speed from the primary, in this case ∼0.3
+m s−1. In contrast, the Monte Carlo models show that larger speeds are required to fit
+the head width of the debris trail. For example, with V = V0β1/2 and V0 = 550 m s−1,
+millimeter sized particles (β = 0.001) would have V ∼ 17 m s−1, about 60 times the escape
+speed. We conjecture that these higher speeds result from gas drag acceleration following
+the exposure and intense sublimation of previously buried ices caused by rotational breakup
+at rH ∼ 0.8 au.
+Very large particles and boulders would not be substantially accelerated by gas drag
+and should leave the disintegrating nucleus at about the escape velocity of the primary.
+In the ∼3 months elapsed between the first signs of breakup and the HST observations,
+such slow-moving fragments would travel ∼2000 km, a distance subtending 1′′ to 2′′ in the
+plane of the sky (c.f. Table 1). Large fragments should therefore be resolvable in the HST
+data (the resolution is ∼0.08′′) but, nevertheless, remain unseen. This might reflect the
+continued disintegration of the fragments, again aided by the new exposure to the heat of
+the Sun of previously buried volatiles. The breakup process would then be catastrophic.
+Smaller fragments produced by breakup of the primary nucleus would have progressively
+shorter and shorter spin-up times, owing to their smaller size (c.f. Equation 7) and to the
+sudden exposure of large areas of previously buried ice which could amplify the moment
+arm, kT, by orders of magnitude. The expected result is a runaway fragmentation cascade.
+4.6.
+Gas Production Resulting from Nucleus Disintegration
+Disintegration of the nucleus must suddenly expose previously buried ices to the heat
+of the Sun, leading to a burst in the gas production rate caused by sublimation. Indeed,
+
+– 19 –
+measurements of the gas production rate in the mid-December to January period are highly
+variable, peaking near QH2O = 2.4 × 1029 s−1 in radio (Crovisier et al. 2021), Lyman-α (M.
+Combi, (private communication)), and near-ultraviolet (Jehin et al. 2021, 2022a, 2022b)
+observations. At break up, A1 was about rH = 0.8 AU from the Sun and ∆ = 0.2 AU from
+the SWAN/SOHO observatory used to take the Lyman-α data. The latter has 1◦ wide
+pixels, corresponding to about w ∼ 6 × 105 km per pixel at the comet and 1.2×106 km
+for the nominal Nyquist (2 pixel) resolution of the data. With an isothermal blackbody
+temperature at 0.8 AU ∼310 K, the thermal velocity of hydrogen atoms is Vth ∼ 2.5 km
+s−1. This, however, is a strong lower limit to the outflow velocity because of photo-electric
+heating (e.g. Combi and Delsemme 1980, Combi et al. 2000). Based on published models,
+we adopt a hydrogen outflow speed Vth ∼ 10 km s−1 and estimate the residence time for
+hydrogen atoms within a Nyquist sampled resolution element as tr ∼ 2w/Vth ∼ 1.2 × 105
+s (about 1.4 days). This means that the peak rate inferred from SWAN/SOHO Lyman-α
+data should be understood as a measure of the production rate averaged over 1.4 days.
+We are interested to see how QH2O compares with estimates of the gas production
+expected from the break up of the nucleus. To this end, we consider an idealized model in
+which the nucleus consists of particles which are either refractory or ice, and in which the
+ratio of ice to refractory masses is fice. Both refractory and ice particles are assumed to
+occupy a differential power size distribution (Equation 4). To render the problem tractable,
+we make the simplifying assumption that the nucleus disintegrates instantaneously into
+power law distributions of ice and refractory particles, each having radii in the range
+a1 ≤ a ≤ a2. The icy component then sublimates at the rate fs [kg m−2 s−1], which we
+calculate from energy balance including terms for radiation and sublimation.
+In the residence time tr, an ice surface will sublimate over a layer thickness
+
+– 20 –
+as = fstr
+ρn
+,
+(8)
+where ρn is the density of the particle, assumed equal to the bulk density of the nucleus.
+All the ice particles with radii a ≤ as will sublimate away, releasing water molecules and,
+eventually, producing by photodissociation the hydrogen atoms detected using the SWAN
+instrument. Ice particles with a > as will also partially sublimate in time tr, but their
+contribution to the gas flux should be small because, for plausible power law distributions
+(in particular, for γ = 3.5 as determined in sections 4.3 and 4.4), large particles present a
+small fraction of the total particle cross-section.
+The fraction of the mass contained in ice particles having a ≤ as is given by
+F =
+� as
+a1 a3−γda
+� a2
+a1 a3−γda
+(9)
+which, for 3 < γ < 4 and as ≫ a1 and a2 ≫ a1, simplifies to
+F =
+�γ − 3
+4 − γ
+� �as
+a2
+�4−γ
+.
+(10)
+The total ice mass in the undisrupted nucleus, assumed to be spherical, is Mi =
+(4π/3)ρnr3
+nfice. The production rate averaged over time tr may be written QH2O =
+FMi/(trµmH), where µ = 18 is the molecular weight of the water molecule and
+mH = 1.67 × 10−27 kg is the mass of the hydrogen atom. Substitution of Equations 8 and
+10 into this expression gives
+QH2O = 4πρnr3
+nfice
+3trµmH
+�γ − 3
+4 − γ
+� � fstr
+ρna2
+�4−γ
+.
+(11)
+The equilibrium sublimation mass flux calculated for a blackbody water ice sphere at 0.8
+
+– 21 –
+AU is fs = 1.7 × 10−4 kg m−2 s−1. The flux could be smaller if the grain albedo is high, or
+larger if the grain is anisothermal (albeit then sublimating from a smaller fraction of the
+grain surface). We set a2 = 60 m, the largest “particle” allowed by the Hubble imaging,
+and a1 = 10−7 m (however, Equation 11 is insensitive to a1 and its value is unimportant
+provided a1 ≪ as). The nominal nucleus radius is rn = 600 m, and the size distribution
+index is γ = 3.5, as deduced above. Measured cometary ice/refractory ratios, fice, show a
+wide range of values, from fice ∼ 1 in 67P/Churyumov-Gerasimenko (Marschall et al. 2020),
+to fice < 0.2 in C/1995 O1 Hale-Bopp (Jewitt and Matthews 1999) and fice = 0.03 to
+0.1 in 2P/Encke (Reach et al. 2000). We adopt fice = 1/4, recognizing that this value is
+substantially uncertain.
+Substitution into Equation 11 gives QH2O = 8.8+12.0
+−6.2 × 1029 s−1, where the error bars
+reflect only the ±200 m uncertainty in the estimated radius of the nucleus. This is larger
+than the measured peak water production rate (2×1029 s−1) but shows acceptable agreement
+given the crude nature of the model calculation and the likelihood that the disintegration
+was in reality spread over a finite period not impulsive, as modeled. We conclude that
+complete disintegration of the nucleus into a power law particle size distribution is consistent
+both with the optical brightness of the debris cloud and with the surge in the water
+production rate measured using Lyman-α.
+Future improvements to this model could include a treatment of the initial, optically-
+thick phase of the expanding disintegration cloud, when self-shielding will suppress and
+delay the sublimation surge relative to the estimate given here. Also needed is a treatment
+of the gas drag interaction with cometary solids in a fully disintegrated body, responsible
+for the size-dependent acceleration of refractory particles into the coma and surviving
+debris field. Furthermore, several of the parameters needed to accurately model nucleus
+disintegration remain unmeasured, and most other disintegrating comets are observationally
+
+– 22 –
+even less-well characterized than A1. It is obvious, even from these simple considerations
+that many more detailed observations, across a wide range of wavelengths and with
+adequate temporal sampling, will be needed to better understand what is likely to be the
+dominant destructive cometary process.
+
+– 23 –
+5.
+SUMMARY
+We present both high resolution and wide field observations of disintegrating
+long-period comet C/2021 A1 (Leonard) taken to study the nature of its demise.
+• The pre-disintegration radius of the nucleus, estimated using two methods, was
+rn = 0.6 ± 0.2 km. After breakup, which began in mid-December 2021 and may have
+continued for weeks, no nucleus fragments larger than about rn = 0.06 km (i.e. < 10−3
+of the primary mass) survived.
+• The observed debris cloud consists of sub-millimeter and larger particles, with a
+differential power law size distribution having index γ = 3.4±0.1 and 3.5±0.1, as
+estimated by two different methods. The observational constraints are consistent with
+equality between the mass of the debris cloud and the mass of the primary nucleus,
+indicating a total disintegration.
+• Tidal disruption, sublimation, collisional disruption, and explosion following internal
+pressure build-up in the nucleus all offer implausible explanations of the disintegration
+of C/2021 A1.
+• The spin-up timescale due to outgassing torques for a 600 m nucleus in the orbit of
+C/2021 A1 is as short as ∼2 months, pointing to rotational instability as the likely
+cause of the disintegration.
+• A simple model of the exposure and rapid sublimation of previously buried ice
+indicates a peak gas production rate (QH2O = 9+12
+−6 × 1029 s−1) of the same order as
+the measured peak value (QH2O = 2.4 × 1029 s−1).
+We thank Michael Combi for a preview of his SWAN data on C/2021 A1 and the
+anonymous referee for prompt comments on the manuscript. Based on observations made
+
+– 24 –
+with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the
+Space Telescope Science Institute. STScI is operated by the Association of Universities for
+Research in Astronomy, Inc. under NASA contract NAS 5-26555. Support for this work
+was provided by NASA through grant number GO-16929 from the Space Telescope Science
+Institute, which is operated by auRA, Inc., under NASA contract NAS 5-26555.
+Facilities: HST.
+
+– 25 –
+REFERENCES
+Bessell, M. S. 1990, PASP, 102, 1181. doi:10.1086/132749
+Bohren, C. F. & Huffman, D. R. 1983, Absorption and scattering of light by small particles.
+New York: Wiley, 1983
+Bottke, W. F., Durda, D. D., Nesvorn´y, D., et al. 2005, Icarus, 179, 63.
+doi:10.1016/j.icarus.2005.05.017
+Blaauw, R. C., Campbell-Brown, M. D., & Weryk, R. J. 2011, MNRAS, 414, 3322.
+doi:10.1111/j.1365-2966.2011.18633.x
+Combi, M. R. & Delsemme, A. H. 1980, ApJ, 237, 633. doi:10.1086/157909
+Combi, M. R., Reinard, A. A., Bertaux, J.-L., et al. 2000, Icarus, 144, 191.
+doi:10.1006/icar.1999.6335
+Crovisier, J., Biver, N., and Bockelee-Morvan, D. 2021, Central Bureau Electronic Telegram
+5087 (2021 December 22)
+Finson, M. J. & Probstein, R. F. 1968, ApJ, 154, 327. doi:10.1086/149761
+Garcia-Trinanes, P., Luding, S. and Shi, H.
+2019. Advanced Powder Technology, 30,
+2868-2880
+Groussin, O., Attree, N., Brouet, Y., et al. 2019, Space Sci. Rev., 215, 29. doi:10.1007/s11214-
+019-0594-x
+Henke, S., Gail, H.-P., Trieloff, M., et al. 2012, A&A, 537, A45. doi:10.1051/0004-
+6361/201117177
+Holmberg, J., Flynn, C., & Portinari, L. 2006, MNRAS, 367, 449. doi:10.1111/j.1365-
+2966.2005.09832.x
+
+– 26 –
+Ishiguro, M., Sarugaku, Y., Ueno, M., et al. 2007, Icarus, 189, 169.
+doi:10.1016/j.icarus.2007.01.003
+Jehin, E., Moulane, Y., & Manfroid, J. 2021, The Astronomer’s Telegram, 15128
+Jehin, E., Moulane, Y., Manfroid, J., et al. 2022a, The Astronomer’s Telegram, 15186
+Jehin, E., Moulane, Y., Manfroid, J., et al. 2022b, The Astronomer’s Telegram, 15189
+Jewitt, D. & Matthews, H. 1999, AJ, 117, 1056. doi:10.1086/300743
+Jewitt, D. & Luu, J. 2019, ApJ, 883, L28. doi:10.3847/2041-8213/ab4135
+Jewitt, D., Kim, Y., Mutchler, M., et al. 2020, ApJ, 896, L39. doi:10.3847/2041-8213/ab99cb
+Jewitt, D. 2021, AJ, 161, 261. doi:10.3847/1538-3881/abf09c
+Jewitt, D. 2022, AJ, 164, 158. doi:10.3847/1538-3881/ac886d
+Kim, Y., Ishiguro, M., Michikami, T., et al. 2017, AJ, 153, 228. doi:10.3847/1538-
+3881/aa69bb
+Knight, M. M., A’Hearn, M. F., Biesecker, D. A., et al. 2010, AJ, 139, 926. doi:10.1088/0004-
+6256/139/3/926
+Leonard, G. J., Aschi, S., Pettarin, E., et al. 2021, Minor Planet Electronic Circulars,
+2021-A99
+Li, J. & Jewitt, D. 2015, AJ, 149, 133. doi:10.1088/0004-6256/149/4/133
+Marschall, R., Markkanen, J., Gerig, S.-B., et al. 2020, Frontiers in Physics, 8, 227.
+doi:10.3389/fphy.2020.00227
+Pansecchi, L. & Fulle, M. 1990, A&A, 239, 369
+
+– 27 –
+Reach, W. T., Sykes, M. V., Lien, D., et al. 2000, Icarus, 148, 80. doi:10.1006/icar.2000.6478
+Samarasinha, N. H. 2001, Icarus, 154, 540. doi:10.1006/icar.2001.6685
+Wolf, C., Onken, C. A., Luvaul, L. C., et al. 2018, PASA, 35, e010. doi:10.1017/pasa.2018.5
+Zhang, Q., Ye, Q., Vissapragada, S., et al. 2021, AJ, 162, 194. doi:10.3847/1538-3881/ac19ba
+Zubko, E., Videen, G. Shkuratov, Y., et al. 2017, JQSRT, 202, 104.
+doi:10.1016/j.jqsrt.2017.07.026
+This manuscript was prepared with the AAS LATEX macros v5.2.
+
+– 28 –
+Table 1.
+Observing Geometry
+UT Date & Time
+νa
+rH b
+∆c
+αd
+θ−⊙e
+θ−V f
+δ⊕g
+Telh
+Scalei
+Uncj
+2022 Mar 31 18:14-18:26
+107.4
+1.756
+1.942
+30.8
+243.6
+90.2
+-20.4
+Swan Hill
+1408
+±1.4
+2022 Apr 05 23:35-24:04
+109.2
+1.833
+1.910
+30.9
+246.4
+91.7
+-19.8
+HST
+1385
+±1.6
+2022 Apr 06 23:32-23:51
+109.5
+1.848
+1.902
+30.9
+246.9
+92.0
+-19.7
+HST
+1379
+±1.6
+2022 Apr 10 19:23-19:53
+110.7
+1.903
+1.875
+30.7
+249.0
+93.2
+-19.1
+HST
+1359
+±1.7
+2022 Jun 7 16:36-17:12
+123.0
+2.698
+1.715
+6.8
+319.3
+137.0
++0.2
+HST
+1243
+±3.7
+aTrue anomaly, in degrees
+bHeliocentric distance, in au
+cGeocentric distance, in au
+dPhase angle, in degrees
+ePosition angle of projected anti-solar direction, in degrees
+fPosition angle of negative heliocentric velocity vector, in degrees
+gAngle from orbital plane, in degrees
+hTelescope
+iImage scale, km arcsecond−1
+j3σ ephemeris uncertainty, arcsecond (from JPL Horizons)
+
+– 29 –
+Fig. 1.— A) Composite of four, 450 s HST images from UT 2022 April 5. Diffuse streaks
+are imperfectly removed field stars and galaxies.
+B) Same image, anotated to show the
+approximate boundary of the debris (white dashed line) and the expected location of the
+nucleus (yellow line segments). Two scale bars of 30′′ and 5×104 km in length are shown, as
+well as the projected anti-solar (−S) and negative heliocentric velocity (−V ) vectors. North
+is to the top, East to the Left.
+
+UT 2022 April 5
+30
+5x104 km
+B– 30 –
+Fig. 2.— Wide field image from Swan Hill Observatory showing C/2021 A1 on UT 2022
+March 31. 10′ and 106 km scale bars are shown, as well as the projected anti-solar (−S) and
+negative heliocentric velocity (−V ) vectors. Yellow lines mark the ephemeris location of the
+nucleus. The white square shows the size of the HST field of view. The image has North to
+the top, East to the left.
+
+10
+.UT 2022 March 31
+106.km– 31 –
+Fig. 3.— (Upper:) Same image as in Figure 2 but rotated to bring the axis of the dust tail
+to the horizontal and shown at a larger scale. Yellow lines mark the ephemeris location of
+the nucleus. (Lower:) Locations of the photometry regions A, B and C used to measure the
+scattering cross-section of particles in the tail.
+
+R
+380″
+1105"– 32 –
+-500
+0
+500
+1000
+1500
+0
+400
+800
+1200
+1600
+Surface Brightness
+Distance [arcsecond]
+Fig. 4.— Surface brightness profile parallel to the long axis of Box A (Figure 3) plotted
+against the distance from the nucleus ephemeris location (axis is reversed relative to Figure
+3). 1000 units correspond to a surface brightness Σ = 24.4 magnitudes arcsec−2. The linear
+distance scale is approximately 1500 km per arcsecond.
+
+– 33 –
+Fig. 5.— (Left:) Same image as Figure 2 with synchrones overplotted, for ejection dates 80,
+100, 120, 140 and 160 days prior to the date of the image. (Right:) Syndynes for particles
+with β = 0.0003, 0.001, 0.003, 0.01 and 0.03, as marked. The axis of the debris cloud is best
+matched by the 110±10 day synchrones, corresponding to ejection on UT 2021 December
+11±10.
+
+UT 2022 March 31
+0.0003
+0.001
+120
+0.003
+100-
+80
+10'0
+0.03– 34 –
+1011
+1012
+1013
+1014
+1015
+2.5
+3.0
+3.5
+4.0
+Debris Mass [kg]
+Differential Size index, γ
+rn = 0.6+/-0.2 km
+Blaauw et al. 2011
+Kreutz Sungrazers
+C/2021 A1
+Fig. 6.— Total mass of the debris cloud (assuming density ρn = 500 kg m−3) plotted as a
+function of the differential power law index, γ, is plotted as a solid black line. The equivalent
+spherical mass of the original 0.6±0.2 km radius nucleus is shown (assuming the same ρn),
+together with its uncertainty, as a yellow horizontal band. The debris and nucleus masses
+are equal at γ = 3.5 ± 0.1, shown by the red filled circle. For comparison we show, as a blue
+square, the size distribution of the Kreutz sungrazing comets (Knight et al. 2010) and, as
+green triangles, several radar-measured meteoroid streams (Blaauw et al. 2011). The vertical
+positions of the Kreutz and radar stream points have no meaning.
+
+– 35 –
+-200
+0
+200
+400
+600
+800
+1000
+1200
+0
+400
+800
+1200
+1600
+Surface Brightness
+Distance [arcsecond]
+3.5
+3.4
+3.3
+3.5
+3.3
+3.4
+Fig. 7.— Axial surface brightness profile on UT 2022 March 31 (yellow diamonds) compared
+with results from a Monte Carlo simulation. The models shown have size index γ = 3.3 (red
+curve), 3.4 (black curve) and 3.5 (blue curve), all with 7 × 10−4 ≤ β ≤ 0.07, corresponding
+to particle radii 14 µm to 1.4 mm.
+
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+page_content='Disintegration of Long-Period Comet C/2021 A1 (Leonard)  David Jewitt1, Yoonyoung Kim2, Michael Mattiazzo3, Max Mutchler4, Jing Li1  and Jessica Agarwal2  1Department of Earth, Planetary and Space Sciences, UCLA  2Institute for Geophysics and Extraterrestrial Physics, TU Braunschweig, D-38106  Braunschweig, Germany  3Swan Hill Observatory, Australia  4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218  jewitt@ucla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='edu  Received  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  accepted  Revised 2022 January 16  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='08673v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='EP]  20 Jan 2023  – 2 –  ABSTRACT  We present imaging observations of the disintegrating long-period comet  C/2021 A1 (Leonard).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' High resolution observations with Hubble Space Tele-  scope show no evidence for surviving fragments, and place a 3σ upper limit to  their possible radius ∼60 m (albedo 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1 assumed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' In contrast, wide field ob-  servations from the Swan Hill Observatory, Australia, show an extensive debris  cloud, the cross-section and estimated mass of which are consistent with com-  plete disintegration of the nucleus near mid- December 2021 (at about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8 au).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Two methods give the pre-disruption nucleus radius, rn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Tidal,  collisional, sublimation and pressure-confined explosion models provide implau-  sible explanations of the disintegration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' However, rotational instability driven  by outgassing torques has a very short timescale (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1 year) given the orbit and  size of the C/2021 A1 nucleus, and offers the most plausible mechanism for the  disruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Initial rotational breakup is accelerated by the exposure and strong  sublimation of previously buried volatiles, leading to catastrophic destruction of  the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Subject headings: comets: general—comets: individual C/2021 A1  – 3 –  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  INTRODUCTION  Comet C/2021 A1 (Leonard), hereafter “A1”, was discovered on UT 2021 January 3 as  a diffuse V ∼ 19 magnitude object inbound to the Sun at heliocentric distance rH = 5 au  (Leonard 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A1 is a long-period comet, with heliocentric osculating semimajor axis a  = -6124 au, eccentricity e = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0001 and inclination i = 132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6◦, reaching perihelion (at rH  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='615 au) on UT 2022 January 03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3, about a year after discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Although presently  following a weakly hyperbolic orbit, the pre-entry orbital elements (corrected for planetary  perturbations to 1900 January 1, when the heliocentric distance was 137 au) are those of a  bound object, a = 2020 au, e = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='999696 and i = 132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A1 is thus not a dynamically new  comet, having passed through the planetary system ∼ 105 years ago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Comet A1 attained naked eye visibility in late 2021 and then displayed spectacular  gas and dust tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' However, images and commentary recorded in public on-line archives1  indicate that A1 became photometrically unstable in 2021 December and 2022 January.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Measurements of the OH production rate from the Nancay radio telescope were steady near  QOH = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6×1028 s−1 between UT 2021 December 9 and 12, but jumped by a factor of ∼8  to QOH = 22×1028 s−1 on December 15, even as the heliocentric distance barely decreased  from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='80 au to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='74 au (Crovisier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The morphology also changed, becoming  more diffuse and with “the tail being more prominent than the head” on UT 2022 January  222 at rH ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='74 au outbound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Based on these early observational reports we requested  Director’s Discretionary Time on the Hubble Space Telescope (HST), with the science  objective being to study the presumed breakup of this long-period comet at the highest  angular resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Independently, coauthor Mattiazzo also obtained wide-field imaging  data using a private telescope at the Swan Hill Observatory in Australia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The wide-field and  1e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' https://britastro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='org/cometobs/2021a1/thumbnails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='html  2https://groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='io/g/comets-ml/message/30541  – 4 –  HST data are highly complementary, with the former providing sensitivity to low surface  brightness debris over a wide angle and the latter providing ultra-high resolution and very  deep imaging of the near-nucleus region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  While the phenomenon of cometary breakup has been known for over a century, very  few physical observations of disintegrating comets are to be found in the refereed literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  In this paper, we present the observations and consider possible causes of the breakup of  comet A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  OBSERVATIONS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Hubble Space Telescope  The 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 m diameter Hubble Space Telescope was used to observe disintegrating A1  under program GO 16929.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We used the WFC3 camera, which houses two 2015×4096 pixel  charge coupled devices separated by a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2′′ wide gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='04′′ pixel−1 image scale gives a  full-frame 162′′×162′′ field of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' HST images were taken using the F350 LP filter in order  to maximize throughput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This filter has an effective central wavelength λc = 6230˚A when  observing a Sun-like (G2V) source and a FWHM ∆λ = 4758˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We secured four images  each of 450 s duration in each of the first three orbits and five frames of 285 s, with a  sub-frame readout, in the fourth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The first three orbits were obtained in 2022 April with  spacings of one and four days, with the intention being to measure the sky-plane motions  of fragments produced by the break-up of A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The fourth orbit was scheduled on UT 2022  June 7 to coincide with the passage of the Earth through the projected orbit plane of the  comet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Observations from this vantage point provide a model-free measure of the thickness  of the dust distribution perpendicular to the plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Unfortunately, the images from the  fourth orbit suffered from extreme field star contamination, as a result of the low (-6◦)  – 5 –  galactic latitude of the comet, and were not useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Swan Hill Observatory  Wide-field observations were taken by co-author Michael Mattiazzo using a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='28 m  diameter, f/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 wide-field telescope at the Swan Hill Observatory (observatory code Q38),  located in Victoria, Australia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A 4655×3522 pixel CMOS imaging device (Panasonic model  QHY163M) provided an image scale of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='27′′ pixel−1, and a field of view approximately  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6◦×1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Each pixel of the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='28 m telescope subtends a solid angle equal to 103 HST  pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Ten images each of 30 s duration were obtained, during which time the comet moved  relative to field stars by about 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7′′, which is small compared to the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1′′ full width at half  maximum of point source objects in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The wide field image shows evidence for loss  of sensitivity due to vignetting, especially near the corners of the device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We removed this  by fitting a cubic spline surface to the image, using the median signal within 50×50 pixel  boxes (after checking that the procedure did not self-subtract the comet).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  No filter was employed in order to maximize the throughput of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The  quantum efficiency of the detector peaks near a central wavelength 5500˚A, and has a  FWHM estimated at ∼4000˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The central wavelength is close to that of Johnson V (see  the discussion in Bessel 1990), but the response is so broad that it captures the same light  as the Johnson B, V and R filters (or, equivalently, the Sloan g and r filters) combined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  The large bandwidth and lack of a standard filter together limit the accuracy with which  the measured magnitudes can be related to, for example, the V band magnitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We  calibrated the data using measurements of field stars on the Sloan filter system, provided  by the Skymapper southern survey (Wolf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' For this purpose we extracted  measurements using circular apertures of projected radius 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7′′, with sky subtraction from  the median signal within a concentric annulus having inner and outer radii 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1′′ and 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1′′,  – 6 –  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' In order to minimize the color term in our photometry, we selected stars with  optical color g-r ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5, so as to approximately match the color of the Sun (given as g-r  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='45±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='02 by Holmberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We further selected these stars to lie within ∼1′ of  the comet in order to minimize spatial variations in the photometry caused by imperfect  flatness of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  The geometrical circumstances of observation are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  RESULTS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  High Resolution Data  We combined the four images from each orbit in order to reject cosmic rays, suppress  trailed field objects, and reach a fainter limiting magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The composite from UT 2022  April 5 is shown in Figure 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' composites from April 6 and 10 look the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The predicted  location of the nucleus is indicated in the Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The JPL Horizons ephemeris for April  5 gives 3σ positional uncertainties of ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3′′ in right ascension and ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0′′ in declination,  both of which are negligible compared to the 160′′ field of view of WFC3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We searched  for the principal nucleus and discrete fragments in the data by comparing image subsets  to identify correlated motion, but found none.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Instead, the images show evidence for  diffuse light scattered from cometary dust, evident in Figure 1 as a region of slightly higher  surface brightness in the south east quadrant of the image (marked by a dashed white  line in the right-hand panel of the figure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Although it at first resembles a flat-field defect  or a smudge of internally scattered light, two lines of evidence show that this region of  diffuse brightness is neither.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' First, the enhanced region is fixed with respect to the daily  predicted ephemeris position of A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Second, the enhanced region moves on the detector as  the telescope orientation angle changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The enhancement appears at the same position in  – 7 –  image composites from all three dates in April, whereas scattered light from bright stars  outside the WFC3 field of view would vary as the background stars are completely different  from day to day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A flat-field defect would not rotate as the telescope orientation changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  We conclude that the diffuse light is sunlight scattered from cometary debris released from  the now invisible nucleus of A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  The on-line WFC3 Exposure Time Calculator3 gives a 3σ limit for detection of point  source objects at V = 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7, in each of our orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This limiting magnitude is consistent  with the measured sky noise in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Corrected to absolute magnitude using phase  coefficient β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='04 magnitude degree−1, we find H ≥ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' For a nominal albedo, pV =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1, this corresponds to a 3σ limit to the fragment radius, r ≤ 60 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Wide Field Data  The composite wide field image is shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A low surface brightness dust  structure extends over at least 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4◦ (2×106 km in the plane of the sky), with a position  angle 120◦±2◦ and no indication of a brightness peak at the expected location of the  nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The latter was determined from the JPL Horizons ephemeris for the mid-time of  the image, and is marked in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Overall, the morphology is similar to that of C/2010  X1 (Elenin), a long period comet which disintegrated when inbound near rH = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6 AU (Li  and Jewitt 2015), and C/2019 J2 (Palomar), which disintegrated pre-perihelion near rH  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='9 au (Jewitt and Luu 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Comparison with Figure 1 shows that the HST, which  was pointed at the expected location of the nucleus, indeed recorded diffuse light from the  western tip of this dust structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  We estimated the total light from the dust as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' First, we rotated the image to  3https://etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='stsci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='edu/etc/input/wfc3uvis/imaging/  – 8 –  bring the long axis of the dust tail to the horizontal (upper panel in Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Next, we  manually replaced field stars with the average of surrounding pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The median signal from  the comet was then computed within a rectangular box, “A” in the lower panel of Figure  3) 1105′′ long by 380′′ tall, and the background sky estimated from equal-sized photometry  boxes contiguous with the comet box but displaced above and below it (“B” and “C” in  Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Figure 3 shows that the tail extends beyond the left edge of the photometry box  “A” but the increased uncertainty imposed by the sky rendered measurements of this very  faint material impractical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The light from the tail was calculated from fT = fA−(fB+fC)/2,  where fx is the flux in box “x”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Then, applying the calibration obtained from field stars,  we find VT = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='9±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5, where the quoted error is our best estimate of the uncertainty  resulting from non-flatness of the data, the transformation from the wide response of the  camera and the effective V magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' With assumed phase function 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='02±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='02 magnitude  degree−1 and the geometry given in Table 1, the corresponding absolute magnitude is H =  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6, where the larger uncertainty is introduced by the phase correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The scattering  cross-section needed to give this absolute magnitude is C = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8 × 1010 m2, assuming  geometric albedo pV = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1 (appropriate for cometary dust;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Zubko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Figure 4 shows the averaged surface brightness profile from the March 31 image,  measured parallel to the long axis of region A in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Most of the scatter in the  surface brightness profile is statistical noise in the data, but larger oscillations (for example  at ∼480′′ and 750′′) result from spatial background variations caused by the digital removal  of field stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' In this plot, the peak of 1000 units corresponds to a surface brightness Σ =  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 magnitudes arcsec−1, about 5% of the surface brightness of the night sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The surface  brightness shows a steep increase, reaching a maximum at about 100′′ from the ephemeris  nucleus location, followed by a steady decline at larger projected angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This profile shape  is indicative of a suddenly terminated dust mass release, with the peak of the profile giving  the distance traveled by the largest, slowest particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  – 9 –  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  DISCUSSION  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Radius and Mass of the Nucleus  We use the effective spherical nucleus radius of A1 ¯r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 km from Jewitt (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  This estimate is based on independent measurements of QH2O(1), the gas production rate  at 1 au, and of α1, the non-gravitational acceleration at 1 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Comet A1 has QH2O(1) =  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='9×1028 s−1 (only pre-perihelion observations are used because post-perihelion rates are  clearly affected by the breakup) and α1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3×10−6 m s−2, provided by JPL Horizons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A  substantially smaller nucleus would have a surface area insufficient to supply the QH2O(1),  while a substantially larger nucleus would have too much mass to be accelerated at α1  given the known gas production rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Using ¯r and nominal nucleus density ρn = 500 kg  m−3 (Groussin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2019), we estimate the nucleus mass Mn = (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5+6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2) × 1011 kg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The  largest surviving fragments, with radii <60 m, individually contain < 10−3 of the mass of  the primary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Time of Disruption  Syndynes (the loci of particles having one size, released with zero initial relative  velocity over a range of times;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Finson & Probstein (1968)) are curved and do not match  the linear shape of the debris cloud in A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Instead, the morphology more resembles a  set of synchrones as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Synchrones trace the loci of particles in the sky  plane having a range of sizes (hence, radiation pressure accelerations) but released from the  nucleus simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The position angle of the debris trail in A1 is most compatible with  ejection 110±10 days before the image was taken, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' on UT 2021 December 11±10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This is  about a month before reports of distinct morphological change appeared but coincides with  a dramatic increase in the OH production rate from 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4×1028 s−1 on UT 2021 December  – 10 –  19 to 14×1028 s−1 on UT 2021 December 21, in unpublished SOHO/SWAN data (personal  communication M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Combi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' It is also close to a reported OH outburst on UT 2021 December  15 (Crovisier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' While we lack continuous coverage of the gas production from  A1, it is likely that the sublimation rate became highly unstable as a result of the breakup  of the nucleus when close to perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  We assume that the disintegration began on UT 2021 December 11±10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' To reach the  far end of the measured debris cloud (an angular distance ∼1500′′, corresponding to linear  distance L = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 × 106 km) under the action of radiation pressure requires an average  acceleration 2L/∆T 2, where ∆T = 111 days (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6×106 s) is the interval between the time  of disintegration and the Swan Hill image from UT 2022 March 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' In units of the solar  gravitational acceleration at the average rH = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3 au heliocentric distance in this period,  β =  2Lr2  H  g⊙(1)∆T 2  (1)  where g⊙(1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='006 m s−2 is the solar gravity at 1 au and rH is expressed in au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Substituting, we obtain β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' With β ∼ 1/aµm, where aµm is the particle radius  expressed in microns (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Bohren & Huffman (1983)), we infer that the particles at the far  end of the tail in the March 31 image had aµm ∼ 75 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' All particles in the visible debris  cloud on UT 2022 March 31 must be larger, while smaller particles were presumably ejected  but have been swept by radiation pressure beyond the visible extent of the tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Particles  near the peak of the surface brightness profile (angular distance ∼100′′, corresponding to  L = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 × 105 km) have β ∼ 10−3 by Equation 1 and, therefore, radii ∼1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  – 11 –  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Mass of the Optical Debris  How does the mass of the debris compare with the mass of the nucleus prior to its  disappearance?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' To answer this question, we treat the debris as consisting of a distribution  of spherical particles with radii between a and a+da written as n(a)da.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Then, the combined  mass of the particles between minimum radius a1 and maximum radius a2 is  Md =  � a2  a1  4  3πρa3n(a)da  (2)  while their combined cross-section is  C =  � a2  a1  πa2n(a)da  (3)  It is useful to represent the size distribution as a power law  n(a)da = Γa−γda  (4)  where γ is the differential size distribution index and Γ is a normalizing constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Substituting equation 4 into equations 2 and 3 and eliminating Γ, we obtain  Md = 4  3ρC  � a2  a1 a3−γda  � a2  a1 a2−γda  (5)  The minimum particle radius is selected as a1 = 75 µm, since all smaller particles  would have been swept out of the image field in the time since ejection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The maximum  radius, a2 = 60 m, is set by the non-detection of larger bodies in our deep HST imaging  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' With these values for a1 and a2, we plot Equation 5 as a function of γ in the range 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  ≤ γ ≤ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0 (Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The particle mass required to account for the measured cross-section,  – 12 –  C, is seen to vary by orders of magnitude for modest changes in the index, γ, with smaller  values (flatter distributions) hiding a larger fraction of the total mass in big bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Also plotted in the figure is the nucleus mass, Mn = (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5+6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2) × 1011 kg, computed from  the effective radius, rn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 km, (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1), and density, ρn = 500 kg m−3, with the  mass uncertainty marked as a horizontal yellow band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The red point marks the intersection  of the two curves where Md = Mn and shows that, for index γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1, the debris mass  and nucleus mass are equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The upper limit to the size distribution could be substantially  smaller than the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6 km limit set by the Hubble data, in which case a smaller value of  the index would be needed for the mass of the debris to equal the mass of the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  A relevant comparison can be made with the size distribution of the Kreutz sungrazing  comets, which are themselves produced by the fragmentation of a precursor body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The  Kreutz objects have γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 in the 5 m to 35 m radius range (Knight et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2010), plotted  as a blue square in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The uncertainty on γ for the Kreutz objects is not stated;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  we have plotted a nominal ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1 error bar for reference and note reasonable agreement  with the index deduced for A1 within the uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Perhaps less relevant are radar  measurements of the debris size distributions in six meteoroid streams, most associated  with decaying comets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' These are plotted for comparison using green triangular symbols  (Blaauw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' (2011)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The formal meteoroid stream index uncertainties are comparable to  the size of the symbols in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The measured indices span the range γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7,  encompassing the values found for A1 and the Kreutz comets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  We conclude that the optical cross-section presented by the debris in 2022 March is  consistent with the complete disintegration of the original ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6 km scale nucleus into a  power law distribution (index γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1) of particle sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We emphasize that we possess  no independent evidence that the debris mass and original nucleus mass are equal, although  a consideration of the particle properties using more detailed considerations (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4)  – 13 –  supports this result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' It should also be noted that 60 m is an upper limit to the size of  the largest post-disruption “particles” and our result would be changed if a2 ≪ 60 m, as  it would if the size distribution of particles is not well represented by a single power law  across the full range of sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' It is also not obvious that the density of the particles should  necessarily be the same as the bulk density of the nucleus, as we have assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' These and  other physically plausible possibilities lie beyond the observational constraints obtained  from the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Monte Carlo Simulation  We next used a Monte Carlo simulation as developed by Ishiguro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' (2007) (see  also Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' (2017)) to model the cometary debris in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The model is  under-constrained and cannot provide unique solutions for the particle properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' It  is nevertheless valuable in allowing us to test the deductions made based on order of  magnitude considerations, and also to more fully explore the range of plausible solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  We particularly examined the effect of the particle size distribution index and the minimum  and maximum particles sizes in the distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Figure 7 shows the data with results of simulations for γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5 and size  parameter in the range 7 × 10−4 ≤ β ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='07, with ejection on 2021 December 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The  upper limit to β (lower limit to particle radius) is set by the field of view, with smaller  particles have already been pushed out of the field by radiation pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We obtain a ≥  14 µm, different by a factor of five from the limit a ≥ 75 µm estimated by the order of  magnitude procedure, above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The lower limit to β (upper limit to the particle size of ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4  mm) is determined from the location of the surface brightness peak in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This is very  small compared to the 60 m upper limit to the radius of the largest possible fragment, set  by non-detection in the HST images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' However, this difference is understandable since, for  – 14 –  commonly measured cometary size distributions, the scattering cross-section is dominated  by the smallest particles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' large particles contribute little to the cross-section and thus are  poorly constrained by scattered light observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' In order to fit the data, we assumed  that the particle ejection speed varies with size parameter as V = V0β1/2, with V0 = 550  m s−1 being the gas thermal speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Unlike the particle trails of weakly active comets and  asteroids, a high ejection speed is required in order to fit the large width of the debris cloud  in A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  As is evident in Figure 7, the plotted models do not perfectly reproduce the measured  surface brightness profile, with larger γ models being 25% to 30% brighter than the data at  large distances from the nucleus and smaller γ models being too sharply peaked compared  to the measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' If they are real, these differences could result from physical effects not  included in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' For example, we have ignored dust released before disintegration,  reasoning that the dramatic outbursts and brightening starting in mid-December would  swamp any signal from older material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' As another example, large aggregate grains in the  tail might break up into smaller particles which would be quickly swept from the field of  view by radiation pressure, perhaps explaining the lower brightness of the tail ≳1000′′ from  the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' On the other hand, the differences between the models and the measured  profile are certainly affected by systematic uncertainties intrinsic to the wide field data,  particularly by imperfect flatness of the data and by the presence of scattered light from  bright background sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Rather than over-interpret the data, we conclude from the  Monte Carlo simulation only that γ ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1 provides a broad match to the profile, while  much steeper and much less steep distributions do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The range of allowable indices  deduced from Monte Carlo models is consistent with γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1 as inferred from the  debris mass in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3 (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Lastly, we used the Monte Carlo model to test the possibility that the debris observed  – 15 –  in 2022 March could be long-lived material released before perihelion, in the form of a  so-called “neck-line” structure (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Pansecchi and Fulle 1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We find that material  ejected in the period 2021 November 15 to December 15 would produce a tail structure  in March having position angle (113◦) distinctly different from that measured (120◦) or  calculated from the impulsive ejection model (119◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' In addition, neck-line structures in  other comets are most prominent when observed from near the projected orbital plane,  whereas our observations were taken ∼20◦ from the orbital plane of C/2021 A1 (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Table  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The combination of the unfavorable observing geometry, the failure to reproduce the  measured position angle of the dust in 2022 March, and the obvious importance of the  outbursts reported in 2021 December together show that pre-perihelion dust is a negligible  contributor to the post-perihelion appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Disintegration Mechanism  The preceding discussion shows that a ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6 km scale nucleus disintegrated into  fragments, the largest of which were no more than about 10% of the radius of the original  body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' What process could lead to such a dramatic outcome?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Tidal Breakup: The 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='615 au perihelion distance of A1 far exceeds the Roche radius  of the Sun (∼10−2 au), negating the possibility of a tidal breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Comet A1 did pass  within a distance rV = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='029 au from Venus on UT 2021 December 18 (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021)  but this is still ∼300 times the Roche radius (∼10−4 au) of the planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' To within a numerical  multiplier, the differential of the gravitational force on opposite sides of the nucleus is  ∆F ∼ (GMV ρnr3  n/r2  V )(rn/rV ) giving an order of magnitude tidal stress S ∼ ∆F/r2  n or  S ∼ GMV ρnr2  n  r3  V  ,  (6)  – 16 –  where G = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='67 × 10−11 N kg−2 m2 is the gravitational constant, MV = 5 × 1024 kg is  the mass of Venus and the other quantities are already defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Substituting ρn = 500 kg  m−3, rn = 600 m, and rV = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='029 au, we estimate S ∼ 10−6 N m−2 at closest approach,  which is orders of magnitude smaller even than the cohesive strengths of fine, unconfined  powders (S ≳ 100 N m−2) measured in the laboratory (Garcia-Trinanes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The  disintegration of A1 is very unlikely to be a consequence of tidally induced stresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Equilibrium Sublimation: The rate of loss of surface material is drn/dt ∼ −fs/ρ,  where fs ∼ 2 × 10−4 kg m−2 s−1, at 1 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Substitution gives drn/dt ∼ -3 cm day−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' At this  rate, the timescale for eroding the whole nucleus would be |rn/(drn/dt)| ∼ 40 years, which  is very large compared to the ∼1 year spent by A1 in the vicinity of the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' In any case,  sublimation would produce steady erosion of the comet not a catastrophic disintegration  like that observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Equilibrium sublimation cannot account for the sudden disintegration  of A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Collisional Disruption: Collisional disruption timescales for 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6 km scale objects,  even in the dense parts of the asteroid belt, are measured in hundreds of millions of years  (Bottke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Comet A1 arrived from a high inclination orbit and disintegrated ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  au from the ecliptic plane where there are no known objects with which to collide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We  confidently dismiss the possibility that A1 was collisionally disrupted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Internal Pressure: Could internal pressure build-up from sublimated gases cause  the nucleus to explode (Samarasinha 2001)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The core temperature of the nucleus of A1  is comparable to the Oort cloud equilibrium temperature of just a few degrees above  absolute zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Heat transport from the surface to the interior by conduction is controlled  by the thermal diffusivity, which is proportional to the conductivity and which, in turn,  is strongly affected by the particulate nature and porosity of the cometary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Laboratory measurements of porous, dielectric powders yield conductivities ∼ 102 to 103  – 17 –  times smaller than the solid material (Henke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The expected high porosities  and low thermal diffusivities of cometary material lead to small thermal skin depths that  make deep conduction impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Heat applied for a time τ will conduct over a distance  d ∼ (κτ)1/2, where κ is the diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' For example, with κ = 10−8 to 10−9 m2 s−1, even in  the year between discovery at rH = 5 au and perihelion at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6 au, conducted heat travelled  into the nucleus by a characteristic distance only d ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 m to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This distance is so  small compared to the nucleus radius that it is difficult to see how subsurface gas produced  by surface heating could have any relevance to the complete disintegration of the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Rotational Instability: The remaining possibility for nucleus break-up is also the  most plausible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The timescale for changing the spin angular momentum of a spherical  nucleus through outgassing torques is (Jewitt 2021)  τs =  �16π2  15  � � ρnr4  n  kTVthP  � � 1  ˙M  �  ,  (7)  where P is the instantaneous spin-period and kT is the dimensionless moment arm, equal  to the fraction of the outflow momentum that exerts a torque on the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The median  values in a sample of short-period comet nuclei with perihelia in the range 1 ≤ q ≤ 2 au  are kT = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='007 and P = 15 hours (5×104 s) (Jewitt 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We substitute  ˙M = 800 kg  s−1, equal to the sublimation rate at 1 au as measured by Combi’s Lyman-α data, on the  understanding that this sets a lower bound to the mass loss rate at smaller distances and  therefore sets an upper limit to τs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' With ρn = 500 kg m−3, rn = 600 m, and Vth = 500  m s−1, substitution into Equation 7 gives τs < 5 × 106 s (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='16 year, or 2 months), which  compares to the 6 weeks (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='12 year) spent by A1 with rH < 1 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' While this is not proof  that A1 disintegrated through a rotational instability, given the nominal nucleus parameters  and measured mass loss rate, rotational instability does offer a plausible mechanism for  nucleus disintegration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  – 18 –  Rotational breakup is expected to launch fragments with a velocity dispersion  comparable to the tangential speed of the nucleus due to its rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' For a strengthless  nucleus, this equals the gravitational escape speed from the primary, in this case ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3  m s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' In contrast, the Monte Carlo models show that larger speeds are required to fit  the head width of the debris trail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' For example, with V = V0β1/2 and V0 = 550 m s−1,  millimeter sized particles (β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='001) would have V ∼ 17 m s−1, about 60 times the escape  speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We conjecture that these higher speeds result from gas drag acceleration following  the exposure and intense sublimation of previously buried ices caused by rotational breakup  at rH ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8 au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Very large particles and boulders would not be substantially accelerated by gas drag  and should leave the disintegrating nucleus at about the escape velocity of the primary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  In the ∼3 months elapsed between the first signs of breakup and the HST observations,  such slow-moving fragments would travel ∼2000 km, a distance subtending 1′′ to 2′′ in the  plane of the sky (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Large fragments should therefore be resolvable in the HST  data (the resolution is ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='08′′) but, nevertheless, remain unseen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This might reflect the  continued disintegration of the fragments, again aided by the new exposure to the heat of  the Sun of previously buried volatiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The breakup process would then be catastrophic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Smaller fragments produced by breakup of the primary nucleus would have progressively  shorter and shorter spin-up times, owing to their smaller size (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Equation 7) and to the  sudden exposure of large areas of previously buried ice which could amplify the moment  arm, kT, by orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The expected result is a runaway fragmentation cascade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Gas Production Resulting from Nucleus Disintegration  Disintegration of the nucleus must suddenly expose previously buried ices to the heat  of the Sun, leading to a burst in the gas production rate caused by sublimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Indeed,  – 19 –  measurements of the gas production rate in the mid-December to January period are highly  variable, peaking near QH2O = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 × 1029 s−1 in radio (Crovisier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021), Lyman-α (M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Combi, (private communication)), and near-ultraviolet (Jehin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021, 2022a, 2022b)  observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' At break up, A1 was about rH = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8 AU from the Sun and ∆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 AU from  the SWAN/SOHO observatory used to take the Lyman-α data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The latter has 1◦ wide  pixels, corresponding to about w ∼ 6 × 105 km per pixel at the comet and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2×106 km  for the nominal Nyquist (2 pixel) resolution of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' With an isothermal blackbody  temperature at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8 AU ∼310 K, the thermal velocity of hydrogen atoms is Vth ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5 km  s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This, however, is a strong lower limit to the outflow velocity because of photo-electric  heating (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Combi and Delsemme 1980, Combi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Based on published models,  we adopt a hydrogen outflow speed Vth ∼ 10 km s−1 and estimate the residence time for  hydrogen atoms within a Nyquist sampled resolution element as tr ∼ 2w/Vth ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 × 105  s (about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 days).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This means that the peak rate inferred from SWAN/SOHO Lyman-α  data should be understood as a measure of the production rate averaged over 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  We are interested to see how QH2O compares with estimates of the gas production  expected from the break up of the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' To this end, we consider an idealized model in  which the nucleus consists of particles which are either refractory or ice, and in which the  ratio of ice to refractory masses is fice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Both refractory and ice particles are assumed to  occupy a differential power size distribution (Equation 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' To render the problem tractable,  we make the simplifying assumption that the nucleus disintegrates instantaneously into  power law distributions of ice and refractory particles, each having radii in the range  a1 ≤ a ≤ a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The icy component then sublimates at the rate fs [kg m−2 s−1], which we  calculate from energy balance including terms for radiation and sublimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  In the residence time tr, an ice surface will sublimate over a layer thickness  – 20 –  as = fstr  ρn  ,  (8)  where ρn is the density of the particle, assumed equal to the bulk density of the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  All the ice particles with radii a ≤ as will sublimate away, releasing water molecules and,  eventually, producing by photodissociation the hydrogen atoms detected using the SWAN  instrument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Ice particles with a > as will also partially sublimate in time tr, but their  contribution to the gas flux should be small because, for plausible power law distributions  (in particular, for γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5 as determined in sections 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4), large particles present a  small fraction of the total particle cross-section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  The fraction of the mass contained in ice particles having a ≤ as is given by  F =  � as  a1 a3−γda  � a2  a1 a3−γda  (9)  which, for 3 < γ < 4 and as ≫ a1 and a2 ≫ a1, simplifies to  F =  �γ − 3  4 − γ  � �as  a2  �4−γ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  (10)  The total ice mass in the undisrupted nucleus, assumed to be spherical, is Mi =  (4π/3)ρnr3  nfice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The production rate averaged over time tr may be written QH2O =  FMi/(trµmH), where µ = 18 is the molecular weight of the water molecule and  mH = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='67 × 10−27 kg is the mass of the hydrogen atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Substitution of Equations 8 and  10 into this expression gives  QH2O = 4πρnr3  nfice  3trµmH  �γ − 3  4 − γ  � � fstr  ρna2  �4−γ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  (11)  The equilibrium sublimation mass flux calculated for a blackbody water ice sphere at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8  – 21 –  AU is fs = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7 × 10−4 kg m−2 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The flux could be smaller if the grain albedo is high, or  larger if the grain is anisothermal (albeit then sublimating from a smaller fraction of the  grain surface).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We set a2 = 60 m, the largest “particle” allowed by the Hubble imaging,  and a1 = 10−7 m (however, Equation 11 is insensitive to a1 and its value is unimportant  provided a1 ≪ as).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The nominal nucleus radius is rn = 600 m, and the size distribution  index is γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5, as deduced above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Measured cometary ice/refractory ratios, fice, show a  wide range of values, from fice ∼ 1 in 67P/Churyumov-Gerasimenko (Marschall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2020),  to fice < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 in C/1995 O1 Hale-Bopp (Jewitt and Matthews 1999) and fice = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='03 to  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1 in 2P/Encke (Reach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We adopt fice = 1/4, recognizing that this value is  substantially uncertain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Substitution into Equation 11 gives QH2O = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8+12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0  −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 × 1029 s−1, where the error bars  reflect only the ±200 m uncertainty in the estimated radius of the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' This is larger  than the measured peak water production rate (2×1029 s−1) but shows acceptable agreement  given the crude nature of the model calculation and the likelihood that the disintegration  was in reality spread over a finite period not impulsive, as modeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' We conclude that  complete disintegration of the nucleus into a power law particle size distribution is consistent  both with the optical brightness of the debris cloud and with the surge in the water  production rate measured using Lyman-α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Future improvements to this model could include a treatment of the initial, optically-  thick phase of the expanding disintegration cloud, when self-shielding will suppress and  delay the sublimation surge relative to the estimate given here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Also needed is a treatment  of the gas drag interaction with cometary solids in a fully disintegrated body, responsible  for the size-dependent acceleration of refractory particles into the coma and surviving  debris field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Furthermore, several of the parameters needed to accurately model nucleus  disintegration remain unmeasured, and most other disintegrating comets are observationally  – 22 –  even less-well characterized than A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' It is obvious, even from these simple considerations  that many more detailed observations, across a wide range of wavelengths and with  adequate temporal sampling, will be needed to better understand what is likely to be the  dominant destructive cometary process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  – 23 –  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  SUMMARY  We present both high resolution and wide field observations of disintegrating  long-period comet C/2021 A1 (Leonard) taken to study the nature of its demise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  The pre-disintegration radius of the nucleus, estimated using two methods, was  rn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' After breakup, which began in mid-December 2021 and may have  continued for weeks, no nucleus fragments larger than about rn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='06 km (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' < 10−3  of the primary mass) survived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  The observed debris cloud consists of sub-millimeter and larger particles, with a  differential power law size distribution having index γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1, as  estimated by two different methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The observational constraints are consistent with  equality between the mass of the debris cloud and the mass of the primary nucleus,  indicating a total disintegration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Tidal disruption, sublimation, collisional disruption, and explosion following internal  pressure build-up in the nucleus all offer implausible explanations of the disintegration  of C/2021 A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  The spin-up timescale due to outgassing torques for a 600 m nucleus in the orbit of  C/2021 A1 is as short as ∼2 months, pointing to rotational instability as the likely  cause of the disintegration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  A simple model of the exposure and rapid sublimation of previously buried ice  indicates a peak gas production rate (QH2O = 9+12  −6 × 1029 s−1) of the same order as  the measured peak value (QH2O = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 × 1029 s−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  We thank Michael Combi for a preview of his SWAN data on C/2021 A1 and the  anonymous referee for prompt comments on the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Based on observations made  – 24 –  with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the  Space Telescope Science Institute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' STScI is operated by the Association of Universities for  Research in Astronomy, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' under NASA contract NAS 5-26555.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Support for this work  was provided by NASA through grant number GO-16929 from the Space Telescope Science  Institute, which is operated by auRA, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', under NASA contract NAS 5-26555.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Facilities: HST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  – 25 –  REFERENCES  Bessell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 1990, PASP, 102, 1181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1086/132749  Bohren, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' & Huffman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 1983, Absorption and scattering of light by small particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  New York: Wiley, 1983  Bottke, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Durda, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Nesvorn´y, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2005, Icarus, 179, 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='icarus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='017  Blaauw, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Campbell-Brown, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', & Weryk, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2011, MNRAS, 414, 3322.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='18633.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='x  Combi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' & Delsemme, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 1980, ApJ, 237, 633.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1086/157909  Combi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Reinard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Bertaux, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2000, Icarus, 144, 191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1006/icar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6335  Crovisier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Biver, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', and Bockelee-Morvan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021, Central Bureau Electronic Telegram  5087 (2021 December 22)  Finson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' & Probstein, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 1968, ApJ, 154, 327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1086/149761  Garcia-Trinanes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Luding, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' and Shi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Advanced Powder Technology, 30,  2868-2880  Groussin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Attree, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Brouet, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2019, Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', 215, 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1007/s11214-  019-0594-x  Henke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Gail, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Trieloff, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2012, A&A, 537, A45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1051/0004-  6361/201117177  Holmberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Flynn, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', & Portinari, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2006, MNRAS, 367, 449.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1365-  2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='09832.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='x  – 26 –  Ishiguro, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Sarugaku, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Ueno, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2007, Icarus, 189, 169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='icarus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='003  Jehin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Moulane, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', & Manfroid, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021, The Astronomer’s Telegram, 15128  Jehin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Moulane, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Manfroid, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2022a, The Astronomer’s Telegram, 15186  Jehin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Moulane, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Manfroid, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2022b, The Astronomer’s Telegram, 15189  Jewitt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' & Matthews, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 1999, AJ, 117, 1056.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1086/300743  Jewitt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' & Luu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2019, ApJ, 883, L28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3847/2041-8213/ab4135  Jewitt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Mutchler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2020, ApJ, 896, L39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3847/2041-8213/ab99cb  Jewitt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021, AJ, 161, 261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3847/1538-3881/abf09c  Jewitt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2022, AJ, 164, 158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3847/1538-3881/ac886d  Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Ishiguro, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Michikami, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2017, AJ, 153, 228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3847/1538-  3881/aa69bb  Knight, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', A’Hearn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Biesecker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2010, AJ, 139, 926.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1088/0004-  6256/139/3/926  Leonard, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Aschi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Pettarin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021, Minor Planet Electronic Circulars,  2021-A99  Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' & Jewitt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2015, AJ, 149, 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1088/0004-6256/149/4/133  Marschall, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Markkanen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Gerig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2020, Frontiers in Physics, 8, 227.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3389/fphy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='00227  Pansecchi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' & Fulle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 1990, A&A, 239, 369  – 27 –  Reach, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Sykes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Lien, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2000, Icarus, 148, 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1006/icar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6478  Samarasinha, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2001, Icarus, 154, 540.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1006/icar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6685  Wolf, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Onken, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Luvaul, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2018, PASA, 35, e010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1017/pasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  Zhang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Ye, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Vissapragada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2021, AJ, 162, 194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3847/1538-3881/ac19ba  Zubko, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', Videen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Shkuratov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2017, JQSRT, 202, 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='jqsrt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='026  This manuscript was prepared with the AAS LATEX macros v5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  – 28 –  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  Observing Geometry  UT Date & Time  νa  rH b  ∆c  αd  θ−⊙e  θ−V f  δ⊕g  Telh  Scalei  Uncj  2022 Mar 31 18:14-18:26  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='756  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='942  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8  243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4  Swan Hill  1408  ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4  2022 Apr 05 23:35-24:04  109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='833  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='910  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='9  246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8  HST  1385  ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6  2022 Apr 06 23:32-23:51  109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='848  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='902  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='9  246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='9  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7  HST  1379  ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6  2022 Apr 10 19:23-19:53  110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='903  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='875  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7  249.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1  HST  1359  ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7  2022 Jun 7 16:36-17:12  123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='698  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='715  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='8  319.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3  137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0  +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2  HST  1243  ±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='7  aTrue anomaly, in degrees  bHeliocentric distance, in au  cGeocentric distance, in au  dPhase angle, in degrees  ePosition angle of projected anti-solar direction, in degrees  fPosition angle of negative heliocentric velocity vector, in degrees  gAngle from orbital plane, in degrees  hTelescope  iImage scale, km arcsecond−1  j3σ ephemeris uncertainty, arcsecond (from JPL Horizons)  – 29 –  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='— A) Composite of four, 450 s HST images from UT 2022 April 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Diffuse streaks  are imperfectly removed field stars and galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  B) Same image, anotated to show the  approximate boundary of the debris (white dashed line) and the expected location of the  nucleus (yellow line segments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Two scale bars of 30′′ and 5×104 km in length are shown, as  well as the projected anti-solar (−S) and negative heliocentric velocity (−V ) vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' North  is to the top, East to the Left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  UT 2022 April 5  30  5x104 km  B– 30 –  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='— Wide field image from Swan Hill Observatory showing C/2021 A1 on UT 2022  March 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 10′ and 106 km scale bars are shown, as well as the projected anti-solar (−S) and  negative heliocentric velocity (−V ) vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Yellow lines mark the ephemeris location of the  nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The white square shows the size of the HST field of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The image has North to  the top, East to the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  10  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='UT 2022 March 31  106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='km– 31 –  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='— (Upper:) Same image as in Figure 2 but rotated to bring the axis of the dust tail  to the horizontal and shown at a larger scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' Yellow lines mark the ephemeris location of  the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' (Lower:) Locations of the photometry regions A, B and C used to measure the  scattering cross-section of particles in the tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  R  380″  1105"– 32 –  500  0  500  1000  1500  0  400  800  1200  1600  Surface Brightness  Distance [arcsecond]  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='— Surface brightness profile parallel to the long axis of Box A (Figure 3) plotted  against the distance from the nucleus ephemeris location (axis is reversed relative to Figure  3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 1000 units correspond to a surface brightness Σ = 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 magnitudes arcsec−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The linear  distance scale is approximately 1500 km per arcsecond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  – 33 –  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='— (Left:) Same image as Figure 2 with synchrones overplotted, for ejection dates 80,  100, 120, 140 and 160 days prior to the date of the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' (Right:) Syndynes for particles  with β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0003, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='003, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='01 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='03, as marked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The axis of the debris cloud is best  matched by the 110±10 day synchrones, corresponding to ejection on UT 2021 December  11±10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  UT 2022 March 31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='001  120  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content="003  100-  80  10'0  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='03– 34 –  1011  1012  1013  1014  1015  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='0  Debris Mass [kg]  Differential Size index, γ  rn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6+/-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 km  Blaauw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2011  Kreutz Sungrazers  C/2021 A1  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='— Total mass of the debris cloud (assuming density ρn = 500 kg m−3) plotted as a  function of the differential power law index, γ, is plotted as a solid black line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The equivalent  spherical mass of the original 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='6±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='2 km radius nucleus is shown (assuming the same ρn),  together with its uncertainty, as a yellow horizontal band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The debris and nucleus masses  are equal at γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='1, shown by the red filled circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' For comparison we show, as a blue  square, the size distribution of the Kreutz sungrazing comets (Knight et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2010) and, as  green triangles, several radar-measured meteoroid streams (Blaauw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The vertical  positions of the Kreutz and radar stream points have no meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='  – 35 –  200  0  200  400  600  800  1000  1200  0  400  800  1200  1600  Surface Brightness  Distance [arcsecond]  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='— Axial surface brightness profile on UT 2022 March 31 (yellow diamonds) compared  with results from a Monte Carlo simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content=' The models shown have size index γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='3 (red  curve), 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 (black curve) and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='5 (blue curve), all with 7 × 10−4 ≤ β ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='07, corresponding  to particle radii 14 µm to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
+page_content='4 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNFAT4oBgHgl3EQfvB44/content/2301.08673v1.pdf'}
diff --git a/M9AzT4oBgHgl3EQfWPwO/content/tmp_files/2301.01296v1.pdf.txt b/M9AzT4oBgHgl3EQfWPwO/content/tmp_files/2301.01296v1.pdf.txt
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+TinyMIM: An Empirical Study of Distilling MIM Pre-trained Models
+Sucheng Ren
+Fangyun Wei*
+Zheng Zhang
+Han Hu
+Microsoft Research Asia
+Abstract
+Masked image modeling (MIM) performs strongly in pre-
+training large vision Transformers (ViTs). However, small
+models that are critical for real-world applications can-
+not or only marginally benefit from this pre-training ap-
+proach. In this paper, we explore distillation techniques to
+transfer the success of large MIM-based pre-trained mod-
+els to smaller ones. We systematically study different op-
+tions in the distillation framework, including distilling tar-
+gets, losses, input, network regularization, sequential dis-
+tillation, etc, revealing that: 1) Distilling token relations
+is more effective than CLS token- and feature-based distil-
+lation; 2) An intermediate layer of the teacher network as
+target perform better than that using the last layer when
+the depth of the student mismatches that of the teacher;
+3) Weak regularization is preferred; etc. With these find-
+ings, we achieve significant fine-tuning accuracy improve-
+ments over the scratch MIM pre-training on ImageNet-1K
+classification, using all the ViT-Tiny, ViT-Small, and ViT-
+base models, with +4.2%/+2.4%/+1.4% gains, respectively.
+Our TinyMIM model of base size achieves 52.2 mIoU in
+AE20K semantic segmentation, which is +4.1 higher than
+the MAE baseline. Our TinyMIM model of tiny size achieves
+79.6% top-1 accuracy on ImageNet-1K image classifica-
+tion, which sets a new record for small vision models of
+the same size and computation budget. This strong perfor-
+mance suggests an alternative way for developing small
+vision Transformer models, that is, by exploring better train-
+ing methods rather than introducing inductive biases into
+architectures as in most previous works. Code is available
+at https://github.com/OliverRensu/TinyMIM.
+1. Introduction
+Masked image modeling (MIM), which masks a large
+portion of the image area and trains a network to recover
+the original signals for the masked area, has proven to be a
+very effective self-supervised method for pre-training vision
+Transformers [2,12,18,53]. Thanks to its strong fine-tuning
+performance, MIM has now been a main-stream pre-training
+*Corresponding author: fawe@microsoft.com.
+ViT-T
+ViT-S
+ViT-B
+70
+74
+78
+82
+86
+Scratch
+MAE
+TinyMIM
+-0.6
++3.6
++0.7
++3.1
++2.4
++3.8
+Acc.
+72.2
+79.9
+81.2
+Figure 1. Comparison among TinyMIM (ours), MAE [18] and
+training from scratch by using ViT-T, -S and -B on ImageNet-1K.
+We report top-1 accuracy. We adopt DeiT [44] when training from
+scratch. For the first time, we successfully perform masked image
+modeling pre-training for smaller ViTs.
+Model
+Param.
+Flops
+Top-1
+mIoU
+(M)
+(G)
+(%)
+DeiT-T [44]
+5.5
+1.3
+72.2
+38.0
+PVT-T [46]
+13.0
+1.9
+75.1
+39.8
+CiT-T [39]
+5.5
+1.3
+75.3
+38.5
+Swin [32]
+8.8
+1.2
+76.9
+40.4
+EdgeViT-XS [35]
+6.4
+1.1
+77.5
+42.1
+MobileViTv1-S [34]
+4.9
+2.0
+78.4
+42.7
+MobileViTv3-S [45]
+4.8
+1.8
+79.3
+43.1
+TinyMIM⋆-T (Ours)
+5.8
+1.3
+79.6
+45.0
+Table 1. Comparison with state-of-the-art tiny Transformers with
+architecture variants. The parameters indicate the backbone pa-
+rameter excluding the parameters of the last classification layer
+in classification or the decoder in segmentation. We report top-1
+accuracy on ImageNet-1K classification and mIoU on ADE20K
+segmentation.
+method for vision Transformers, and numerous follow-ups
+have been carried out in this research line, such as study-
+ing how to set decoding architectures [25], reconstruction
+targets [11,36,48,60], etc., as well as revealing its proper-
+ties [49,52,54].
+1
+arXiv:2301.01296v1  [cs.CV]  3 Jan 2023
+
+Method
+ViT-T
+ViT-S
+ViT-B
+ViT-L
+Scratch
+72.2
+79.9
+81.2
+82.6
+MAE
+71.6
+80.6
+83.6
+85.9
+Gap
+-0.6
++0.7
++2.4
++3.3
+Table 2. Comparison between MAE pre-trained ViTs and ViTs
+trained from scratch by using ViT-T, -S, -B and -L on ImageNet-
+1K. We adopt DeiT when training from scratch. We report top-1
+accuracy. As model size shrinks, the superiority of MAE gradually
+vanishes. MAE even hurts the performance of ViT-T.
+However, as shown in Table 2, MIM pre-training [18]
+mainly effects for relatively large models. When the model
+size is as small as ViT-Tiny (5 million parameters), which
+is critical for real-world applications, MIM pre-training can
+even hurt the fine-tuning accuracy on ImageNet-1K classifi-
+cation. In fact, the accuracy drops by -0.6 compared to the
+counterpart trained from scratch. This raises a question: can
+small models also benefit from MIM pre-training, and how
+can this be achieved?
+In addition, the existing study on small vision Transform-
+ers mainly focus on introducing certain inductive bias into
+architecture design [6,26,34,35]. The additional architec-
+tural inductive biases facilitate optimization yet limit the
+expressive capacity. It’s natural to ask whether we can boost
+plain small vision Transformers to perform just as well.
+In this work, we present TinyMIM, which answers the
+above questions. Instead of directly training small ViT mod-
+els using a MIM pretext task, TinyMIM uses distillation
+technology [24] to transfer the knowledge of larger MIM
+pre-trained models to smaller ones. Distillation endows the
+nice properties of larger MIM pre-trained models to smaller
+ones while avoiding solving a “too” difficult MIM task. Not-
+ing that knowledge distillation has been well developed,
+especially for supervised models [16], our main work is to
+systematically study for the first time the effects of different
+design options in a distillation framework when using MIM
+pre-trained models as teachers. Specifically, we consider dis-
+tillation targets, data augmentation, network regularization,
+auxiliary losses, macro distillation strategy, etc., and draw
+several useful findings:
+• Distillation targets. There are two main findings re-
+lated to distillation targets: 1) Distilling token relations
+is more effective than distilling the CLS token and fea-
+ture maps. 2) Using intermediate layers as the target
+may perform better than using the last layer, and the
+optimal target layer for different down-stream tasks,
+e.g., classification and segmentation, can be different.
+• Data and network regularization. Weak augmentation
+and regularization is preferred: 1) The performance of
+using a masked image is worse than using the original
+image; 2) Relatively small drop path rate (0 for teacher
+and 0.1 for student) performs best.
+• auxiliary losses. We find that an auxiliary MIM loss
+does not improve fine-tuning accuracy.
+• Macro distillation strategy. We find that using a se-
+quential distillation strategy, i.e., “ViT-B → ViT-S →
+ViT-T”, performs better than that distilling directly from
+ViT-B to ViT-T.
+By selecting the best framework options, we achieve sig-
+nificant fine-tuning accuracy improvements over the direct
+MIM pre-training on ImageNet-1K classification, using ViT
+models of different sizes, as shown in Figure 1. Specifi-
+cally, the gains of TinyMIM on the ViT-Tiny, ViT-Small, and
+ViT-base models are +4.2%/+2.4%/+1.4%, respectively.
+In particular, our TinyMIM⋆-T model with knowledge
+distillation during finetune-tuning achieves a top-1 accuracy
+of 79.6% on ImageNet-1K classification (see Table 1), which
+performs better than all previous works that develop small
+vision Transformer models by introducing architectural in-
+ductive biases or smaller feature resolutions. It sets a new
+accuracy record using similar model size and computation
+budget. On ADE20K semantic segmentation, TinyMIM-T
+achieves 45.0 mIoU, which is +1.9 higher than the second
+best method, MobileViTv3-S [45]. The strong fine-tuning
+accuracy by TinyMIM⋆-T suggests an alternative way for
+developing small vision Transformer models, that is, by
+exploring better training methods rather than introducing
+inductive biases into architectures as most previous works
+have done.
+2. Related Works
+2.1. Masked Image Modeling
+Masked Language Modeling (MLM) [10] for self-
+supervised Transformer pre-training has achieved incredible
+success in natural language processing (NLP) field. Inspired
+by the same idea of masking and reconstruction, BEiT [2]
+is the pioneer to bring such success to computer vision filed
+by encoding masked images and predicting masked tokens
+generated by DALL-E [38]. SimMIM [53] and MAE [18]
+find that reconstructing RGB pixels results in favorable rep-
+resentations. MAE adopts an asymmetric encoder-decoder
+architecture. The encoder only encodes the visible tokens
+and drops a high portion of masked tokens to reduce the com-
+putation burden. A lightweight decoder then produces recon-
+structed patches. Different from tokens in natural language
+processing that have rich semantics, pixels in computer vi-
+sion are low-level information, therefore, a lot of recent
+works aim at looking for better supervisions. MaskFeat [48]
+takes local gradient features produced by the manually-
+crafted HOG descriptor [9] as supervisions. PeCo [11] trains
+2
+
+Masked Image
+Raw Image
+Factors
+Input
+Target 
+Feature
+Relation
+𝑄·𝑄𝑇
+𝐾·𝐾𝑇
+𝑉·𝑉𝑇
+𝑄·𝐾𝑇
+Head Number
+w/ or w/o Softmax
+Output Feature
+Block Feature
+QKV Features
+Attention Feature
+FFN Feature
+Res. Connection of FFN
+Block
+Last
+Intermediate
+…
+…
+Transformer Block-N
+Output Feature
+Multi-Head 
+Attention
+Add & Norm
+FFN
+Add & Norm
+Attention Feature
+FFN Feature
+Block Feature
+Raw Image
+Masked Image
+Feature of Last Block
+𝑄·𝑄𝑇
+𝐾·𝐾𝑇
+𝑉·𝑉𝑇
+𝑄·𝐾𝑇
+𝑄
+𝐾
+𝑉
+Softmax
+Transformer Block-n
+Transformer Block-1
+Teacher
+(Highlight 
+by Blue)
+Relations
+Figure 2. We comprehensively study a variety of factors (highlighted by Royal Blue) that may affect TinyMIM pre-training including input,
+distillation target (feature or relation) and target block.
+a new tokenizer by enforcing perceptual similarity. iBot [60]
+and data2vec [1] take exponential moving average (EMA)
+updated models as tokenizers. MILAN [25] adopts a pre-
+trained CLIP as the teacher. Similarly, BeiTv2 [36] also uses
+CLIP [37] for tokenizer training. Different from these works
+that use various tokenizers/teachers, we adopt a masked im-
+age modeling pre-trained model as our teacher.
+The MIM pre-training performs very well on relatively
+large models from base size to giant size [31,53]. However,
+it will hurt the fine-tuning when the model is as small as
+tiny size, probably because the limited capthe MIM task is
+“too” difficult for small model. This paper explores how to
+make small vision Transformer models also benefit from
+MIM training, through a systematic study of the distillation
+technology.
+2.2. Knowledge Distillation
+Knowledge distillation is a classical method to transfer
+the knowledge from cumbersome models to a small one, pi-
+oneered by [24]. The original knowledge distillation frame-
+work adopts the annealed classification logits of the teacher
+as the distilling target for the student. Since then, extensive
+variants have been carried out to improve the distilling ef-
+fectiveness [16], including changing the distilling targets as
+intermediate features [22,23,28,40] and relations [29,56],
+data augmentations of teacher and students [39, 50], regu-
+larization [50], distilling strategies [47, 55, 57, 58] and so
+on.
+While almost all studies are made for CNN architec-
+tures under supervised settings, recently, there have been
+a few works performing distilling technologies for vision
+Transformers [44,50] and contrastive learning based meth-
+ods [14, 50]. In DeiT [44], the teacher is set as a CNN
+architecture so as to transfer the inductive bias involved in
+CNNs to vision Transformers. It also propose to use hard
+distillation which uses hard pseudo class labels of the teacher
+network as the distilling targets, which performs better than
+the naive knowledge distillation [24]. In [14], a distillation
+method regarding the similarities between instances is ap-
+plied to transfer the power of contrastive pre-trained large
+CNN models to small CNNs. In [50], a method based on
+feature map distillation is proposed to generally improve
+vision transformers by different pre-training approaches in-
+cluding image classification, instance contrastive based self-
+sueprvised learning [3] and CLIP pre-training [37]. However,
+it shows no gains for MIM pre-trained models.
+This paper for the first time studies the distillation frame-
+work for MIM pre-trained vision Transformers. Through
+a systematic study, it draws several useful findings and the
+best options, under which, significant gains are achieved for
+vision Transformers of various sizes.
+2.3. Small Vision Transformers
+Designing efficient CNN models [27,42] has been widely
+studied in recent years.
+With the emergence of Vision
+Transformer (ViT), there have been several works study-
+ing how to develop efficient vision Transformer, with the
+majority focus on introduing inductive biases into the archi-
+tectures [17,26,30,34,35].
+Different from these works that develop small vision
+Transformers by introducing sophisticated components into
+architectures, we demonstrate that a plain vision Trans-
+former [12] at a small scale can perform just as well, or
+even better. Our main insight is that the MIM pre-training
+can implicitly incorporate necessary inductive biases, and
+thus avoids the need of explicit architecture bias. Our plain
+3
+
+vision Transformer of tiny size achieves the state-of-the-art
+accuracy for both ImageNet-1K image classification and
+ADE20K semantic segmentation using similar model size
+and computation budget.
+3. TinyMIM
+We adopt a larger, MIM pre-trained model as the teacher,
+and a smaller ViT as the student. The objective of TinyMIM
+is to train the randomly initialized student by mimicking the
+target produced by the teacher in a knowledge distillation
+manner. After pre-training, the TinyMIM pre-trained model
+can be transferred to various downstream tasks. In this work,
+we adopt MAE [18] as the MIM model due to its popularity
+and simplicity.
+In this section, we first describe the factors that may affect
+TinyMIM pre-training: distillation target in Section 3.1.1;
+input in Section 3.1.2; target block in Section 3.1.3. Then we
+present a series of distillation losses for different distillation
+target in Section 3.1.3. At last, a sequential distillation strat-
+egy is introduced to facilitate the performance in Section 3.3.
+3.1. Factors
+3.1.1
+Distillation Target
+Block Feature and Output Feature. Given an input image
+x, we first divide it into N non-overlapping patches and use
+a linear projection layer to map N patches into patch em-
+beddings F0 ∈ RN×D, where D is the dimension of hidden
+features. Suppose we have a ViT containing L Transformer
+blocks. Each Transformer block takes the output Fi−1 of the
+last Transformer block as the input and generates the feature
+Fi of the current block, which can be formulated as:
+Fi = Transformer(Fi−1), i ∈ [1, L].
+(1)
+We term Fi as the block feature of the i-th Transformer
+block. In particular, we name the feature FL from the last
+Transformer block as the output feature.
+Attention Feature and FFN Feature. Each Transformer
+block is composed of a self-attention layer and a feed for-
+ward layer, which can be defined as:
+Hi = Attention(LN(Fi−1)),
+�Hi = Hi + Fi−1,
+�Hi = FFN(LN( �Hi)),
+F i = �Hi + �Hi,
+(2)
+where Attention(·), FFN(·) and LN(·) denotes self-
+attention layer, feed forward layer and layer norm, respec-
+tively. We term �Hi and �Hi as attention feature and FFN
+feature of the i-th Transformer block.
+Query/Key/Value Features. Each self-attention layer con-
+sists of M head networks, each of which maps input feature
+Fi−1 to query (Q), key (K) and value (V):
+Qm
+i = LN(Fi−1)W Q
+i ,
+Km
+i
+= LN(Fi−1)W K
+i ,
+V m
+i
+= LN(Fi−1)W V
+i ,
+(3)
+where Qi, Ki, Vi ∈ RN× D
+M represent the query, key and
+value of the m-th head network. The query/key/value fea-
+tures (Qi, Ki, Vi ∈ RN×D) are the concatenation of M
+Qm
+i /Km
+i /V m
+i , respectively.
+Relations. For the m-th head network from the i-th Trans-
+former block, we could calculate its Q-Q, K-K, V-V and
+Q-K relations (RQQ
+i,m, RKK
+i,m , RV V
+i,m, RQK
+i,m ∈ RN×N), which
+are implemented as the scaled product relation:
+RQQ
+i,m = Softmax
+�
+Qm
+i Qm
+i
+T
+�
+D/M
+�
+,
+RKK
+i,m = Softmax
+�
+Km
+i Km
+i
+T
+�
+D/M
+�
+,
+RV V
+i,m = Softmax
+�
+V m
+i V m
+i
+T
+�
+D/M
+�
+,
+RQK
+i,m = Softmax
+�
+Qm
+i Km
+i
+T
+�
+D/M
+�
+.
+(4)
+The Q-Q/K-K/V-V/Q-K relations (RQQ
+i
+, RKK
+i
+, RV V
+i
+,
+RQK
+i
+∈ RM×N×N) of the i-th Transformer block is the
+stack of M RQQ
+i,m/RKK
+i,m /RV V
+i,m/RQK
+i,m , respectively.
+3.1.2
+Input
+MIM models randomly mask a high proportion of image
+patches on an input image x, yielding a masked image �x
+for pre-training. We also investigate the input of TinyMIM
+when performing knowledge distillation— the input could
+be either a raw image x or a masked image �x.
+3.1.3
+Target Block
+Consider a situation where we tend to use an MAE pre-
+trained ViT-L (teacher) containing 24 blocks to distill a ViT-
+B (student) containing 12 blocks. In this scenario, the block
+number of the student does not match that of the teacher. We
+investigate which block of the teacher can provide the most
+appropriate target. The selected block is referred to as the
+target block.
+3.2. Knowledge Distillation as MIM Pre-training
+In Section 3.1.1, we describe a variety of distillation target
+candidates. In this section, we introduce different knowledge
+distillation losses for various distillation targets. Let x de-
+note an input image, ft and fs represent a teacher model and
+4
+
+…
+Teacher
+𝑉·𝑉𝑇
+𝑄·𝐾𝑇
+Raw Image
+#Head
+𝑄·𝐾𝑇
+…
+…
+𝑉·𝑉𝑇
+#Head
+𝑉·𝑉𝑇
+𝑄·𝐾𝑇
+#Head
+𝑄·𝐾𝑇
+…
+…
+𝑉·𝑉𝑇
+#Head
+Block-1
+Block-n
+Block-N
+…
+…
+Student
+Block-1
+Block-L (Adaptive Block) 
+Loss
+…
+: Forward
+: Backward
+Figure 3. The default knowledge distillation strategy of TinyMIM. The student (e.g. ViT-B) is optimized to mimic the relations generated by
+the intermediate block of a MIM pre-trained teacher (e.g. ViT-L) with raw image as input. We replace the last block of the student with an
+adaptive block to match teacher’s head number (no extra computational cost). After pre-training (knowledge distillation), the student model
+can be transferred to various downstream tasks.
+a student model, respectively. The objective of knowledge
+distillation is to transfer the knowledge from ft to fs by
+optimizing fs while freezing ft. In general, the training is
+supervised by the KL divergence, which is defined as:
+LKL(p, t) = tlog t
+p,
+(5)
+where t denotes the target generated by ft(x), and p is the
+prediction produced by fs(x).
+Class Token Distillation. We use ct and cs to denote class
+token feature of ft and fs, respectively. The loss of class
+token distillation is formulated as:
+L = LKL(cs, ct).
+(6)
+Feature Distillation. In general, the feature dimension of
+the teacher network and the student network are mismatched.
+To tackle this problem, we adopt an extra linear layer on the
+output of the student network to match the feature dimension
+of the teacher’s target. Let F t and F s denote the target
+feature and the prediction yielded by the student followed by
+a linear projection layer, respectively. We could formulate
+the loss of feature distillation as follows:
+L = L1(F s, Norm(F t)),
+(7)
+where Norm(·) is the whitening operation implemented by
+layer norm without affiliation, and L1 is the smooth L1 loss
+defined as:
+L1(y, ˆy) =
+�
+1
+2(ˆy − y)2/β,
+|ˆy − y| ≤ β
+(|ˆy − y| − 1
+2β),
+otherwise
+,
+(8)
+where β is set to 2.0.
+Relation Distillation. This is our default knowledge distilla-
+tion strategy as illustrated in Figure 3. For the sake of clarity,
+we use RQK
+t→m to denote the m-th head generated Q-K rela-
+tion target (see Eq 4) from the teacher network, and RQK
+s→m to
+represent the corresponding Q-K relation prediction from the
+student network. We define RV V
+t→m and RV V
+s→m in a similar
+way. The loss of relation distillation is formulated as:
+LQK = 1
+M
+M
+�
+m=1
+LKL(RQK
+s→m, RQK
+t→m),
+LV V = 1
+M
+M
+�
+m=1
+LKL(RV V
+s→m, RV V,S
+t→m ),
+L = LQK + LV V .
+(9)
+Head Alignment for Relation Distillation. In general, the
+head number of the student network is lower than that of the
+teacher network. For instance, ViT-L (teacher) contains 16
+heads per block while ViT-B (student) only contains 12 heads
+per block. Recall that the relation distillation loss (Eq. 9)
+is calculated head by head, thus we have to solve the head
+misalignment issue before performing relation distillation.
+To this end, we replace the last block of the student with an
+adaptive block, which keeps the original hidden dimension
+but adjusts the head number to the teacher. Concretely, given
+a teacher network with Mt heads per block, and a student
+network with Ms heads per block, a hidden dimension of
+Ds, and a head dimension of Ds/Ms, the adaptive block is
+designed to be a Transformer block with Mt heads per block,
+a hidden dimension of Ds and a head dimension of Ds/Mt.
+3.3. Sequential Distillation
+When training a small model like ViT-S, the teacher has
+two options: a pre-trained ViT-B and a pre-trained ViT-
+L. Intuitively, the pre-trained ViT-L is a good teacher due
+to its higher representation capability. However, there is
+5
+
+a huge capacity gap between ViT-L and ViT-S, resulting
+in poor distillation results. Following [8, 15], we adopt a
+sequential distillation strategy to improve pre-training. For
+instance, when pre-training a ViT-S, the teacher is selected
+as a TinyMIM pre-trained ViT-B, which has been trained by
+TinyMIM with ViT-L as the teacher.
+4. Experiments
+4.1. Implementation Details
+Pre-training.
+All models are pre-trained under a 100-
+epoch schedule on ImageNet-1K [41] training set.
+We
+use a batch size of 4096 and a learning rate of lr=1.5e-
+4×batchsize/256. We adopt a cosine decay schedule with
+a warm-up for 5 epochs. We adopt AdamW [33] optimizer
+with a weight decay of 0.05. We use random resized crop-
+ping random horizontal flipping, color jitter for student only.
+The input size is set to 224 × 224.
+Fine-tuning. We transfer TinyMIM pre-trained models to
+ImageNet [41] image classification and ADE20K [59] se-
+mantic segmentation. For ImageNet, we use AdamW op-
+timizer with weight decay of 0.05. For data augmentation,
+we follow the settings in MAE [18]. We fine-tune ViT-B
+for 100 epochs with a batch size of 1024, a learning rate of
+2e-3, and a drop path rate of 0.1. We fine-tune ViT-S and
+ViT-T for 200 epochs with a batch size of 2048, a learning
+rate of 5e-3, and a drop path rate of 0.1. For ADE20K, we
+follow the same setting in MAE and adopt UperNet [51]
+as our framework with a TinyMIM pre-trained backbone.
+The input image resolution is 512 × 512 for training and
+evaluating. We use mIoU as the evaluation metric.
+Besides, we evaluate the robustness of TinyMIM on var-
+ious out-of-domain ImageNet datasets [19–21] which are
+generated by applying different perturbations on ImageNet,
+e.g. natural adversarial examples (ImageNet-A), semantic
+shift (ImageNet-R), common image corruptions (ImageNet-
+C). We report top-1 accuracy on ImageNet-A/R and mCE
+error on ImageNet-C (lower is better).
+Default Setting. By default, we adopt relation distillation
+formulated in Eq. 9, head alignment, raw image as input, se-
+quential distillation and the 18-th block of MAE pre-trained
+ViT-L as the target block for TinyMIM-ViT-B pre-training.
+4.2. Main Results
+As shown in Table 3, we compare our TinyMIM with
+previous methods on ImageNet image classification and
+ADE20K semantic segmentation using different ViTs. In
+particular, TinyMIM pre-trained ViT-T achieves 75.8% top-
+1 accuracy, outperforming MAE baseline by +4.2.
+An
+enhanced model named TinyMIM⋆-T, which retains the
+plain architecture and computation budget of ViT-T, fur-
+ther achieves 79.6% top-1 accuracy. See appendix for the
+details of TinyMIM⋆-T. Moreover, TinyMIM pre-trained
+ViT-S achieves 83.0% top-1 accuracy, outperforming MAE
+baseline and previous best method CIM [13] by +2.4, +1.4,
+respectively. By transferring the knowledge of an MAE pre-
+trained ViT-L, TinyMIM pre-trained ViT-B achieves 85.0%
+top-1 accuracy on ImageNet-1K.
+As for semantic segmentation, TinyMIM pre-trained ViT-
+B surpasses MAE baseline and state-of-the-art CAE [4] by
++4.1 and +2.0, respectively. An intermediate fine-tuning on
+ImageNet-1K classification before ADE20K segmentation
+fine-tuning further boosts the performance.
+We also evaluate our models on out-of-domain datasets
+in Table 4. Our TinyMIM pretrained models are more robust
+than MAE pre-trained ones. Specifically, TinyMIM-ViT-B
+outperforms MAE-ViT-B by +6.4 and +4.6 on ImageNet-A
+and ImageNet-R, respectively, and lower the mCE by -5.1.
+4.3. Ablation Study
+Unless otherwise specified, all ablation studies are con-
+ducted on TinyMIM-ViT-B, with a teacher of being an MAE
+pre-trained ViT-L, relation distillation strategy, raw image as
+input, the 18-th block of ViT-L as the target block, under a
+100-epoch pre-training schedule. We report top-1 accuracy
+on ImageNet-1K.
+Class Token Distillation. For this distillation strategy, we
+study two variants: 1) class token distillation as formulated
+in Eq.6; 2) class token distillation with an extra MAE re-
+construction loss. The results are shown in Table 5. Both
+variants perform worse than MAE baseline, indicting that
+the class token is improper to be served as the distillation
+target since there is no explicit supervision applied on class
+token during teacher’s pre-training.
+Feature Distillation. As described in Section 3.1.1, there
+are four types of features can be served as the targets for
+feature distillation formulated in Eq. 7: output feature, FFN
+feature, attention feature and Q/K/V features. Table 6 com-
+pares the results of using different features as distillation
+targets. We also report the results of FFN feature and atten-
+tion feature before the residual connection (see Eq. 2). An
+interesting finding is that distilling FFN feature and attention
+feature after the residual connection significantly degrades
+the performance.
+Relation Distillation. Eq. 9 formulates our default relation
+distillation, which jointly distills Q-K relation and V-V re-
+lation (see Eq. 4). Here we study a variant by changing the
+target relations from Q-K/V-V to Q-K/K-K/V-V. We also
+investigate that whether to apply a Softmax operator on each
+relation. The results are shown in Table 7.
+Comparison of Different Distillation Strategies. In this
+study, all models are pre-trained under a 300-epoch schedule.
+We compare three distillation strategies on ImageNet image
+classification (Table 8) and ADE20K semantic segmentation
+(Table 9). For each strategy, we use the target that yields
+the best result. We also highlight the improvements over the
+6
+
+Method
+Pretraining
+Tokenizer/
+Tokenizer/Teacher
+Classification
+Segmentation
+Epochs
+Teacher
+Data
+Top-1 Acc (%)
+mIoU
+Tiny-size models (ViT-T/16)
+Scratch [44]
+300
+Label
+IN1K
+72.2
+38.0
+MAE† [18]
+1600
+Pixel
+IN1K
+71.6
+37.6
+MoCo [5]
+1600
+EMA
+IN1K
+73.3
+39.3
+TinyMIM (Ours)
+300
+TinyMIM-ViT-S
+IN1K
+75.8
+44.0/44.6‡
+TinyMIM⋆ (Ours)
+300
+TinyMIM-ViT-S
+IN1K
+79.6
+45.0‡
+Small-size models (ViT-S/16)
+Scratch [44]
+300
+Label
+IN1K
+79.9
+43.1
+MAE† [18]
+1600
+Pixel
+IN1K
+80.6
+42.8
+MoCo [5]
+1600
+EMA
+IN1K
+81.4
+43.9
+DINO [3]
+1600
+EMA
+IN1K
+81.5
+45.3
+CIM [13]
+1600
+Pixel
+IN1K
+81.6
+-
+TinyMIM (Ours)
+300
+TinyMIM-ViT-B
+IN1K
+83.0
+48.4/48.9‡
+Base-size models (ViT-B/16)
+Scratch [44]
+300
+Label
+IN1K
+81.2
+47.2
+BeiT [2]
+800
+DALL-E
+DALLE250M+IN22K+IN1K
+83.2
+45.6
+MAE [18]
+1600
+Pixel
+IN1K
+83.6
+48.1
+SIM [43]
+1600
+EMA
+IN1K
+83.8
+-
+CAE [4]
+1600
+DALL-E
+DALLE250M+IN22K+IN1K
+83.9
+50.2
+MaskFeat [48]
+1600
+HOG
+IN1K
+84.0
+-
+SdAE [7]
+300
+EMA
+IN1K
+84.1
+48.6
+data2vec [1]
+800
+EMA
+IN1K
+84.2
+-
+PeCo [11]
+300
+VQGAN
+IN1K
+84.1
+46.7
+PeCo [11]
+800
+VQGAN
+IN1K
+84.5
+48.5
+TinyMIM (Ours)
+300
+MAE-ViT-L
+IN1K
+85.0
+52.2/52.6‡
+Table 3. Fine-tuning results on ImageNet-1K and ADE20K. All models are pre-trained on ImageNet-1K. “Tokenizer/Teacher Data”: training
+data of teacher and tokenizer. †: reproduced result using official code. ⋆: the model is fine-tuned for 1000 epochs with DeiT-style [44]
+knowledge distillation. ‡: the model adopts an intermediate fine-tuning on ImageNet-1K classification before ADE20K segmentation
+fine-tuning.
+Method
+Model Size
+ImageNet ↑
+IN-Adversarial↑
+IN-Rendition↑
+IN-Corruption ↓
+DeiT [44]
+ViT-T
+72.2
+8.0
+32.7
+54.0
+MAE [18]
+71.8
+7.0
+36.5
+55.2
+TinyMIM
+75.8
+11.0
+39.8
+50.1
+DeiT [44]
+ViT-S
+79.9
+18.3
+42.3
+41.4
+MAE [18]
+80.6
+20.1
+45.6
+40.6
+TinyMIM
+83.0
+27.5
+48.8
+35.8
+DeiT [44]
+ViT-B
+81.2
+25.8
+45.4
+36.8
+MAE [18]
+83.6
+33.6
+50.0
+37.8
+TinyMIM
+85.0
+43.0
+54.6
+32.7
+Table 4. Robustness evaluation on out-of-domain datasets.
+MAE baseline.
+Target Block. As described in Section 3.1.3, we consider
+a situation where the block number of the student does not
+match that of the teacher. Here we use an MAE pre-trained
+ViT-L containing 24 blocks to distill a ViT-B containing
+12 blocks. Here we examine the effects of using the 12th,
+15th, 18th, 21th and 24th (last) blocks of the ViT-L as the
+target blocks. The comparison is shown in Table 10. We
+7
+
+Method
+Reconstruction Loss
+Top-1 Acc.
+MAE
+✓
+83.6
+TinyMIM w/ Cls
+80.6
+TinyMIM w/ Cls
+✓
+82.1
+Table 5. Study of class token distillation formulated in Eq.6.
+Feature
+Res. Connection
+Top-1 Acc.
+MAE
+83.6
+Output Feature
+83.7
+FFN Feature
+84.2
+FFN Feature
+✓
+81.8
+Attention Feature
+84.1
+Attention Feature
+✓
+81.3
+Q/K/V Features
+84.3
+Table 6. Study of feature distillation formulated in Eq.7. See
+Section 3.1.1 and Eq. 2 for the definitions of different features.
+Relation
+Softmax
+Top-1 Acc.
+MAE
+83.6
+Q-Q, K-K, V-V
+84.4
+Q-Q, K-K, V-V
+✓
+84.5
+Q-K, V-V
+84.4
+Q-K, V-V
+✓
+84.6
+Table 7. Study of relation distillation formulated in Eq. 9. See
+Section 3.1.1 and Eq. 4 for the definitions of different relations.
+experimentally find that using 18th block yields the best
+result.
+Sequential Distillation. In Section 3.3, we advocate to
+adopt a sequential distillation strategy to enable distillation
+from a larger model (e.g. ViT-L) to a smaller model (e.g.
+ViT-S). Table 11 compares the result of adopting different
+teachers with or without the sequential distillation. We have
+two conclusions: 1) using a larger teacher (MAE-ViT-L) to
+distill a smaller student (ViT-S) degrades the performance; 2)
+sequential distillation significantly boosts the performance
+of ViT-T (MAE-ViT-B→TinyMIM-ViT-S as the teacher and
+ViT-T as the student).
+Integrating MAE into TinyMIM. MAE is a simple but ef-
+fective self-supervised pre-training paradigm that trains a
+model by requiring it to predict masked inputs. In contrast,
+TinyMIM pre-trains smaller ViTs in a knowledge distilla-
+tion manner. Here we integrate MAE into our TinyMIM,
+yielding an integrated model. This model is optimized under
+two losses: knowledge distillation loss from TinyMIM, and
+Method
+Model Size
+Top-1 Acc.
+Supervised (DeiT)
+ViT-T
+72.2
+MAE
+71.6
+Class Token Distillation
+70.6
+Feature Distillation
+73.4
+Relation Distillation
+75.8 (+4.2)
+Supervised (DeiT)
+ViT-S
+79.9
+MAE
+80.6
+Class Token Distillation
+79.6
+Feature Distillation
+80.8
+Relation Distillation
+83.0 (+3.1)
+Supervised (DeiT)
+ViT-B
+81.2
+MAE
+83.6
+Class Token Distillation
+82.6
+Feature Distillation
+83.8
+Relation Distillation
+85.0 (+1.6)
+Table 8. Comparison of three distillation strategies on ImageNet-1K
+image classification. The models are pre-trained under a 300-epoch
+schedule.
+Method
+Model Size
+mIoU
+Supervised (DeiT)
+ViT-B
+47.2
+MAE
+48.1
+Class Token Distillation
+46.2
+Feature Distillation
+47.7
+Relation Distillation
+52.2 (+4.1)
+Table 9. Comparison of three distillation strategies on ADE20K
+semantic segmentation. The models are pre-trained under a 300-
+epoch schedule.
+Task
+12th
+15th
+18th
+21th
+24th
+Classification
+83.6
+84.1
+84.6
+84.8
+84.4
+Segmentation
+48.7
+49.8
+52.2
+50.6
+50.0
+Table 10. Study of target block on ImageNet-1K and ADE20K.
+Student
+Teacher
+Acc.
+ViT-S
+MAE-ViT-B
+82.3
+MAE-ViT-L
+82.1
+MAE-ViT-L → TinyMIM-ViT-B
+82.6
+ViT-T
+MAE-ViT-S
+74.1
+MAE-ViT-B
+74.4
+MAE-ViT-B → TinyMIM-ViT-S
+75.0
+Table 11. Study of sequential distillation.
+8
+
+Masked Image
+Reconstruction Loss
+Top-1 Acc.
+84.6
+✓
+83.9
+✓
+✓
+84.0
+Table 12. Comparison between the TinyMIM-ViT-B (the first row)
+and the integrated model (the third row). We also study the input
+of TinyMIM-ViT-B, which could be raw image (the first row) or
+masked image (the second row).
+DPR (Teacher)
+DPR (Student)
+Top-1 Acc.
+0.0
+0.0
+84.3
+0.0
+0.1
+84.6
+0.0
+0.2
+84.3
+0.0
+0.3
+84.1
+0.1
+0.1
+83.9
+Table 13. Ablation study of drop path rate (DPR) used in teacher
+and student.
+reconstruction loss from MAE. To enable MAE pre-training,
+we randomly mask 75% image patches, and feed the visi-
+ble patches into the network to initiate the pre-training of
+the integrated model. Table 12 shows the comparison be-
+tween TinyMIM-ViT-B and the integrated model. From the
+Table, we could draw a conclusion—integrating MAE into
+our TinyMIM does not improve the performance. In addi-
+tion, we also investigate the input of TinyMIM-ViT-B, which
+could be either raw image or masked image, as shown in
+Table 12—taking raw image as input yields better result.
+Drop Path. Drop path is one of the most critical techniques
+in training Transformers [44]. Using an appropriate drop
+path rate could significantly alleviate the over-fitting issue.
+However, MAE disables this technique in its implementation.
+Here we verify the effects of applying drop path to our
+TinyMIM. The results are shown in Table 13. For the student
+model, the optimal drop path rate is 0.1. For the teacher
+model, disabling drop path yields best result.
+5. Conclusion
+In this paper, we present TinyMIM, which is the first to
+successfully perform masked image modeling (MIM) pre-
+training for smaller ViT models. In stead of adopting a
+mask-and-predict pretext task, we pre-train a small ViT by
+mimicking the relations of a large ViT in a knowledge dis-
+tillation manner. The success of TinyMIM can be attributed
+to a comprehensive study of various factors that may affect
+TinyMIM pretraining including distillation target, distillation
+input and target block. With extensive experiments, we draw
+a series of conclusions. For instance, relation distillation is
+superior than feature distillation and class token distillation;
+taking raw image as input is optimal; a sequential distillation
+is necessary for training smaller ViTs; etc. With its simplic-
+ity and strong performance, we hope our approach can serve
+as a solid baseline for future research.
+References
+[1] Alexei Baevski, Wei-Ning Hsu, Qiantong Xu, Arun Babu,
+Jiatao Gu, and Michael Auli. Data2vec: A general framework
+for self-supervised learning in speech, vision and language.
+arXiv preprint arXiv:2202.03555, 2022. 3, 7
+[2] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. BEiT:
+BERT pre-training of image transformers. In International
+Conference on Learning Representations, 2022. 1, 2, 7
+[3] Mathilde Caron, Hugo Touvron, Ishan Misra, Herv´e J´egou,
+Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerg-
+ing properties in self-supervised vision transformers. arXiv
+preprint arXiv:2104.14294, 2021. 3, 7
+[4] Xiaokang Chen, Mingyu Ding, Xiaodi Wang, Ying Xin, Shen-
+tong Mo, Yunhao Wang, Shumin Han, Ping Luo, Gang Zeng,
+and Jingdong Wang. Context autoencoder for self-supervised
+representation learning. arXiv preprint arXiv:2202.03026,
+2022. 6, 7
+[5] Xinlei Chen, Saining Xie, and Kaiming He. An empirical
+study of training self-supervised vision transformers. ArXiv,
+abs/2104.02057, 2021. 7
+[6] Yinpeng Chen, Xiyang Dai, Dongdong Chen, Mengchen
+Liu, Xiaoyi Dong, Lu Yuan, and Zicheng Liu.
+Mobile-
+former: Bridging mobilenet and transformer. In Proceedings
+of the IEEE/CVF Conference on Computer Vision and Pattern
+Recognition, pages 5270–5279, 2022. 2
+[7] Yabo Chen, Yuchen Liu, Dongsheng Jiang, Xiaopeng Zhang,
+Wenrui Dai, Hongkai Xiong, and Qi Tian.
+Sdae: Self-
+distillated masked autoencoder. ArXiv, abs/2208.00449, 2022.
+7
+[8] Jang Hyun Cho and Bharath Hariharan. On the efficacy of
+knowledge distillation. In Proceedings of the IEEE/CVF
+international conference on computer vision, pages 4794–
+4802, 2019. 6
+[9] Navneet Dalal and Bill Triggs. Histograms of oriented gra-
+dients for human detection. In 2005 IEEE computer soci-
+ety conference on computer vision and pattern recognition
+(CVPR’05), volume 1, pages 886–893. Ieee, 2005. 2
+[10] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina
+Toutanova. BERT: pre-training of deep bidirectional trans-
+formers for language understanding. In Proceedings of the
+2019 Conference of the North American Chapter of the As-
+sociation for Computational Linguistics: Human Language
+Technologies, pages 4171–4186. Association for Computa-
+tional Linguistics, 2019. 2
+[11] Xiaoyi Dong, Jianmin Bao, Ting Zhang, Dongdong Chen,
+Weiming Zhang, Lu Yuan, Dong Chen, Fang Wen, and Neng-
+hai Yu. Peco: Perceptual codebook for bert pre-training of
+vision transformers. arXiv preprint arXiv:2111.12710, 2021.
+1, 2, 7
+[12] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov,
+Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner,
+9
+
+Mostafa Dehghani, Matthias Minderer, Georg Heigold, Syl-
+vain Gelly, et al. An image is worth 16x16 words: Transform-
+ers for image recognition at scale. preprint arXiv:2010.11929,
+2020. 1, 3
+[13] Yuxin Fang, Li Dong, Hangbo Bao, Xinggang Wang, and
+Furu Wei. Corrupted image modeling for self-supervised
+visual pre-training. arXiv preprint arXiv:2202.03382, 2022.
+6, 7
+[14] Zhiyuan Fang, Jianfeng Wang, Lijuan Wang, Lei Zhang,
+Yezhou Yang, and Zicheng Liu. Seed: Self-supervised distil-
+lation for visual representation. 2021. 3
+[15] Tommaso Furlanello, Zachary Lipton, Michael Tschannen,
+Laurent Itti, and Anima Anandkumar. Born again neural
+networks. In International Conference on Machine Learning,
+pages 1607–1616. PMLR, 2018. 6
+[16] Jianping Gou, Baosheng Yu, Stephen J. Maybank, and
+Dacheng Tao. Knowledge distillation: A survey. International
+Journal of Computer Vision, 2021. 2, 3
+[17] Benjamin Graham, Alaaeldin El-Nouby, Hugo Touvron,
+Pierre Stock, Armand Joulin, Herv´e J´egou, and Matthijs
+Douze. Levit: a vision transformer in convnet’s clothing
+for faster inference. In Proceedings of the IEEE/CVF inter-
+national conference on computer vision, pages 12259–12269,
+2021. 3
+[18] Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr
+Doll´ar, and Ross Girshick. Masked autoencoders are scalable
+vision learners. In CVPR, 2022. 1, 2, 4, 6, 7
+[19] Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kada-
+vath, Frank Wang, Evan Dorundo, Rahul Desai, Tyler Zhu,
+Samyak Parajuli, Mike Guo, Dawn Song, Jacob Steinhardt,
+and Justin Gilmer. The many faces of robustness: A critical
+analysis of out-of-distribution generalization. ICCV, 2021. 6
+[20] Dan Hendrycks and Thomas Dietterich. Benchmarking neural
+network robustness to common corruptions and perturbations.
+ICLR, 2019. 6
+[21] Dan Hendrycks, Kevin Zhao, Steven Basart, Jacob Steinhardt,
+and Dawn Song. Natural adversarial examples. CVPR, 2021.
+6
+[22] Byeongho Heo, Jeesoo Kim, Sangdoo Yun, Hyojin Park, No-
+jun Kwak, and Jin Young Choi. A comprehensive overhaul
+of feature distillation. In Proceedings of the IEEE/CVF Inter-
+national Conference on Computer Vision, pages 1921–1930,
+2019. 3
+[23] Byeongho Heo, Minsik Lee, Sangdoo Yun, and Jin Young
+Choi. Knowledge transfer via distillation of activation bound-
+aries formed by hidden neurons. In Proceedings of the AAAI
+Conference on Artificial Intelligence, volume 33, pages 3779–
+3787, 2019. 3
+[24] Geoffrey Hinton, Oriol Vinyals, Jeff Dean, et al. Distill-
+ing the knowledge in a neural network.
+arXiv preprint
+arXiv:1503.02531, 2(7), 2015. 2, 3
+[25] Zejiang Hou, Fei Sun, Yen-Kuang Chen, Yuan Xie, and S. Y.
+Kung. Milan: Masked image pretraining on language assisted
+representation. ArXiv, abs/2208.06049, 2022. 1, 3
+[26] Andrew Howard, Mark Sandler, Grace Chu, Liang-Chieh
+Chen, Bo Chen, Mingxing Tan, Weijun Wang, Yukun Zhu,
+Ruoming Pang, Vijay Vasudevan, et al. Searching for mo-
+bilenetv3. In Proceedings of the IEEE/CVF international
+conference on computer vision, pages 1314–1324, 2019. 2, 3,
+12
+[27] Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry
+Kalenichenko, Weijun Wang, Tobias Weyand, Marco An-
+dreetto, and Hartwig Adam. Mobilenets: Efficient convolu-
+tional neural networks for mobile vision applications. arXiv
+preprint arXiv:1704.04861, 2017. 3
+[28] Jangho Kim, SeongUk Park, and Nojun Kwak. Paraphrasing
+complex network: Network compression via factor transfer.
+Advances in neural information processing systems, 31, 2018.
+3
+[29] Seung Hyun Lee, Dae Ha Kim, and Byung Cheol Song. Self-
+supervised knowledge distillation using singular value de-
+composition. In Proceedings of the European Conference on
+Computer Vision (ECCV), pages 335–350, 2018. 3
+[30] Yanyu Li, Geng Yuan, Yang Wen, Eric Hu, Georgios Evan-
+gelidis, Sergey Tulyakov, Yanzhi Wang, and Jian Ren. Effi-
+cientformer: Vision transformers at mobilenet speed. arXiv
+preprint arXiv:2206.01191, 2022. 3
+[31] Ze Liu, Han Hu, Yutong Lin, Zhuliang Yao, Zhenda Xie,
+Yixuan Wei, Jia Ning, Yue Cao, Zheng Zhang, Li Dong,
+Furu Wei, and Baining Guo. Swin transformer v2: Scaling
+up capacity and resolution. In International Conference on
+Computer Vision and Pattern Recognition (CVPR), 2022. 3
+[32] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng
+Zhang, Stephen Lin, and Baining Guo. Swin Transformer:
+Hierarchical vision transformer using shifted windows. arXiv
+preprint arXiv:2103.14030, 2021. 1
+[33] Ilya Loshchilov and Frank Hutter. Decoupled weight de-
+cay regularization. In International Conference on Learning
+Representations, 2019. 6
+[34] Sachin Mehta and Mohammad Rastegari. Mobilevit: Light-
+weight, general-purpose, and mobile-friendly vision trans-
+former. In International Conference on Learning Representa-
+tions, 2021. 1, 2, 3
+[35] Junting Pan, Adrian Bulat, Fuwen Tan, Xiatian Zhu, Lukasz
+Dudziak, Hongsheng Li, Georgios Tzimiropoulos, and Brais
+Martinez. Edgevits: Competing light-weight cnns on mobile
+devices with vision transformers. In European Conference on
+Computer Vision, pages 294–311. Springer, 2022. 1, 2, 3
+[36] Zhiliang Peng, Li Dong, Hangbo Bao, Qixiang Ye, and Furu
+Wei. BEiT v2: Masked image modeling with vector-quantized
+visual tokenizers. arXiv preprint arXiv:2208.06366, 2022. 1,
+3
+[37] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya
+Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry,
+Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning
+transferable visual models from natural language supervision.
+In ICML, pages 8748–8763. PMLR, 2021. 3
+[38] A. Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea
+Voss, Alec Radford, Mark Chen, and Ilya Sutskever. Zero-
+shot text-to-image generation. ArXiv, abs/2102.12092, 2021.
+2
+[39] Sucheng Ren, Zhengqi Gao, Tianyu Hua, Zihui Xue, Yong-
+long Tian, Shengfeng He, and Hang Zhao. Co-advise: Cross
+inductive bias distillation. In Proceedings of the IEEE/CVF
+Conference on Computer Vision and Pattern Recognition
+(CVPR), pages 16773–16782, June 2022. 1, 3
+10
+
+[40] Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou,
+Antoine Chassang, Carlo Gatta, and Yoshua Bengio. Fitnets:
+Hints for thin deep nets. arXiv preprint arXiv:1412.6550,
+2014. 3
+[41] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, San-
+jeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy,
+Aditya Khosla, Michael Bernstein, Alexander C Berg, and Li
+Fei-Fei. Imagenet large scale visual recognition challenge.
+IJCV, 2015. 6
+[42] Mingxing Tan and Quoc Le. Efficientnet: Rethinking model
+scaling for convolutional neural networks. In International
+conference on machine learning, pages 6105–6114. PMLR,
+2019. 3
+[43] Chenxin Tao, Xizhou Zhu, Gao Huang, Yu Qiao, Xiaogang
+Wang, and Jifeng Dai. Siamese image modeling for self-
+supervised vision representation learning. arXiv preprint
+arXiv:2206.01204, 2022. 7
+[44] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco
+Massa, Alexandre Sablayrolles, and Herv´e J´egou. Training
+data-efficient image transformers & distillation through atten-
+tion. preprint arXiv:2012.12877, 2020. 1, 3, 7, 9, 12
+[45] Shakti N Wadekar and Abhishek Chaurasia. Mobilevitv3:
+Mobile-friendly vision transformer with simple and effective
+fusion of local, global and input features. arXiv preprint
+arXiv:2209.15159, 2022. 1, 2
+[46] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao
+Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pyra-
+mid vision transformer: A versatile backbone for dense predic-
+tion without convolutions. In Proceedings of the IEEE/CVF
+International Conference on Computer Vision, pages 568–
+578, 2021. 1
+[47] Xiaojie Wang, Rui Zhang, Yu Sun, and Jianzhong Qi. Kdgan:
+Knowledge distillation with generative adversarial networks.
+Advances in neural information processing systems, 31, 2018.
+3
+[48] Chen Wei, Haoqi Fan, Saining Xie, Chao-Yuan Wu, Alan
+Yuille, and Christoph Feichtenhofer. Masked feature predic-
+tion for self-supervised visual pre-training. arXiv preprint
+arXiv:2112.09133, 2021. 1, 2, 7
+[49] Yixuan Wei, Han Hu, Zhenda Xie, Zheng Zhang, Yue Cao,
+Jianmin Bao, Dong Chen, and Baining Guo. Contrastive
+learning rivals masked image modeling in fine-tuning via
+feature distillation. arXiv preprint arXiv:2205.14141, 2022.
+1
+[50] Yixuan Wei, Han Hu, Zhenda Xie, Zheng Zhang, Yue Cao,
+Jianmin Bao, Dong Chen, and Baining Guo. Contrastive
+learning rivals masked image modeling in fine-tuning via
+feature distillation. arXiv preprint arXiv:2205.14141, 2022.
+3
+[51] Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, and
+Jian Sun. Unified perceptual parsing for scene understanding.
+In ECCV, 2018. 6
+[52] Zhenda Xie, Zigang Geng, Jingcheng Hu, Zheng Zhang, Han
+Hu, and Yue Cao. Revealing the dark secrets of masked image
+modeling. arXiv preprint arXiv:2205.13543, 2022. 1
+[53] Zhenda Xie, Zheng Zhang, Yue Cao, Yutong Lin, Jianmin
+Bao, Zhuliang Yao, Qi Dai, and Han Hu. Simmim: A simple
+framework for masked image modeling. In Proceedings of
+the IEEE/CVF Conference on Computer Vision and Pattern
+Recognition, pages 9653–9663, 2022. 1, 2, 3
+[54] Zhenda Xie, Zheng Zhang, Yue Cao, Yutong Lin, Yixuan
+Wei, Qi Dai, and Han Hu. On data scaling in masked image
+modeling. arXiv preprint arXiv:2206.04664, 2022. 1
+[55] Zihui Xue, Sucheng Ren, Zhengqi Gao, and Hang Zhao.
+Multimodal knowledge expansion. In Proceedings of the
+IEEE/CVF International Conference on Computer Vision,
+pages 854–863, 2021. 3
+[56] Junho Yim, Donggyu Joo, Jihoon Bae, and Junmo Kim. A
+gift from knowledge distillation: Fast optimization, network
+minimization and transfer learning. In Proceedings of the
+IEEE conference on computer vision and pattern recognition,
+pages 4133–4141, 2017. 3
+[57] Shan You, Chang Xu, Chao Xu, and Dacheng Tao. Learn-
+ing from multiple teacher networks. In Proceedings of the
+23rd ACM SIGKDD International Conference on Knowledge
+Discovery and Data Mining, pages 1285–1294, 2017. 3
+[58] Shan You, Chang Xu, Chao Xu, and Dacheng Tao. Learning
+with single-teacher multi-student. In Proceedings of the AAAI
+Conference on Artificial Intelligence, volume 32, 2018. 3
+[59] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler,
+Adela Barriuso, and Antonio Torralba. Semantic understand-
+ing of scenes through the ADE20K dataset. Int. J. Comput.
+Vis., 127(3):302–321, 2019. 6
+[60] Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang
+Xie, Alan Yuille, and Tao Kong. ibot: Image bert pre-training
+with online tokenizer. arXiv preprint arXiv:2111.07832, 2021.
+1, 3
+11
+
+A. Hyper-parameters
+Hyper-parameters of ImageNet-1K Pre-training. See Ta-
+ble 14.
+Hyper-parameters of ImageNet-1K Image Classification
+Fine-tuning. See Table 15. TinyMIM⋆-T retains the plain
+architecture and computation budget of ViT-T. We fine-tune
+TinyMIM⋆ for 1000 epochs with DeiT-style [44] knowledge
+distillation on ImageNet-1K. Following MobileNetV3 [26],
+an extra fully connected layer is placed before the classifi-
+cation layer to increase the feature dimension from 192 to
+1280. The head number is set to 12 instead of the default 3.
+Hyper-parameters for ADE20K Semantic Segmentation
+Fine-tuning. See Table 16.
+Hyperparameter
+ViT-T
+ViT-S
+ViT-B
+Layers
+12
+Hidden size
+192
+384
+768
+FFN inner hidden size
+768
+1536
+3072
+Attention heads
+3
+6
+12
+Patch size
+16 × 16
+Pre-training epochs
+100/300
+Batch size
+4096
+Adam ϵ
+1e-8
+Adam β
+(0.9, 0.999)
+Peak learning rate
+2.4e-3
+Minimal learning rate
+1e-5
+Learning rate schedule
+Cosine
+Warmup epochs
+5/15
+Stochastic depth
+0.1
+Dropout
+�
+Weight decay
+0.05
+Data augment
+RandomResizeAndCrop
+Input resolution
+224 × 224
+Color jitter (student only)
+0.4
+Table 14. Hyper-parameters of ImageNet-1K Pre-training.
+Hyperparameter
+ViT-T
+ViT-S
+ViT-B
+Peak learning rate
+5e-3
+5e-3
+2e-3
+Fine-tuning epochs
+200
+200
+100
+Warmup epochs
+5
+Layer-wise learning rate decay
+0.65
+0.65
+0.65/0.6∗
+Batch size
+2048
+2048
+1024
+Adam ϵ
+1e-8
+Adam β
+(0.9, 0.999)
+Minimal learning rate
+1e-6
+Learning rate schedule
+Cosine
+Stochastic depth
+0.1
+Weight decay
+0.05
+Label smoothing ε
+0.1
+Dropout
+�
+Gradient clipping
+�
+Erasing
+0.25
+Input resolution
+224 × 224
+Rand augment
+9/0.5
+Mixup
+0.8
+Cutmix
+1.0
+Table 15. Hyper-parameters of ImageNet-1K image classification
+fine-tuning. ∗ indicates that we use 0.65 and 0.6 for 100-epoch and
+300-epoch pre-trained models, respectively.
+Hyperparameter
+ViT-S
+ViT-B
+Input resolution
+512 × 512
+Peak learning rate
+1e-4
+Fine-tuning steps
+160K
+Batch size
+16
+Adam ϵ
+1e-8
+Adam β
+(0.9, 0.999)
+Layer-wise learning rate decay
+{0.65, 0.75, 0.8}
+Minimal learning rate
+0
+Learning rate schedule
+Linear
+Warmup steps
+1500
+Dropout
+�
+Stochastic depth
+0.1
+Weight decay
+0.05
+Table 16. Hyper-parameters of ADE20K semantic segmentation
+fine-tuning.
+12
+
diff --git a/M9AzT4oBgHgl3EQfWPwO/content/tmp_files/load_file.txt b/M9AzT4oBgHgl3EQfWPwO/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,874 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf,len=873
+page_content='TinyMIM: An Empirical Study of Distilling MIM Pre-trained Models  Sucheng Ren  Fangyun Wei*  Zheng Zhang  Han Hu  Microsoft Research Asia  Abstract  Masked image modeling (MIM) performs strongly in pre-  training large vision Transformers (ViTs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' However, small  models that are critical for real-world applications can-  not or only marginally benefit from this pre-training ap-  proach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In this paper, we explore distillation techniques to  transfer the success of large MIM-based pre-trained mod-  els to smaller ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We systematically study different op-  tions in the distillation framework, including distilling tar-  gets, losses, input, network regularization, sequential dis-  tillation, etc, revealing that: 1) Distilling token relations  is more effective than CLS token- and feature-based distil-  lation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2) An intermediate layer of the teacher network as  target perform better than that using the last layer when  the depth of the student mismatches that of the teacher;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3) Weak regularization is preferred;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' With these find-  ings, we achieve significant fine-tuning accuracy improve-  ments over the scratch MIM pre-training on ImageNet-1K  classification, using all the ViT-Tiny, ViT-Small, and ViT-  base models, with +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2%/+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4%/+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4% gains, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Our TinyMIM model of base size achieves 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2 mIoU in  AE20K semantic segmentation, which is +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1 higher than  the MAE baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Our TinyMIM model of tiny size achieves  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6% top-1 accuracy on ImageNet-1K image classifica-  tion, which sets a new record for small vision models of  the same size and computation budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' This strong perfor-  mance suggests an alternative way for developing small  vision Transformer models, that is, by exploring better train-  ing methods rather than introducing inductive biases into  architectures as in most previous works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Code is available  at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='com/OliverRensu/TinyMIM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Introduction  Masked image modeling (MIM), which masks a large  portion of the image area and trains a network to recover  the original signals for the masked area, has proven to be a  very effective self-supervised method for pre-training vision  Transformers [2,12,18,53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Thanks to its strong fine-tuning  performance, MIM has now been a main-stream pre-training  Corresponding author: fawe@microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  ViT-T  ViT-S  ViT-B  70  74  78  82  86  Scratch  MAE  TinyMIM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Comparison among TinyMIM (ours), MAE [18] and  training from scratch by using ViT-T, -S and -B on ImageNet-1K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  We report top-1 accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We adopt DeiT [44] when training from  scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For the first time, we successfully perform masked image  modeling pre-training for smaller ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Model  Param.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Flops  Top-1  mIoU  (M)  (G)  (%)  DeiT-T [44]  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  PVT-T [46]  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  CiT-T [39]  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  Swin [32]  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  EdgeViT-XS [35]  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  MobileViTv1-S [34]  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  MobileViTv3-S [45]  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  TinyMIM⋆-T (Ours)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Comparison with state-of-the-art tiny Transformers with  architecture variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The parameters indicate the backbone pa-  rameter excluding the parameters of the last classification layer  in classification or the decoder in segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We report top-1  accuracy on ImageNet-1K classification and mIoU on ADE20K  segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  method for vision Transformers, and numerous follow-ups  have been carried out in this research line, such as study-  ing how to set decoding architectures [25], reconstruction  targets [11,36,48,60], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=', as well as revealing its proper-  ties [49,52,54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='01296v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='CV]  3 Jan 2023  Method  ViT-T  ViT-S  ViT-B  ViT-L  Scratch  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  MAE  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  Gap  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Comparison between MAE pre-trained ViTs and ViTs  trained from scratch by using ViT-T, -S, -B and -L on ImageNet-  1K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We adopt DeiT when training from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We report top-1  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' As model size shrinks, the superiority of MAE gradually  vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' MAE even hurts the performance of ViT-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  However, as shown in Table 2, MIM pre-training [18]  mainly effects for relatively large models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' When the model  size is as small as ViT-Tiny (5 million parameters), which  is critical for real-world applications, MIM pre-training can  even hurt the fine-tuning accuracy on ImageNet-1K classifi-  cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In fact, the accuracy drops by -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6 compared to the  counterpart trained from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' This raises a question: can  small models also benefit from MIM pre-training, and how  can this be achieved?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  In addition, the existing study on small vision Transform-  ers mainly focus on introducing certain inductive bias into  architecture design [6,26,34,35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The additional architec-  tural inductive biases facilitate optimization yet limit the  expressive capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' It’s natural to ask whether we can boost  plain small vision Transformers to perform just as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  In this work, we present TinyMIM, which answers the  above questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Instead of directly training small ViT mod-  els using a MIM pretext task, TinyMIM uses distillation  technology [24] to transfer the knowledge of larger MIM  pre-trained models to smaller ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Distillation endows the  nice properties of larger MIM pre-trained models to smaller  ones while avoiding solving a “too” difficult MIM task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Not-  ing that knowledge distillation has been well developed,  especially for supervised models [16], our main work is to  systematically study for the first time the effects of different  design options in a distillation framework when using MIM  pre-trained models as teachers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Specifically, we consider dis-  tillation targets, data augmentation, network regularization,  auxiliary losses, macro distillation strategy, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=', and draw  several useful findings:  Distillation targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' There are two main findings re-  lated to distillation targets: 1) Distilling token relations  is more effective than distilling the CLS token and fea-  ture maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2) Using intermediate layers as the target  may perform better than using the last layer, and the  optimal target layer for different down-stream tasks,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=', classification and segmentation, can be different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Data and network regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Weak augmentation  and regularization is preferred: 1) The performance of  using a masked image is worse than using the original  image;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2) Relatively small drop path rate (0 for teacher  and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1 for student) performs best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  auxiliary losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We find that an auxiliary MIM loss  does not improve fine-tuning accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Macro distillation strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We find that using a se-  quential distillation strategy, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=', “ViT-B → ViT-S →  ViT-T”, performs better than that distilling directly from  ViT-B to ViT-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  By selecting the best framework options, we achieve sig-  nificant fine-tuning accuracy improvements over the direct  MIM pre-training on ImageNet-1K classification, using ViT  models of different sizes, as shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Specifi-  cally, the gains of TinyMIM on the ViT-Tiny, ViT-Small, and  ViT-base models are +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2%/+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4%/+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  In particular, our TinyMIM⋆-T model with knowledge  distillation during finetune-tuning achieves a top-1 accuracy  of 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6% on ImageNet-1K classification (see Table 1), which  performs better than all previous works that develop small  vision Transformer models by introducing architectural in-  ductive biases or smaller feature resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' It sets a new  accuracy record using similar model size and computation  budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' On ADE20K semantic segmentation, TinyMIM-T  achieves 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0 mIoU, which is +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9 higher than the second  best method, MobileViTv3-S [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The strong fine-tuning  accuracy by TinyMIM⋆-T suggests an alternative way for  developing small vision Transformer models, that is, by  exploring better training methods rather than introducing  inductive biases into architectures as most previous works  have done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Related Works  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Masked Image Modeling  Masked Language Modeling (MLM) [10] for self-  supervised Transformer pre-training has achieved incredible  success in natural language processing (NLP) field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Inspired  by the same idea of masking and reconstruction, BEiT [2]  is the pioneer to bring such success to computer vision filed  by encoding masked images and predicting masked tokens  generated by DALL-E [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' SimMIM [53] and MAE [18]  find that reconstructing RGB pixels results in favorable rep-  resentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' MAE adopts an asymmetric encoder-decoder  architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The encoder only encodes the visible tokens  and drops a high portion of masked tokens to reduce the com-  putation burden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' A lightweight decoder then produces recon-  structed patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Different from tokens in natural language  processing that have rich semantics, pixels in computer vi-  sion are low-level information, therefore, a lot of recent  works aim at looking for better supervisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' MaskFeat [48]  takes local gradient features produced by the manually-  crafted HOG descriptor [9] as supervisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' PeCo [11] trains  2  Masked Image  Raw Image  Factors  Input  Target  Feature  Relation  𝑄·𝑄𝑇  𝐾·𝐾𝑇  𝑉·𝑉𝑇  𝑄·𝐾𝑇  Head Number  w/ or w/o Softmax  Output Feature  Block Feature  QKV Features  Attention Feature  FFN Feature  Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Connection of FFN  Block  Last  Intermediate  …  …  Transformer Block-N  Output Feature  Multi-Head  Attention  Add & Norm  FFN  Add & Norm  Attention Feature  FFN Feature  Block Feature  Raw Image  Masked Image  Feature of Last Block  𝑄·𝑄𝑇  𝐾·𝐾𝑇  𝑉·𝑉𝑇  𝑄·𝐾𝑇  𝑄  𝐾  𝑉  Softmax  Transformer Block-n  Transformer Block-1  Teacher  (Highlight  by Blue)  Relations  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We comprehensively study a variety of factors (highlighted by Royal Blue) that may affect TinyMIM pre-training including input,  distillation target (feature or relation) and target block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  a new tokenizer by enforcing perceptual similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' iBot [60]  and data2vec [1] take exponential moving average (EMA)  updated models as tokenizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' MILAN [25] adopts a pre-  trained CLIP as the teacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Similarly, BeiTv2 [36] also uses  CLIP [37] for tokenizer training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Different from these works  that use various tokenizers/teachers, we adopt a masked im-  age modeling pre-trained model as our teacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  The MIM pre-training performs very well on relatively  large models from base size to giant size [31,53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' However,  it will hurt the fine-tuning when the model is as small as  tiny size, probably because the limited capthe MIM task is  “too” difficult for small model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' This paper explores how to  make small vision Transformer models also benefit from  MIM training, through a systematic study of the distillation  technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Knowledge Distillation  Knowledge distillation is a classical method to transfer  the knowledge from cumbersome models to a small one, pi-  oneered by [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The original knowledge distillation frame-  work adopts the annealed classification logits of the teacher  as the distilling target for the student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Since then, extensive  variants have been carried out to improve the distilling ef-  fectiveness [16], including changing the distilling targets as  intermediate features [22,23,28,40] and relations [29,56],  data augmentations of teacher and students [39, 50], regu-  larization [50], distilling strategies [47, 55, 57, 58] and so  on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  While almost all studies are made for CNN architec-  tures under supervised settings, recently, there have been  a few works performing distilling technologies for vision  Transformers [44,50] and contrastive learning based meth-  ods [14, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In DeiT [44], the teacher is set as a CNN  architecture so as to transfer the inductive bias involved in  CNNs to vision Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' It also propose to use hard  distillation which uses hard pseudo class labels of the teacher  network as the distilling targets, which performs better than  the naive knowledge distillation [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In [14], a distillation  method regarding the similarities between instances is ap-  plied to transfer the power of contrastive pre-trained large  CNN models to small CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In [50], a method based on  feature map distillation is proposed to generally improve  vision transformers by different pre-training approaches in-  cluding image classification, instance contrastive based self-  sueprvised learning [3] and CLIP pre-training [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' However,  it shows no gains for MIM pre-trained models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  This paper for the first time studies the distillation frame-  work for MIM pre-trained vision Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Through  a systematic study, it draws several useful findings and the  best options, under which, significant gains are achieved for  vision Transformers of various sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Small Vision Transformers  Designing efficient CNN models [27,42] has been widely  studied in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  With the emergence of Vision  Transformer (ViT), there have been several works study-  ing how to develop efficient vision Transformer, with the  majority focus on introduing inductive biases into the archi-  tectures [17,26,30,34,35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Different from these works that develop small vision  Transformers by introducing sophisticated components into  architectures, we demonstrate that a plain vision Trans-  former [12] at a small scale can perform just as well, or  even better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Our main insight is that the MIM pre-training  can implicitly incorporate necessary inductive biases, and  thus avoids the need of explicit architecture bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Our plain  3  vision Transformer of tiny size achieves the state-of-the-art  accuracy for both ImageNet-1K image classification and  ADE20K semantic segmentation using similar model size  and computation budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' TinyMIM  We adopt a larger, MIM pre-trained model as the teacher,  and a smaller ViT as the student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The objective of TinyMIM  is to train the randomly initialized student by mimicking the  target produced by the teacher in a knowledge distillation  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' After pre-training, the TinyMIM pre-trained model  can be transferred to various downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In this work,  we adopt MAE [18] as the MIM model due to its popularity  and simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  In this section, we first describe the factors that may affect  TinyMIM pre-training: distillation target in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  input in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' target block in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Then we  present a series of distillation losses for different distillation  target in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' At last, a sequential distillation strat-  egy is introduced to facilitate the performance in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Factors  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  Distillation Target  Block Feature and Output Feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Given an input image  x, we first divide it into N non-overlapping patches and use  a linear projection layer to map N patches into patch em-  beddings F0 ∈ RN×D, where D is the dimension of hidden  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Suppose we have a ViT containing L Transformer  blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Each Transformer block takes the output Fi−1 of the  last Transformer block as the input and generates the feature  Fi of the current block, which can be formulated as:  Fi = Transformer(Fi−1), i ∈ [1, L].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  (1)  We term Fi as the block feature of the i-th Transformer  block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In particular, we name the feature FL from the last  Transformer block as the output feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Attention Feature and FFN Feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Each Transformer  block is composed of a self-attention layer and a feed for-  ward layer, which can be defined as:  Hi = Attention(LN(Fi−1)),  �Hi = Hi + Fi−1,  �Hi = FFN(LN( �Hi)),  F i = �Hi + �Hi,  (2)  where Attention(·), FFN(·) and LN(·) denotes self-  attention layer, feed forward layer and layer norm, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We term �Hi and �Hi as attention feature and FFN  feature of the i-th Transformer block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Query/Key/Value Features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Each self-attention layer con-  sists of M head networks, each of which maps input feature  Fi−1 to query (Q), key (K) and value (V):  Qm  i = LN(Fi−1)W Q  i ,  Km  i  = LN(Fi−1)W K  i ,  V m  i  = LN(Fi−1)W V  i ,  (3)  where Qi, Ki, Vi ∈ RN× D  M represent the query, key and  value of the m-th head network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The query/key/value fea-  tures (Qi, Ki, Vi ∈ RN×D) are the concatenation of M  Qm  i /Km  i /V m  i , respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For the m-th head network from the i-th Trans-  former block, we could calculate its Q-Q, K-K, V-V and  Q-K relations (RQQ  i,m, RKK  i,m , RV V  i,m, RQK  i,m ∈ RN×N), which  are implemented as the scaled product relation:  RQQ  i,m = Softmax  �  Qm  i Qm  i  T  �  D/M  �  ,  RKK  i,m = Softmax  �  Km  i Km  i  T  �  D/M  �  ,  RV V  i,m = Softmax  �  V m  i V m  i  T  �  D/M  �  ,  RQK  i,m = Softmax  �  Qm  i Km  i  T  �  D/M  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  (4)  The Q-Q/K-K/V-V/Q-K relations (RQQ  i  , RKK  i  , RV V  i  ,  RQK  i  ∈ RM×N×N) of the i-th Transformer block is the  stack of M RQQ  i,m/RKK  i,m /RV V  i,m/RQK  i,m , respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  Input  MIM models randomly mask a high proportion of image  patches on an input image x, yielding a masked image �x  for pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We also investigate the input of TinyMIM  when performing knowledge distillation— the input could  be either a raw image x or a masked image �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  Target Block  Consider a situation where we tend to use an MAE pre-  trained ViT-L (teacher) containing 24 blocks to distill a ViT-  B (student) containing 12 blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In this scenario, the block  number of the student does not match that of the teacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We  investigate which block of the teacher can provide the most  appropriate target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The selected block is referred to as the  target block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Knowledge Distillation as MIM Pre-training  In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1, we describe a variety of distillation target  candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In this section, we introduce different knowledge  distillation losses for various distillation targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Let x de-  note an input image, ft and fs represent a teacher model and  4  …  Teacher  𝑉·𝑉𝑇  𝑄·𝐾𝑇  Raw Image  #Head  𝑄·𝐾𝑇  …  …  𝑉·𝑉𝑇  #Head  𝑉·𝑉𝑇  𝑄·𝐾𝑇  #Head  𝑄·𝐾𝑇  …  …  𝑉·𝑉𝑇  #Head  Block-1  Block-n  Block-N  …  …  Student  Block-1  Block-L (Adaptive Block)  Loss  …  : Forward  : Backward  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The default knowledge distillation strategy of TinyMIM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The student (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ViT-B) is optimized to mimic the relations generated by  the intermediate block of a MIM pre-trained teacher (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ViT-L) with raw image as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We replace the last block of the student with an  adaptive block to match teacher’s head number (no extra computational cost).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' After pre-training (knowledge distillation), the student model  can be transferred to various downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  a student model, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The objective of knowledge  distillation is to transfer the knowledge from ft to fs by  optimizing fs while freezing ft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In general, the training is  supervised by the KL divergence, which is defined as:  LKL(p, t) = tlog t  p,  (5)  where t denotes the target generated by ft(x), and p is the  prediction produced by fs(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Class Token Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We use ct and cs to denote class  token feature of ft and fs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The loss of class  token distillation is formulated as:  L = LKL(cs, ct).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  (6)  Feature Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In general, the feature dimension of  the teacher network and the student network are mismatched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  To tackle this problem, we adopt an extra linear layer on the  output of the student network to match the feature dimension  of the teacher’s target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Let F t and F s denote the target  feature and the prediction yielded by the student followed by  a linear projection layer, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We could formulate  the loss of feature distillation as follows:  L = L1(F s, Norm(F t)),  (7)  where Norm(·) is the whitening operation implemented by  layer norm without affiliation, and L1 is the smooth L1 loss  defined as:  L1(y, ˆy) =  �  1  2(ˆy − y)2/β,  |ˆy − y| ≤ β  (|ˆy − y| − 1  2β),  otherwise  ,  (8)  where β is set to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Relation Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' This is our default knowledge distilla-  tion strategy as illustrated in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For the sake of clarity,  we use RQK  t→m to denote the m-th head generated Q-K rela-  tion target (see Eq 4) from the teacher network, and RQK  s→m to  represent the corresponding Q-K relation prediction from the  student network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We define RV V  t→m and RV V  s→m in a similar  way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The loss of relation distillation is formulated as:  LQK = 1  M  M  �  m=1  LKL(RQK  s→m, RQK  t→m),  LV V = 1  M  M  �  m=1  LKL(RV V  s→m, RV V,S  t→m ),  L = LQK + LV V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  (9)  Head Alignment for Relation Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In general, the  head number of the student network is lower than that of the  teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For instance, ViT-L (teacher) contains 16  heads per block while ViT-B (student) only contains 12 heads  per block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Recall that the relation distillation loss (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 9)  is calculated head by head, thus we have to solve the head  misalignment issue before performing relation distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  To this end, we replace the last block of the student with an  adaptive block, which keeps the original hidden dimension  but adjusts the head number to the teacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Concretely, given  a teacher network with Mt heads per block, and a student  network with Ms heads per block, a hidden dimension of  Ds, and a head dimension of Ds/Ms, the adaptive block is  designed to be a Transformer block with Mt heads per block,  a hidden dimension of Ds and a head dimension of Ds/Mt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Sequential Distillation  When training a small model like ViT-S, the teacher has  two options: a pre-trained ViT-B and a pre-trained ViT-  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Intuitively, the pre-trained ViT-L is a good teacher due  to its higher representation capability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' However, there is  5  a huge capacity gap between ViT-L and ViT-S, resulting  in poor distillation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Following [8, 15], we adopt a  sequential distillation strategy to improve pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For  instance, when pre-training a ViT-S, the teacher is selected  as a TinyMIM pre-trained ViT-B, which has been trained by  TinyMIM with ViT-L as the teacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Experiments  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Implementation Details  Pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  All models are pre-trained under a 100-  epoch schedule on ImageNet-1K [41] training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  We  use a batch size of 4096 and a learning rate of lr=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5e-  4×batchsize/256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We adopt a cosine decay schedule with  a warm-up for 5 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We adopt AdamW [33] optimizer  with a weight decay of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We use random resized crop-  ping random horizontal flipping, color jitter for student only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  The input size is set to 224 × 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We transfer TinyMIM pre-trained models to  ImageNet [41] image classification and ADE20K [59] se-  mantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For ImageNet, we use AdamW op-  timizer with weight decay of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For data augmentation,  we follow the settings in MAE [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We fine-tune ViT-B  for 100 epochs with a batch size of 1024, a learning rate of  2e-3, and a drop path rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We fine-tune ViT-S and  ViT-T for 200 epochs with a batch size of 2048, a learning  rate of 5e-3, and a drop path rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For ADE20K, we  follow the same setting in MAE and adopt UperNet [51]  as our framework with a TinyMIM pre-trained backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  The input image resolution is 512 × 512 for training and  evaluating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We use mIoU as the evaluation metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Besides, we evaluate the robustness of TinyMIM on var-  ious out-of-domain ImageNet datasets [19–21] which are  generated by applying different perturbations on ImageNet,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' natural adversarial examples (ImageNet-A), semantic  shift (ImageNet-R), common image corruptions (ImageNet-  C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We report top-1 accuracy on ImageNet-A/R and mCE  error on ImageNet-C (lower is better).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Default Setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' By default, we adopt relation distillation  formulated in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 9, head alignment, raw image as input, se-  quential distillation and the 18-th block of MAE pre-trained  ViT-L as the target block for TinyMIM-ViT-B pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Main Results  As shown in Table 3, we compare our TinyMIM with  previous methods on ImageNet image classification and  ADE20K semantic segmentation using different ViTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In  particular, TinyMIM pre-trained ViT-T achieves 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8% top-  1 accuracy, outperforming MAE baseline by +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  An  enhanced model named TinyMIM⋆-T, which retains the  plain architecture and computation budget of ViT-T, fur-  ther achieves 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6% top-1 accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' See appendix for the  details of TinyMIM⋆-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Moreover, TinyMIM pre-trained  ViT-S achieves 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0% top-1 accuracy, outperforming MAE  baseline and previous best method CIM [13] by +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4, +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' By transferring the knowledge of an MAE pre-  trained ViT-L, TinyMIM pre-trained ViT-B achieves 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0%  top-1 accuracy on ImageNet-1K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  As for semantic segmentation, TinyMIM pre-trained ViT-  B surpasses MAE baseline and state-of-the-art CAE [4] by  +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1 and +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' An intermediate fine-tuning on  ImageNet-1K classification before ADE20K segmentation  fine-tuning further boosts the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  We also evaluate our models on out-of-domain datasets  in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Our TinyMIM pretrained models are more robust  than MAE pre-trained ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Specifically, TinyMIM-ViT-B  outperforms MAE-ViT-B by +6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4 and +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6 on ImageNet-A  and ImageNet-R, respectively, and lower the mCE by -5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Ablation Study  Unless otherwise specified, all ablation studies are con-  ducted on TinyMIM-ViT-B, with a teacher of being an MAE  pre-trained ViT-L, relation distillation strategy, raw image as  input, the 18-th block of ViT-L as the target block, under a  100-epoch pre-training schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We report top-1 accuracy  on ImageNet-1K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Class Token Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For this distillation strategy, we  study two variants: 1) class token distillation as formulated  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2) class token distillation with an extra MAE re-  construction loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The results are shown in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Both  variants perform worse than MAE baseline, indicting that  the class token is improper to be served as the distillation  target since there is no explicit supervision applied on class  token during teacher’s pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Feature Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' As described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1, there  are four types of features can be served as the targets for  feature distillation formulated in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 7: output feature, FFN  feature, attention feature and Q/K/V features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Table 6 com-  pares the results of using different features as distillation  targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We also report the results of FFN feature and atten-  tion feature before the residual connection (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' An  interesting finding is that distilling FFN feature and attention  feature after the residual connection significantly degrades  the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Relation Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 9 formulates our default relation  distillation, which jointly distills Q-K relation and V-V re-  lation (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Here we study a variant by changing the  target relations from Q-K/V-V to Q-K/K-K/V-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We also  investigate that whether to apply a Softmax operator on each  relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The results are shown in Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Comparison of Different Distillation Strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In this  study, all models are pre-trained under a 300-epoch schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  We compare three distillation strategies on ImageNet image  classification (Table 8) and ADE20K semantic segmentation  (Table 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For each strategy, we use the target that yields  the best result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We also highlight the improvements over the  6  Method  Pretraining  Tokenizer/  Tokenizer/Teacher  Classification  Segmentation  Epochs  Teacher  Data  Top-1 Acc (%)  mIoU  Tiny-size models (ViT-T/16)  Scratch [44]  300  Label  IN1K  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  MAE† [18]  1600  Pixel  IN1K  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  MoCo [5]  1600  EMA  IN1K  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  TinyMIM (Ours)  300  TinyMIM-ViT-S  IN1K  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0/44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6‡  TinyMIM⋆ (Ours)  300  TinyMIM-ViT-S  IN1K  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0‡  Small-size models (ViT-S/16)  Scratch [44]  300  Label  IN1K  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  MAE† [18]  1600  Pixel  IN1K  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  MoCo [5]  1600  EMA  IN1K  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  DINO [3]  1600  EMA  IN1K  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  CIM [13]  1600  Pixel  IN1K  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6 TinyMIM (Ours)  300  TinyMIM-ViT-B  IN1K  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4/48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9‡  Base-size models (ViT-B/16)  Scratch [44]  300  Label  IN1K  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  BeiT [2]  800  DALL-E  DALLE250M+IN22K+IN1K  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  MAE [18]  1600  Pixel  IN1K  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  SIM [43]  1600  EMA  IN1K  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8 CAE [4]  1600  DALL-E  DALLE250M+IN22K+IN1K  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  MaskFeat [48]  1600  HOG  IN1K  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0 SdAE [7]  300  EMA  IN1K  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  data2vec [1]  800  EMA  IN1K  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2 PeCo [11]  300  VQGAN  IN1K  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  PeCo [11]  800  VQGAN  IN1K  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  TinyMIM (Ours)  300  MAE-ViT-L  IN1K  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2/52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6‡  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Fine-tuning results on ImageNet-1K and ADE20K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' All models are pre-trained on ImageNet-1K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' “Tokenizer/Teacher Data”: training  data of teacher and tokenizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' †: reproduced result using official code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ⋆: the model is fine-tuned for 1000 epochs with DeiT-style [44]  knowledge distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ‡: the model adopts an intermediate fine-tuning on ImageNet-1K classification before ADE20K segmentation  fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Method  Model Size  ImageNet ↑  IN-Adversarial↑  IN-Rendition↑  IN-Corruption ↓  DeiT [44]  ViT-T  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  MAE [18]  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  TinyMIM  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  DeiT [44]  ViT-S  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  MAE [18]  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  TinyMIM  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  DeiT [44]  ViT-B  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  MAE [18]  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  TinyMIM  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Robustness evaluation on out-of-domain datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  MAE baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Target Block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' As described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3, we consider  a situation where the block number of the student does not  match that of the teacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Here we use an MAE pre-trained  ViT-L containing 24 blocks to distill a ViT-B containing  12 blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Here we examine the effects of using the 12th,  15th, 18th, 21th and 24th (last) blocks of the ViT-L as the  target blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The comparison is shown in Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We  7  Method  Reconstruction Loss  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  MAE  ✓  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  TinyMIM w/ Cls  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  TinyMIM w/ Cls  ✓  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Study of class token distillation formulated in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Feature  Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Connection  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  MAE  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Output Feature  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  FFN Feature  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  FFN Feature  ✓  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  Attention Feature  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  Attention Feature  ✓  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  Q/K/V Features  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Study of feature distillation formulated in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' See  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2 for the definitions of different features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Relation  Softmax  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  MAE  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Q-Q, K-K, V-V  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  Q-Q, K-K, V-V  ✓  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  Q-K, V-V  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  Q-K, V-V  ✓  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Study of relation distillation formulated in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' See  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 4 for the definitions of different relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  experimentally find that using 18th block yields the best  result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Sequential Distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3, we advocate to  adopt a sequential distillation strategy to enable distillation  from a larger model (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ViT-L) to a smaller model (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  ViT-S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Table 11 compares the result of adopting different  teachers with or without the sequential distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We have  two conclusions: 1) using a larger teacher (MAE-ViT-L) to  distill a smaller student (ViT-S) degrades the performance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2)  sequential distillation significantly boosts the performance  of ViT-T (MAE-ViT-B→TinyMIM-ViT-S as the teacher and  ViT-T as the student).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Integrating MAE into TinyMIM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' MAE is a simple but ef-  fective self-supervised pre-training paradigm that trains a  model by requiring it to predict masked inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In contrast,  TinyMIM pre-trains smaller ViTs in a knowledge distilla-  tion manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Here we integrate MAE into our TinyMIM,  yielding an integrated model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' This model is optimized under  two losses: knowledge distillation loss from TinyMIM, and  Method  Model Size  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Supervised (DeiT)  ViT-T  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  MAE  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Class Token Distillation  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Feature Distillation  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  Relation Distillation  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8 (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2)  Supervised (DeiT)  ViT-S  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  MAE  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Class Token Distillation  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Feature Distillation  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  Relation Distillation  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1)  Supervised (DeiT)  ViT-B  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  MAE  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Class Token Distillation  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  Feature Distillation  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  Relation Distillation  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0 (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6)  Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Comparison of three distillation strategies on ImageNet-1K  image classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The models are pre-trained under a 300-epoch  schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Method  Model Size  mIoU  Supervised (DeiT)  ViT-B  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  MAE  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  Class Token Distillation  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  Feature Distillation  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  Relation Distillation  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2 (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1)  Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Comparison of three distillation strategies on ADE20K  semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The models are pre-trained under a 300-  epoch schedule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Task  12th  15th  18th  21th  24th  Classification  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  Segmentation  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='7  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Study of target block on ImageNet-1K and ADE20K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Student  Teacher  Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  ViT-S  MAE-ViT-B  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  MAE-ViT-L  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  MAE-ViT-L → TinyMIM-ViT-B  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  ViT-T  MAE-ViT-S  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  MAE-ViT-B  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  MAE-ViT-B → TinyMIM-ViT-S  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  Table 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Study of sequential distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  8  Masked Image  Reconstruction Loss  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  ✓  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  ✓  ✓  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  Table 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Comparison between the TinyMIM-ViT-B (the first row)  and the integrated model (the third row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We also study the input  of TinyMIM-ViT-B, which could be raw image (the first row) or  masked image (the second row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  DPR (Teacher)  DPR (Student)  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='2  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='3  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9  Table 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Ablation study of drop path rate (DPR) used in teacher  and student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  reconstruction loss from MAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' To enable MAE pre-training,  we randomly mask 75% image patches, and feed the visi-  ble patches into the network to initiate the pre-training of  the integrated model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Table 12 shows the comparison be-  tween TinyMIM-ViT-B and the integrated model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' From the  Table, we could draw a conclusion—integrating MAE into  our TinyMIM does not improve the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In addi-  tion, we also investigate the input of TinyMIM-ViT-B, which  could be either raw image or masked image, as shown in  Table 12—taking raw image as input yields better result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Drop Path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Drop path is one of the most critical techniques  in training Transformers [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Using an appropriate drop  path rate could significantly alleviate the over-fitting issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  However, MAE disables this technique in its implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Here we verify the effects of applying drop path to our  TinyMIM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The results are shown in Table 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For the student  model, the optimal drop path rate is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For the teacher  model, disabling drop path yields best result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Conclusion  In this paper, we present TinyMIM, which is the first to  successfully perform masked image modeling (MIM) pre-  training for smaller ViT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In stead of adopting a  mask-and-predict pretext task, we pre-train a small ViT by  mimicking the relations of a large ViT in a knowledge dis-  tillation manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The success of TinyMIM can be attributed  to a comprehensive study of various factors that may affect  TinyMIM pretraining including distillation target, distillation  input and target block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' With extensive experiments, we draw  a series of conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' For instance, relation distillation is  superior than feature distillation and class token distillation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  taking raw image as input is optimal;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' a sequential distillation  is necessary for training smaller ViTs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' With its simplic-  ity and strong performance, we hope our approach can serve  as a solid baseline for future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  References  [1] Alexei Baevski, Wei-Ning Hsu, Qiantong Xu, Arun Babu,  Jiatao Gu, and Michael Auli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Data2vec: A general framework  for self-supervised learning in speech, vision and language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='03555, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3, 7  [2] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' BEiT:  BERT pre-training of image transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In International  Conference on Learning Representations, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 2, 7  [3] Mathilde Caron, Hugo Touvron, Ishan Misra, Herv´e J´egou,  Julien Mairal, Piotr Bojanowski, and Armand Joulin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Emerg-  ing properties in self-supervised vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv  preprint arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='14294, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3, 7  [4] Xiaokang Chen, Mingyu Ding, Xiaodi Wang, Ying Xin, Shen-  tong Mo, Yunhao Wang, Shumin Han, Ping Luo, Gang Zeng,  and Jingdong Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Context autoencoder for self-supervised  representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='03026,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6, 7  [5] Xinlei Chen, Saining Xie, and Kaiming He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' An empirical  study of training self-supervised vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ArXiv,  abs/2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='02057, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 7  [6] Yinpeng Chen, Xiyang Dai, Dongdong Chen, Mengchen  Liu, Xiaoyi Dong, Lu Yuan, and Zicheng Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Mobile-  former: Bridging mobilenet and transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings  of the IEEE/CVF Conference on Computer Vision and Pattern  Recognition, pages 5270–5279, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2  [7] Yabo Chen, Yuchen Liu, Dongsheng Jiang, Xiaopeng Zhang,  Wenrui Dai, Hongkai Xiong, and Qi Tian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Sdae: Self-  distillated masked autoencoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ArXiv, abs/2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='00449, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  7  [8] Jang Hyun Cho and Bharath Hariharan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' On the efficacy of  knowledge distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF  international conference on computer vision, pages 4794–  4802, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6  [9] Navneet Dalal and Bill Triggs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Histograms of oriented gra-  dients for human detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In 2005 IEEE computer soci-  ety conference on computer vision and pattern recognition  (CVPR’05), volume 1, pages 886–893.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Ieee, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2  [10] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina  Toutanova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' BERT: pre-training of deep bidirectional trans-  formers for language understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the  2019 Conference of the North American Chapter of the As-  sociation for Computational Linguistics: Human Language  Technologies, pages 4171–4186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Association for Computa-  tional Linguistics, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2  [11] Xiaoyi Dong, Jianmin Bao, Ting Zhang, Dongdong Chen,  Weiming Zhang, Lu Yuan, Dong Chen, Fang Wen, and Neng-  hai Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Peco: Perceptual codebook for bert pre-training of  vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='12710, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  1, 2, 7  [12] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov,  Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner,  9  Mostafa Dehghani, Matthias Minderer, Georg Heigold, Syl-  vain Gelly, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' An image is worth 16x16 words: Transform-  ers for image recognition at scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='11929,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 3  [13] Yuxin Fang, Li Dong, Hangbo Bao, Xinggang Wang, and  Furu Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Corrupted image modeling for self-supervised  visual pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='03382, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  6, 7  [14] Zhiyuan Fang, Jianfeng Wang, Lijuan Wang, Lei Zhang,  Yezhou Yang, and Zicheng Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Seed: Self-supervised distil-  lation for visual representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [15] Tommaso Furlanello, Zachary Lipton, Michael Tschannen,  Laurent Itti, and Anima Anandkumar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Born again neural  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In International Conference on Machine Learning,  pages 1607–1616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6  [16] Jianping Gou, Baosheng Yu, Stephen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Maybank, and  Dacheng Tao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Knowledge distillation: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' International  Journal of Computer Vision, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2, 3  [17] Benjamin Graham, Alaaeldin El-Nouby, Hugo Touvron,  Pierre Stock, Armand Joulin, Herv´e J´egou, and Matthijs  Douze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Levit: a vision transformer in convnet’s clothing  for faster inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF inter-  national conference on computer vision, pages 12259–12269,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [18] Kaiming He, Xinlei Chen, Saining Xie, Yanghao Li, Piotr  Doll´ar, and Ross Girshick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Masked autoencoders are scalable  vision learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In CVPR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 2, 4, 6, 7  [19] Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kada-  vath, Frank Wang, Evan Dorundo, Rahul Desai, Tyler Zhu,  Samyak Parajuli, Mike Guo, Dawn Song, Jacob Steinhardt,  and Justin Gilmer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The many faces of robustness: A critical  analysis of out-of-distribution generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6  [20] Dan Hendrycks and Thomas Dietterich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Benchmarking neural  network robustness to common corruptions and perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  ICLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6  [21] Dan Hendrycks, Kevin Zhao, Steven Basart, Jacob Steinhardt,  and Dawn Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Natural adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  6  [22] Byeongho Heo, Jeesoo Kim, Sangdoo Yun, Hyojin Park, No-  jun Kwak, and Jin Young Choi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' A comprehensive overhaul  of feature distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Inter-  national Conference on Computer Vision, pages 1921–1930,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [23] Byeongho Heo, Minsik Lee, Sangdoo Yun, and Jin Young  Choi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Knowledge transfer via distillation of activation bound-  aries formed by hidden neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the AAAI  Conference on Artificial Intelligence, volume 33, pages 3779–  3787, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [24] Geoffrey Hinton, Oriol Vinyals, Jeff Dean, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Distill-  ing the knowledge in a neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  arXiv preprint  arXiv:1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='02531, 2(7), 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2, 3  [25] Zejiang Hou, Fei Sun, Yen-Kuang Chen, Yuan Xie, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Kung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Milan: Masked image pretraining on language assisted  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ArXiv, abs/2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='06049, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 3  [26] Andrew Howard, Mark Sandler, Grace Chu, Liang-Chieh  Chen, Bo Chen, Mingxing Tan, Weijun Wang, Yukun Zhu,  Ruoming Pang, Vijay Vasudevan, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Searching for mo-  bilenetv3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF international  conference on computer vision, pages 1314–1324, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 2, 3,  12  [27] Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry  Kalenichenko, Weijun Wang, Tobias Weyand, Marco An-  dreetto, and Hartwig Adam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Mobilenets: Efficient convolu-  tional neural networks for mobile vision applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv  preprint arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='04861, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [28] Jangho Kim, SeongUk Park, and Nojun Kwak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Paraphrasing  complex network: Network compression via factor transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Advances in neural information processing systems, 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3  [29] Seung Hyun Lee, Dae Ha Kim, and Byung Cheol Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Self-  supervised knowledge distillation using singular value de-  composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the European Conference on  Computer Vision (ECCV), pages 335–350, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [30] Yanyu Li, Geng Yuan, Yang Wen, Eric Hu, Georgios Evan-  gelidis, Sergey Tulyakov, Yanzhi Wang, and Jian Ren.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Effi-  cientformer: Vision transformers at mobilenet speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv  preprint arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='01191, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [31] Ze Liu, Han Hu, Yutong Lin, Zhuliang Yao, Zhenda Xie,  Yixuan Wei, Jia Ning, Yue Cao, Zheng Zhang, Li Dong,  Furu Wei, and Baining Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Swin transformer v2: Scaling  up capacity and resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In International Conference on  Computer Vision and Pattern Recognition (CVPR), 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [32] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng  Zhang, Stephen Lin, and Baining Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Swin Transformer:  Hierarchical vision transformer using shifted windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv  preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='14030, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1  [33] Ilya Loshchilov and Frank Hutter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Decoupled weight de-  cay regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In International Conference on Learning  Representations, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6  [34] Sachin Mehta and Mohammad Rastegari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Mobilevit: Light-  weight, general-purpose, and mobile-friendly vision trans-  former.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In International Conference on Learning Representa-  tions, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 2, 3  [35] Junting Pan, Adrian Bulat, Fuwen Tan, Xiatian Zhu, Lukasz  Dudziak, Hongsheng Li, Georgios Tzimiropoulos, and Brais  Martinez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Edgevits: Competing light-weight cnns on mobile  devices with vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In European Conference on  Computer Vision, pages 294–311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Springer, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 2, 3  [36] Zhiliang Peng, Li Dong, Hangbo Bao, Qixiang Ye, and Furu  Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' BEiT v2: Masked image modeling with vector-quantized  visual tokenizers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='06366, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1,  3  [37] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya  Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry,  Amanda Askell, Pamela Mishkin, Jack Clark, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Learning  transferable visual models from natural language supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  In ICML, pages 8748–8763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea  Voss, Alec Radford, Mark Chen, and Ilya Sutskever.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Zero-  shot text-to-image generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ArXiv, abs/2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='12092, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  2  [39] Sucheng Ren, Zhengqi Gao, Tianyu Hua, Zihui Xue, Yong-  long Tian, Shengfeng He, and Hang Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Co-advise: Cross  inductive bias distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF  Conference on Computer Vision and Pattern Recognition  (CVPR), pages 16773–16782, June 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 3  10  [40] Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou,  Antoine Chassang, Carlo Gatta, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Fitnets:  Hints for thin deep nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6550,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [41] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, San-  jeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy,  Aditya Khosla, Michael Bernstein, Alexander C Berg, and Li  Fei-Fei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Imagenet large scale visual recognition challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  IJCV, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6  [42] Mingxing Tan and Quoc Le.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Efficientnet: Rethinking model  scaling for convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In International  conference on machine learning, pages 6105–6114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' PMLR,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [43] Chenxin Tao, Xizhou Zhu, Gao Huang, Yu Qiao, Xiaogang  Wang, and Jifeng Dai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Siamese image modeling for self-  supervised vision representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint  arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='01204, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 7  [44] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco  Massa, Alexandre Sablayrolles, and Herv´e J´egou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Training  data-efficient image transformers & distillation through atten-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' preprint arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='12877, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 3, 7, 9, 12  [45] Shakti N Wadekar and Abhishek Chaurasia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Mobilevitv3:  Mobile-friendly vision transformer with simple and effective  fusion of local, global and input features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint  arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='15159, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 2  [46] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao  Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Pyra-  mid vision transformer: A versatile backbone for dense predic-  tion without convolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF  International Conference on Computer Vision, pages 568–  578, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1  [47] Xiaojie Wang, Rui Zhang, Yu Sun, and Jianzhong Qi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Kdgan:  Knowledge distillation with generative adversarial networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Advances in neural information processing systems, 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3  [48] Chen Wei, Haoqi Fan, Saining Xie, Chao-Yuan Wu, Alan  Yuille, and Christoph Feichtenhofer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Masked feature predic-  tion for self-supervised visual pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint  arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='09133, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 2, 7  [49] Yixuan Wei, Han Hu, Zhenda Xie, Zheng Zhang, Yue Cao,  Jianmin Bao, Dong Chen, and Baining Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Contrastive  learning rivals masked image modeling in fine-tuning via  feature distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='14141, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  1  [50] Yixuan Wei, Han Hu, Zhenda Xie, Zheng Zhang, Yue Cao,  Jianmin Bao, Dong Chen, and Baining Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Contrastive  learning rivals masked image modeling in fine-tuning via  feature distillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='14141, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  3  [51] Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, and  Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Unified perceptual parsing for scene understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  In ECCV, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6  [52] Zhenda Xie, Zigang Geng, Jingcheng Hu, Zheng Zhang, Han  Hu, and Yue Cao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Revealing the dark secrets of masked image  modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='13543, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1  [53] Zhenda Xie, Zheng Zhang, Yue Cao, Yutong Lin, Jianmin  Bao, Zhuliang Yao, Qi Dai, and Han Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Simmim: A simple  framework for masked image modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of  the IEEE/CVF Conference on Computer Vision and Pattern  Recognition, pages 9653–9663, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1, 2, 3  [54] Zhenda Xie, Zheng Zhang, Yue Cao, Yutong Lin, Yixuan  Wei, Qi Dai, and Han Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' On data scaling in masked image  modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='04664, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 1  [55] Zihui Xue, Sucheng Ren, Zhengqi Gao, and Hang Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Multimodal knowledge expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the  IEEE/CVF International Conference on Computer Vision,  pages 854–863, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [56] Junho Yim, Donggyu Joo, Jihoon Bae, and Junmo Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' A  gift from knowledge distillation: Fast optimization, network  minimization and transfer learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the  IEEE conference on computer vision and pattern recognition,  pages 4133–4141, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [57] Shan You, Chang Xu, Chao Xu, and Dacheng Tao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Learn-  ing from multiple teacher networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the  23rd ACM SIGKDD International Conference on Knowledge  Discovery and Data Mining, pages 1285–1294, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [58] Shan You, Chang Xu, Chao Xu, and Dacheng Tao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Learning  with single-teacher multi-student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' In Proceedings of the AAAI  Conference on Artificial Intelligence, volume 32, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 3  [59] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler,  Adela Barriuso, and Antonio Torralba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Semantic understand-  ing of scenes through the ADE20K dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=', 127(3):302–321, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' 6  [60] Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang  Xie, Alan Yuille, and Tao Kong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ibot: Image bert pre-training  with online tokenizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' arXiv preprint arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='07832, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  1, 3  11  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Hyper-parameters  Hyper-parameters of ImageNet-1K Pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' See Ta-  ble 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Hyper-parameters of ImageNet-1K Image Classification  Fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' See Table 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' TinyMIM⋆-T retains the plain  architecture and computation budget of ViT-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' We fine-tune  TinyMIM⋆ for 1000 epochs with DeiT-style [44] knowledge  distillation on ImageNet-1K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Following MobileNetV3 [26],  an extra fully connected layer is placed before the classifi-  cation layer to increase the feature dimension from 192 to  1280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' The head number is set to 12 instead of the default 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Hyper-parameters for ADE20K Semantic Segmentation  Fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' See Table 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Hyperparameter  ViT-T  ViT-S  ViT-B  Layers  12  Hidden size  192  384  768  FFN inner hidden size  768  1536  3072  Attention heads  3  6  12  Patch size  16 × 16  Pre-training epochs  100/300  Batch size  4096  Adam ϵ  1e-8  Adam β  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='999)  Peak learning rate  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4e-3  Minimal learning rate  1e-5  Learning rate schedule  Cosine  Warmup epochs  5/15  Stochastic depth  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  Dropout  �  Weight decay  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='05  Data augment  RandomResizeAndCrop  Input resolution  224 × 224  Color jitter (student only)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='4  Table 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Hyper-parameters of ImageNet-1K Pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Hyperparameter  ViT-T  ViT-S  ViT-B  Peak learning rate  5e-3  5e-3  2e-3  Fine-tuning epochs  200  200  100  Warmup epochs  5  Layer-wise learning rate decay  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='65/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6∗  Batch size  2048  2048  1024  Adam ϵ  1e-8  Adam β  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='999)  Minimal learning rate  1e-6  Learning rate schedule  Cosine  Stochastic depth  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  Weight decay  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='05  Label smoothing ε  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  Dropout  �  Gradient clipping  �  Erasing  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='25  Input resolution  224 × 224  Rand augment  9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='5  Mixup  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8  Cutmix  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='0  Table 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Hyper-parameters of ImageNet-1K image classification  fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' ∗ indicates that we use 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='65 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='6 for 100-epoch and  300-epoch pre-trained models, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  Hyperparameter  ViT-S  ViT-B  Input resolution  512 × 512  Peak learning rate  1e-4  Fine-tuning steps  160K  Batch size  16  Adam ϵ  1e-8  Adam β  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='9, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='999)  Layer-wise learning rate decay  {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='65, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='75, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='8}  Minimal learning rate  0  Learning rate schedule  Linear  Warmup steps  1500  Dropout  �  Stochastic depth  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='1  Weight decay  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='05  Table 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content=' Hyper-parameters of ADE20K semantic segmentation  fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
+page_content='  12' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/M9AzT4oBgHgl3EQfWPwO/content/2301.01296v1.pdf'}
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+Draft version January 3, 2023
+Typeset using LATEX twocolumn style in AASTeX631
+MHD simulation of Solar Eruption from Active Region 11429 Driven by Photospheric Velocity Field
+Xinyi Wang,1, 2 Chaowei Jiang,3 and Xueshang Feng1, 3
+1SIGMA Weather Group, State Key Laboratory for Space Weather, National Space Science Center, Chinese Academy of Sciences,Beijing
+100190, PR China
+2College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
+3Institute of Space Science and Applied Technology, Harbin Institute of Technology, Shenzhen 518055, PR China, chaowei@hit.edu.cn
+ABSTRACT
+Data-driven simulation is becoming an important approach for realistically characterizing the con-
+figuration and evolution of solar active regions, revealing the onset mechanism of solar eruption events
+and hopefully achieving the goal of accurate space weather forecast, which is beyond the scope of any
+existing theoretical modelling. Here we performed a full 3D MHD simulation using the data-driven
+approach and followed the whole evolution process from quasi-static phase to eruption successfully for
+solar active region NOAA 11429. The MHD system was driven at the bottom boundary by photospheric
+velocity field, which is derived by the DAVE4VM method from the observed vector magnetograms.
+The simulation shows that a magnetic flux rope was generated by persistent photospheric flow be-
+fore the flare onset and then triggered to erupt by torus instability. Our simulation demonstrates a
+high degree of consistency with observations in the pre-eruption magnetic structure, the time scale
+of quasi-static stage, the pattern of flare ribbons as well as the time evolution of magnetic energy
+injection and total unsigned magnetic flux. We further found that an eruption can also be initiated
+in the simulation as driven by only the horizontal components of photospheric flow, but a comparison
+of the different simulations indicates that the vertical flow at the bottom boundary is necessary in
+reproducing more realistically these observed features, emphasizing the importance of flux emergence
+during the development of this AR.
+Keywords: Magnetohydrodynamic (MHD) — Sun: corona — Methods: numerical — Sun: magnetic
+fields
+1. INTRODUCTION
+As driven by solar eruptions, the solar-terrestrial envi-
+ronment often experiences variations, which are known
+as space weather, and forecasting the space weather pre-
+cisely is not only an important scientific topic but can
+also avoid damage of the sensitive on-ground and space-
+based critical infrastructures. Though many theoretical
+models have been proposed and significant process has
+been made in understanding the triggering mechanism
+of solar eruptions (Forbes 2000; Chen 2011; Schmieder
+et al. 2013; Priest 2014), reproducing the whole life-span
+from quasi-static stage to eruption using numerical mod-
+els constrained and driven by observed vector magne-
+togram possess unprecedented capabilities in revealing
+the onset mechanism of the real eruption events, and can
+potentially be used for accurate space weather forecast
+(Jiang et al. 2022; Jiang 2022).
+Previous study reproduced the whole process of en-
+ergy accumulation and release successfully (Jiang et al.
+2016), showing an MHD system can be driven to erupt
+by inputting time series of vector magnetograms at the
+bottom boundary (B-driven). There are also other data-
+driven models, in which the evolution of MHD system
+is driven by the electric field (E-driven, e.g., Cheung &
+DeRosa 2012; Hayashi et al. 2018; Pomoell et al. 2019;
+Price et al. 2019) or the velocity field (V-driven, e.g.,
+Hayashi et al. 2019; Guo et al. 2019; Liu et al. 2019;
+He et al. 2020; Zhong et al. 2021) on the photosphere
+(bottom boundary). Though the B-driven method can
+fully match the magnetogram, it will introduce consid-
+erable errors of magnetic divergence from the bottom
+boundary. This shortage will vanish in E-driven model,
+however, deriving both the induction and potential com-
+ponents of the electric field on the photosphere is not an
+easy task (Fisher et al. 2010, 2012, 2015, 2020), and the
+photospheric flow also needs to be properly set to fol-
+low the Ohm’s law. In most of the theoretical models of
+solar eruption, the key structure in favor of eruption is
+arXiv:2301.00144v1  [astro-ph.SR]  31 Dec 2022
+
+2
+assumed to be formed through the movement of the foot-
+points of magnetic field lines (Moore & Labonte 1980;
+Moore & Roumeliotis 1992; Antiochos et al. 1999; Lin
+& Forbes 2000; Jiang et al. 2021b), which is driven by
+the horizontal flow, and the vertical component of the
+photospheric flow will be responsible for the flux emer-
+gence process. Therefore, with the photospheric velocity
+field determined, the photospheric magnetic field can
+be generated self-consistently. Furthermore, in the V-
+driven approach, there is no need to solve the complex
+momentum equation at the bottom boundary (which is
+the most time-consuming part in solving MHD equa-
+tions). Due to these advantages, the V-driven method
+has attracted many previous studies to focus on this
+topic. For example, with the velocity field derived by
+DAVE4VM method (Schuck 2008), Hayashi et al. (2019)
+used the projected normal characteristics method to up-
+date the physical variables other than velocity at the
+bottom boundary. However, the total magnetic energy
+kept almost the same level of that of the initial state
+without obvious magnetic energy injection. Jiang et al.
+(2021a) updated the magnetic field by solving directly
+the magnetic induction equation at the bottom bound-
+ary and their model can inject the magnetic energy from
+bottom boundary successfully. He et al. (2020) drove the
+magnetic evolution by inputting the DAVE4VM velocity
+field and vector magnetogram simultaneously. The for-
+mation process of an magnetic flux rope (MFR) was ob-
+tained in their model. Unfortunately, these simulations
+didn’t drive the system to erupt. The only work we know
+that obtained an eruption by the velocity field derived
+from observation was shown in Kaneko et al. (2021).
+The velocity field was derived from the electric field on
+the photosphere using Ohm’s law and then was input at
+the bottom boundary in their zero-beta model to drive
+the system to erupt. Two eruptions they produced were
+identified from the evolution curves of the magnetic and
+kinetic energies, however, the kinetic energy showed an
+overall increase without obvious quasi-static evolution
+during the pre-eruption stage. Before the first eruption,
+the kinetic energy was comparable with its peak dur-
+ing the first eruption and the amount of the release of
+the magnetic energy was also too small, which didn’t
+show the feature of a typical eruption event, i.e., a large
+amount of magnetic energy was converted into kinetic
+energy impulsively. As described above, the whole en-
+ergy accumulation process from quasi-static evolution
+(of typically tens of hours) to impulsive eruption has
+not been realized in a self-consistent way using the V-
+driven MHD model, and this is one of the motivations
+of this work.
+In this Letter, we applied a V-driven model to inves-
+tigate the evolution and eruption of a well-studied ac-
+tive region (AR) NOAA 11429. Previous studies found
+persistent shearing flow and flux cancellation near the
+main polarity inversion line (PIL) of this AR (Shimizu
+et al. 2014; Zheng et al. 2017), which were suggested
+to be responsible for the eruptions on 2012 March 7,
+9 and 10 (Dhakal et al. 2018, 2020).
+An analysis of
+the MFR reconstructed from vector magnetograms us-
+ing the nonlinear force-free field (NLFFF) model sug-
+gests that the homologous eruptions are triggered by
+torus instability (TI) of the MFR (Chintzoglou et al.
+2015). Zhang et al. (2021) suggested the helical kink
+instability may also take effect. Nevertheless, whether
+these mechanisms were at work requires to be further
+studied using dynamic modeling of this AR evolution
+and eruption, which is absent in all the previous stud-
+ies and is the other motivation of this work.
+In our
+simulation, the dynamic process from the beginning of
+2012 March 4 to the eruption on March 5 in this AR
+was reproduced self-consistently as driven by the pho-
+tospheric velocity derived from vector magnetogram us-
+ing DAVE4VM method. Our simulation shows that an
+MFR was generated near the main PIL before the flare
+onset and the initiation of this eruption event depended
+mainly on TI of the preformed MFR.
+2. DATA AND MODEL
+AR 11429 showed a complex βγδ configuration and
+is very flare-productive, which has produced 3 X-class
+flares from 2012 March 5 to 7. It first appeared on the
+eastern solar limb on March 4 and was located on the
+eastern part of the solar disk before March 8. During
+this period, the AR kept developing as characterized by
+the increasing total unsigned magnetic flux, indicating
+the obvious flux emergence by vertical flow on the pho-
+tosphere. Since it was the first X-class flare of this AR,
+here we focus on the initiation process of the X1.1 flare
+(which is accompanied with a halo CME moving at a
+speed of 1531 km s−1) around 04:00 UT on March 5 as
+shown in the white box in Figure 1A. Before the flare on-
+set, there was persistent shearing flow near the main PIL
+(Figure 1B) and as a result, the horizontal magnetic field
+there was highly sheared (Figure 1C), which indicates
+that a large amount of free magnetic energy is stored
+ready for an eruption. An hot loop first erupted away
+as shown in AIA 94 ˚A (Lemen et al. 2012) at around
+03:31 UT (Figure 1D and E) and after that a pair of
+hook shape flare ribbons appeared near the main PIL
+in AIA 1600 ˚A at 03:36 UT (Figure 1F), i.e., the flare
+event started.
+
+Simulation of AR 11429 eruption
+3
+To understand the formation of the pre-eruptive coro-
+nal magnetic field and the triggering mechanism of this
+eruption, we used the DARE-MHD model (Jiang et al.
+2016) to study the dynamic evolution of this AR. For
+saving the computational time, the strength of magnetic
+field from the magnetograms were reduced by a factor of
+25 before being input into our code. The initial plasma
+density was set as a hydrostatic isothermal model with a
+fixed temperature as T = 1×106 K and a modified solar
+gravity (Jiang et al. 2021b) to get a plasma background
+that mimics the real environment in the solar corona
+basing on two key parameters, the plasma β and the
+Alfv´en speed (in particular, the minimum β is 6.3×10−4
+and maximum Alfv´en speed VA ∼ 4800 km s−1 in the
+final equilibrium we obtained below). We chose to use
+the magnetograms of HMI SHARP data set (Schou et al.
+2012; Bobra et al. 2014) at 00:00UT on March 4 to
+reconstruct the initial magnetic field since there were
+no obvious MFR at that time. This magnetogram was
+smoothed first using Gaussian smoothing with FWHM
+of 6 pixels and a NLFFF model from this smoothed
+magnetogram was extrapolated by our CESE-NLFFF-
+MHD code (Jiang & Feng 2012, 2013). Since the code
+(like many other NLFFF codes) does not give a per-
+fect force-free solution but with residual Lorentz forces,
+we input the extrapolated field into the DARE-MHD
+model, along with the initial background plasma, to let
+the MHD system relax until the kinetic and magnetic
+energies were almost unchanged, i.e., an MHD equilib-
+rium was obtained, and the initial state was ready.
+At the bottom boundary, we solve the magnetic induc-
+tion equation to update the magnetic field with the ve-
+locity field derived by DAVE4VM method to update the
+magnetic field on the photosphere. The DAVE4VM ve-
+locity was strengthened by a factor of 13.7 (determined
+by the ratio of the time series magnetograms’ original
+time cadence as 720 seconds to the time cadence in our
+simulation as 0.5 × 105 seconds, i.e.,
+720
+0.5×105) to speed
+up our simulation and thus the time scale of quasi-static
+evolution prior to the eruption onset is shorten by the
+same times.
+At the side and top boundaries, all the
+variables are extrapolated from the neighboring inner
+points with zero gradient along the normal direction
+of the boundary surface and the normal component of
+magnetic field is further modified by the divergence-free
+condition. The Powell-source terms and diffusion con-
+trol terms was used to deal with the divergence error of
+the magnetic field as described in Jiang et al. (2010).
+We set the computational domain sufficiently large as
+[−368, 368] Mm in both x and y direction and [0, 736]
+Mm in z direction with grid resolution varies from 1′′ to
+8′′ using adaptive mesh refinement. The highest resolu-
+tion is used mainly for the regions with strong magnetic
+gradients and current density, in particular, the current
+sheets (CSs). Explicit value of magnetic resistivity was
+not used in our simulation and the magnetic reconnec-
+tion was controlled by the resistivity of the numerical
+method only, which mimicked the low-resistivity plasma
+better. As the total unsigned flux of this AR kept in-
+creasing before the flare onset, we energized the MHD
+system by full 3D DAVE4VM velocity field (vD
+x , vD
+y , vD
+z )
+(will be referred to as V3D simulation) and horizontal
+component (vD
+x , vD
+y , 0) (V2D) respectively, and a com-
+parison of the results for these two simulations will show
+the importance of flux emergence through the vertical
+flow on the photosphere.
+3. RESULTS
+3.1. Overall Process
+The evolution curves of the total magnetic and kinetic
+energies in the computational domain as well as the to-
+tal unsigned magnetic flux at the bottom boundary are
+shown in Figure 2. For the ‘V3D’ simulation, as driven
+by the time-series velocity field (V3D) for a time dura-
+tion of 150 minutes, the total magnetic energy in our
+simulation model experienced an overall increase firstly
+and then a rapid decrease, which is associated with an
+eruption event. The eruption can be identified from the
+energy evolution with onset time tE,V3D = 120 minutes.
+At the very beginning from t = 0 to t = 22 minutes,
+the magnetic energy injection curve (black dashed line,
+which is computed by the time integration of the to-
+tal Poynting flux of the ‘V3D’ simulation at the bottom
+surface) matches well with the solid ‘V3D’ curve (the
+magnetic energy increase of the ‘V3D’ simulation) and
+‘OB’ curve (the magnetic energy injection computed by
+DAVE4VM velocity and magnetograms) in Figure 2A.
+However, in the time duration of t ∈ [97, 122] minutes,
+the total magnetic energy (blue solid line) is higher than
+the magnetic energy injection. Such an unphysical mis-
+match of the inputted energy from the boundary and the
+cumulative energy in the volume is likely owing to the in-
+sufficient resolution for the bottom boundary, since the
+magnetic field at the bottom boundary has accumulated
+a very large gradient in this phase (see Discussions). The
+kinetic energy keeps a very low value of around 10−3Ep0
+(which is the potential field energy corresponding to the
+magnetic field at t=0) before the major eruption be-
+gins at tE,V3D = 120 minutes when the magnetic energy
+reaches about 1.85 Ep0. The magnetic energy decreases
+to about 1.7 Ep0 at the peak of the total kinetic energy
+(i.e., Ek = 5.6 × 10−2Ep0), and keeps decreasing to 1.45
+Ep0 in total through this eruption (0.4 Ep0 free energy
+loss). That is, about one third of the magnetic energy
+
+4
+loss has been converted to kinetic energy in 10 minutes.
+If multiplied by a factor of 13.7 determined by the rate of
+speeding up in our velocity-driven simulation, the quasi-
+static evolution time of ‘V3D’ run is 27.4 hours. This
+time scale is very close to the observation one which is
+27.6 hours.
+We have also driven the simulation by the horizontal
+velocity (V2D) and found that it can also produce an
+eruption with rather similar onset time. However, com-
+paring the different curves of magnetic energy evolution
+in Figure 2A and the curves of total unsigned magnetic
+flux in Figure 2B respectively, the blue solid lines labeled
+by ‘V2D’ are obvious lower than those from the ’V3D’
+simulation. This clearly shows that though horizontal
+velocity can also drive the field to erupt (with a delayed
+onset time for about 6 minutes compared with ‘V3D’),
+the vertical velocity vD
+z is necessary in accounting for the
+larger increase of the total magnetic energy and total un-
+signed flux as shown in observations, therefore leading
+to a stronger eruption. The evolution of the simulated
+magnetic energy, total unsigned flux and the time scale
+of the ‘V3D’ run before the major eruption are more
+consistent with observations, showing the importance of
+the vertical photospheric plasma flow in the numerical
+modeling of solar eruptions.
+Our simulated magnetic
+structure (the first panel in Figure 3E) has reasonable
+consistency with observations in the pre-eruption image
+of AIA 171 ˚A (the second panel in Figure 3E), and the
+synthetic image of coronal emission from current den-
+sity of our simulation (the last panel in Figure 3E) is
+reasonable consistent with the image of AIA 131 ˚A (the
+third panel in Figure 3E). Also the quasi separatrix lay-
+ers (QSLs), where the magnetic reconnection is most
+likely to take place and thus represent the position of
+the flare ribbons (Titov et al. 2002; Liu et al. 2016),
+at the bottom boundary (Figure 4F) has approximately
+the same patterns as the flare ribbons in AIA 1600 ˚A
+(Figure 4E). These results confirm the validity of our
+V-driven DARE-MHD model as well as the DAVE4VM
+method.
+3.2. Eruption Initiation Mechanism
+Since the actual velocity field must contain vz, here we
+analyzed the ‘V3D’ run to study the onset mechanism
+of this eruption. As we can see, a group of twisted field
+lines (represented by the blue solid lines in Figure 3A
+and B) formed and was embedded in the surrounding
+shear arcades, which is similar to an MFR in morphol-
+ogy. In addition, the ejection of the hot loop (also called
+hot channel) as observed in AIA 94 ˚A (shown by the
+white arrows in Figure 1D and E) also suggested the ex-
+istence of an MFR (Cheng et al. 2017) before the flare
+onset.
+To identify the formation of MFR before the eruption,
+we calculated the QSLs and the twist number (Berger
+& Prior 2006) of our simulated magnetic fields, which
+are given in Figure 3D, Figure 5A and B, respectively.
+As shown in the third panel of Figure 3D, a strong QSL
+appeared near the core field and grew up to be a QSL
+ring in the last panel, which separated the MFR and the
+background magnetic field, thus representing the exis-
+tence of an MFR in topology. The QSL ring intersects
+itself below the MFR, forming a typical hyperbolic flux
+tube (HFT), where the CS developed and magnetic re-
+connection took place subsequently to further drive the
+eruption (Jiang et al. 2018). The isosurface of Tw = −1,
+which represents the position and shape of the MFR, are
+shown in Figure 5A and B respectively. It became larger
+and higher, illustrating more magnetic flux were twisted
+as driven by persistent photospheric flow. However, the
+isosurface of Tw = −2, which is the lower threshold of
+kink instability (KI) according to the statistics of Duan
+et al. (2019), is barely visible and KI may take little
+effect.
+Among different triggering mechanisms, TI is consid-
+ered as an efficient way of MFR eruption. In Figure 5D,
+we plot the key controlling parameter that determines
+the onset of TI, i.e., the decay index of the strapping
+field. The variation of the decay index n was calculated
+along the z direction of the overlying field at t = 119
+minutes before the eruption onset. Since the potential
+field is not always the good approximation of the strap-
+ping field (especially when the strapping field is highly
+sheared), we calculated the decay index of our simu-
+lated field instead and plotted the decay index of the
+corresponding potential field at the same time for com-
+parison. The critical height (above which n > 1.5) of
+the simulated field is located at 60 Mm as labeled by
+the vertical black dashed line in Figure 5D. When the
+MFR was just formed, it is small and it’s apex was at a
+low height (about 40 Mm in Figure 5A). About 14 min-
+utes later, it had grown up to be a huge twist structure
+and entered the unstable zone (above 60 Mm as shown
+in Figure 5B), after which it erupted violently.
+The formation and the evolution of the MFR, i.e.,
+there was an preformed MFR and the MFR erupted af-
+ter it entered the unstable zone, strongly suggest that TI
+is the triggering mechanism of this eruption. To further
+test this assumption, we used the V3D-driven data at
+t = 100 minutes as the initial condition and ran our code
+without bottom velocity driven (by setting all the three
+velocity components as zero at the bottom boundary,
+thus referred to as ‘V0D’) to see whether the magnetic
+
+Simulation of AR 11429 eruption
+5
+field will erupt. The evolution of energies of this ‘V0D’
+run are shown as the red solid lines in Figure 2A. During
+the time duration of t ∈ [100, 124] minutes, the magnetic
+energy kept almost unchanged, while the toroidal flux of
+the MFR (defined as
+�
+s Bzds, where s denotes the region
+of Tw < −1 and Bz < 0 at the bottom boundary) kept
+increasing as shown in Figure 5C. In ‘V3D’ simulation,
+the MFR (the isosurface of Tw = −1) became larger
+and higher than the critical height before the eruption
+onset (Figure 5A and B) as the toroidal flux increas-
+ing (Figure 5C), after which TI took effect and finally
+led to a strong eruption. Similarly, the toroidal flux of
+‘V0D’ simulation increased before and decreased after
+the eruption (Figure 5C), showing the slow reconnec-
+tion can took place spontaneously without velocity driv-
+ing and made the MFR larger until the eruption started
+at tE,V0D = 124 minutes as identified from the energy
+evolution curve. Since the current density was weaker
+and the current layer was thicker (as shown in the third
+panel in Figure 3C) than a true CS (the first panel in
+Figure 4C), the magnetic gradient was lower in the cur-
+rent layer than in the CS, and thus the diffusivity was
+relatively uniform, which only allowed slow reconnection
+(i.e., a slow dissipation of the current) to take place with-
+out impulsive energy release (i.e., not a Pescheck-type
+reconnection, Yokoyama & Shibata 1994). The eruption
+of this ‘V0D’ run has the similar onset time and strength
+with the ‘V3D’ run, which further indicates that after
+t = 100 minutes in ‘V3D’ run, the velocity field on the
+bottom boundary is not necessary and the instability is
+sufficient to trigger the eruption.
+It follows the basic
+developing stage of TI, i.e., the rising MFR stretched
+the overlying field and consequently the flare CS formed
+below the MFR. Since we didn’t use any explicit value
+of magnetic resistivity, and since the CS formed in a
+dynamic way, the width of CS could become very thin
+to trigger the fast reconnection easily as pointed out by
+Jiang et al. (2021b), which further drives the eruption.
+Based on the analysis of our simulation and the sup-
+plementary numerical experiment (‘V0D’ simulation),
+along with the consistency between our simulation re-
+sults and observations that have been shown above, we
+conclude that TI is the initiation mechanism of the X1.1
+flare in AR 11429 on 2012 March 5.
+4. CONCLUSIONS AND DISCUSSIONS
+We have carried out a full 3D MHD simulation of
+an X-class flare eruption event on 2012 March 5 in AR
+11429 using the V-driven DARE-MHD model. An MHD
+equilibrium was obtained by relaxing the NLFFF recon-
+structed by the CESE-MHD-NLFFF code and was set as
+the initial condition. Then the initial state was driven
+to evolve by the DAVE4VM velocity field on the bot-
+tom boundary of our simulation box. The analysis of
+the quasi-static evolution stage before the eruption on-
+set shows the gradual formation of an MFR above the
+main PIL. When the MFR first appeared, it was rela-
+tively low and then it grew up into the torus unstable
+region, after which TI was triggered. Then the energy
+conversion process was accomplished by reconnection in
+the CS that is formed due to the stretching effect of
+the erupting MFR. The images of SDO observation and
+the important physical quantities computed from the
+magnetograms are reasonably consistent with our result
+in the pre-flare magnetic structure, the morphology of
+flare ribbons, evolution curves of the magnetic and ki-
+netic energies as well as the total unsigned magnetic flux.
+The time duration of the quasi-static evolution process
+before the simulated eruption is also very close to the
+actual time scale before the flare onset.
+Nevertheless, our simulation does not reproduce accu-
+rately the evolution of magnetic field as shown in the ob-
+served magnetograms. As can be seen in the last panel of
+Figure 3A, part of the magnetic flux was transported to
+and concentrated at the edge of the AR, while this pileup
+was not observed in HMI magnetograms. One likely rea-
+son for this flux pileup is that, the DAVE4VM method
+only solves the normal component of the magnetic in-
+duction equation in the least-square sense (Lumme et al.
+2019), which may not reproduce the velocity precisely
+at every point and can only be used to approximate the
+overall distribution and evolution of magnetic flux in
+the AR. In addition, the magnetic flux on the photo-
+sphere should be dispersed and dissipated by granular
+and supergranular convection (Wang et al. 1989) as well
+as small scale turbulent diffusion in practical situation.
+Therefore, without dealing properly with these effects,
+the flux pileup will be more obvious than observations
+and as a result the magnetic energy injection rate of
+‘V3D’ run will be overall higher than the ‘OB’ one as
+shown in Figure 2A (comparing the black dashed line
+and the black solid line). This unrealistic flux pileup
+may also contribute to the overshoot of the magnetic
+energy increase (Figure 2A, the mismatch of the black
+dashed line and the green line before the eruption), be-
+cause it results in a very large magnetic gradient at the
+bottom boundary, thus even the finest spatial resolution
+in our simulation was inadequate to capture the too high
+gradient during the time duration close to the eruption
+onset (i.e., t ∈ [97, 122] minutes). The insufficient grid
+resolution led to the considerable numerical error there,
+which thus makes the magnetic energy increase higher
+than the magnetic energy injection in ‘V3D’ simulation.
+The proper settings of numerical diffusion and grid res-
+
+6
+olution, along with the improved methods for deriving
+the photospheric flow will need to be considered in fu-
+ture works for a more accurate data-driven simulation
+of solar eruptions.
+To summarize, our simulation shows that, besides
+inputting the time series of vector magnetogram, the
+numerical model of solar corona can be driven to erupt
+by inputting the time series velocity field at the bot-
+tom boundary, in which the driver, i.e., the bottom
+velocity field is derived from time series of vector mag-
+netograms.
+The numerical model we established here
+shows the possibility of driving the evolution of solar
+corona using different physical variables, which offers
+a straightforward way for revealing the eruption mech-
+anisms in real events.
+Thus, such model has a great
+potentiality in forecasting the onset time as well as the
+strength of solar eruptions and evaluating the quantita-
+tive impact on space weather.
+This
+work
+is
+jointly
+supported
+by
+the
+Na-
+tional Natural Science Foundation of China (NSFC
+41731067, 42030204, 42174200), the Fundamental Re-
+search Funds for the Central Universities (grant No.
+HIT.OCEF.2021033), and Shenzhen Science and Tech-
+nology Program (grant Nos. RCJC20210609104422048
+and JCYJ20190806142609035).
+The computational
+work was carried out on TianHe-1(A), National Super-
+computer Center in Tianjin, China, and we thank Jun
+Chen for his informative and helpful discussions.
+REFERENCES
+Antiochos, S. K., DeVore, C. R., & Klimchuk, J. A. 1999,
+ApJ, 510, 485, doi: 10.1086/306563
+Berger, M. A., & Prior, C. 2006, Journal of Physics A
+Mathematical General, 39, 8321,
+doi: 10.1088/0305-4470/39/26/005
+Bobra, M. G., Sun, X., Hoeksema, J. T., et al. 2014, SoPh,
+289, 3549, doi: 10.1007/s11207-014-0529-3
+Chen, P. F. 2011, Living Reviews in Solar Physics, 8, 1,
+doi: 10.12942/lrsp-2011-1
+Cheng, X., Guo, Y., & Ding, M. 2017, Science China Earth
+Sciences, 60, 1383, doi: 10.1007/s11430-017-9074-6
+Cheung, M. C. M., & DeRosa, M. L. 2012, ApJ, 757, 147,
+doi: 10.1088/0004-637X/757/2/147
+Chintzoglou, G., Patsourakos, S., & Vourlidas, A. 2015,
+ApJ, 809, 34, doi: 10.1088/0004-637X/809/1/34
+Dhakal, S. K., Chintzoglou, G., & Zhang, J. 2018, ApJ,
+860, 35, doi: 10.3847/1538-4357/aac028
+Dhakal, S. K., Zhang, J., Vemareddy, P., & Karna, N. 2020,
+ApJ, 901, 40, doi: 10.3847/1538-4357/abacbc
+Duan, A., Jiang, C., He, W., et al. 2019, ApJ, 884, 73,
+doi: 10.3847/1538-4357/ab3e33
+Fisher, G. H., Kazachenko, M. D., Welsch, B. T., et al.
+2020, ApJS, 248, 2, doi: 10.3847/1538-4365/ab8303
+Fisher, G. H., Welsch, B. T., & Abbett, W. P. 2012, SoPh,
+277, 153, doi: 10.1007/s11207-011-9816-4
+Fisher, G. H., Welsch, B. T., Abbett, W. P., & Bercik, D. J.
+2010, ApJ, 715, 242, doi: 10.1088/0004-637X/715/1/242
+Fisher, G. H., Abbett, W. P., Bercik, D. J., et al. 2015,
+Space Weather, 13, 369, doi: 10.1002/2015SW001191
+Forbes, T. G. 2000, J. Geophys. Res., 105, 23153,
+doi: 10.1029/2000JA000005
+Guo, Y., Xia, C., Keppens, R., Ding, M. D., & Chen, P. F.
+2019, ApJL, 870, L21, doi: 10.3847/2041-8213/aafabf
+Hayashi, K., Feng, X., Xiong, M., & Jiang, C. 2018, The
+Astrophysical Journal, 855, 11,
+doi: 10.3847/1538-4357/aaacd8
+Hayashi, K., Feng, X., Xiong, M., & Jiang, C. 2019, ApJL,
+871, L28, doi: 10.3847/2041-8213/aaffcf
+He, W., Jiang, C., Zou, P., et al. 2020, ApJ, 892, 9,
+doi: 10.3847/1538-4357/ab75ab
+Jiang, C. 2022, Reviews of Geophysics and Planetary
+Physics, 53, 497, doi: 10.19975/j.dqyxx.2022-022
+Jiang, C., Bian, X., Sun, T., & Feng, X. 2021a, Frontiers in
+Physics, 9, 224, doi: 10.3389/fphy.2021.646750
+Jiang, C., & Feng, X. 2012, ApJ, 749, 135,
+doi: 10.1088/0004-637X/749/2/135
+—. 2013, ApJ, 769, 144, doi: 10.1088/0004-637X/769/2/144
+Jiang, C., Feng, X., Guo, Y., & Hu, Q. 2022, The
+Innovation, 3, 100236,
+doi: https://doi.org/10.1016/j.xinn.2022.100236
+Jiang, C., Feng, X., Zhang, J., & Zhong, D. 2010, SoPh,
+267, 463, doi: 10.1007/s11207-010-9649-6
+Jiang, C., Wu, S. T., Feng, X., & Hu, Q. 2016, Nature
+Communications, 7, 11522, doi: 10.1038/ncomms11522
+Jiang, C., Zou, P., Feng, X., et al. 2018, The Astrophysical
+Journal, 869, 13, doi: 10.3847/1538-4357/aaeacc
+Jiang, C., Feng, X., Liu, R., et al. 2021b, Nature
+Astronomy, 5, 1126, doi: 10.1038/s41550-021-01414-z
+Kaneko, T., Park, S.-H., & Kusano, K. 2021, ApJ, 909, 155,
+doi: 10.3847/1538-4357/abe414
+Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, SoPh,
+275, 17, doi: 10.1007/s11207-011-9776-8
+Lin, J., & Forbes, T. G. 2000, J. Geophys. Res., 105, 2375,
+doi: 10.1029/1999JA900477
+Liu, C., Chen, T., & Zhao, X. 2019, A&A, 626, A91,
+doi: 10.1051/0004-6361/201935225
+
+Simulation of AR 11429 eruption
+7
+Liu, R., Kliem, B., Titov, V. S., et al. 2016, ApJ, 818, 148,
+doi: 10.3847/0004-637X/818/2/148
+Lumme, E., Kazachenko, M. D., Fisher, G. H., et al. 2019,
+SoPh, 294, 84, doi: 10.1007/s11207-019-1475-x
+Moore, R. L., & Labonte, B. J. 1980, in Solar and
+Interplanetary Dynamics, ed. M. Dryer &
+E. Tandberg-Hanssen, Vol. 91, 207–210
+Moore, R. L., & Roumeliotis, G. 1992, Triggering of
+Eruptive Flares - Destabilization of the Preflare Magnetic
+Field Configuration, ed. Z. Svestka, B. V. Jackson, &
+M. E. Machado, Vol. 399, 69,
+doi: 10.1007/3-540-55246-4 79
+Pomoell, J., Lumme, E., & Kilpua, E. 2019, SoPh, 294, 41,
+doi: 10.1007/s11207-019-1430-x
+Price, D. J., Pomoell, J., Lumme, E., & Kilpua, E. K. J.
+2019, A&A, 628, A114,
+doi: 10.1051/0004-6361/201935535
+Priest, E. 2014, Magnetohydrodynamics of the Sun,
+doi: 10.1017/CBO9781139020732
+Schmieder, B., D´emoulin, P., & Aulanier, G. 2013,
+Advances in Space Research, 51, 1967,
+doi: 10.1016/j.asr.2012.12.026
+Schou, J., Scherrer, P. H., Bush, R. I., et al. 2012, SoPh,
+275, 229, doi: 10.1007/s11207-011-9842-2
+Schuck, P. W. 2008, ApJ, 683, 1134, doi: 10.1086/589434
+Shimizu, T., Lites, B. W., & Bamba, Y. 2014, Publications
+of the Astronomical Society of Japan, 66, S14,
+doi: 10.1093/pasj/psu089
+Titov, V. S., Hornig, G., & D´emoulin, P. 2002, Journal of
+Geophysical Research (Space Physics), 107, 1164,
+doi: 10.1029/2001JA000278
+Wang, Y. M., Nash, A. G., & Sheeley, N. R., J. 1989,
+Science, 245, 712, doi: 10.1126/science.245.4919.712
+Yokoyama, T., & Shibata, K. 1994, ApJL, 436, L197,
+doi: 10.1086/187666
+Zhang, Y., Bastian, T. S., Liu, J. H., et al. 2021, ApJ, 910,
+40, doi: 10.3847/1538-4357/abded6
+Zheng, J.-C., Yang, Z.-L., Guo, J.-P., et al. 2017, Research
+in Astronomy and Astrophysics, 17, 081,
+doi: 10.1088/1674-4527/17/8/81
+Zhong, Z., Guo, Y., & Ding, M. D. 2021, Nature
+Communications, 12, 2734,
+doi: 10.1038/s41467-021-23037-8
+
+8
+2012-03-05T03:58:14
+AR11429
+A
+D
+E
+F
+AIA-094
+2012-03-05T03:25:38
+AIA-094
+2012-03-05T03:31:50
+AIA-1600
+2012-03-05T03:36:18
+N
+P
+2000 G
+2012-03-05T03:36:00
+C
+500 m/s
+2012-03-05T03:36:00
+B
+Figure 1.
+(A): A full-disk composite image of SDO AIA 171 ˚A and HMI magnetogram.
+The white box shows the AR
+11429. (B): The vectors denote the time average horizontal velocity from 2012 March 4 00:00 UT to March 5 03:36 UT on
+the photosphere. The background shows the magnetic flux distribution, in which black and white represents the negative and
+positive polarity respectively. (C): The vectors denote the transverse magnetic field on the photosphere. (D): Pre-flare image
+of AIA 94˚A. The white arrow shows the erupting structure. (E): Same as D, but at a time closer to eruption before the
+flare onset. (F): The first image of flare ribbons observed in AIA 1600˚A. Letter P labels the positive ribbon and N labels the
+negative ribbon.
+
+Simulation of AR 11429 eruption
+9
+0
+50
+100
+150
+Time (min)
+0.9
+1.0
+1.1
+1.2
+Relative flux
+0.9
+1.0
+1.1
+1.2
+V3D
+OB
+V2D
+0
+50
+100
+150
+1.0
+1.2
+1.4
+1.6
+1.8
+2.0
+EM (Ep0)
+tE,V2D = 126 min
+tE,V3D = 120 min
+tE,V0D = 124 min
+tE,OB = 121 min
+Magnetic energy injection
+V2D
+V3D
+OB
+V0D
+Kinetic energy
+(V0D/V2D/V3D )
+A
+B
+0
+2
+4
+6
+EK × 10-2 (Ep0)
+Figure 2. (A): Magnetic and kinetic energy evolution during the whole process. The unit of x-axis is in minutes. The solid
+curves in different colors denote the corresponding evolution of different energies and the vertical dashed lines in different colors
+denote the eruption onset time of different runs. The vertical black solid line shows the flare onset time in observations. The
+black curve ‘OB’ denotes the magnetic energy injection computed by DAVE4VM velocity and magnetograms, thus representing
+the actual magnetic energy evolution. In our simulation, magnetic energy of the potential field of the initial magnetogram is
+Ep0 = 2.52 × 1030 erg (which is a fixed value and is used for normalization here). This value should be multiplied by a factor
+of 625=252 if scaling to the realistic value, thus being 1.57 × 1033 erg. (B): Time evolution of the total unsigned magnetic
+flux in our simulations. The ‘OB’ curve is computed by the magnetograms and the other labels ‘V3D’, ‘V2D’ and the vertical
+black solid line have the same meanings as in A. All curves are normalized by their initial value at t = 0. The corresponding
+animation is attached for the V3D run, and it starts at t = 0 and ends at t = 147 minutes in simulation time, which corresponds
+to 33.6 hours in real-time duration. Panel a in the animation corresponds to rows A in Figure 3 and 4. Panel b corresponds
+to the rows C in Figure 3 and 4 in time series. Panel c shows the corresponding evolution as in the row D in Figure 4, and
+panel d represents the evolution of QSLs as in Figure 4F. We only plotted the kinetic energy in panel e, with the vertical solid
+line showing the current simulation time; the magnetic flux evolution is not included in the animation. The cadence between
+each snapshot used in the animation is 210 s in the quasi-static period (t ∈ [0, 119] minutes) and 21 s in the eruption period
+(t ∈ (119, 147] minutes) in simulation time, respectively.
+
+10
+-120
+-60
+0
+x (Mm)
+-50
+0
+50
+y (Mm)
+A
+t = 000 min 00 s
+B
+-50
+0
+50
+y (Mm)
+0
+50
+100
+150
+ z (Mm)
+-50
+0
+50
+0
+50
+100
+150
+C
+0
+25
+50
+75
+100
+z (Mm)
+D
+t=119 min
+E
+-120
+-60
+0
+x (Mm)
+t = 070 min 00 s
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+2012-03-05T02:31:24
+-120
+-60
+0
+x (Mm)
+t = 105 min 00 s
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+2012-03-05T03:14:33
+-120
+-60
+0
+x (Mm)
+-36
+-18
+0
+18
+36
+Bz (G)
+t = 119 min 00 s
+-1.00
+-0.75
+-0.50
+-0.25
+0.00
+Tw
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+0.00
+0.05
+0.10
+J/B (Mm-1)
+1
+7
+log10 Q
+t=119 min
+0
+1
+2
+3
+4
+5
+log10 Em
+AIA-171
+AIA-131
+Figure 3. The magnetic evolution during the pre-eruption stage. (A): Top view of 3 bunches of field lines with the footpoints
+approximately following the movement of the magnetic flux. The white solid line denotes the position of the slices in C and in
+Figure 4C and D. The red solid line segment shows the position of the slices in D, which is almost perpendicular to the PIL and
+at the middle of MFR. (B): Side view of the same 3D magnetic field lines as in A. (C): Vertical cross section of the current
+layer near the main PIL. The position of these slices are labeled by the white solid line in A. (D): Magnetic squashing factor
+Q on the same cross section of C and the region with high Q denotes the QSLs. The position of these slices are labeled by the
+red solid line segment in A. (E): The first 2 panels show the comparison between our simulation and observations in AIA 171
+˚A. The last 2 panels show comparison between the synthetic image of coronal emission from current density of our simulation
+and observations in AIA 131 ˚A. Row A is shown at panel a, and rows C is shown at panel c in the animation of Figure 2,
+respectively.
+
+X
+5X
+人X
+人XX
+人XX
+人XHEIX
+人Simulation of AR 11429 eruption
+11
+-240
+-120
+0
+x (Mm)
+-100
+-50
+0
+50
+100
+150
+y (Mm)
+A
+t = 120 min 45 s
+B
+-50
+0
+50
+y (Mm)
+0
+50
+100
+150
+ z (Mm)
+-50
+0
+50
+0
+50
+100
+150
+C
+-50
+0
+50
+y (Mm)
+0
+50
+100
+150
+z (Mm)
+-50
+0
+50
+0
+50
+100
+150
+D
+Vmax =  401.7 km s-1
+MA, max = 0.2
+Vmax =  401.7 km s-1
+MA, max = 0.2
+E
+F
+-240
+-120
+0
+x (Mm)
+t = 122 min 30 s
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+Vmax =  848.0 km s-1
+MA, max = 0.6
+Vmax =  848.0 km s-1
+MA, max = 0.6
+-240
+-120
+0
+x (Mm)
+t = 124 min 15 s
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+Vmax = 1216.7 km s-1
+MA, max = 1.2
+Vmax = 1216.7 km s-1
+MA, max = 1.2
+-240
+-120
+0
+x (Mm)
+-36
+-18
+0
+18
+36
+Bz (G)
+t = 127 min 45 s
+-2.0
+-1.5
+-1.0
+-0.5
+0.0
+Tw
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+0.00
+0.05
+0.10
+J/B (Mm-1)
+-50
+0
+50
+y (Mm)
+-50
+0
+50
+0
+250
+500
+750
+1000
+v (km s-1)
+Vmax = 1141.1 km s-1
+MA, max = 1.7
+Vmax = 1141.1 km s-1
+MA, max = 1.7
+-5
+0
+5
+sgn(Bz) × log10 Q
+2012-03-05T03:54:42
+2012-03-05T04:07:06
+2012-03-05T04:19:30
+2012-03-05T05:09:30
+N
+P
+AIA-1600
+N
+P
+AIA-1600
+N
+P
+AIA-1600
+N
+P
+AIA-1600
+t=119 min
+t=122 min 30 s
+t=126 min 00 s
+t=129 min 30 s
+N
+P
+N
+P
+N
+P
+N
+P
+Figure 4. The magnetic evolution of the eruption stage. (A), (B) and (C): All settings are the same as in Figure 3A, B
+and C, except the footpoints of the magnetic field lines are fixed and the current layer in Figure 3C turns into a current sheet
+here. (D): Outflows at the position of current sheet. (E): Projection corrected images of the flare ribbons observed in AIA
+1600 ˚A. The letter P denotes the positive ribbon and N denotes the negative ribbon. (F): Evolution of the bottom QSL of our
+simulation, where sgn(Bz) denotes the sign of Bz. The letter P denotes the positive QSL and N denotes the negative QSL. The
+slices in C and D are located at the position labeled by the white solid line in the first panel of Figure 3A. Row A is shown at
+panel a, and rows C and D are shown at panel c and panel d in the animation of Figure 2, respectively. The QSL evolution in
+row F is shown at panel b.
+
+XX
+人XX
+人X
+人XX
+人12
+t = 105 min 00 s
+t = 119 min 00 s
+A
+B
+0
+15
+30
+45
+60
+Z (Mm)
+100
+110
+120
+130
+t (min)
+0
+5
+10
+15
+Relative toroidal flux
+V3D
+V0D
+C
+0
+50
+100
+150
+200
+z (Mm)
+0
+1
+2
+3
+n
+D
+potential(V3D)
+simulation(V3D)
+Figure 5. (A): The isosurface of Tw = −1 and Tw is the twist number of the magnetic field in ‘V3D’ simulation. The red ‘X’
+labels the position where we calculate the decay index. (B): Same as A but at a different time. (C): The green solid curve
+denotes the relative toroidal flux of the MFR in ‘V3D’ simulation and the red solid curve in ‘V0D’ simulation with both curves
+normalized by their initial values respectively. Two vertical dashed lines in different colors denotes the onset time of ‘V0D’
+and ‘V3D’ simulations, respectively. The toroidal flux is defined as
+�
+s Bzds, where ‘s’ is the region of Tw < −1 and Bz < 0 at
+the bottom boundary. (D): The decay index n of the magnetic field in ‘V3D’ simulation (solid curve) and the corresponding
+potential field (dashed curve) at the same time of t = 119 minutes. The horizontal dashed line denotes the critical value of
+n = 1.5 and the vertical dashed line denotes the critical height, above which n > 1.5.
+
+XX
\ No newline at end of file
diff --git a/S9AyT4oBgHgl3EQfVfdE/content/tmp_files/load_file.txt b/S9AyT4oBgHgl3EQfVfdE/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..338aebd2003709399aa36803bcb76a357da9b163
--- /dev/null
+++ b/S9AyT4oBgHgl3EQfVfdE/content/tmp_files/load_file.txt
@@ -0,0 +1,656 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf,len=655
+page_content='Draft version January 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2023  Typeset using LATEX twocolumn style in AASTeX631  MHD simulation of Solar Eruption from Active Region 11429 Driven by Photospheric Velocity Field  Xinyi Wang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2 Chaowei Jiang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3 and Xueshang Feng1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 3  1SIGMA Weather Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' State Key Laboratory for Space Weather,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' National Space Science Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='Beijing  100190,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' PR China  2College of Earth and Planetary Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' University of Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Beijing 100049,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' PR China  3Institute of Space Science and Applied Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Harbin Institute of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Shenzhen 518055,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' PR China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' chaowei@hit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='cn  ABSTRACT  Data-driven simulation is becoming an important approach for realistically characterizing the con-  figuration and evolution of solar active regions, revealing the onset mechanism of solar eruption events  and hopefully achieving the goal of accurate space weather forecast, which is beyond the scope of any  existing theoretical modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Here we performed a full 3D MHD simulation using the data-driven  approach and followed the whole evolution process from quasi-static phase to eruption successfully for  solar active region NOAA 11429.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The MHD system was driven at the bottom boundary by photospheric  velocity field, which is derived by the DAVE4VM method from the observed vector magnetograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  The simulation shows that a magnetic flux rope was generated by persistent photospheric flow be-  fore the flare onset and then triggered to erupt by torus instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Our simulation demonstrates a  high degree of consistency with observations in the pre-eruption magnetic structure, the time scale  of quasi-static stage, the pattern of flare ribbons as well as the time evolution of magnetic energy  injection and total unsigned magnetic flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' We further found that an eruption can also be initiated  in the simulation as driven by only the horizontal components of photospheric flow, but a comparison  of the different simulations indicates that the vertical flow at the bottom boundary is necessary in  reproducing more realistically these observed features, emphasizing the importance of flux emergence  during the development of this AR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Keywords: Magnetohydrodynamic (MHD) — Sun: corona — Methods: numerical — Sun: magnetic  fields  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' INTRODUCTION  As driven by solar eruptions, the solar-terrestrial envi-  ronment often experiences variations, which are known  as space weather, and forecasting the space weather pre-  cisely is not only an important scientific topic but can  also avoid damage of the sensitive on-ground and space-  based critical infrastructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Though many theoretical  models have been proposed and significant process has  been made in understanding the triggering mechanism  of solar eruptions (Forbes 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Chen 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Schmieder  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Priest 2014), reproducing the whole life-span  from quasi-static stage to eruption using numerical mod-  els constrained and driven by observed vector magne-  togram possess unprecedented capabilities in revealing  the onset mechanism of the real eruption events, and can  potentially be used for accurate space weather forecast  (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Jiang 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Previous study reproduced the whole process of en-  ergy accumulation and release successfully (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2016), showing an MHD system can be driven to erupt  by inputting time series of vector magnetograms at the  bottom boundary (B-driven).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' There are also other data-  driven models, in which the evolution of MHD system  is driven by the electric field (E-driven, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Cheung &  DeRosa 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Hayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Pomoell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Price et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019) or the velocity field (V-driven, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=',  Hayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Guo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Zhong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2021) on the photosphere  (bottom boundary).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Though the B-driven method can  fully match the magnetogram, it will introduce consid-  erable errors of magnetic divergence from the bottom  boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' This shortage will vanish in E-driven model,  however, deriving both the induction and potential com-  ponents of the electric field on the photosphere is not an  easy task (Fisher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2010, 2012, 2015, 2020), and the  photospheric flow also needs to be properly set to fol-  low the Ohm’s law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' In most of the theoretical models of  solar eruption, the key structure in favor of eruption is  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='00144v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='SR]  31 Dec 2022  2  assumed to be formed through the movement of the foot-  points of magnetic field lines (Moore & Labonte 1980;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Moore & Roumeliotis 1992;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Antiochos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Lin  & Forbes 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2021b), which is driven by  the horizontal flow, and the vertical component of the  photospheric flow will be responsible for the flux emer-  gence process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Therefore, with the photospheric velocity  field determined, the photospheric magnetic field can  be generated self-consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Furthermore, in the V-  driven approach, there is no need to solve the complex  momentum equation at the bottom boundary (which is  the most time-consuming part in solving MHD equa-  tions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Due to these advantages, the V-driven method  has attracted many previous studies to focus on this  topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' For example, with the velocity field derived by  DAVE4VM method (Schuck 2008), Hayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (2019)  used the projected normal characteristics method to up-  date the physical variables other than velocity at the  bottom boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' However, the total magnetic energy  kept almost the same level of that of the initial state  without obvious magnetic energy injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  (2021a) updated the magnetic field by solving directly  the magnetic induction equation at the bottom bound-  ary and their model can inject the magnetic energy from  bottom boundary successfully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (2020) drove the  magnetic evolution by inputting the DAVE4VM velocity  field and vector magnetogram simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The for-  mation process of an magnetic flux rope (MFR) was ob-  tained in their model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Unfortunately, these simulations  didn’t drive the system to erupt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The only work we know  that obtained an eruption by the velocity field derived  from observation was shown in Kaneko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  The velocity field was derived from the electric field on  the photosphere using Ohm’s law and then was input at  the bottom boundary in their zero-beta model to drive  the system to erupt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Two eruptions they produced were  identified from the evolution curves of the magnetic and  kinetic energies, however, the kinetic energy showed an  overall increase without obvious quasi-static evolution  during the pre-eruption stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Before the first eruption,  the kinetic energy was comparable with its peak dur-  ing the first eruption and the amount of the release of  the magnetic energy was also too small, which didn’t  show the feature of a typical eruption event, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', a large  amount of magnetic energy was converted into kinetic  energy impulsively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' As described above, the whole en-  ergy accumulation process from quasi-static evolution  (of typically tens of hours) to impulsive eruption has  not been realized in a self-consistent way using the V-  driven MHD model, and this is one of the motivations  of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  In this Letter, we applied a V-driven model to inves-  tigate the evolution and eruption of a well-studied ac-  tive region (AR) NOAA 11429.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Previous studies found  persistent shearing flow and flux cancellation near the  main polarity inversion line (PIL) of this AR (Shimizu  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2017), which were suggested  to be responsible for the eruptions on 2012 March 7,  9 and 10 (Dhakal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2018, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  An analysis of  the MFR reconstructed from vector magnetograms us-  ing the nonlinear force-free field (NLFFF) model sug-  gests that the homologous eruptions are triggered by  torus instability (TI) of the MFR (Chintzoglou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (2021) suggested the helical kink  instability may also take effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Nevertheless, whether  these mechanisms were at work requires to be further  studied using dynamic modeling of this AR evolution  and eruption, which is absent in all the previous stud-  ies and is the other motivation of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  In our  simulation, the dynamic process from the beginning of  2012 March 4 to the eruption on March 5 in this AR  was reproduced self-consistently as driven by the pho-  tospheric velocity derived from vector magnetogram us-  ing DAVE4VM method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Our simulation shows that an  MFR was generated near the main PIL before the flare  onset and the initiation of this eruption event depended  mainly on TI of the preformed MFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' DATA AND MODEL  AR 11429 showed a complex βγδ configuration and  is very flare-productive, which has produced 3 X-class  flares from 2012 March 5 to 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' It first appeared on the  eastern solar limb on March 4 and was located on the  eastern part of the solar disk before March 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' During  this period, the AR kept developing as characterized by  the increasing total unsigned magnetic flux, indicating  the obvious flux emergence by vertical flow on the pho-  tosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Since it was the first X-class flare of this AR,  here we focus on the initiation process of the X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1 flare  (which is accompanied with a halo CME moving at a  speed of 1531 km s−1) around 04:00 UT on March 5 as  shown in the white box in Figure 1A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Before the flare on-  set, there was persistent shearing flow near the main PIL  (Figure 1B) and as a result, the horizontal magnetic field  there was highly sheared (Figure 1C), which indicates  that a large amount of free magnetic energy is stored  ready for an eruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' An hot loop first erupted away  as shown in AIA 94 ˚A (Lemen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2012) at around  03:31 UT (Figure 1D and E) and after that a pair of  hook shape flare ribbons appeared near the main PIL  in AIA 1600 ˚A at 03:36 UT (Figure 1F), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', the flare  event started.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Simulation of AR 11429 eruption  3  To understand the formation of the pre-eruptive coro-  nal magnetic field and the triggering mechanism of this  eruption, we used the DARE-MHD model (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2016) to study the dynamic evolution of this AR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' For  saving the computational time, the strength of magnetic  field from the magnetograms were reduced by a factor of  25 before being input into our code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The initial plasma  density was set as a hydrostatic isothermal model with a  fixed temperature as T = 1×106 K and a modified solar  gravity (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2021b) to get a plasma background  that mimics the real environment in the solar corona  basing on two key parameters, the plasma β and the  Alfv´en speed (in particular, the minimum β is 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3×10−4  and maximum Alfv´en speed VA ∼ 4800 km s−1 in the  final equilibrium we obtained below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' We chose to use  the magnetograms of HMI SHARP data set (Schou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Bobra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2014) at 00:00UT on March 4 to  reconstruct the initial magnetic field since there were  no obvious MFR at that time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' This magnetogram was  smoothed first using Gaussian smoothing with FWHM  of 6 pixels and a NLFFF model from this smoothed  magnetogram was extrapolated by our CESE-NLFFF-  MHD code (Jiang & Feng 2012, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Since the code  (like many other NLFFF codes) does not give a per-  fect force-free solution but with residual Lorentz forces,  we input the extrapolated field into the DARE-MHD  model, along with the initial background plasma, to let  the MHD system relax until the kinetic and magnetic  energies were almost unchanged, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', an MHD equilib-  rium was obtained, and the initial state was ready.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  At the bottom boundary, we solve the magnetic induc-  tion equation to update the magnetic field with the ve-  locity field derived by DAVE4VM method to update the  magnetic field on the photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The DAVE4VM ve-  locity was strengthened by a factor of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7 (determined  by the ratio of the time series magnetograms’ original  time cadence as 720 seconds to the time cadence in our  simulation as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='5 × 105 seconds, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=',  720  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='5×105) to speed  up our simulation and thus the time scale of quasi-static  evolution prior to the eruption onset is shorten by the  same times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  At the side and top boundaries, all the  variables are extrapolated from the neighboring inner  points with zero gradient along the normal direction  of the boundary surface and the normal component of  magnetic field is further modified by the divergence-free  condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The Powell-source terms and diffusion con-  trol terms was used to deal with the divergence error of  the magnetic field as described in Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  We set the computational domain sufficiently large as  [−368, 368] Mm in both x and y direction and [0, 736]  Mm in z direction with grid resolution varies from 1′′ to  8′′ using adaptive mesh refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The highest resolu-  tion is used mainly for the regions with strong magnetic  gradients and current density, in particular, the current  sheets (CSs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Explicit value of magnetic resistivity was  not used in our simulation and the magnetic reconnec-  tion was controlled by the resistivity of the numerical  method only, which mimicked the low-resistivity plasma  better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' As the total unsigned flux of this AR kept in-  creasing before the flare onset, we energized the MHD  system by full 3D DAVE4VM velocity field (vD  x , vD  y , vD  z )  (will be referred to as V3D simulation) and horizontal  component (vD  x , vD  y , 0) (V2D) respectively, and a com-  parison of the results for these two simulations will show  the importance of flux emergence through the vertical  flow on the photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' RESULTS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Overall Process  The evolution curves of the total magnetic and kinetic  energies in the computational domain as well as the to-  tal unsigned magnetic flux at the bottom boundary are  shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' For the ‘V3D’ simulation, as driven  by the time-series velocity field (V3D) for a time dura-  tion of 150 minutes, the total magnetic energy in our  simulation model experienced an overall increase firstly  and then a rapid decrease, which is associated with an  eruption event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The eruption can be identified from the  energy evolution with onset time tE,V3D = 120 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  At the very beginning from t = 0 to t = 22 minutes,  the magnetic energy injection curve (black dashed line,  which is computed by the time integration of the to-  tal Poynting flux of the ‘V3D’ simulation at the bottom  surface) matches well with the solid ‘V3D’ curve (the  magnetic energy increase of the ‘V3D’ simulation) and  ‘OB’ curve (the magnetic energy injection computed by  DAVE4VM velocity and magnetograms) in Figure 2A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  However, in the time duration of t ∈ [97, 122] minutes,  the total magnetic energy (blue solid line) is higher than  the magnetic energy injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Such an unphysical mis-  match of the inputted energy from the boundary and the  cumulative energy in the volume is likely owing to the in-  sufficient resolution for the bottom boundary, since the  magnetic field at the bottom boundary has accumulated  a very large gradient in this phase (see Discussions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The  kinetic energy keeps a very low value of around 10−3Ep0  (which is the potential field energy corresponding to the  magnetic field at t=0) before the major eruption be-  gins at tE,V3D = 120 minutes when the magnetic energy  reaches about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='85 Ep0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The magnetic energy decreases  to about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7 Ep0 at the peak of the total kinetic energy  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Ek = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='6 × 10−2Ep0), and keeps decreasing to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='45  Ep0 in total through this eruption (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='4 Ep0 free energy  loss).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' That is, about one third of the magnetic energy  4  loss has been converted to kinetic energy in 10 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  If multiplied by a factor of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7 determined by the rate of  speeding up in our velocity-driven simulation, the quasi-  static evolution time of ‘V3D’ run is 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='4 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' This  time scale is very close to the observation one which is  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='6 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  We have also driven the simulation by the horizontal  velocity (V2D) and found that it can also produce an  eruption with rather similar onset time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' However, com-  paring the different curves of magnetic energy evolution  in Figure 2A and the curves of total unsigned magnetic  flux in Figure 2B respectively, the blue solid lines labeled  by ‘V2D’ are obvious lower than those from the ’V3D’  simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' This clearly shows that though horizontal  velocity can also drive the field to erupt (with a delayed  onset time for about 6 minutes compared with ‘V3D’),  the vertical velocity vD  z is necessary in accounting for the  larger increase of the total magnetic energy and total un-  signed flux as shown in observations, therefore leading  to a stronger eruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The evolution of the simulated  magnetic energy, total unsigned flux and the time scale  of the ‘V3D’ run before the major eruption are more  consistent with observations, showing the importance of  the vertical photospheric plasma flow in the numerical  modeling of solar eruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Our simulated magnetic  structure (the first panel in Figure 3E) has reasonable  consistency with observations in the pre-eruption image  of AIA 171 ˚A (the second panel in Figure 3E), and the  synthetic image of coronal emission from current den-  sity of our simulation (the last panel in Figure 3E) is  reasonable consistent with the image of AIA 131 ˚A (the  third panel in Figure 3E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Also the quasi separatrix lay-  ers (QSLs), where the magnetic reconnection is most  likely to take place and thus represent the position of  the flare ribbons (Titov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2016),  at the bottom boundary (Figure 4F) has approximately  the same patterns as the flare ribbons in AIA 1600 ˚A  (Figure 4E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' These results confirm the validity of our  V-driven DARE-MHD model as well as the DAVE4VM  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Eruption Initiation Mechanism  Since the actual velocity field must contain vz, here we  analyzed the ‘V3D’ run to study the onset mechanism  of this eruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' As we can see, a group of twisted field  lines (represented by the blue solid lines in Figure 3A  and B) formed and was embedded in the surrounding  shear arcades, which is similar to an MFR in morphol-  ogy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' In addition, the ejection of the hot loop (also called  hot channel) as observed in AIA 94 ˚A (shown by the  white arrows in Figure 1D and E) also suggested the ex-  istence of an MFR (Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2017) before the flare  onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  To identify the formation of MFR before the eruption,  we calculated the QSLs and the twist number (Berger  & Prior 2006) of our simulated magnetic fields, which  are given in Figure 3D, Figure 5A and B, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  As shown in the third panel of Figure 3D, a strong QSL  appeared near the core field and grew up to be a QSL  ring in the last panel, which separated the MFR and the  background magnetic field, thus representing the exis-  tence of an MFR in topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The QSL ring intersects  itself below the MFR, forming a typical hyperbolic flux  tube (HFT), where the CS developed and magnetic re-  connection took place subsequently to further drive the  eruption (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The isosurface of Tw = −1,  which represents the position and shape of the MFR, are  shown in Figure 5A and B respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' It became larger  and higher, illustrating more magnetic flux were twisted  as driven by persistent photospheric flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' However, the  isosurface of Tw = −2, which is the lower threshold of  kink instability (KI) according to the statistics of Duan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (2019), is barely visible and KI may take little  effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Among different triggering mechanisms, TI is consid-  ered as an efficient way of MFR eruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' In Figure 5D,  we plot the key controlling parameter that determines  the onset of TI, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', the decay index of the strapping  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The variation of the decay index n was calculated  along the z direction of the overlying field at t = 119  minutes before the eruption onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Since the potential  field is not always the good approximation of the strap-  ping field (especially when the strapping field is highly  sheared), we calculated the decay index of our simu-  lated field instead and plotted the decay index of the  corresponding potential field at the same time for com-  parison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The critical height (above which n > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='5) of  the simulated field is located at 60 Mm as labeled by  the vertical black dashed line in Figure 5D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' When the  MFR was just formed, it is small and it’s apex was at a  low height (about 40 Mm in Figure 5A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' About 14 min-  utes later, it had grown up to be a huge twist structure  and entered the unstable zone (above 60 Mm as shown  in Figure 5B), after which it erupted violently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  The formation and the evolution of the MFR, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=',  there was an preformed MFR and the MFR erupted af-  ter it entered the unstable zone, strongly suggest that TI  is the triggering mechanism of this eruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' To further  test this assumption, we used the V3D-driven data at  t = 100 minutes as the initial condition and ran our code  without bottom velocity driven (by setting all the three  velocity components as zero at the bottom boundary,  thus referred to as ‘V0D’) to see whether the magnetic  Simulation of AR 11429 eruption  5  field will erupt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The evolution of energies of this ‘V0D’  run are shown as the red solid lines in Figure 2A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' During  the time duration of t ∈ [100, 124] minutes, the magnetic  energy kept almost unchanged, while the toroidal flux of  the MFR (defined as  �  s Bzds, where s denotes the region  of Tw < −1 and Bz < 0 at the bottom boundary) kept  increasing as shown in Figure 5C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' In ‘V3D’ simulation,  the MFR (the isosurface of Tw = −1) became larger  and higher than the critical height before the eruption  onset (Figure 5A and B) as the toroidal flux increas-  ing (Figure 5C), after which TI took effect and finally  led to a strong eruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Similarly, the toroidal flux of  ‘V0D’ simulation increased before and decreased after  the eruption (Figure 5C), showing the slow reconnec-  tion can took place spontaneously without velocity driv-  ing and made the MFR larger until the eruption started  at tE,V0D = 124 minutes as identified from the energy  evolution curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Since the current density was weaker  and the current layer was thicker (as shown in the third  panel in Figure 3C) than a true CS (the first panel in  Figure 4C), the magnetic gradient was lower in the cur-  rent layer than in the CS, and thus the diffusivity was  relatively uniform, which only allowed slow reconnection  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', a slow dissipation of the current) to take place with-  out impulsive energy release (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', not a Pescheck-type  reconnection, Yokoyama & Shibata 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The eruption  of this ‘V0D’ run has the similar onset time and strength  with the ‘V3D’ run, which further indicates that after  t = 100 minutes in ‘V3D’ run, the velocity field on the  bottom boundary is not necessary and the instability is  sufficient to trigger the eruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  It follows the basic  developing stage of TI, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', the rising MFR stretched  the overlying field and consequently the flare CS formed  below the MFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Since we didn’t use any explicit value  of magnetic resistivity, and since the CS formed in a  dynamic way, the width of CS could become very thin  to trigger the fast reconnection easily as pointed out by  Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (2021b), which further drives the eruption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Based on the analysis of our simulation and the sup-  plementary numerical experiment (‘V0D’ simulation),  along with the consistency between our simulation re-  sults and observations that have been shown above, we  conclude that TI is the initiation mechanism of the X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1  flare in AR 11429 on 2012 March 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' CONCLUSIONS AND DISCUSSIONS  We have carried out a full 3D MHD simulation of  an X-class flare eruption event on 2012 March 5 in AR  11429 using the V-driven DARE-MHD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' An MHD  equilibrium was obtained by relaxing the NLFFF recon-  structed by the CESE-MHD-NLFFF code and was set as  the initial condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Then the initial state was driven  to evolve by the DAVE4VM velocity field on the bot-  tom boundary of our simulation box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The analysis of  the quasi-static evolution stage before the eruption on-  set shows the gradual formation of an MFR above the  main PIL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' When the MFR first appeared, it was rela-  tively low and then it grew up into the torus unstable  region, after which TI was triggered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Then the energy  conversion process was accomplished by reconnection in  the CS that is formed due to the stretching effect of  the erupting MFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The images of SDO observation and  the important physical quantities computed from the  magnetograms are reasonably consistent with our result  in the pre-flare magnetic structure, the morphology of  flare ribbons, evolution curves of the magnetic and ki-  netic energies as well as the total unsigned magnetic flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  The time duration of the quasi-static evolution process  before the simulated eruption is also very close to the  actual time scale before the flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Nevertheless, our simulation does not reproduce accu-  rately the evolution of magnetic field as shown in the ob-  served magnetograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' As can be seen in the last panel of  Figure 3A, part of the magnetic flux was transported to  and concentrated at the edge of the AR, while this pileup  was not observed in HMI magnetograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' One likely rea-  son for this flux pileup is that, the DAVE4VM method  only solves the normal component of the magnetic in-  duction equation in the least-square sense (Lumme et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2019), which may not reproduce the velocity precisely  at every point and can only be used to approximate the  overall distribution and evolution of magnetic flux in  the AR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' In addition, the magnetic flux on the photo-  sphere should be dispersed and dissipated by granular  and supergranular convection (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 1989) as well  as small scale turbulent diffusion in practical situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Therefore, without dealing properly with these effects,  the flux pileup will be more obvious than observations  and as a result the magnetic energy injection rate of  ‘V3D’ run will be overall higher than the ‘OB’ one as  shown in Figure 2A (comparing the black dashed line  and the black solid line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' This unrealistic flux pileup  may also contribute to the overshoot of the magnetic  energy increase (Figure 2A, the mismatch of the black  dashed line and the green line before the eruption), be-  cause it results in a very large magnetic gradient at the  bottom boundary, thus even the finest spatial resolution  in our simulation was inadequate to capture the too high  gradient during the time duration close to the eruption  onset (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', t ∈ [97, 122] minutes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The insufficient grid  resolution led to the considerable numerical error there,  which thus makes the magnetic energy increase higher  than the magnetic energy injection in ‘V3D’ simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  The proper settings of numerical diffusion and grid res-  6  olution, along with the improved methods for deriving  the photospheric flow will need to be considered in fu-  ture works for a more accurate data-driven simulation  of solar eruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  To summarize, our simulation shows that, besides  inputting the time series of vector magnetogram, the  numerical model of solar corona can be driven to erupt  by inputting the time series velocity field at the bot-  tom boundary, in which the driver, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', the bottom  velocity field is derived from time series of vector mag-  netograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  The numerical model we established here  shows the possibility of driving the evolution of solar  corona using different physical variables, which offers  a straightforward way for revealing the eruption mech-  anisms in real events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Thus, such model has a great  potentiality in forecasting the onset time as well as the  strength of solar eruptions and evaluating the quantita-  tive impact on space weather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  This  work  is  jointly  supported  by  the  Na-  tional Natural Science Foundation of China (NSFC  41731067, 42030204, 42174200), the Fundamental Re-  search Funds for the Central Universities (grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  HIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='OCEF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2021033), and Shenzhen Science and Tech-  nology Program (grant Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' RCJC20210609104422048  and JCYJ20190806142609035).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  The computational  work was carried out on TianHe-1(A), National Super-  computer Center in Tianjin, China, and we thank Jun  Chen for his informative and helpful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  REFERENCES  Antiochos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', DeVore, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Klimchuk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 1999,  ApJ, 510, 485, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1086/306563  Berger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Prior, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2006, Journal of Physics A  Mathematical General, 39, 8321,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1088/0305-4470/39/26/005  Bobra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Sun, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Hoeksema, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2014, SoPh,  289, 3549, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/s11207-014-0529-3  Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2011, Living Reviews in Solar Physics, 8, 1,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='12942/lrsp-2011-1  Cheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Ding, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2017, Science China Earth  Sciences, 60, 1383, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/s11430-017-9074-6  Cheung, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & DeRosa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2012, ApJ, 757, 147,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1088/0004-637X/757/2/147  Chintzoglou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Patsourakos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Vourlidas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2015,  ApJ, 809, 34, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1088/0004-637X/809/1/34  Dhakal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Chintzoglou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2018, ApJ,  860, 35, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4357/aac028  Dhakal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Vemareddy, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Karna, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2020,  ApJ, 901, 40, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4357/abacbc  Duan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019, ApJ, 884, 73,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4357/ab3e33  Fisher, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Kazachenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Welsch, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2020, ApJS, 248, 2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4365/ab8303  Fisher, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Welsch, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Abbett, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2012, SoPh,  277, 153, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/s11207-011-9816-4  Fisher, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Welsch, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Abbett, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Bercik, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2010, ApJ, 715, 242, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1088/0004-637X/715/1/242  Fisher, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Abbett, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Bercik, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2015,  Space Weather, 13, 369, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1002/2015SW001191  Forbes, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2000, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', 105, 23153,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1029/2000JA000005  Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Xia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Keppens, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Ding, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2019, ApJL, 870, L21, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/2041-8213/aafabf  Hayashi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Xiong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2018, The  Astrophysical Journal, 855, 11,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4357/aaacd8  Hayashi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Xiong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019, ApJL,  871, L28, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/2041-8213/aaffcf  He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Zou, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2020, ApJ, 892, 9,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4357/ab75ab  Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2022, Reviews of Geophysics and Planetary  Physics, 53, 497, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='19975/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='dqyxx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2022-022  Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Bian, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Sun, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2021a, Frontiers in  Physics, 9, 224, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3389/fphy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='646750  Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2012, ApJ, 749, 135,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1088/0004-637X/749/2/135  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2013, ApJ, 769, 144, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1088/0004-637X/769/2/144  Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Hu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2022, The  Innovation, 3, 100236,  doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='xinn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='100236  Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Zhong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2010, SoPh,  267, 463, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/s11207-010-9649-6  Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Hu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2016, Nature  Communications, 7, 11522, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1038/ncomms11522  Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Zou, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2018, The Astrophysical  Journal, 869, 13, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4357/aaeacc  Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Liu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2021b, Nature  Astronomy, 5, 1126, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1038/s41550-021-01414-z  Kaneko, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Kusano, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2021, ApJ, 909, 155,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4357/abe414  Lemen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Title, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Akin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2012, SoPh,  275, 17, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/s11207-011-9776-8  Lin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Forbes, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2000, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', 105, 2375,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1029/1999JA900477  Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Zhao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019, A&A, 626, A91,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1051/0004-6361/201935225  Simulation of AR 11429 eruption  7  Liu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Kliem, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Titov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2016, ApJ, 818, 148,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/0004-637X/818/2/148  Lumme, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Kazachenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Fisher, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019,  SoPh, 294, 84, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/s11207-019-1475-x  Moore, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Labonte, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 1980, in Solar and  Interplanetary Dynamics, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Dryer &  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Tandberg-Hanssen, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 91, 207–210  Moore, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Roumeliotis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 1992, Triggering of  Eruptive Flares - Destabilization of the Preflare Magnetic  Field Configuration, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Svestka, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Jackson, &  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Machado, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 399, 69,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/3-540-55246-4 79  Pomoell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Lumme, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Kilpua, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2019, SoPh, 294, 41,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/s11207-019-1430-x  Price, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Pomoell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Lumme, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Kilpua, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  2019, A&A, 628, A114,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1051/0004-6361/201935535  Priest, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2014, Magnetohydrodynamics of the Sun,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1017/CBO9781139020732  Schmieder, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', D´emoulin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Aulanier, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2013,  Advances in Space Research, 51, 1967,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='asr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='026  Schou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Scherrer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Bush, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2012, SoPh,  275, 229, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1007/s11207-011-9842-2  Schuck, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2008, ApJ, 683, 1134, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1086/589434  Shimizu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Lites, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Bamba, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2014, Publications  of the Astronomical Society of Japan, 66, S14,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1093/pasj/psu089  Titov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Hornig, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & D´emoulin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2002, Journal of  Geophysical Research (Space Physics), 107, 1164,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1029/2001JA000278  Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Nash, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Sheeley, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 1989,  Science, 245, 712, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='4919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='712  Yokoyama, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Shibata, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 1994, ApJL, 436, L197,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1086/187666  Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Bastian, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2021, ApJ, 910,  40, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='3847/1538-4357/abded6  Zheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Guo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2017, Research  in Astronomy and Astrophysics, 17, 081,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1088/1674-4527/17/8/81  Zhong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=', & Ding, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' 2021, Nature  Communications, 12, 2734,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1038/s41467-021-23037-8  8  2012-03-05T03:58:14  AR11429  A  D  E  F  AIA-094  2012-03-05T03:25:38  AIA-094  2012-03-05T03:31:50  AIA-1600  2012-03-05T03:36:18  N  P  2000 G  2012-03-05T03:36:00  C  500 m/s  2012-03-05T03:36:00  B  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  (A): A full-disk composite image of SDO AIA 171 ˚A and HMI magnetogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  The white box shows the AR  11429.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (B): The vectors denote the time average horizontal velocity from 2012 March 4 00:00 UT to March 5 03:36 UT on  the photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The background shows the magnetic flux distribution, in which black and white represents the negative and  positive polarity respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (C): The vectors denote the transverse magnetic field on the photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (D): Pre-flare image  of AIA 94˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The white arrow shows the erupting structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (E): Same as D, but at a time closer to eruption before the  flare onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (F): The first image of flare ribbons observed in AIA 1600˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Letter P labels the positive ribbon and N labels the  negative ribbon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  Simulation of AR 11429 eruption  9  0  50  100  150  Time (min)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2  Relative flux  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2  V3D  OB  V2D  0  50  100  150  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0  EM (Ep0)  tE,V2D = 126 min  tE,V3D = 120 min  tE,V0D = 124 min  tE,OB = 121 min  Magnetic energy injection  V2D  V3D  OB  V0D  Kinetic energy  (V0D/V2D/V3D )  A  B  0  2  4  6  EK × 10-2 (Ep0)  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (A): Magnetic and kinetic energy evolution during the whole process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The unit of x-axis is in minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The solid  curves in different colors denote the corresponding evolution of different energies and the vertical dashed lines in different colors  denote the eruption onset time of different runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The vertical black solid line shows the flare onset time in observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The  black curve ‘OB’ denotes the magnetic energy injection computed by DAVE4VM velocity and magnetograms, thus representing  the actual magnetic energy evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' In our simulation, magnetic energy of the potential field of the initial magnetogram is  Ep0 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='52 × 1030 erg (which is a fixed value and is used for normalization here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' This value should be multiplied by a factor  of 625=252 if scaling to the realistic value, thus being 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='57 × 1033 erg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (B): Time evolution of the total unsigned magnetic  flux in our simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The ‘OB’ curve is computed by the magnetograms and the other labels ‘V3D’, ‘V2D’ and the vertical  black solid line have the same meanings as in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' All curves are normalized by their initial value at t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The corresponding  animation is attached for the V3D run, and it starts at t = 0 and ends at t = 147 minutes in simulation time, which corresponds  to 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='6 hours in real-time duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Panel a in the animation corresponds to rows A in Figure 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Panel b corresponds  to the rows C in Figure 3 and 4 in time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Panel c shows the corresponding evolution as in the row D in Figure 4, and  panel d represents the evolution of QSLs as in Figure 4F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' We only plotted the kinetic energy in panel e, with the vertical solid  line showing the current simulation time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' the magnetic flux evolution is not included in the animation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The cadence between  each snapshot used in the animation is 210 s in the quasi-static period (t ∈ [0, 119] minutes) and 21 s in the eruption period  (t ∈ (119, 147] minutes) in simulation time, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  10  120  60  0  x (Mm)  50  0  50  y (Mm)  A  t = 000 min 00 s  B  50  0  50  y (Mm)  0  50  100  150  z (Mm)  50  0  50  0  50  100  150  C  0  25  50  75  100  z (Mm)  D  t=119 min  E  120  60  0  x (Mm)  t = 070 min 00 s  50  0  50  y (Mm)  50  0  50  2012-03-05T02:31:24  120  60  0  x (Mm)  t = 105 min 00 s  50  0  50  y (Mm)  50  0  50  2012-03-05T03:14:33  120  60  0  x (Mm)  36  18  0  18  36  Bz (G)  t = 119 min 00 s  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='00  Tw  50  0  50  y (Mm)  50  0  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='10  J/B (Mm-1)  1  7  log10 Q  t=119 min  0  1  2  3  4  5  log10 Em  AIA-171  AIA-131  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The magnetic evolution during the pre-eruption stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (A): Top view of 3 bunches of field lines with the footpoints  approximately following the movement of the magnetic flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The white solid line denotes the position of the slices in C and in  Figure 4C and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The red solid line segment shows the position of the slices in D, which is almost perpendicular to the PIL and  at the middle of MFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (B): Side view of the same 3D magnetic field lines as in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (C): Vertical cross section of the current  layer near the main PIL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The position of these slices are labeled by the white solid line in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (D): Magnetic squashing factor  Q on the same cross section of C and the region with high Q denotes the QSLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The position of these slices are labeled by the  red solid line segment in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (E): The first 2 panels show the comparison between our simulation and observations in AIA 171  ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The last 2 panels show comparison between the synthetic image of coronal emission from current density of our simulation  and observations in AIA 131 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Row A is shown at panel a, and rows C is shown at panel c in the animation of Figure 2,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  X  5X  人X  人XX  人XX  人XHEIX  人Simulation of AR 11429 eruption  11  240  120  0  x (Mm)  100  50  0  50  100  150  y (Mm)  A  t = 120 min 45 s  B  50  0  50  y (Mm)  0  50  100  150  z (Mm)  50  0  50  0  50  100  150  C  50  0  50  y (Mm)  0  50  100  150  z (Mm)  50  0  50  0  50  100  150  D  Vmax =  401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7 km s-1  MA, max = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2  Vmax =  401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7 km s-1  MA, max = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2  E  F  240  120  0  x (Mm)  t = 122 min 30 s  50  0  50  y (Mm)  50  0  50  50  0  50  y (Mm)  50  0  50  Vmax =  848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0 km s-1  MA, max = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='6  Vmax =  848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0 km s-1  MA, max = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='6  240  120  0  x (Mm)  t = 124 min 15 s  50  0  50  y (Mm)  50  0  50  50  0  50  y (Mm)  50  0  50  Vmax = 1216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7 km s-1  MA, max = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2  Vmax = 1216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7 km s-1  MA, max = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='2  240  120  0  x (Mm)  36  18  0  18  36  Bz (G)  t = 127 min 45 s  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='0  Tw  50  0  50  y (Mm)  50  0  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='10  J/B (Mm-1)  50  0  50  y (Mm)  50  0  50  0  250  500  750  1000  v (km s-1)  Vmax = 1141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1 km s-1  MA, max = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7  Vmax = 1141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='1 km s-1  MA, max = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='7  5  0  5  sgn(Bz) × log10 Q  2012-03-05T03:54:42  2012-03-05T04:07:06  2012-03-05T04:19:30  2012-03-05T05:09:30  N  P  AIA-1600  N  P  AIA-1600  N  P  AIA-1600  N  P  AIA-1600  t=119 min  t=122 min 30 s  t=126 min 00 s  t=129 min 30 s  N  P  N  P  N  P  N  P  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The magnetic evolution of the eruption stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (A), (B) and (C): All settings are the same as in Figure 3A, B  and C, except the footpoints of the magnetic field lines are fixed and the current layer in Figure 3C turns into a current sheet  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (D): Outflows at the position of current sheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (E): Projection corrected images of the flare ribbons observed in AIA  1600 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The letter P denotes the positive ribbon and N denotes the negative ribbon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (F): Evolution of the bottom QSL of our  simulation, where sgn(Bz) denotes the sign of Bz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The letter P denotes the positive QSL and N denotes the negative QSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The  slices in C and D are located at the position labeled by the white solid line in the first panel of Figure 3A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Row A is shown at  panel a, and rows C and D are shown at panel c and panel d in the animation of Figure 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The QSL evolution in  row F is shown at panel b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  XX  人XX  人X  人XX  人12  t = 105 min 00 s  t = 119 min 00 s  A  B  0  15  30  45  60  Z (Mm)  100  110  120  130  t (min)  0  5  10  15  Relative toroidal flux  V3D  V0D  C  0  50  100  150  200  z (Mm)  0  1  2  3  n  D  potential(V3D)  simulation(V3D)  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (A): The isosurface of Tw = −1 and Tw is the twist number of the magnetic field in ‘V3D’ simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The red ‘X’  labels the position where we calculate the decay index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (B): Same as A but at a different time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (C): The green solid curve  denotes the relative toroidal flux of the MFR in ‘V3D’ simulation and the red solid curve in ‘V0D’ simulation with both curves  normalized by their initial values respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' Two vertical dashed lines in different colors denotes the onset time of ‘V0D’  and ‘V3D’ simulations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The toroidal flux is defined as  �  s Bzds, where ‘s’ is the region of Tw < −1 and Bz < 0 at  the bottom boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' (D): The decay index n of the magnetic field in ‘V3D’ simulation (solid curve) and the corresponding  potential field (dashed curve) at the same time of t = 119 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content=' The horizontal dashed line denotes the critical value of  n = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='5 and the vertical dashed line denotes the critical height, above which n > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
+page_content='  XX' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AyT4oBgHgl3EQfVfdE/content/2301.00144v1.pdf'}
diff --git a/SdFAT4oBgHgl3EQf1h7S/content/tmp_files/2301.08710v1.pdf.txt b/SdFAT4oBgHgl3EQf1h7S/content/tmp_files/2301.08710v1.pdf.txt
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+Turbulence Driving by Interstellar Pickup Ions in the Outer Solar Wind 
+Philip A. Isenberg, Bernard J. Vasquez, and Charles W. Smith 
+Space Science Center and Department of Physics and Astronomy 
+University of New Hampshire, Durham, NH 03824, USA 
+ 
+ 
+ 
+ 
+Abstract.  We revisit the question of how the unstable scattering of interstellar pickup ions 
+(PUIs) may drive turbulence in the outer solar wind, and why the energy released into 
+fluctuations by this scattering appears to be significantly less than the standard bispherical 
+prediction. We suggest that energization of the newly picked-up ions by the ambient turbulence 
+during the scattering process can result in a more spherical distribution of PUIs, and reduce the 
+generated fluctuation energy to a level consistent with the observations of turbulent intensities 
+and core solar wind heating. This scenario implies the operation of a self-regulation mechanism 
+that maintains the observed conditions of turbulence and heating in the PUI-dominated solar 
+wind. 
+ 
+ 
+ 
+ 
+1.  Introduction 
+ 
+The neutral component of the partially ionized local interstellar medium (LISM) 
+penetrates the boundaries of the heliopause and termination shock and flows slowly through the 
+supersonic solar wind (Axford 1972; Holzer 1972; Isenberg 1986). These neutral particles, 
+primarily hydrogen atoms, fill most of the heliosphere, being excluded only from a region near 
+the Sun due to increased ionization from solar photons and charge-exchange interactions with the 
+solar wind protons. As the solar wind expands away from the Sun, the interactions between the 
+streaming plasma and the relatively stationary LISM atoms become energetically important, 
+resulting in a deceleration and heating of the solar wind, as well as significant modifications of 
+the termination shock. 
+ 
+The detailed interaction begins when an LISM atom is ionized, creating a new ion that is 
+temporarily nearly at rest with respect to the supersonic solar wind. In the reference frame of the 
+solar wind plasma, this new ion is streaming toward the Sun at the solar wind speed, Vsw. 
+Suddenly subject to the electromagnetic fields of the flowing plasma, the new ion is “picked up” 
+as its motion across the local magnetic field, B, is forced into a gyration with a speed 
+perpendicular to the field equal to Vsw sin Y, where Y is the angle between B and Vsw. The 
+distribution of these ring-beam particles is highly unstable, and will generate parallel-
+propagating ion-cyclotron waves (ICWs), while scattering to a nearly isotropic distribution of hot 
+pickup ions (PUIs) around a cooler proton core of solar origin. 
+ 
+Early consideration of this scattering process predicted a substantial ICW enhancement at 
+frequencies above the spacecraft frame proton gyrofrequency due to the PUI isotropization (Wu 
+& Davidson 1972; Lee & Ip 1987). However, these waves were only observed sporadically 
+(Murphy et al. 1995), despite the expected continual production of new PUIs. Eventually, it 
+became clear that the predicted waves were being dispersed and masked by the background 
+turbulence in the outer solar wind (Cannon et al. 2014a; Cannon et al. 2014b; Joyce et al. 2010; 
+
+Aggarwal et al. 2016; Argall et al. 2015; Argall et al. 2017; Fisher et al. 2016; Marchuk et al. 
+2021). The distinctive wave enhancements would appear during quiet periods in the solar wind 
+when the level of ambient turbulence was low, but were not detectable during times of stronger 
+turbulence (Hollick et al. 2018a, b; Pine et al. 2020a). 
+ 
+These ICWs are also presumed to drive the turbulent motions in the expanding solar 
+wind, supplementing and eventually replacing the standard energy inputs from shocks and shears 
+that diminish far from the Sun. This turbulent driving by PUIs was first proposed by Zank, 
+Matthaeus, and co-workers (Matthaeus et al. 1999; Williams et al. 1995; Zank et al. 1996). They 
+presented a model for turbulent evolution from the Sun to the termination shock, based on the 
+“engineering model” concepts of von Kármán & Howarth (von Kármán & Howarth 1938; 
+Kolmogorov 1941a, b). Within several AU of the Sun, this model turbulence was driven by a 
+phenomenological shear source, and further away incorporated the energy released by PUI 
+isotropization. The dissipation of this turbulence was taken to heat the core solar wind protons, 
+which measurements from Voyager 2 showed were not cooling adiabatically (Gazis & Lazarus 
+1982; Gazis 1984).  
+ 
+The early models predicted that the core solar wind temperatures would increase 
+dramatically beyond ~ 40 AU where the PUI driving finally dominated the adiabatic cooling. 
+This prediction arose from the assumption that new PUIs would scatter into a “bispherical” 
+distribution as a result of their instability (Galeev & Sagdeev 1988; Johnstone et al. 1991; 
+Williams & Zank 1994). This distribution (described in the next section) corresponds to a 
+reduction of the particle energy per mass by a factor ~ VA/Vsw from the initial Vsw2/2 of the newly 
+ionized ring-beam in the solar wind frame, where VA is the local Alfvén speed. In these models, 
+the energy lost by each newly ionized pickup proton was added to the turbulent fluctuations as 
+the solar wind continued outward, and the dissipation of this turbulence produced a temperature 
+increase with increasing radial distance from the Sun. 
+ 
+However, as Voyager 2 traveled further outward, the measured proton temperature 
+showed only a modest increase, at a fraction of the predicted magnitude (Smith et al. 2001). We 
+proposed an explanation for this discrepancy, suggesting that half of the unstable ICWs could be 
+transformed by the ambient turbulence into parallel-propagating fast-mode waves as they were 
+being generated by the instability (Isenberg et al. 2003; Isenberg 2005). Cyclotron-resonant 
+scattering by the combined ICWs and fast-mode waves led to a distribution of new PUIs which 
+was much more isotropic than the bispherical distribution, so less energy was supplied to the 
+turbulence. Models of the distant solar wind under this hypothesis could reproduce the Voyager 2 
+observations reasonably well, even under time-dependent solar wind conditions (Isenberg et al. 
+2010; Smith et al. 2006). 
+ 
+Since that work, many further models of increasing rigor and complexity have been 
+constructed (Adhikari et al. 2014; Adhikari et al. 2017; Adhikari et al. 2020; Zank et al. 2018; 
+Oughton et al. 2011; Usmanov & Goldstein 2006; Usmanov et al. 2011; Usmanov et al. 2012, 
+2014, 2016; Pine et al. 2020d, c, b; Pine et al. 2020a; Ng et al. 2010; Wiengarten et al. 2016), 
+exploring the evolution and behavior of various turbulent quantities as the solar wind advects 
+into the outer heliosphere. Of course, the more elaborate models contain more free parameters, 
+so a decent agreement with the Voyager 2 observations has been maintained. The newer 
+measurements from the Solar Wind around Pluto (SWAP) instrument on New Horizons, 
+(McComas et al. 2008) which includes information on the PUI component, are also generally 
+consistent with the behavior of these models (McComas et al. 2021; Elliott et al. 2019; 
+McComas et al. 2017; Zank et al. 2018). 
+
+ 
+In all this more recent work, the specific character of the PUI driving has not been 
+addressed. In fact, most of the models have retreated from the detailed kinetic model of Isenberg 
+(2005), and simply taken the fractional decrease of the driving from the bispherical value to be a 
+constant, usually designated fD. In this context, values of fD between 0.15 - 0.25 have led to 
+plausible agreement with the observations. 
+ 
+In this paper, we revisit the question of PUI driven turbulence and take a new look at how 
+the isotropization process could release less energy than the bispherical expectation. We note 
+that, in the years since our suggestion of fast-mode PUI scattering, there has been no evidence 
+that fast-mode waves play a major role in the establishment of strong plasma turbulence (Yang et 
+al. 2018; Brodiano et al. 2021). That original hypothesis may have seemed plausible in the rigid 
+context of resonant scattering of unstable PUIs by strictly parallel-propagating waves, but newer 
+conceptions of solar wind turbulence have prompted another look at this question.  
+ 
+Here, we will explore the possibility that the ambient turbulence in the outer solar wind 
+reduces the energy lost from isotropizing interstellar PUIs, and self-consistently modulates the 
+subsequent driving of the cascade, dissipation and heating. The simultaneous and comparable 
+kinetic influence of quasilinear pitch-angle scattering and turbulent dissipation is not a familiar 
+concept in the magnetosphere or inner heliosphere, where the plasmas are more active and the 
+unstable ion gradients are often well established. In the outer solar wind, however, the 
+production of newly ionized PUIs is very slow and their unstable pitch-angle gradient is only 
+weakly maintained. Thus, the operation of the ring-beam instability, which would scatter the new 
+PUIs to a bispherical shell, can be modified by other kinetic processes in the plasma. In 
+particular, the ambient turbulent fluctuations themselves could influence the PUI isotropization 
+process as they dissipate and heat the rest of the plasma. 
+ 
+This point is consistent with the prevailing explanation for the sporadic nature of the 
+observed PUI excited waves in the outer solar wind (Cannon et al. 2014b; Hollick et al. 2018b; 
+Pine et al. 2020a). Those observations have shown that the turbulent cascade rate is roughly 
+comparable to the PUI production rate, and that PUI excited wave enhancements are only 
+evident when the cascade rate is too small to disperse them. Here, we extend this picture to 
+suggest that the turbulence heats the PUIs as they scatter, interfering with the formation of the 
+bispherical shell.  
+ 
+In the next section, we describe the wave-particle interactions and the solar wind 
+conditions that are relevant to the isotropization of PUIs. In Section 3, we present an idealized 
+demonstration of how combined PUI scattering and turbulent diffusion can modify the energy 
+available for turbulence driving in the outer solar wind. In Section 4, we outline how these 
+combined processes can balance each other, creating a self-regulating system to maintain the 
+levels of turbulence and heating consistent with observations. Section 5 contains a summary and 
+our conclusions. 
+ 
+2.  PUI Isotropization in the Outer Solar Wind 
+ 
+The ring-beam instability of newly picked up ions has been extensively studied in many 
+different contexts (Lee & Ip 1987; Galeev & Sagdeev 1988; Min et al. 2017; Min & Liu 2018; 
+Cowee et al. 2008; Huddleston et al. 1992; Huddleston et al. 1998; Szegö et al. 2000). The 
+resulting waves have been observed at comets, in planetary magnetospheres, and in the solar 
+wind. Further studies in the context of the IBEX ribbon in the outer heliosheath have been 
+focused on the possibility that this wave generation might be somehow prevented in that very 
+quiet medium, in order to allow the accumulation of ribbon ions (Florinski et al. 2010; Florinski 
+
+et al. 2016; Liu et al. 2012; Summerlin et al. 2014). At this time, an inhibition sufficient to justify 
+that hypothesis has yet to be demonstrated.  
+ 
+We do not have direct observations of this instability in the distant supersonic solar wind, 
+in that we cannot detect PUI gradients and resonant ICWs simultaneously. However, the 
+persistent operation of this instability to isotropize interstellar PUIs has been indirectly verified 
+by the observation of wave enhancements in the measured spectra (Cannon et al. 2014a; Cannon 
+et al. 2014b; Hollick et al. 2018a, b; Pine et al. 2020d, c), by the analysis of isotropic PUI 
+distributions at New Horizons (Elliott et al. 2019; McComas et al. 2017; McComas et al. 2021), 
+and by the increasing temperature of core solar wind protons plausibly heated by the turbulence 
+as it is continuously driven by the instability (Adhikari et al. 2017; Isenberg et al. 2010; Smith et 
+al. 2006; Usmanov et al. 2014). 
+ 
+The ring-beam instability is a form of the well-known quasilinear (QL) anisotropy 
+instability (Gary 1993) which occurs when ions exhibit a pitch-angle gradient perpendicular to 
+the large-scale magnetic field. The gradient represents a form of free energy, which generates 
+ICWs propagating primarily along the field. In the generation process, these waves self-
+consistently scatter the cyclotron resonant ions to reduce the pitch-angle gradient. The final 
+bispherical shell configuration results from the details of the QL resonant cyclotron interaction 
+with these waves. 
+ 
+The cyclotron resonance condition for an ion in a transverse wave is written 
+ 
+ 
+ 
+ 
+ 
+ , 
+ 
+ 
+ 
+ 
+(1) 
+ 
+which arises from equating the ion cyclotron frequency, Wi, with the Doppler-shifted wave 
+frequency encountered by the ion streaming at v||. With the appropriate polarization, the wave 
+fields rotate about the large-scale magnetic field in phase with the ion gyration, and energy 
+exchange between the wave and the ion is efficient. A resonant ion viewed in the reference frame 
+propagating with the parallel phase speed of the wave, w/k||, will see a zero wave electric field, 
+since dB/dt = 0 in that frame. Thus, the ion will interact with the wave so as to conserve its 
+energy in that wave frame. Back in the plasma frame, this means that resonant ions will scatter 
+through their phase space along a particular curved path, determined by the initial ring-beam and 
+the wave dispersion relation, w (k). In the distant solar wind, the Parker spiral field, on average, 
+is azimuthally-directed (Y  = p/2) so the initial PUIs will appear in the ring at v^= Vsw and v|| = 
+0.  
+ 
+If the resonant waves can be taken dispersionless, w /k|| = ±VA, this energy-conserving 
+path follows symmetric spherical sections in (v||, v^) space with centers at (±VA, 0), and the final 
+closed ion shell has the standard bispherical shape, as shown by the blue curve in Figure 1. 
+Including the effects of ICW dispersion will modify this shape, typically making it somewhat 
+more energetic since the resonant waves will propagate slower and less energy is taken from the 
+scattering ions.  (As a limiting case, consider the diagram in Figure 1 for a wave phase speed 
+equal to zero. In this case, the center of curvature of each path would be at the origin, and the 
+scattered shell shape in the plasma frame would be a sphere. In this limit, the PUIs would retain 
+all their initial energy and yield none to the waves.) 
+  ω − k!v! = Ωi
+
+ 
+An analytical solution including dispersion can be obtained by taking the dispersion 
+relation for parallel ICWs in a cold proton-electron plasma, 
+, resulting in a 
+scattered shell shape given by the parametric expressions 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+(2) 
+ 
+ 
+ 
+ 
+ 
+where y = k|| VA/Wp. This more realistic shape, termed a “dispersive bispherical” by Isenberg & 
+Lee (1996),  corresponds to less generated wave energy than the standard bispherical, but the 
+reduction is not large enough to resolve the outer solar wind heating problem on its own. 
+ 
+As stated above, turbulent heating from waves generated by PUI isotropization is 
+plausibly responsible for the observed core solar wind temperatures in the outer solar wind, but 
+only if this wave generation is somehow reduced by a factor of 5 or more from the expected QL 
+values. These QL calculations are made in isolation, assuming an otherwise undisturbed, 
+homogeneous background plasma. In the outer solar wind, though, this isotropization must 
+proceed in the presence of a well-developed turbulence, which can act simultaneously to 
+energize the scattering PUIs. We suggest here that this energization is responsible for the 
+reduced wave generation required by the models. This effect is shown schematically by the red 
+dashed curve in Figure 1. 
+ 
+In the outer solar wind, the PUI anisotropy as such is maintained only by the production 
+of new PUIs appearing in the ring position at v^= Vsw. The proton production rate is given by the 
+local density of interstellar neutral hydrogen multiplied by their ionization rate  
+ 
+ 
+ 
+ 
+cm–3 s–1, 
+ 
+ 
+(3) 
+where No = 0.1 cm–3 is the inflowing hydrogen density at the solar wind termination shock, L = 
+5.6 AU is the size of the hydrogen ionization cavity in the upwind direction, and no = 7.5 ´ 10–7 
+s–1 is the hydrogen ionization rate at ro = 1 AU taken to fall off as r–2. At r = 40 AU, we 
+estimate this rate to be ~ 4 ´ 10–11 particles cm–3 s–1, so about one new proton/m3 every 7 hours. 
+In contrast, the proton gyroperiod at this distance will be about 1 minute or less. 
+ 
+The associated rate per mass of energy input to the fluctuations is then  
+ 
+ 
+ 
+ 
+ 
+, 
+ 
+ 
+ 
+ 
+(4)
+ 
+ 
+where we follow Smith et al. (2001) in parameterizing the effective fraction of bispherical wave 
+generation by the factor fD. Taking Vsw = 400 km/s and VA = 50 km/s at r = 40 AU, the energy 
+input rate is dEw/dt  = 4 ´ 10–7 fD (km/s)2 cm–3 s–1. 
+ 
+This energy input rate should be compared with the rate of energy cascade through the 
+inertial range of the turbulent spectrum. This rate is estimated by Vasquez et al. (2007) from the 
+Kolmogorov theory to be 
+ 
+ω = k||VA 1−ω / Ω p
+ 
+v⊥
+2 = Vsw
+2 −VA
+2
+1
+y2 + ln y − sinh−1 y
+2
+⎡
+⎣
+⎢
+⎤
+⎦
+⎥
+  
+v! = VA
+1
+y +
+y2 + 4 − y
+2
+⎡
+⎣
+⎢
+⎢
+⎤
+⎦
+⎥
+⎥
+dN
+dt = No exp −L / r
+(
+) νo
+ro
+r
+⎛
+⎝⎜
+⎞
+⎠⎟
+2
+dEw
+dt
+= 1
+2 fDVAVsw
+dN
+dt
+
+ 
+ 
+ 
+ 
+, 
+ 
+ 
+(5) 
+ 
+where E(fsc) is the magnetic field power spectral density in units of nT2/Hz, which is assumed to 
+vary with the measured spacecraft-frame frequency, fsc, as fsc–5/3, np is the solar wind density in 
+units of cm–3, and the factors of np and 21.8 convert the magnetic field to Alfvén units. At 40 
+AU, we estimate E at fsc = 3 mHz from Figure 4 of Pine et al. (2020a) to be 10–2 nT/Hz. We 
+multiply the expression in (5) by the solar wind density np = 3.125 ´ 10–3 cm–3 (corresponding 
+to 5 cm–3 at 1 AU) to obtain a cascade rate per volume of 2.28 ´ 10–7 (km/s)2 cm–3 s–1. In 
+steady state, the turbulent dissipation rate is equal to the cascade rate, so the solar wind protons 
+including the PUIs will be heated by this rate - comparable to the turbulent driving rate (4) due to 
+PUIs. 
+ 
+The order-of-magnitude equality of these two rates is one of the foundational factors of 
+the prevailing scenario for turbulence driving and solar wind heating in the outer heliosphere. 
+Observational studies (e.g. Cannon et al. 2014b; Hollick et al. 2018b; Pine et al. 2020d; Pine et 
+al. 2020a) have found that the PUI-generated waves due to isotropization, as predicted by Lee & 
+Ip (1987), are observable when the level of background turbulence is low, and are not detected 
+during times of higher turbulence. Since interstellar PUIs are ionized and picked up 
+continuously, independent of the solar wind turbulence level, it is understood that the 
+isotropization continues to take place, and that the turbulence continues to be driven by this 
+process.  
+ 
+Previous models have all assumed that the isotropization process is rapid and not affected 
+by the turbulence. However, the proton gradient assumed to generate the anisotropy instability 
+will not be firmly established when new ring distribution ions only appear every few hours. 
+Although these new ions apparently do scatter toward isotropy, since they do still drive the 
+turbulence, this scattering cannot be rapid and is not likely to be independent of other ongoing 
+processes.  
+ 
+The interplay between anisotropy instabilities and background turbulence has been 
+investigated in various simulation studies in the magnetosphere and inner heliosphere (Hellinger 
+et al. 2015; Hellinger & Trávnícek 2015; Markovskii et al. 2019, 2020; Markovskii & Vasquez 
+2022). The typical conclusion is that, while the growth rates and saturation levels of the 
+instability may be affected, the unstable wave-particle evolution is not strongly suppressed by the 
+turbulence.  
+ 
+Additionally, several hybrid simulations (Hellinger & Trávnícek 2016; Liu et al. 2012) 
+have demonstrated the continued operation of this instability under conditions of slow PUI 
+production rate. Unfortunately, neither study was concerned with the shape of the closed shells 
+that resulted from the scattering or with the energy lost by the scattered particles. Furthermore, 
+both these studies were spatially one-dimensional, so all fluctuations were forced to propagate 
+along the magnetic field, and true turbulence could not develop.  
+ 
+Previous models of turbulence in the outer solar wind have also assumed that PUIs would 
+not be heated by the turbulent dissipation. It is generally argued (e.g. Zank et al. 2018) that a 
+resonant heating of suprathermal ions requires large-wavelength fluctuations, while dissipation-
+range turbulence is characterized by very short wavelengths. However, to the extent that the 
+dominant turbulent fluctuations can be represented as highly oblique kinetic Alfvén waves in 
+εK = fsc
+5/2 E( fsc)
+[
+]3/2 (21.8)3
+Vswnp
+3/2
+km2s−3
+
+critical balance, the short perpendicular scales in the dissipation range can easily coexist with 
+larger parallel scales (Goldreich & Sridhar 1995, 1997; Isenberg & Vasquez 2019; TenBarge & 
+Howes 2012; Oughton et al. 2015). In any case, we also point out that the PUIs observed at New 
+Horizons in the outer solar wind appear to be heated in situ (Elliott et al. 2019; McComas et al. 
+2021; Zank et al. 2018) in a manner that has not been fully explained.  
+ 
+In the next section, we present an idealized demonstration that is meant to illustrate the 
+effects of slow QL scattering by the instability combined with ambient heating by dissipation of 
+the background turbulence.  
+ 
+3.  An Idealized Demonstration 
+ 
+A rigorous demonstration of these combined processes would require a full kinetic 
+simulation of very slow PUI production in an otherwise turbulent plasma, which is beyond the 
+scope of this paper. We present here an idealized demonstration of how this interaction might 
+work, using particle diffusion operators to represent the processes of scattering and heating. 
+ 
+This idealization has a number of limitations. Since diffusion only produces a directed 
+result - such as scattering toward isotropy or net ion heating - in response to a directed density 
+gradient, we need to impose a specific background particle distribution. Additionally, we will 
+specify diffusion coefficients for the two processes, but these effects will then be independent 
+and will not be able to affect each other.  
+ 
+We will represent the QL scattering using the “dispersive bispherical” description of Eq. 
+(2), and model this process on the very slow time scale by taking the magnitude of this diffusion 
+coefficient to be very small. In the absence of a clearly accepted form for the dissipative 
+turbulent heating, we will choose the diffusion coefficient for heating to be a simple isotropic 
+function of particle speed. Then, to assess the evolution of newly ionized PUIs, we will insert a 
+“slug” of additional protons in a ring at the solar wind speed and compare the energization of the 
+total distribution to that without the slug. 
+ 
+With this procedure, the pickup of newly ionized protons is not continuous, but rather the 
+new particles are dumped into the system at once. We do not compute the QL anisotropy 
+instability or the self-consistent particle response. Rather, we define the QL diffusion to follow 
+the dispersive bispherical path through phase space, taking this diffusion to be slow. 
+ 
+Our demonstration will also neglect the effects of adiabatic deceleration in the expanding 
+solar wind, which proceeds on an even longer time scale than the particle effects of interest. This 
+neglect means that the distinctive solar wind speed cutoff in the PUI distributions, to be imposed 
+on the initial distribution, will not be maintained in this model. Consequently, the kinetic 
+behavior of the model PUI distribution is not expected to be physically realistic after the initial 
+pitch-angle scattering time period. 
+ 
+Taking a grid in spherical coordinates (µ, v), where µ is the cosine of the particle pitch 
+angle, we solve the two-dimensional time-dependent diffusion equation 
+ 
+ 
+ 
+  
+(6) 
+ 
+in a system symmetric about µ = 0. 
+ 
+The QL diffusion coefficients for the cyclotron resonant scattering due to parallel-
+propagating ICWs are (Isenberg 2005; Lee 1971; Schlickeiser 1989) 
+ 
+ 
+∂ f
+∂t = ∂
+∂µ Dµµ
+∂ f
+∂µ + Dµv
+∂ f
+∂v
+⎛
+⎝⎜
+⎞
+⎠⎟ + 1
+v2
+∂
+∂v v2 Dµv
+∂ f
+∂µ + Dvv
+∂ f
+∂v
+⎛
+⎝⎜
+⎞
+⎠⎟
+⎡
+⎣⎢
+⎤
+⎦⎥
+
+ 
+ 
+ 
+ 
+ 
+(7) 
+where the spectral intensity of the ICWs at the resonant wavenumber is  AIC I(kres), and their 
+phase and group speeds are Vph and Vgr, respectively. For diffusion coefficients specific to PUI 
+scattering in an azimuthal magnetic field, we take the shape of the ICW spectrum from the 
+dispersive bispherical formalism (Isenberg & Lee 1996) for perpendicular pickup. The wave-
+particle interaction is assumed symmetric about µ = 0, so the spectrum is taken symmetric about 
+k = 0.  
+ 
+The turbulent heating here is modeled by an isotropic power-law diffusion in v, with a 
+Gaussian decrease to zero in the diffusion coefficient for small v,  
+ 
+ 
+ 
+  
+ 
+(8) 
+The total diffusion coefficients in (6) will be the sums of the expressions in (7) and (8), where 
+AIC I(ko = W/VA) and Aturb are constants to be set for various runs. 
+ 
+We perform these computations on a grid with 2000 x 4000 points between 0 ≤ µ ≤ 1 and 
+0 ≤ v/VA ≤ 10. As appropriate for the outer solar wind, where the magnetic field is essentially 
+azimuthal, we assume that new PUIs appear near µ = 0, v = Vsw, and that the particle distribution 
+is symmetric about µ = 0. We take Vsw/VA = 6 rather than a more typical value ~ 10, in order to 
+reduce the necessary computational volume in phase space. 
+ 
+The background proton distribution is composed of a thermal core with the ratio of 
+kinetic to magnetic pressure b = 0.2, a halo of previously picked up PUIs in a Vasyliunas & 
+Siscoe (1976) configuration, and a sharp cutoff above v = Vsw: 
+ 
+  
+(9) 
+where b is chosen to give a PUI halo density that is 10% of the total. This distribution is shown 
+in Figure 2. 
+ 
+With the initial condition given by (9), we solve (6) on the grid using the biconjugate 
+gradient stabilized method. We take reflecting boundary conditions at µ = 0 and 1, and place an 
+absorbing boundary at v = 10 VA. Given the presence of this outer boundary in phase space, 
+ 
+Dµµ
+Dµv
+Dvv
+⎧
+⎨
+⎪⎪
+⎩
+⎪
+⎪
+⎫
+⎬
+⎪⎪
+⎭
+⎪
+⎪
+= AIC
+1– µ2
+(
+)I(kres)
+µv −Vgr
+1– µVph
+v
+⎛
+⎝⎜
+⎞
+⎠⎟
+2
+Vph 1– µVph
+v
+⎛
+⎝⎜
+⎞
+⎠⎟
+Vph
+2
+⎧
+⎨
+⎪
+⎪
+⎪
+⎪
+⎩
+⎪
+⎪
+⎪
+⎪
+⎫
+⎬
+⎪
+⎪
+⎪
+⎪
+⎭
+⎪
+⎪
+⎪
+⎪
+ 
+Dvv = Aturb
+(v /VA)−5/3
+v /VA ≥1
+exp − (v −VA)2
+(VA / 5)2
+⎡
+⎣
+⎢
+⎢
+⎤
+⎦
+⎥
+⎥
+v /VA ≤1
+⎧
+⎨
+⎪⎪
+⎩
+⎪
+⎪
+ 
+f (v) =
+exp − 5v2
+VA
+2
+⎡
+⎣
+⎢
+⎢
+⎤
+⎦
+⎥
+⎥
++ b
+v
+Vsw
+⎛
+⎝⎜
+⎞
+⎠⎟
+−3/2
+exp −0.1
+v
+Vsw
+⎛
+⎝⎜
+⎞
+⎠⎟
+−3/2
+⎡
+⎣
+⎢
+⎢
+⎤
+⎦
+⎥
+⎥
+v ≤ Vsw
+b
+v
+Vsw
+⎛
+⎝⎜
+⎞
+⎠⎟
+−30
+exp (−0.1)
+v ≥ Vsw
+⎧
+⎨
+⎪
+⎪⎪
+⎩
+⎪
+⎪
+⎪
+
+along with the neglect of adiabatic deceleration, we expect this idealized model to only yield 
+physically reasonable distributions for a period near the beginning of the computation. The 
+results for an initial time period, which are shorter for larger values of Aturb, will be qualitatively 
+illustrative of the combined scattering and diffusive heating of newly ionized PUIs in the outer 
+solar wind. 
+ 
+We first consider the case of Aturb = 0, which should reproduce the conditions treated in 
+the original dispersive bispherical calculation (Isenberg & Lee 1996). In keeping with the slow 
+time scale for pickup in the outer solar wind, we take AIC I(ko) = 10–5 in computational units.1 
+Starting with the background distribution (9), we follow the total kinetic energy of the protons as 
+a function of time, Eb (t), which is shown by the blue curve in Figure 3.   
+ 
+We then repeat this computation starting with an additional slug of particles, representing 
+newly ionized PUIs. These additional PUIs are confined to the pitch angle range 0 ≤ µ ≤ 0.03 and 
+the speed range 5.85 ≤ v/VA ≤ 6.05, which straddles the model solar wind speed at Vsw = 6 VA. In 
+this region, the we take the value of  f to be a constant equal to the value from (9) at v = 5.85 VA. 
+With this shelf of extra particles in the distribution, the total proton density is increased by a 
+factor of 10–4. The total proton energy in this case, Es (t), is shown by the red curve in Figure 3.  
+ 
+To quantify the energetics of QL scattering of the newly ionized PUIs, we compare the 
+evolution of the total energy of the proton distributions in these two computations. Ideally, one 
+might prefer to track the actual scattered particles, but in this diffusive system the discernable 
+density enhancement in the slug quickly disappears and we are unable to follow the behavior of 
+that small portion of the distribution.  
+ 
+Figure 4 shows the quantity Q º DE(t)/DE(0), where DE = Es – Eb for this case. In this 
+context, (1 – Q) represents the normalized net energy lost by the new PUIs as they scatter toward 
+isotropy in the undisturbed QL interaction. The normalized energy change levels off at Q = 
+0.893, which is the same value predicted by the dispersive bispherical calculation of Isenberg & 
+Lee (1996) for Vsw/VA = 6. In the turbulent driving scenario for the outer solar wind (Isenberg et 
+al. 2003; Isenberg 2005; Smith et al. 2001; Smith et al. 2006; Zank et al. 1996; Pine et al. 2020a), 
+this proton energy loss appears in ICWs that proceed to drive the turbulence, but the observations 
+at Pioneer 11 and Voyager 2 show that this amount of driving is too large.  
+ 
+When turbulent heating is added to the system, the combined 2-D diffusion proceeds 
+somewhat faster than the effectively 1-D pitch-angle scattering that occurs when Aturb = 0. The 
+total proton energy rises approximately linearly with time for all cases. Keeping AIC I(ko) = 10–5, 
+we choose five values of Aturb = 0.0001, 0.0005, 0.001, 0.002, and 0.003. In Figure 5, we show 
+the results of the normalized energy difference, Q (t), between the computations made with and 
+without the slug of new PUIs for these cases. The computed energy difference reaches a 
+minimum depending on the value of Aturb, before increasing due to further diffusive heating. We 
+interpret these minimum values to indicate the normalized energy of the slug once it has 
+completely scattered to a closed shell in phase space, corresponding to the end state of the QL 
+anisotropy instability. The curves in Figure 5 show that the cases with larger values of Aturb lose 
+less energy in the process of scattering. The minimum values for each case are given in Table 1.  
+ 
+1 This illustrative computation only addresses the relative effects of isotropization and turbulent heating. As such, it 
+is sufficient to work in dimensionless computational, or grid, units. All velocities are normalized to VA, and total 
+proton kinetic energies per proton mass are then defined as ½ f ´ (v/VA)4, summed over all grid points. The time 
+parameter then scales as VA (W AIC I (ko))–1. 
+
+ 
+These computations suggest that the resolution to the discrepancy between the predicted 
+energy loss of new PUIs and the observed turbulent heating of the core solar wind can be found 
+in the influence of the background turbulence on the weak QL scattering of these PUIs. In this 
+example, the new PUIs can be scattered to a stable closed shell while giving up a fraction of their 
+energy, which can range from 11% down to 1%, depending on the strength of the background 
+turbulence. Defining fD = (1 – Qmin)(Vsw/VA), this range corresponds to effective fD reductions for 
+these cases from the dispersive bispherical value of fD = 0.642 to fD = 0.060. Table 1 lists these 
+effective values of fD for each case. The values used to reproduce the observed properties of the 
+outer solar wind lie within this range (Smith et al. 2006). 
+ 
+Our suggestion here that interstellar PUIs are continually heated by the ambient 
+turbulence in the outer solar wind is relatively new, in that previous models of solar wind heating 
+and the large-scale turbulent evolution have not included such an effect (Adhikari et al. 2014; 
+Adhikari et al. 2017; Adhikari et al. 2020; Zank et al. 2018; Oughton et al. 2011; Usmanov & 
+Goldstein 2006; Usmanov et al. 2011; Usmanov et al. 2012, 2014, 2016; Pine et al. 2020d, c, b; 
+Pine et al. 2020a; Ng et al. 2010; Wiengarten et al. 2016; Isenberg 2005; Isenberg et al. 2003, 
+2010; Smith et al. 2006). However, the observations of PUI out to ~52 AU from the New 
+Horizons mission (Elliot et al. 2019; McComas et al. 2021, 2022) have found that PUIs are not 
+cooled as much as would be predicted by the Vasyliunas & Siscoe (1976) model, which 
+incorporates the effects of adiabatic deceleration under conditions of the radial expansion of a 
+constant-speed solar wind. The New Horizons data show that the PUI distribution still generally 
+exhibits a cutoff in speed at the solar wind value in the solar wind frame (apart from indications 
+of local shock heating downstream of observed shocks (Zirnstein et al. 2018)), but that the 
+“cooling index” (Chen et al. 2013; Swaczyna et al. 2020; McComas et al. 2021) indicates that the 
+observed PUIs have been heated since their pickup and isotropization. This heating appears to be 
+in addition to, and independent of, the localized energization seen at these interplanetary shocks 
+(McComas et al. 2021, 2022). 
+ 
+4.  A Self-Regulating System  
+ 
+Given the substantial variability of the solar wind, the scenario presented here allows for 
+an intriguing possibility of self-regulation. The ambient turbulence in the expanding wind will 
+decay with increasing heliocentric distance if it is not actively driven by the fluctuations from the 
+PUI instability. If the turbulence in some region is temporarily weak, due perhaps to a faster 
+expansion, the QL scattering can proceed to a bispherical-like shape as originally envisioned by 
+Zank, Matthaeus, and Smith. This interaction will generate fluctuations at the level ~ VA/Vsw 
+times the initial PUI energy, leading to a stronger turbulent driving than that indicated over the 
+large scale by the observations.  
+ 
+In some other region where the turbulence is strong, the turbulent energization will 
+modify the scattering to reduce the QL energy loss from the PUI instability, leading to a 
+corresponding reduction in the turbulent driving. More generally, a parcel of solar wind, 
+advecting outward, could cycle between these two circumstances, actively maintaining a level of 
+turbulent driving which, on average, would be some fraction of the bispherical prediction. A 
+schematic diagram of this regulation is shown in Figure 6. 
+ 
+We do not know the details of the specific mechanism by which the parallel ICWs 
+generated by the PUI instability are transformed into turbulent fluctuations in the distant solar 
+wind. Thus, it is difficult to theoretically establish the fraction of QL intensity that would result 
+from this self-regulation. We show here that a fraction consistent with the observed solar wind 
+
+heating can be attained within an order-of-magnitude intensity variation of the background 
+turbulence. Future theoretical research and simulation modeling would be extremely valuable in 
+understanding this complicated interaction. 
+  
+5.  Summary and Conclusions  
+ 
+Interstellar PUIs, formed from the ionization of inflowing interstellar neutral atoms, 
+dominate the plasma behavior of the supersonic solar wind beyond ~ 40 AU from the Sun. They 
+accumulate with increasing radial position to make up a large fraction of the thermal energy of 
+the outer solar wind, and their properties strongly influence the details of the solar wind 
+termination shock. The energy released when newly ionized PUIs are scattered toward isotropy 
+is thought to drive the observed turbulent heating of the core solar wind protons. However, the 
+interaction predicted from standard QL scattering due to the conventional operation of the 
+anisotropy instability provides far too much energy to the turbulence in the outflowing plasma.  
+ 
+We have suggested that the energizing effects of the ambient background turbulence on 
+the weakly scattering PUIs should be taken into account in the determination of the generated 
+unstable fluctuations. We have illustrated the possible form of this turbulent modification with an 
+idealized computation, using a combined QL diffusive description. We identify a potential self-
+regulation mechanism in these combined effects, which may explain the observed level of 
+turbulence and solar wind heating in the distant solar wind. Further theoretical work and 
+simulation studies specifically addressing the details of PUI scattering and turbulent driving 
+under realistic conditions are needed to accurately model these interactions in the outer solar 
+wind. 
+ 
+ 
+We are grateful for valuable conversations with E. Möbius, P. Swaczyna, and D. 
+Verscharen. PAI, BJV and CWS are supported by NASA grant 80NSSC18K1215. PAI and BJV 
+are also supported by NSF grant AGS2005982. PAI is further supported by NASA grant 
+80NSSC18K0655. 
+ 
+ 
+References 
+ 
+Adhikari, L., Zank, G. P., Hu, Q., & Dosch, A. 2014, Astrophys. J., 793, 52 
+Adhikari, L., Zank, G. P., Zhao, L.-L., & Webb, G. M. 2020, Astrophys. J., 891, 34 
+Adhikari, L., Zank, G. P., Hunana, P., et al. 2017, Astrophys. J., 841, 85 
+Aggarwal, P., Taylor, D. K., Smith, C. W., et al. 2016, Astrophys. J., 822, 94 
+Argall, M. R., Fisher, M. K., Joyce, C. J., et al. 2015, Geophys. Res. Lett., 42, 9617 
+Argall, M. R., Hollick, S. J., Pine, Z. B., et al. 2017, Astrophys. J., 849, 61 
+Axford, W. I. 1972, in Solar Wind, ed. C. P. Sonett, P. J. Coleman, & J. M. Wilcox (Washington, 
+D.C.: NASA Spec. Pub. SP-308), 609 
+Brodiano, M., Andrés, N., & Dmitruk, P. 2021, Astrophys. J., 922, 240 
+Cannon, B. E., Smith, C. W., Isenberg, P. A., et al. 2014a, Astrophys. J., 784, 150 
+Cannon, B. E., Smith, C. W., Isenberg, P. A., et al. 2014b, Astrophys. J., 787, 133 
+Chen, J. H., Möbius, E., Gloeckler, G., et al. 2013, J. Geophys. Res., 118, 3946 
+Cowee, M. M., Russell, C. T., & Strangeway, R. J. 2008, J. Geophys. Res., 113, A08220 
+Elliott, H. A., McComas, D. J., Zirnstein, E. J., et al. 2019, Astrophys. J., 885, 156 
+Fisher, M. K., Argall, M. R., Joyce, C. J., et al. 2016, Astrophys. J., 830, 47 
+
+Florinski, V., Heerikhuisen, J., Niemiec, J., & Ernst, A. 2016, Astrophys. J., 826, 197 
+Florinski, V., Zank, G. P., Heerikhuisen, J., Hu, Q., & Khazanov, I. 2010, Astrophys. J., 719, 
+1097 
+Galeev, A. A., & Sagdeev, R. Z. 1988, Astrophys. Space Sci., 144, 427 
+Gary, S. P. 1993, Theory of Space Plasma Microinstabilities (Cambridge, England:  
+Gazis, P. R. 1984, J. Geophys. Res., 89, 775 
+Gazis, P. R., & Lazarus, A. J. 1982, Geophys. Res. Lett., 9, 431 
+Goldreich, P., & Sridhar, S. 1995, Astrophys. J., 438, 763 
+–––––. 1997, Astrophys. J., 485, 680 
+Hellinger, P., & Trávnícek, P. 2015, J. Plasma Phys., 81, 305810103 
+–––––. 2016, Astrophys. J., 832, 32 
+Hellinger, P., Matteini, L., Landi, S., et al. 2015, Astrophys. J., 811, L32 
+Hollick, S. J., Smith, C. W., Pine, Z. B., et al. 2018a, Astrophys. J., 863, 75 
+–––––. 2018b, Astrophys. J., 863, 76 
+Holzer, T. E. 1972, J. Geophys. Res., 77, 5407 
+Huddleston, D. E., Coates, A. J., & Johnstone, A. D. 1992, J. Geophys. Res., 97, 19,163 
+Huddleston, D. E., Strangeway, R. J., Warnecke, J., Russell, C. T., & Kivelson, M. G. 1998, J. 
+Geophys. Res., 103, 19887 
+Isenberg, P. A. 1986, J. Geophys. Res., 91, 9965 
+Isenberg, P. A. 2005, Astrophys. J., 623, 502 
+Isenberg, P. A., & Lee, M. A. 1996, J. Geophys. Res., 101, 11,055 
+Isenberg, P. A., & Vasquez, B. J. 2019, Astrophys. J., in press, arXiv: 1910.11366 
+Isenberg, P. A., Smith, C. W., & Matthaeus, W. H. 2003, Astrophys. J., 592, 564 
+Isenberg, P. A., Smith, C. W., Matthaeus, W. H., & Richardson, J. D. 2010, Astrophys. J., 719, 
+716 
+Johnstone, A. D., Huddleston, D. E., & Coates, A. J. 1991, in Cometary Plasma Processes, ed. A. 
+D. Johnstone (Washington, DC: AGU), 259 
+Joyce, C. J., Smith, C. W., Isenberg, P. A., Murphy, N., & Schwadron, N. A. 2010, Astrophys. J., 
+724, 1256 
+Kolmogorov, A. N. 1941a, C. R. Acad. Sci. URSS, 32, 16 
+–––––. 1941b, C. R. Acad. Sci. URSS, 30, 301 
+Lee, M. A. 1971, Plasma Phys., 13, 1079 
+Lee, M. A., & Ip, W.-H. 1987, J. Geophys. Res., 92, 11,041 
+Liu, K., Möbius, E., Gary, S. P., & Winske, D. 2012, J. Geophys. Res., 117, A10102 
+Marchuk, A. V., Smith, C. W., Watson, A. S., et al. 2021, Astrophys. J., 923, 185 
+Markovskii, S. A., & Vasquez, B. J. 2022, Astrophys. J., 924, 111 
+Markovskii, S. A., Vasquez, B. J., & Chandran, B. D. G. 2019, Astrophys. J., 875, 125 
+–––––. 2020, Astrophys. J., 889, 7 
+Matthaeus, W. H., Zank, G. P., Smith, C. W., & Oughton, S. 1999, Phys. Rev. Lett., 82, 3444 
+McComas, D.J., Shrestha, B. L., Swaczyna, P., et al. 2022, Astrophys. J., 934, 147 
+McComas, D. J., Swaczyna, P., Szalay, J. R., et al. 2021, Astrophys. J. Suppl., 254, 19 
+McComas, D. J., Zirnstein, E. J., Bzowski, M., et al. 2017, Astrophys. J. Suppl., 233, 8 
+McComas, D. J., Allegrini, F., Bagenal, F., et al. 2008, Space Sci. Rev., 140, 261 
+Min, K., & Liu, K. 2018, Astrophys. J., 852, 39 
+Min, K., Liu, K., & Gary, S. P. 2017, J. Geophys. Res., 122, 7891 
+
+Murphy, N., Smith, E. J., Tsurutani, B. T., Balogh, A., & Southwood, D. J. 1995, Space Sci. 
+Rev., 72, 447 
+Ng, C. S., Bhattacharjee, A., Munsi, D., Isenberg, P. A., & Smith, C. W. 2010, J. Geophys. Res., 
+115, A02101 
+Oughton, S., Matthaeus, W. H., Wan, M., & Osman, K. T. 2015, Phil. Trans. R. Soc. A, 373, 
+201401152 
+Oughton, S., Matthaeus, W. H., Smith, C. W., Breech, B., & Isenberg, P. A. 2011, J. Geophys. 
+Res., 116, A08105 
+Pine, Z. B., Smith, C. W., Hollick, S. J., et al. 2020a, Astrophys. J., 900, 94 
+Pine, Z. B., Smith, C. W., Hollick, S. J., et al. 2020b, Astrophys. J., 900, 93 
+–––––. 2020c, Astrophys. J., 900, 92 
+–––––. 2020d, Astrophys. J., 900, 91 
+Schlickeiser, R. 1989, Astrophys. J., 336, 243 
+Smith, C. W., Isenberg, P. A., Matthaeus, W. H., & Richardson, J. D. 2006, Astrophys. J., 638, 
+508 
+Smith, C. W., Matthaeus, W. H., Zank, G. P., et al. 2001, J. Geophys. Res., 106, 8253 
+Swaczyna, P., McComas, D. J., Zirnstein, E. J. et al. 2020, Astrophys. J., 903, 48 
+Summerlin, E. J., Viñas, A. F., Moore, T. E., Christian, E. R., & Cooper, J. F. 2014, Astrophys. 
+J., 793, 93 
+Szegö, K., Glassmeier, K.-H., Bingham, R., et al. 2000, Space Sci. Rev., 94, 429 
+TenBarge, J. M., & Howes, G. G. 2012, Phys. Plasmas, 19, 055901 
+Usmanov, A. V., & Goldstein, M. L. 2006, J. Geophys. Res., 111, A07101 
+Usmanov, A. V., Goldstein, M. L., & Matthaeus, W. H. 2012, Astrophys. J., 754, 40 
+–––––. 2014, Astrophys. J., 788, 43 
+–––––. 2016, Astrophys. J., 820, 17 
+Usmanov, A. V., Matthaeus, W. H., Breech, B., & Goldstein, M. L. 2011, Astrophys. J., 727, 84 
+Vasquez, B. J., Smith, C. W., Hamilton, K., MacBride, B. T., & Leamon, R. J. 2007, J. Geophys. 
+Res., 112, A07101 
+Vasyliunas, V. M., & Siscoe, G. L. 1976, J. Geophys. Res., 81, 1247 
+von Kármán, T., & Howarth, L. 1938, Proc. R. Soc. London, Ser. A, 164, 192 
+Wiengarten, T., Oughton, S., Engelbrecht, N. E., et al. 2016, Astrophys. J., 833, 17 
+Williams, L. L., & Zank, G. P. 1994, J. Geophys. Res., 99, 19,229 
+Williams, L. L., Zank, G. P., & Matthaeus, W. H. 1995, J. Geophys. Res., 100, 17,059 
+Wu, C. S., & Davidson, R. C. 1972, J. Geophys. Res., 77, 5399 
+Yang, L., Zhang, L., He, J., et al. 2018, Astrophys. J., 866, 41 
+Zank, G. P., Matthaeus, W. H., & Smith, C. W. 1996, J. Geophys. Res., 101, 17,093 
+Zank, G. P., Adhikari, L., Zhao, L.-L., et al. 2018, Astrophys. J., 869, 23 
+Zirnstein, E. J., McComas, D. J., Kumar, R., et al. 2018, PhRvL, 121, 075102 
+ 
+ 
+
+Table 1.  Minimum Values of the Normalized Energy Loss, Q, and the Corresponding Effective 
+Values of fD for the Cases of Section 3. 
+ 
+Aturb 
+Qmin 
+eff fD 
+0.0 
+0.893 
+0.642 
+0.0001 
+0.910 
+0.540 
+0.0005 
+0.945 
+0.330 
+0.001 
+0.962 
+0.228 
+0.002 
+0.984 
+0.096 
+0.003 
+0.990 
+0.060 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure 1.  Sketch of the plasma response of newly ionized PUIs in the azimuthal magnetic field 
+of the outer solar wind. The ions initially form an unstable ring distribution, depicted by the red 
+dot, which scatters to a closed shell in phase space. The conventional QL theory predicts a 
+bispherical shell, given by the blue curve as reflected into the other quadrants of the figure. The 
+red dashed curve indicates a possible modification of the shell due to interaction with the 
+ambient turbulence. 
+ 
+ 
+VA
+v
+v||
+Vsw
+bispherical
+turbulent
+dissipation
+
+ 
+ 
+ 
+Figure 2.  Normalized initial proton distribution function (8).  
+ 
+ 
+ 
+ 
+0.0001
+0.001
+0.01
+0.1
+1
+0
+2
+4
+6
+8
+10
+f (v)
+v/V
+A
+
+ 
+ 
+Figure 3. Evolution of the total proton energy in grid units, when Aturb = 0. The blue curve uses 
+the initial distribution (8), and the red curve has the additional slug of new PUIs. 
+ 
+ 
+ 
+ 
+388
+390
+392
+394
+0
+10000
+20000
+30000
+40000
+50000
+E
+tot
+t
+
+ 
+ 
+ 
+Figure 4.  Evolution of the normalized energy difference, Q, between the computations with and 
+without the slug of new PUIs, for Aturb = 0. 
+ 
+ 
+ 
+ 
+ 
+Figure 5. Evolution of the normalized energy difference, Q, for increasing values of Aturb, while 
+AIC I(ko) is fixed at 10–5. The values are Aturb = 0.0001 (green), 0.0005 (light blue), 0.001 (red), 
+0.002 (dark blue), and 0.003 (black). The respective minima are given in Table 1.  
+0.88
+0.9
+0.92 0.94 0.96 0.98
+1
+0
+10000
+20000
+30000
+40000
+50000
+Q
+t
+0.9
+0.92
+0.94
+0.96
+0.98
+1
+0
+5000
+10000
+15000
+20000
+25000
+30000
+Q
+t
+
+  r = Ro  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+r = Ro + dr 
+ 
+  
+ 
+ 
+High <δB2> 
+Low <δB2> 
+More 
+Spherical 
+More Bi- 
+spherical 
+Less E-loss 
+ 
+Less Driving 
+More E-loss 
+ 
+More Driving 
+Reduced 
+<δB2> 
+Increased 
+<δB2> 
+Local 
+SW 
+with 
+with 
+Turbulent 
+Self-Regulation 
+with a 
+with a 
+New 
+PUIs 
+Figure 6.  Schematic diagram of 
+the self-regulation mechanism. 
+
diff --git a/SdFAT4oBgHgl3EQf1h7S/content/tmp_files/load_file.txt b/SdFAT4oBgHgl3EQf1h7S/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7c79220b2aaca18a0b79d4d57908ab617415cb35
--- /dev/null
+++ b/SdFAT4oBgHgl3EQf1h7S/content/tmp_files/load_file.txt
@@ -0,0 +1,1102 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf,len=1101
+page_content='Turbulence Driving by Interstellar Pickup Ions in the Outer Solar Wind Philip A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Isenberg, Bernard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Vasquez, and Charles W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Smith Space Science Center and Department of Physics and Astronomy University of New Hampshire, Durham, NH 03824, USA  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We revisit the question of how the unstable scattering of interstellar pickup ions (PUIs) may drive turbulence in the outer solar wind, and why the energy released into fluctuations by this scattering appears to be significantly less than the standard bispherical prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We suggest that energization of the newly picked-up ions by the ambient turbulence during the scattering process can result in a more spherical distribution of PUIs, and reduce the generated fluctuation energy to a level consistent with the observations of turbulent intensities and core solar wind heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This scenario implies the operation of a self-regulation mechanism that maintains the observed conditions of turbulence and heating in the PUI-dominated solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Introduction  The neutral component of the partially ionized local interstellar medium (LISM) penetrates the boundaries of the heliopause and termination shock and flows slowly through the supersonic solar wind (Axford 1972;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Holzer 1972;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Isenberg 1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' These neutral particles, primarily hydrogen atoms, fill most of the heliosphere, being excluded only from a region near the Sun due to increased ionization from solar photons and charge-exchange interactions with the solar wind protons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' As the solar wind expands away from the Sun, the interactions between the streaming plasma and the relatively stationary LISM atoms become energetically important, resulting in a deceleration and heating of the solar wind, as well as significant modifications of the termination shock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The detailed interaction begins when an LISM atom is ionized, creating a new ion that is temporarily nearly at rest with respect to the supersonic solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In the reference frame of the solar wind plasma, this new ion is streaming toward the Sun at the solar wind speed, Vsw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Suddenly subject to the electromagnetic fields of the flowing plasma, the new ion is “picked up” as its motion across the local magnetic field, B, is forced into a gyration with a speed perpendicular to the field equal to Vsw sin Y, where Y is the angle between B and Vsw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The distribution of these ring-beam particles is highly unstable, and will generate parallel- propagating ion-cyclotron waves (ICWs), while scattering to a nearly isotropic distribution of hot pickup ions (PUIs) around a cooler proton core of solar origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Early consideration of this scattering process predicted a substantial ICW enhancement at frequencies above the spacecraft frame proton gyrofrequency due to the PUI isotropization (Wu & Davidson 1972;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Lee & Ip 1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' However, these waves were only observed sporadically (Murphy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1995), despite the expected continual production of new PUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Eventually, it became clear that the predicted waves were being dispersed and masked by the background turbulence in the outer solar wind (Cannon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Cannon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Joyce et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Aggarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Argall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Argall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Fisher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Marchuk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The distinctive wave enhancements would appear during quiet periods in the solar wind when the level of ambient turbulence was low, but were not detectable during times of stronger turbulence (Hollick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018a, b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  These ICWs are also presumed to drive the turbulent motions in the expanding solar wind, supplementing and eventually replacing the standard energy inputs from shocks and shears that diminish far from the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This turbulent driving by PUIs was first proposed by Zank, Matthaeus, and co-workers (Matthaeus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Williams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1995;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Zank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' They presented a model for turbulent evolution from the Sun to the termination shock, based on the “engineering model” concepts of von Kármán & Howarth (von Kármán & Howarth 1938;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Kolmogorov 1941a, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Within several AU of the Sun, this model turbulence was driven by a phenomenological shear source, and further away incorporated the energy released by PUI isotropization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The dissipation of this turbulence was taken to heat the core solar wind protons, which measurements from Voyager 2 showed were not cooling adiabatically (Gazis & Lazarus 1982;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Gazis 1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The early models predicted that the core solar wind temperatures would increase dramatically beyond ~ 40 AU where the PUI driving finally dominated the adiabatic cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This prediction arose from the assumption that new PUIs would scatter into a “bispherical” distribution as a result of their instability (Galeev & Sagdeev 1988;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Johnstone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Williams & Zank 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This distribution (described in the next section) corresponds to a reduction of the particle energy per mass by a factor ~ VA/Vsw from the initial Vsw2/2 of the newly ionized ring-beam in the solar wind frame, where VA is the local Alfvén speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In these models, the energy lost by each newly ionized pickup proton was added to the turbulent fluctuations as the solar wind continued outward, and the dissipation of this turbulence produced a temperature increase with increasing radial distance from the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  However, as Voyager 2 traveled further outward, the measured proton temperature showed only a modest increase, at a fraction of the predicted magnitude (Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We proposed an explanation for this discrepancy, suggesting that half of the unstable ICWs could be transformed by the ambient turbulence into parallel-propagating fast-mode waves as they were being generated by the instability (Isenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Isenberg 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Cyclotron-resonant scattering by the combined ICWs and fast-mode waves led to a distribution of new PUIs which was much more isotropic than the bispherical distribution, so less energy was supplied to the turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Models of the distant solar wind under this hypothesis could reproduce the Voyager 2 observations reasonably well, even under time-dependent solar wind conditions (Isenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Since that work, many further models of increasing rigor and complexity have been constructed (Adhikari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Adhikari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Adhikari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Zank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Oughton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Usmanov & Goldstein 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Usmanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Usmanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2012, 2014, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020d, c, b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Wiengarten et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016), exploring the evolution and behavior of various turbulent quantities as the solar wind advects into the outer heliosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Of course, the more elaborate models contain more free parameters, so a decent agreement with the Voyager 2 observations has been maintained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The newer measurements from the Solar Wind around Pluto (SWAP) instrument on New Horizons, (McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2008) which includes information on the PUI component, are also generally consistent with the behavior of these models (McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Elliott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Zank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  In all this more recent work, the specific character of the PUI driving has not been addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In fact, most of the models have retreated from the detailed kinetic model of Isenberg (2005), and simply taken the fractional decrease of the driving from the bispherical value to be a constant, usually designated fD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In this context, values of fD between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='15 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='25 have led to plausible agreement with the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  In this paper, we revisit the question of PUI driven turbulence and take a new look at how the isotropization process could release less energy than the bispherical expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We note that, in the years since our suggestion of fast-mode PUI scattering, there has been no evidence that fast-mode waves play a major role in the establishment of strong plasma turbulence (Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Brodiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' That original hypothesis may have seemed plausible in the rigid context of resonant scattering of unstable PUIs by strictly parallel-propagating waves, but newer conceptions of solar wind turbulence have prompted another look at this question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Here, we will explore the possibility that the ambient turbulence in the outer solar wind reduces the energy lost from isotropizing interstellar PUIs, and self-consistently modulates the subsequent driving of the cascade, dissipation and heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The simultaneous and comparable kinetic influence of quasilinear pitch-angle scattering and turbulent dissipation is not a familiar concept in the magnetosphere or inner heliosphere, where the plasmas are more active and the unstable ion gradients are often well established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In the outer solar wind, however, the production of newly ionized PUIs is very slow and their unstable pitch-angle gradient is only weakly maintained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Thus, the operation of the ring-beam instability, which would scatter the new PUIs to a bispherical shell, can be modified by other kinetic processes in the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In particular, the ambient turbulent fluctuations themselves could influence the PUI isotropization process as they dissipate and heat the rest of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  This point is consistent with the prevailing explanation for the sporadic nature of the observed PUI excited waves in the outer solar wind (Cannon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Hollick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Those observations have shown that the turbulent cascade rate is roughly comparable to the PUI production rate, and that PUI excited wave enhancements are only evident when the cascade rate is too small to disperse them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Here, we extend this picture to suggest that the turbulence heats the PUIs as they scatter, interfering with the formation of the bispherical shell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  In the next section, we describe the wave-particle interactions and the solar wind conditions that are relevant to the isotropization of PUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In Section 3, we present an idealized demonstration of how combined PUI scattering and turbulent diffusion can modify the energy available for turbulence driving in the outer solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In Section 4, we outline how these combined processes can balance each other, creating a self-regulating system to maintain the levels of turbulence and heating consistent with observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Section 5 contains a summary and our conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' PUI Isotropization in the Outer Solar Wind  The ring-beam instability of newly picked up ions has been extensively studied in many different contexts (Lee & Ip 1987;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Galeev & Sagdeev 1988;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Min et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Min & Liu 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Cowee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Huddleston et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1992;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Huddleston et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Szegö et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The resulting waves have been observed at comets, in planetary magnetospheres, and in the solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Further studies in the context of the IBEX ribbon in the outer heliosheath have been focused on the possibility that this wave generation might be somehow prevented in that very quiet medium, in order to allow the accumulation of ribbon ions (Florinski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Florinski  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Summerlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' At this time, an inhibition sufficient to justify that hypothesis has yet to be demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  We do not have direct observations of this instability in the distant supersonic solar wind, in that we cannot detect PUI gradients and resonant ICWs simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' However, the persistent operation of this instability to isotropize interstellar PUIs has been indirectly verified by the observation of wave enhancements in the measured spectra (Cannon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Cannon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Hollick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018a, b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020d, c), by the analysis of isotropic PUI distributions at New Horizons (Elliott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021), and by the increasing temperature of core solar wind protons plausibly heated by the turbulence as it is continuously driven by the instability (Adhikari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Isenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Usmanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The ring-beam instability is a form of the well-known quasilinear (QL) anisotropy instability (Gary 1993) which occurs when ions exhibit a pitch-angle gradient perpendicular to the large-scale magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The gradient represents a form of free energy, which generates ICWs propagating primarily along the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In the generation process, these waves self- consistently scatter the cyclotron resonant ions to reduce the pitch-angle gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The final bispherical shell configuration results from the details of the QL resonant cyclotron interaction with these waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The cyclotron resonance condition for an ion in a transverse wave is written  ,  (1)  which arises from equating the ion cyclotron frequency, Wi, with the Doppler-shifted wave frequency encountered by the ion streaming at v||.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' With the appropriate polarization, the wave fields rotate about the large-scale magnetic field in phase with the ion gyration, and energy exchange between the wave and the ion is efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A resonant ion viewed in the reference frame propagating with the parallel phase speed of the wave, w/k||, will see a zero wave electric field, since dB/dt = 0 in that frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Thus, the ion will interact with the wave so as to conserve its energy in that wave frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Back in the plasma frame, this means that resonant ions will scatter through their phase space along a particular curved path, determined by the initial ring-beam and the wave dispersion relation, w (k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In the distant solar wind, the Parker spiral field, on average, is azimuthally-directed (Y  = p/2) so the initial PUIs will appear in the ring at v^= Vsw and v|| = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  If the resonant waves can be taken dispersionless, w /k|| = ±VA, this energy-conserving path follows symmetric spherical sections in (v||, v^) space with centers at (±VA, 0), and the final closed ion shell has the standard bispherical shape, as shown by the blue curve in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Including the effects of ICW dispersion will modify this shape, typically making it somewhat more energetic since the resonant waves will propagate slower and less energy is taken from the scattering ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' (As a limiting case, consider the diagram in Figure 1 for a wave phase speed equal to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In this case, the center of curvature of each path would be at the origin, and the scattered shell shape in the plasma frame would be a sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In this limit, the PUIs would retain all their initial energy and yield none to the waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=') ω − k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='v!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' = Ωi  An analytical solution including dispersion can be obtained by taking the dispersion relation for parallel ICWs in a cold proton-electron plasma, , resulting in a scattered shell shape given by the parametric expressions  (2)  where y = k|| VA/Wp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This more realistic shape, termed a “dispersive bispherical” by Isenberg & Lee (1996),  corresponds to less generated wave energy than the standard bispherical, but the reduction is not large enough to resolve the outer solar wind heating problem on its own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  As stated above, turbulent heating from waves generated by PUI isotropization is plausibly responsible for the observed core solar wind temperatures in the outer solar wind, but only if this wave generation is somehow reduced by a factor of 5 or more from the expected QL values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' These QL calculations are made in isolation, assuming an otherwise undisturbed, homogeneous background plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In the outer solar wind, though, this isotropization must proceed in the presence of a well-developed turbulence, which can act simultaneously to energize the scattering PUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We suggest here that this energization is responsible for the reduced wave generation required by the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This effect is shown schematically by the red dashed curve in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  In the outer solar wind, the PUI anisotropy as such is maintained only by the production of new PUIs appearing in the ring position at v^= Vsw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The proton production rate is given by the local density of interstellar neutral hydrogen multiplied by their ionization rate  cm–3 s–1,  (3) where No = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='1 cm–3 is the inflowing hydrogen density at the solar wind termination shock, L = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='6 AU is the size of the hydrogen ionization cavity in the upwind direction, and no = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='5 ´ 10–7 s–1 is the hydrogen ionization rate at ro = 1 AU taken to fall off as r–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' At r = 40 AU, we estimate this rate to be ~ 4 ´ 10–11 particles cm–3 s–1, so about one new proton/m3 every 7 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In contrast, the proton gyroperiod at this distance will be about 1 minute or less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The associated rate per mass of energy input to the fluctuations is then  ,  (4)  where we follow Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' (2001) in parameterizing the effective fraction of bispherical wave generation by the factor fD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Taking Vsw = 400 km/s and VA = 50 km/s at r = 40 AU, the energy input rate is dEw/dt  = 4 ´ 10–7 fD (km/s)2 cm–3 s–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  This energy input rate should be compared with the rate of energy cascade through the inertial range of the turbulent spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This rate is estimated by Vasquez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' (2007) from the Kolmogorov theory to be  ω = k||VA 1−ω / Ω p  v⊥ 2 = Vsw 2 −VA 2 1 y2 + ln y − sinh−1 y 2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥  v!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' = VA 1 y + y2 + 4 − y 2 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ dN dt = No exp −L / r ( ) νo ro r ⎛ ⎝⎜ ⎞ ⎠⎟ 2 dEw dt = 1 2 fDVAVsw dN dt  ,  (5)  where E(fsc) is the magnetic field power spectral density in units of nT2/Hz, which is assumed to vary with the measured spacecraft-frame frequency, fsc, as fsc–5/3, np is the solar wind density in units of cm–3, and the factors of np and 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='8 convert the magnetic field to Alfvén units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' At 40 AU, we estimate E at fsc = 3 mHz from Figure 4 of Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' (2020a) to be 10–2 nT/Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We multiply the expression in (5) by the solar wind density np = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='125 ´ 10–3 cm–3 (corresponding to 5 cm–3 at 1 AU) to obtain a cascade rate per volume of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='28 ´ 10–7 (km/s)2 cm–3 s–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In steady state, the turbulent dissipation rate is equal to the cascade rate, so the solar wind protons including the PUIs will be heated by this rate - comparable to the turbulent driving rate (4) due to PUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The order-of-magnitude equality of these two rates is one of the foundational factors of the prevailing scenario for turbulence driving and solar wind heating in the outer heliosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Observational studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Cannon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Hollick et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020a) have found that the PUI-generated waves due to isotropization, as predicted by Lee & Ip (1987), are observable when the level of background turbulence is low, and are not detected during times of higher turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Since interstellar PUIs are ionized and picked up continuously, independent of the solar wind turbulence level, it is understood that the isotropization continues to take place, and that the turbulence continues to be driven by this process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Previous models have all assumed that the isotropization process is rapid and not affected by the turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' However, the proton gradient assumed to generate the anisotropy instability will not be firmly established when new ring distribution ions only appear every few hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Although these new ions apparently do scatter toward isotropy, since they do still drive the turbulence, this scattering cannot be rapid and is not likely to be independent of other ongoing processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The interplay between anisotropy instabilities and background turbulence has been investigated in various simulation studies in the magnetosphere and inner heliosphere (Hellinger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Hellinger & Trávnícek 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Markovskii et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2019, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Markovskii & Vasquez 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The typical conclusion is that, while the growth rates and saturation levels of the instability may be affected, the unstable wave-particle evolution is not strongly suppressed by the turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Additionally, several hybrid simulations (Hellinger & Trávnícek 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2012) have demonstrated the continued operation of this instability under conditions of slow PUI production rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Unfortunately, neither study was concerned with the shape of the closed shells that resulted from the scattering or with the energy lost by the scattered particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Furthermore, both these studies were spatially one-dimensional, so all fluctuations were forced to propagate along the magnetic field, and true turbulence could not develop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Previous models of turbulence in the outer solar wind have also assumed that PUIs would not be heated by the turbulent dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' It is generally argued (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Zank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018) that a resonant heating of suprathermal ions requires large-wavelength fluctuations, while dissipation- range turbulence is characterized by very short wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' However, to the extent that the dominant turbulent fluctuations can be represented as highly oblique kinetic Alfvén waves in εK = fsc 5/2 E( fsc) [ ]3/2 (21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='8)3 Vswnp 3/2 km2s−3  critical balance, the short perpendicular scales in the dissipation range can easily coexist with larger parallel scales (Goldreich & Sridhar 1995, 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Isenberg & Vasquez 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' TenBarge & Howes 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Oughton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In any case, we also point out that the PUIs observed at New Horizons in the outer solar wind appear to be heated in situ (Elliott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Zank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018) in a manner that has not been fully explained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  In the next section, we present an idealized demonstration that is meant to illustrate the effects of slow QL scattering by the instability combined with ambient heating by dissipation of the background turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' An Idealized Demonstration  A rigorous demonstration of these combined processes would require a full kinetic simulation of very slow PUI production in an otherwise turbulent plasma, which is beyond the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We present here an idealized demonstration of how this interaction might work, using particle diffusion operators to represent the processes of scattering and heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  This idealization has a number of limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Since diffusion only produces a directed result - such as scattering toward isotropy or net ion heating - in response to a directed density gradient, we need to impose a specific background particle distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Additionally, we will specify diffusion coefficients for the two processes, but these effects will then be independent and will not be able to affect each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  We will represent the QL scattering using the “dispersive bispherical” description of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' (2), and model this process on the very slow time scale by taking the magnitude of this diffusion coefficient to be very small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In the absence of a clearly accepted form for the dissipative turbulent heating, we will choose the diffusion coefficient for heating to be a simple isotropic function of particle speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Then, to assess the evolution of newly ionized PUIs, we will insert a “slug” of additional protons in a ring at the solar wind speed and compare the energization of the total distribution to that without the slug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  With this procedure, the pickup of newly ionized protons is not continuous, but rather the new particles are dumped into the system at once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We do not compute the QL anisotropy instability or the self-consistent particle response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Rather, we define the QL diffusion to follow the dispersive bispherical path through phase space, taking this diffusion to be slow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Our demonstration will also neglect the effects of adiabatic deceleration in the expanding solar wind, which proceeds on an even longer time scale than the particle effects of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This neglect means that the distinctive solar wind speed cutoff in the PUI distributions, to be imposed on the initial distribution, will not be maintained in this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Consequently, the kinetic behavior of the model PUI distribution is not expected to be physically realistic after the initial pitch-angle scattering time period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Taking a grid in spherical coordinates (µ, v), where µ is the cosine of the particle pitch angle, we solve the two-dimensional time-dependent diffusion equation  (6)  in a system symmetric about µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The QL diffusion coefficients for the cyclotron resonant scattering due to parallel- propagating ICWs are (Isenberg 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Lee 1971;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Schlickeiser 1989)  ∂ f  ∂t = ∂  ∂µ Dµµ  ∂ f  ∂µ + Dµv  ∂ f  ∂v  ⎛  ⎝⎜  ⎞  ⎠⎟ + 1  v2  ∂  ∂v v2 Dµv  ∂ f  ∂µ + Dvv  ∂ f  ∂v  ⎛  ⎝⎜  ⎞  ⎠⎟  ⎡  ⎣⎢  ⎤  ⎦⎥  (7) where the spectral intensity of the ICWs at the resonant wavenumber is  AIC I(kres), and their phase and group speeds are Vph and Vgr, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' For diffusion coefficients specific to PUI scattering in an azimuthal magnetic field, we take the shape of the ICW spectrum from the dispersive bispherical formalism (Isenberg & Lee 1996) for perpendicular pickup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The wave- particle interaction is assumed symmetric about µ = 0, so the spectrum is taken symmetric about k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The turbulent heating here is modeled by an isotropic power-law diffusion in v, with a Gaussian decrease to zero in the diffusion coefficient for small v,  (8) The total diffusion coefficients in (6) will be the sums of the expressions in (7) and (8), where AIC I(ko = W/VA) and Aturb are constants to be set for various runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  We perform these computations on a grid with 2000 x 4000 points between 0 ≤ µ ≤ 1 and 0 ≤ v/VA ≤ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' As appropriate for the outer solar wind, where the magnetic field is essentially azimuthal, we assume that new PUIs appear near µ = 0, v = Vsw, and that the particle distribution is symmetric about µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We take Vsw/VA = 6 rather than a more typical value ~ 10, in order to reduce the necessary computational volume in phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  The background proton distribution is composed of a thermal core with the ratio of kinetic to magnetic pressure b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='2, a halo of previously picked up PUIs in a Vasyliunas & Siscoe (1976) configuration, and a sharp cutoff above v = Vsw:  (9) where b is chosen to give a PUI halo density that is 10% of the total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This distribution is shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  With the initial condition given by (9), we solve (6) on the grid using the biconjugate gradient stabilized method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We take reflecting boundary conditions at µ = 0 and 1, and place an absorbing boundary at v = 10 VA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Given the presence of this outer boundary in phase space,  Dµµ  Dµv  Dvv  ⎧  ⎨  ⎪⎪  ⎩  ⎪  ⎪  ⎫  ⎬  ⎪⎪  ⎭  ⎪  ⎪  = AIC  1– µ2  (  )I(kres)  µv −Vgr  1– µVph  v  ⎛  ⎝⎜  ⎞  ⎠⎟  2  Vph 1– µVph  v  ⎛  ⎝⎜  ⎞  ⎠⎟  Vph  2  ⎧  ⎨  ⎪  ⎪  ⎪  ⎪  ⎩  ⎪  ⎪  ⎪  ⎪  ⎫  ⎬  ⎪  ⎪  ⎪  ⎪  ⎭  ⎪  ⎪  ⎪  ⎪  Dvv = Aturb  (v /VA)−5/3  v /VA ≥1  exp − (v −VA)2  (VA / 5)2  ⎡  ⎣  ⎢  ⎢  ⎤  ⎦  ⎥  ⎥  v /VA ≤1  ⎧  ⎨  ⎪⎪  ⎩  ⎪  ⎪  f (v) =  exp − 5v2  VA  2  ⎡  ⎣  ⎢  ⎢  ⎤  ⎦  ⎥  ⎥  + b  v  Vsw  ⎛  ⎝⎜  ⎞  ⎠⎟  −3/2  exp −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='1  v  Vsw  ⎛  ⎝⎜  ⎞  ⎠⎟  −3/2  ⎡  ⎣  ⎢  ⎢  ⎤  ⎦  ⎥  ⎥  v ≤ Vsw  b  v  Vsw  ⎛  ⎝⎜  ⎞  ⎠⎟  −30  exp (−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='1)  v ≥ Vsw  ⎧  ⎨  ⎪  ⎪⎪  ⎩  ⎪  ⎪  ⎪  along with the neglect of adiabatic deceleration, we expect this idealized model to only yield physically reasonable distributions for a period near the beginning of the computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The results for an initial time period, which are shorter for larger values of Aturb, will be qualitatively illustrative of the combined scattering and diffusive heating of newly ionized PUIs in the outer solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  We first consider the case of Aturb = 0, which should reproduce the conditions treated in the original dispersive bispherical calculation (Isenberg & Lee 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In keeping with the slow time scale for pickup in the outer solar wind, we take AIC I(ko) = 10–5 in computational units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='1 Starting with the background distribution (9), we follow the total kinetic energy of the protons as a function of time, Eb (t), which is shown by the blue curve in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  We then repeat this computation starting with an additional slug of particles, representing newly ionized PUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' These additional PUIs are confined to the pitch angle range 0 ≤ µ ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='03 and the speed range 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='85 ≤ v/VA ≤ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='05, which straddles the model solar wind speed at Vsw = 6 VA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In this region, the we take the value of  f to be a constant equal to the value from (9) at v = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='85 VA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' With this shelf of extra particles in the distribution, the total proton density is increased by a factor of 10–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The total proton energy in this case, Es (t), is shown by the red curve in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  To quantify the energetics of QL scattering of the newly ionized PUIs, we compare the evolution of the total energy of the proton distributions in these two computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Ideally, one might prefer to track the actual scattered particles, but in this diffusive system the discernable density enhancement in the slug quickly disappears and we are unable to follow the behavior of that small portion of the distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Figure 4 shows the quantity Q º DE(t)/DE(0), where DE = Es – Eb for this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In this context, (1 – Q) represents the normalized net energy lost by the new PUIs as they scatter toward isotropy in the undisturbed QL interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The normalized energy change levels off at Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='893, which is the same value predicted by the dispersive bispherical calculation of Isenberg & Lee (1996) for Vsw/VA = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In the turbulent driving scenario for the outer solar wind (Isenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Isenberg 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Zank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020a), this proton energy loss appears in ICWs that proceed to drive the turbulence, but the observations at Pioneer 11 and Voyager 2 show that this amount of driving is too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  When turbulent heating is added to the system, the combined 2-D diffusion proceeds somewhat faster than the effectively 1-D pitch-angle scattering that occurs when Aturb = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The total proton energy rises approximately linearly with time for all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Keeping AIC I(ko) = 10–5, we choose five values of Aturb = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='0001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='0005, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='002, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In Figure 5, we show the results of the normalized energy difference, Q (t), between the computations made with and without the slug of new PUIs for these cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The computed energy difference reaches a minimum depending on the value of Aturb, before increasing due to further diffusive heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We interpret these minimum values to indicate the normalized energy of the slug once it has completely scattered to a closed shell in phase space, corresponding to the end state of the QL anisotropy instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The curves in Figure 5 show that the cases with larger values of Aturb lose less energy in the process of scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The minimum values for each case are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  1 This illustrative computation only addresses the relative effects of isotropization and turbulent heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' As such, it is sufficient to work in dimensionless computational, or grid, units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' All velocities are normalized to VA, and total proton kinetic energies per proton mass are then defined as ½ f ´ (v/VA)4, summed over all grid points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The time parameter then scales as VA (W AIC I (ko))–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  These computations suggest that the resolution to the discrepancy between the predicted energy loss of new PUIs and the observed turbulent heating of the core solar wind can be found in the influence of the background turbulence on the weak QL scattering of these PUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' In this example, the new PUIs can be scattered to a stable closed shell while giving up a fraction of their energy, which can range from 11% down to 1%, depending on the strength of the background turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Defining fD = (1 – Qmin)(Vsw/VA), this range corresponds to effective fD reductions for these cases from the dispersive bispherical value of fD = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='642 to fD = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='060.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Table 1 lists these effective values of fD for each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The values used to reproduce the observed properties of the outer solar wind lie within this range (Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Our suggestion here that interstellar PUIs are continually heated by the ambient turbulence in the outer solar wind is relatively new, in that previous models of solar wind heating and the large-scale turbulent evolution have not included such an effect (Adhikari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Adhikari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Adhikari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Zank et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Oughton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Usmanov & Goldstein 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Usmanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Usmanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2012, 2014, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020d, c, b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Wiengarten et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Isenberg 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Isenberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2003, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' However, the observations of PUI out to ~52 AU from the New Horizons mission (Elliot et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021, 2022) have found that PUIs are not cooled as much as would be predicted by the Vasyliunas & Siscoe (1976) model, which incorporates the effects of adiabatic deceleration under conditions of the radial expansion of a constant-speed solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The New Horizons data show that the PUI distribution still generally exhibits a cutoff in speed at the solar wind value in the solar wind frame (apart from indications of local shock heating downstream of observed shocks (Zirnstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018)), but that the “cooling index” (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Swaczyna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021) indicates that the observed PUIs have been heated since their pickup and isotropization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  This heating appears to be in addition to, and independent of, the localized energization seen at these interplanetary shocks (McComas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A Self Regulating System  Given the substantial variability of the solar wind, the scenario presented here allows for an intriguing possibility of self-regulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The ambient turbulence in the expanding wind will decay with increasing heliocentric distance if it is not actively driven by the fluctuations from the PUI instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' If the turbulence in some region is temporarily weak, due perhaps to a faster expansion, the QL scattering can proceed to a bispherical-like shape as originally envisioned by Zank, Matthaeus, and Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' This interaction will generate fluctuations at the level ~ VA/Vsw times the initial PUI energy, leading to a stronger turbulent driving than that indicated over the large scale by the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  In some other region where the turbulence is strong, the turbulent energization will modify the scattering to reduce the QL energy loss from the PUI instability, leading to a corresponding reduction in the turbulent driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' More generally, a parcel of solar wind, advecting outward, could cycle between these two circumstances, actively maintaining a level of turbulent driving which, on average, would be some fraction of the bispherical prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A schematic diagram of this regulation is shown in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  We do not know the details of the specific mechanism by which the parallel ICWs generated by the PUI instability are transformed into turbulent fluctuations in the distant solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Thus, it is difficult to theoretically establish the fraction of QL intensity that would result from this self-regulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We show here that a fraction consistent with the observed solar wind  heating can be attained within an order-of-magnitude intensity variation of the background turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Future theoretical research and simulation modeling would be extremely valuable in understanding this complicated interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Summary and Conclusions  Interstellar PUIs, formed from the ionization of inflowing interstellar neutral atoms, dominate the plasma behavior of the supersonic solar wind beyond ~ 40 AU from the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' They accumulate with increasing radial position to make up a large fraction of the thermal energy of the outer solar wind, and their properties strongly influence the details of the solar wind termination shock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The energy released when newly ionized PUIs are scattered toward isotropy is thought to drive the observed turbulent heating of the core solar wind protons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' However, the interaction predicted from standard QL scattering due to the conventional operation of the anisotropy instability provides far too much energy to the turbulence in the outflowing plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  We have suggested that the energizing effects of the ambient background turbulence on the weakly scattering PUIs should be taken into account in the determination of the generated unstable fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We have illustrated the possible form of this turbulent modification with an idealized computation, using a combined QL diffusive description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' We identify a potential self- regulation mechanism in these combined effects, which may explain the observed level of turbulence and solar wind heating in the distant solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Further theoretical work and simulation studies specifically addressing the details of PUI scattering and turbulent driving under realistic conditions are needed to accurately model these interactions in the outer solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  We are grateful for valuable conversations with E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Möbius, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Swaczyna, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Verscharen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' PAI, BJV and CWS are supported by NASA grant 80NSSC18K1215.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' PAI and BJV are also supported by NSF grant AGS2005982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' PAI is further supported by NASA grant 80NSSC18K0655.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  References  Adhikari, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Hu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Dosch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 793, 52 Adhikari, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Webb, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 891, 34 Adhikari, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Hunana, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 841, 85 Aggarwal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Taylor, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 822, 94 Argall, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Fisher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Joyce, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2015, Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 42, 9617 Argall, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Hollick, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Pine, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 849, 61 Axford, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1972, in Solar Wind, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Sonett, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Coleman, & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Wilcox (Washington, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=': NASA Spec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Pub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' SP-308), 609 Brodiano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Andrés, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Dmitruk, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 922, 240 Cannon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014a, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 784, 150 Cannon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014b, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 787, 133 Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Möbius, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Gloeckler, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2013, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 118, 3946 Cowee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Russell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Strangeway, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2008, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 113, A08220 Elliott, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', McComas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zirnstein, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2019, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 885, 156 Fisher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Argall, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Joyce, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 830, 47  Florinski, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Heerikhuisen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Niemiec, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Ernst, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 826, 197 Florinski, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Heerikhuisen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Hu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Khazanov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 719, 1097 Galeev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Sagdeev, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1988, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 144, 427 Gary, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1993, Theory of Space Plasma Microinstabilities (Cambridge, England: Gazis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1984, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 89, 775 Gazis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Lazarus, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1982, Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 9, 431 Goldreich, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Sridhar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1995, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 438, 763 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1997, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 485, 680 Hellinger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Trávnícek, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2015, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 81, 305810103 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 832, 32 Hellinger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Matteini, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Landi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2015, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 811, L32 Hollick, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Pine, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018a, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 863, 75 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018b, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 863, 76 Holzer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1972, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 77, 5407 Huddleston, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Coates, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Johnstone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1992, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 97, 19,163 Huddleston, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Strangeway, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Warnecke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Russell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Kivelson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1998, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 103, 19887 Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1986, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 91, 9965 Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2005, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 623, 502 Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1996, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 101, 11,055 Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Vasquez, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2019, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', in press, arXiv: 1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='11366 Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2003, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 592, 564 Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Richardson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 719, 716 Johnstone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Huddleston, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Coates, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1991, in Cometary Plasma Processes, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Johnstone (Washington, DC: AGU), 259 Joyce, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Murphy, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Schwadron, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 724, 1256 Kolmogorov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1941a, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' URSS, 32, 16 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1941b, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' URSS, 30, 301 Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1971, Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 13, 1079 Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Ip, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1987, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 92, 11,041 Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Möbius, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Gary, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Winske, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2012, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 117, A10102 Marchuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Watson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 923, 185 Markovskii, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Vasquez, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2022, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 924, 111 Markovskii, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Vasquez, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Chandran, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2019, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 875, 125 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 889, 7 Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Oughton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1999, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 82, 3444 McComas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Shrestha, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Swaczyna, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2022, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 934, 147 McComas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Swaczyna, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Szalay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2021, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 254, 19 McComas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zirnstein, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Bzowski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 233, 8 McComas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Allegrini, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Bagenal, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2008, Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 140, 261 Min, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 852, 39 Min, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Gary, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2017, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 122, 7891  Murphy, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Tsurutani, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Balogh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Southwood, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1995, Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 72, 447 Ng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Bhattacharjee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Munsi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2010, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 115, A02101 Oughton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Wan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Osman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2015, Phil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A, 373, 201401152 Oughton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Breech, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2011, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 116, A08105 Pine, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Hollick, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020a, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 900, 94 Pine, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Hollick, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020b, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 900, 93 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020c, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 900, 92 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020d, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 900, 91 Schlickeiser, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1989, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 336, 243 Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Isenberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Richardson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2006, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 638, 508 Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2001, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 106, 8253 Swaczyna, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', McComas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zirnstein, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2020, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 903, 48 Summerlin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Viñas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Moore, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Christian, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Cooper, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 793, 93 Szegö, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Glassmeier, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Bingham, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2000, Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 94, 429 TenBarge, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Howes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2012, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Plasmas, 19, 055901 Usmanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Goldstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2006, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 111, A07101 Usmanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Goldstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2012, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 754, 40 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2014, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 788, 43 –––––.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 820, 17 Usmanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Breech, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Goldstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2011, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 727, 84 Vasquez, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Hamilton, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', MacBride, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Leamon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2007, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 112, A07101 Vasyliunas, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Siscoe, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1976, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 81, 1247 von Kármán, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Howarth, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1938, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' London, Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' A, 164, 192 Wiengarten, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Oughton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Engelbrecht, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2016, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 833, 17 Williams, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1994, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 99, 19,229 Williams, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1995, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 100, 17,059 Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Davidson, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1972, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 77, 5399 Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', He, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 866, 41 Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Matthaeus, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', & Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 1996, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 101, 17,093 Zank, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Adhikari, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', 869, 23 Zirnstein, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', McComas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 2018, PhRvL, 121, 075102  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Minimum Values of the Normalized Energy Loss, Q, and the Corresponding Effective Values of fD for the Cases of Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Aturb  Qmin  eff fD  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='893  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='642  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='0001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='910  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='540  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
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+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='990  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='060  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Sketch of the plasma response of newly ionized PUIs in the azimuthal magnetic field of the outer solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The ions initially form an unstable ring distribution, depicted by the red dot, which scatters to a closed shell in phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The conventional QL theory predicts a bispherical shell, given by the blue curve as reflected into the other quadrants of the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The red dashed curve indicates a possible modification of the shell due to interaction with the ambient turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  VA  v  v||  Vsw  bispherical  turbulent  dissipation  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Normalized initial proton distribution function (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='0001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='1  1  0  2  4  6  8  10  f (v)  v/V  A  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Evolution of the total proton energy in grid units, when Aturb = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The blue curve uses the initial distribution (8), and the red curve has the additional slug of new PUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  388  390  392  394  0  10000  20000  30000  40000  50000  E  tot  t  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Evolution of the normalized energy difference, Q, between the computations with and without the slug of new PUIs, for Aturb = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Evolution of the normalized energy difference, Q, for increasing values of Aturb, while AIC I(ko) is fixed at 10–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The values are Aturb = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='0001 (green), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='0005 (light blue), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='001 (red), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='002 (dark blue), and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='003 (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' The respective minima are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='92 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='94 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='98 1 0 10000 20000 30000 40000 50000 Q t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='92 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='94 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content='98 1 0 5000 10000 15000 20000 25000 30000 Q t  r = Ro  r = Ro + dr  High <δB2>  Low <δB2>  More  Spherical  More Bi spherical  Less E loss  Less Driving  More E loss  More Driving Reduced <δB2> Increased <δB2> Local SW with with Turbulent Self-Regulation with a with a New PUIs Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
+page_content=' Schematic diagram of the self-regulation mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdFAT4oBgHgl3EQf1h7S/content/2301.08710v1.pdf'}
diff --git a/T9E5T4oBgHgl3EQfbA-t/content/tmp_files/2301.05593v1.pdf.txt b/T9E5T4oBgHgl3EQfbA-t/content/tmp_files/2301.05593v1.pdf.txt
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+Scalable Estimation for Structured Additive
+Distributional Regression
+Nikolaus Umlauf
+Universität Innsbruck
+Johannes Seiler
+Universität Innsbruck
+Mattias Wetscher
+Universität Innsbruck
+Thorsten Simon
+Universität Innsbruck
+Stefan Lang
+Universität Innsbruck
+Nadja Klein
+Technische Universität Dortmund
+Abstract
+Recently, fitting probabilistic models have gained importance in many areas but es-
+timation of such distributional models with very large data sets is a difficult task. In
+particular, the use of rather complex models can easily lead to memory-related efficiency
+problems that can make estimation infeasible even on high-performance computers. We
+therefore propose a novel backfitting algorithm, which is based on the ideas of stochastic
+gradient descent and can deal virtually with any amount of data on a conventional laptop.
+The algorithm performs automatic selection of variables and smoothing parameters, and
+its performance is in most cases superior or at least equivalent to other implementations
+for structured additive distributional regression, e.g., gradient boosting, while maintain-
+ing low computation time. Performance is evaluated using an extensive simulation study
+and an exceptionally challenging and unique example of lightning count prediction over
+Austria. A very large dataset with over 9 million observations and 80 covariates is used,
+so that a prediction model cannot be estimated with standard distributional regression
+methods but with our new approach.
+Keywords: Generalized additive models for location, scale and shape; gradient descent; itera-
+tively weighted least squares; stochastic optimization.
+1. Introduction
+Fitting distributional regression models of high complexity to large data is challenging with
+respect to storage and computational feasibility due to data volume or very high-dimensional
+vectors of model parameters required to define sufficiently flexible models. Moreover, in many
+applications, solving the problem also requires automatic selection of variables since manual
+or stepwise searches in such model spaces are impossible to be conducted. In recent years,
+techniques have already been developed to efficiently estimate generalized additive models
+(GAM; Hastie and Tibshirani 1990; Fahrmeir, Kneib, and Lang 2004) and generalized additive
+models for location scale and shape (GAMLSS; Rigby and Stasinopoulos 2005; Klein, Kneib,
+and Lang 2015b). For example, Wood, Li, Shaddick, and Augustin (2017); Li and Wood (2020)
+show how to decompose the iterative estimation algorithm for GAMs to be able to compute
+models for large data and gigadata with coefficients up to 104 and up to 108 observations.
+arXiv:2301.05593v1  [stat.CO]  13 Jan 2023
+
+2
+Scalable Estimation for Structured Additive Distributional Regression
+Lang, Umlauf, Wechselberger, Harttgen, and Kneib (2014) present efficient algorithms for
+Bayesian multilevel models for example by, discretization and indexing to significantly reduce
+the number of floating point operations. These ideas are carried over to estimate fully Bayesian
+structured additive distributional regression models (Klein, Kneib, Lang, and Sohn 2015c),
+the Bayesian version of GAMLSS, such that e.g. modelling the precipitation climatology
+across Austria with over 1.2 million daily observations is possible (Umlauf, Klein, and Zeileis
+2018). While in principle being easily trainable in terms of data size with the approach of Li
+and Wood (2020), GAMs are not suited here given the censored nature of the response daily
+precipitation with a spike at zero. Nevertheless, for more complicated probabilistic models
+or larger n, techniques such as Umlauf et al. (2018) also reach their limits. On the one hand,
+such models can no longer be computed on conventional computers since there is simply a
+lack of random-access memory (RAM); on the other hand, the computing time increases so
+much that modeling with many variables is not possible in a foreseeable time.
+To break down these barriers in structured additive distributional regression models, we
+propose a novel estimation algorithm, which we call batchwise backfitting and which combines
+the ideas of the classic backfitting optimization with stochastic gradient descent (SGD), an
+efficient algorithm based on a stochastic approximation to gradient descent for finding local
+maxima of an objective function J(θ) of a parameter vector θ ∈ Rp (Robbins and Monro
+1951).
+Compared to costly gradient descent methods, which involve updates of the form
+θ = θ − η∇θJ(θ) based on the whole data set, SGD replaces the gradient ∇θJ(θ) by a noisy
+(yet unbiased) estimate thereof, thus being much faster to compute. However, convergence
+to a local optimum, which is theoretically guaranteed as long as the learning rate vector η
+fulfils the Robbins-Monroe conditions (Robbins and Monro 1951) can be extremely slow.
+We show that our batchwise backfitting algorithm induces a learning rate that can be de-
+composed into the product of a scalar step length ν and an adaptive learning rate vector δ
+based on second order information of the objective function through an unbiased estimate
+of the Hessian, similar to the concept of natural gradients motivated from information the-
+ory (Amari 1998; Duan, Anand, Ding, Thai, Basu, Ng, and Schuler 2020). The result is
+an algorithm that requires little manual tuning and ensures fast convergence. Depending on
+the choice of ν we show that our algorithm closely mimics special cases such as resampling
+or gradient boosting (Efron and Tibshirani 1993; Mayr, Fenske, Hofner, Kneib, and Schmid
+2012). In addition, we demonstrate that our new algorithm does not only significantly reduce
+computation time and requires extremely little memory, it also has excellent properties in
+terms of variable selection; thus markedly contributing to a wider applicability of structured
+additive distributional regression to big data and highly parameterized models.
+The remainder of the paper is structured as follows. In Section 2, structured additive distri-
+butional regression models are briefly reviewed. In Section 3, the new batchwise backfitting
+algorithm and its implementation for distributional regression models is presented. In an
+extensive simulation study in Section 4, the performance of the algorithm is investigated,
+whereas in Section 5 we further highlight the usefulness of the algorithm developing a distri-
+butional model for lightning count forecasting using a very large data set with ≈ 9.1 million
+observations and 80 covariates. The final Section 6 concludes. Additional details on how to
+use our software implementation and further simulation results are contained in the Appendix.
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+3
+2. Structured Additive Distributional Regression Models
+2.1. Model Specification
+The idea in structured additive distributional regression (or GAMLSS; Rigby and Stasinopou-
+los 2005; Klein, Kneib, Klasen, and Lang 2015a) is to model all distributional parameters
+of an arbitrary parametric response distribution (rather than just the mean) through co-
+variates.
+Based on data (Yi, xi) of responses Yi (possibly non-continuous or multivariate,
+i.e. Yi = Y i ∈ RD, D > 1) and available covariate information xi, for i = 1, . . . , n ob-
+servations, we assume conditional independence of individual response observations given
+covariates. Specifically
+Y |x ∼ DY
+�
+θ1(x)) = h−1
+1 (η1(x)), θ2(x)) = h−1
+2 (η2(x)), . . . θK(x)) = h−1
+K (ηK(x))
+�
+where DY denotes a parametric distribution with K parameters θk ≡ θk(x), k = 1, . . . , K,
+and parametric density dY (·; θ1, . . . , θK). Each parameter θk is linked to an additive predictor
+ηk ≡ ηk(x) using known monotonic and twice differentiable functions hk(·) (with inverses h−1
+k
+also known as link- and response functions) to ensure potential parameter space restrictions
+on θk. The additive predictor for the k-th parameter is modeled as
+ηk = ηk(x; βk) = f1k(x; β1k) + . . . + fJkk(x; βJkk),
+(1)
+based on j = 1, . . . , Jk unspecified (possibly non-linear) functions fjk(·), applied to a subset
+of x. For a data set of i = 1, . . . , n observations, let X be the covariate matrix with rows xi,
+and ηk = (η1,k, . . . , ηn,k)⊤ be the corresponding n dimensional vector of predictors each entry
+containing the sum of evaluations of fjk(·) at xi. The parameters βk = (β1k, . . . , βJkk)⊤ are
+the regression coefficients and we denote furthermore Xk = (X1k, . . . , XJkk) the predictor
+specific design matrices, whose structure only depend on the type of covariate(s) and as-
+sumptions about fjk(·). For the models discussed here, matrices Xjk are typically based on a
+basis function approach, e.g., using B-spline basis functions (Eilers and Marx 1996) or thin-
+plate splines (Wood 2003) for modeling smooth effects. Therefore, each function fjk(·) may
+be represented by the linear combination fjk(Xjk, βjk) = Xjkβjk which leads to so-called
+GAM-type or structured additive predictors ηk (STAR, Fahrmeir et al. 2004).
+2.2. Penalized Likelihood Estimation
+Likelihood-based estimation in this flexible model class is typically based on the penalized
+log-likelihood function
+ℓpen(β, τ; y, X) = ℓ(β; y, X) +
+K
+�
+k=1
+Jk
+�
+j=1
+Pjk(βjk, τ jk),
+(2)
+where ℓ(β; y, X) is log-likelihood function
+ℓ(β; y, X) =
+n
+�
+i=1
+log dY (yi; θi,1 = h−1
+1 (η1(xi; β1)), . . . , θi,K = h−1
+K (ηK(xi; βK))),
+θk = (θ1,k, . . . , θn,k)⊤ are the parameter vectors and β = (β⊤
+1 , . . . , β⊤
+K)⊤ the stacked vector
+of regression coefficients to be estimated. The overall design matrix is X = (X1, . . . , XK),
+
+4
+Scalable Estimation for Structured Additive Distributional Regression
+where each Xk consists of rows xi,k. To avoid the problem of overfitting, each function fjk(·)
+is regularized through the penalty terms Pjk(βjk, τ jk), where τ jk controls the amount of
+smoothness and Pjk(·) is specific to fjk(·). In general, the penalty terms are assumed to be
+of the following quadratic form
+Pjk(βjk, τ jk) = β⊤
+jkKjk(τ jk)βjk.
+(3)
+For instance, when using P-splines, Pjk(·) is computed by a penalty matrix τ jkKjk formed
+by the cross-product of difference matrices. This then penalizes too abrupt jumps of neigh-
+boring coefficients to achieve a smooth functional form (a similar penalty structure results
+from, e.g., thin-plate splines or tensor splines; Fahrmeir, Kneib, Lang, and Marx 2013; Wood
+2017). Groll, Hambuckers, Kneib, and Umlauf (2019) extend the classical smoothing penalty
+for GAMLSS to (fused) LASSO-type penalties Pjk(βjk, τ jk) = β⊤
+jkKjk(τ jk)βjk, where the
+penalty Kjk(·) is also a function of the regression coefficients accounting for (approximate) L1-
+regularization (Tibshirani, Saunders, Rosset, Zhu, and Knight 2005; Oelker and Tutz 2017).
+In the following, we will describe the algorithms with the “classic” penalization (3) for the
+sake of simplicity, but more complex penalties can be implemented just as straightforwardly.
+2.3. Backfitting
+To maximize (2), Rigby and Stasinopoulos (2005) proposed a modified backfitting algorithm
+based on iteratively reweighted (penalized) least squares (IRPLS; Marx 1996), which similar
+to the backfitting algorithm of Umlauf et al. (2018) employs updates based on iteratively
+weighted least squares (IWLS; Gamerman 1997). The updating equation for the jk-th model
+term of (1) is given by
+β[t+1]
+jk
+= (X⊤
+jkWkkXjk + Kjk(τ jk))−1X⊤
+jkWkk(zk − η[t+1]
+k,−j ),
+(4)
+with vector of working observations zk = η[t]
+k + W−1
+kk uk, score vectors uk = ∂ℓ(β; y, X)/∂ηk
+and working weights Wkk = −diag(∂2ℓ(β; y, X)∂ηk∂η⊤
+k ). Here, ηk,−j represents the pre-
+dictor without the j-th model term. The backfitting iterations at (4) are computed until a
+certain termination criterion is met, e.g., when the relative change of the coefficients becomes
+very small. The optimal smoothing parameters can be estimated using e.g. stepwise selection
+(Belitz and Lang 2008), where in each updating step at (4) each τ jk = (τ1jk, . . . , τLjkjk)⊤ is
+optimized one after the other using adaptive search intervals, e.g., using the Akaike (AIC)
+or Bayesian information criterion (BIC), noting that in many cases, τ jk is just a scalar. For
+a detailed description of the algorithm see Umlauf et al. (2018). Moreover, for numerical
+reasons it is oftentimes better to replace the Hessian by the expected Fisher information with
+weights Wkk = −diag(E(∂2ℓ(β; y, X)/∂ηk∂η⊤
+k )) (Klein et al. 2015b). To reduce computation
+times, the design matrix Xjk can be modified by using only the unique values of the covariate
+data, which in many cases have much less observations than the number of observations in
+the whole data set. This leads to an updating step with reduced working observations and
+weights, which can be calculated quickly via a simple sum with indices of the unique values
+(Lang et al. 2014). Although this method can save quite a bit of computing time, memory
+issues can still occur very quickly in the GAMLSS model class.
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+5
+3. Scalable Estimation
+As a solution to large-scale data, we present our batchwise backfitting algorithm as part of
+this section first. Then we discuss some interesting properties of our algorithm depending on
+the step length choice but also further computational details.
+3.1. Batchwise Backfitting
+Instead of using all observations of the data, we replace score vector and Hessian in (4)
+through unbiased estimates thereof, which are readily available based on a random batch of
+the data. That is, we use a randomly chosen subset denoted by the subindex [i] ⊆ {1, . . . , n}
+to arrive at a stochastic updating step of the form
+β[t+1]
+jk
+=
+(1 − ν) · β[t]
+jk +
+(5)
+ν · (X⊤
+[i],jkW[i],kkX[i],jk + Kjk(τ jk))−1X⊤
+[i],jkW[i],kk(z[i],k − η[t+1]
+[i],k,−j)
+=
+(1 − ν) · β[t]
+jk + ν · β[i],jk
+and introduce a step length control parameter ν (or learning rate) specifying the amount of
+which β[t]
+jk is updated to β[t+1]
+jk
+in the direction of the new estimate β[i],jk on batch [i]. In
+each iteration, (5) is evaluated on exactly one batch [i], such that computational burden can
+be reduced considerably . As mentioned in the introduction, this mimics a second order SGD
+algorithm (Bottou 2012) since
+β[t+1]
+jk
+= β[t]
+jk + ν · (β[i],jk − β[t]
+jk) = β[t]
+jk + ν · δ[t]
+jk,
+(6)
+where the difference δ[t]
+jk between parameter updates from iteration t and batch [i] is a de-
+composition of first and second order derivative information with
+δ[t]
+jk
+=
+β[i],jk − β[t]
+jk
+=
+�
+β[t]
+jk − H[i],kk
+�
+β[t]
+jk
+�−1 s[i]
+�
+β[t]
+jk
+��
+− β[t]
+jk
+=
+−H[i],kk
+�
+β[t]
+jk
+�−1 s[i]
+�
+β[t]
+jk
+�
+,
+where s[i](·) and H[i],kk(·) are unbiased estimates of the score and Hessian (see also Umlauf
+et al. 2018) evaluated on batch [i]
+s[i](βjk)
+=
+∂ℓpen(β, τ; y[i], X[i])
+∂βjk
+= ∂ℓ(β; y[i], X[i])
+∂βjk
++
+K
+�
+k=1
+Jk
+�
+j=1
+�
+∂P(βjk, τ jk)
+∂βjk
+�
+,
+H[i],kk(βjk)
+=
+∂s[i](βjk)
+∂β⊤
+jk
+= ∂2ℓpen(β, τ; y[i], X[i])
+∂βjk∂β⊤
+jk
+=
+∂2ℓ(β, τ; y[i], X[i])
+∂βjk∂β⊤
+jk
++
+K
+�
+k=1
+Jk
+�
+j=1
+�
+∂P(βjk, τ jk)
+∂βjk∂β⊤
+jk
+�
+.
+Using second order information can speed up convergence considerably and our updating
+rule resembles that of natural gradients (Amari 1998). In each iteration of the batchwise
+
+6
+Scalable Estimation for Structured Additive Distributional Regression
+backfitting algorithm the update step length is adaptive, because of the curvature information
+provided in δ[t]
+jk.
+The working weights W[i],kk, the working responses z[i],k and the predictors η[i],k are computed
+based on the current states β[t]
+k . For each batch [i], the algorithm subsequently cycles over
+all parameters of the response distribution, the outer loop, and all model terms, the inner
+loop, in the typical backfitting manner, i.e., the predictors η[i],k and model terms fjk(·)
+are updated instantly within the inner loop. By iteration through the batches the batchwise
+backfitting algorithm updates in a memory efficient manner from batch to batch either until all
+observations are included once, or the algorithm runs through the data a prespecified number
+of epochs. This design principle makes the batchwise backfitting optimizer computationally
+simple and thus scaleable.
+3.2. Choosing the Batch Size
+The size of the batches is application specific. In general, a good strategy is to first estimate
+intercept only models, with ηk = β0k, using batchwise backfitting and small batches, e.g.,
+about 1000 observations, and then inspect the coefficient paths. If these are stationary after
+a certain runtime, the batch size is sufficient and if not it should be increased successively. For
+examples of coefficient paths that are stationary after a certain “burn-in” phase, see Figure 1.
+This approach has proven successful, e.g., in the application Section 5.
+3.3. Choosing the Step Length
+Our default batchwise backfitting works with a fixed step length ν = 0.1, which is a good
+compromise between fast updates and numerical stability and has also been shown to be
+very robust in simulations. In addition, we consider the following two variants of the basic
+algorithm.
+Resampling Variant
+If ν = 1, the algorithm can be interpreted as a resampling method
+and each update β[t+1]
+jk
+resembles a “sample” of the “distribution” of βjk, and convergence is
+achieved in distribution, i.e., once the estimates are fluctuating around a certain level. The
+final estimate ˆβ is then computed by taking the means or medians of the resulting coefficient
+paths after convergence.
+Boosting Variant
+In addition, (6) can also be utilized to enforce complete variable selection
+in a boosting type algorithm when only the model term with the best improvement in the out-
+of-sample log-likelihood is updated. An important innovation of this variant over classical
+gradient boosting for GAMLSS is that the smoothing parameters τ jk are also updated in
+each iteration (see Section 3.4), i.e., the last iteration already leads to the final model. In
+contrast, in classical boosting for GAMLSS the optimal stopping iteration is crucial and
+has to be determined separately (commonly based on costly cross validation (CV); see, e.g.,
+Mayr et al. 2012; Thomas, Mayr, Bischl, Schmid, Smith, and Hofner 2018).
+The costly
+CV makes boosting GAMLSS infeasible for big data. A further considerable advantage of
+our algorithm is that it makes the selection of the best model term relatively fair, unlike
+boosting variants with fixed prechosen degrees of freedom for fjk(·). For example, with more
+complicated distributions, it can easily happen that certain parameters are never selected
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+7
+Figure 1:
+Examples of coefficient paths for βjk of a spline model term fjk(·) using the three
+different variants of the batchwise backfitting algorithm.
+because of too large differences in the gradients. Zhang, Hepp, Greven, and Bergherr (2022)
+try to circumvent this problem by adaptive step length selection for ν in the linear normal
+location-scale model, however, for the general class of GAMLSS this procedure seems to be
+difficult or even impossible to implement.
+Graphical Illustration
+The three different variants of the algorithm are illustrated in
+Figure 1. Here, the coefficient paths are shown for a model term estimated with a thin-plate
+spline. The left plot shows coefficient paths of the batchwise backfitting with ν = 0.1, it
+takes approximately 50 iterations for the coefficients to reach a steady state. The middle plot
+illustrates coefficients paths for the boosting version with ν = 0.1 of the algorithm and possible
+updating only if the relative improvement of the log-likelihood on the next batch [˜i] is larger
+than a prespecified constant c. In the first few iterations, the model term is not selected, all
+coefficients are zero. Around iteration 10, coefficients start to deviate from zero and converge
+to a steady state shortly after iteration 150. After that, the coefficients are no longer updated,
+as indicated by the strict horizontal movements. The right plot shows coefficient paths if the
+step length is set to ν = 1 and updates are always allowed in combination with slice sampling
+of the smoothing parameters τ jk under the AIC using the next batch [˜i]. Similar to the basic
+batchwise backfitting algorithm, the coefficients require about 50 iterations to reach a steady
+state. randomly from a proposal density and an acceptance step is not required.
+3.4. Estimation of Hyperparameters
+As described in Section 2.2, the smoothness of fjk(·) is controlled by parameters τ jk. In the
+proposed implementation these parameters are either estimated according to an information
+criterion like the AIC or BIC, which is computed on an out-of-sample batch [˜i], or by slice
+
+Classic SGD
+Boosting
+Resampling
+1.5
+5.
+1.0
+Coefficients
+Coefficients
+Coefficients
+0.5
+0.5
+0.5
+0.0
+0.0
+-0.5
+5
+5
+1
+50
+100
+150
+200
+1
+50
+100
+150
+200
+50
+100
+150
+200
+Iteration
+Iteration
+Iteration8
+Scalable Estimation for Structured Additive Distributional Regression
+sampling under the information criterion (Neal 2003).
+Using the out-of-sample batch for
+selection is a novelty, aiming to improve the predictive performance of the model. Moreover,
+in addition to commonly used penalties in Pjk(·), complete model term selection can also be
+incorporated by an additional LASSO-type penalty for coefficients βjk (Groll et al. 2019).
+3.5. Computational Details and Implementation
+The complete algorithm is described in pseudo code in Algorithm 1 and is implemented in
+the R package bamlss (Umlauf, Klein, Zeileis, and Köhler 2022) within the optimizer function
+opt_bbfit(). It supports all commonly used model terms for GAMs, as implemented in
+the mgcv package (Wood 2022). In addition, to overcome memory issues with very large
+data, the bamlss package now supports the binary flat file format for data frames, which is
+implemented in the ff package (Adler, Gläser, Nenadic, Oehlschlägel, Schuemie, and Zucchini
+2022).
+By processing data and design matrices with ff, the usual memory limitations of
+the R ecosystem are circumvented. This is achieved by loading the data sequentially, using
+chunks that fit in memory, so that the complete data is never in the RAM. This means
+that the batchwise backfitting optimizer opt_bbfit() can work directly with ff objects, i.e.,
+the batches are loaded directly by the ff infrastructure, which usually means only very little
+additional processing time. This makes it possible to use almost arbitrarily large data sets
+for the estimation of structured additive distributional regression models. In Appendix A, we
+give detailed examples on how to fit models with the new optimizer function and its handling
+within the bamlss framework using simulated data with 107 observations.
+4. Simulation Study
+To investigate the performance of the proposed batchwise backfitting algorithm in terms
+of variable selection, mean squared error (MSE), prediction and runtimes, we conduct a
+benchmark study against classical Markov chain Monte Carlo (MCMC) and gradient boosting
+algorithms for GAMLSS for which we give details next before describing the simulation design
+and results.
+4.1. Estimation Approaches
+In the following, we refer to our proposed approach of batchwise backfitting throughout as
+opt_bbfit (as the model fitting function is called in the bamlss package). Our batchwise
+backfitting combines the boosting and the resampling variant as described in Section 3.1.
+The boosting step is run for 400 iterations including all possible covariates. This first step is
+used to preselect the covariates, and only covariates that are updated at least once are included
+in the subsequent resampling variant of the algorithm, which is run for 1500 iterations. The
+batch indices are drawn randomly, for the very small datasets of 500 observations we use a
+batchsize of 400, for larger datasets up to 10000 observations the batchsize is 63% of the data,
+for settings with ≥ 10000 observations, the batchsize is fixed constant at 10000.
+We investigate the performance of our batchwise backfitting opt_bbfit approach compared
+to the following very popular methods in distributional regression.
+1. MCMC (sam_mcmc). The default MCMC implementation of the bamlss package (Um-
+lauf et al. 2022) in R based on IWLS proposals is used. Note that the sam_mcmc method
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+9
+Algorithm 1 Batchwise backfitting.
+Input: y, X, α.
+Set: Step length ν ∈ [0, 1], batch index B = (b1, . . . , bT )⊤, goodness-of-fit criterion C,
+scaling constant c ∈ R, e.g., c = 1.
+Initialize: β, τ, e.g., β = 0, τ = 0.001 · 1.
+for t in 1 to number of batches T − 1. do
+Set current batch index i = bt.
+Set next batch index, e.g., with ˜i = bt+1.
+for k = 1 to K do
+Initialize η[i],k = 0.
+for j = 1 to Jk do
+Compute state η[i],k = η[i],k + X[i],jkβ[t]
+jk on current batch.
+end for
+end for
+Likewise compute η[˜i],k on next batch.
+for k = 1 to K do
+for j = 1 to Jk do
+Compute old log-likelihood on next batch ℓ(β[t]; y[˜i], X[˜i]).
+Set the working response z[i],k = η[i],k + W−1
+[i],kku[i],k.
+IWLS step
+β[i],jk = (X⊤
+[i],jkW[i],kkX[i],jk + Kjk))−1X⊤
+[i],jkW[i],kk(z[i],k − η[i],−j,k).
+Therefore find new τ [t+1]
+jk
+on next batch.
+for l = 1 to Ljk do
+Set search interval for τ [t+1]
+ljk
+, e.g., Iljk = [τ [t]
+ljk · 10−1, τ [t]
+ljk · 10].
+Find τ [t+1]
+ljk
+← arg min
+τ ⋆
+ljk∈Iljk
+C(β[i],jk, τ ⋆
+ljk; y[˜i], X[˜i]), or slice sample under C(·).
+end for
+Now set ˚βjk = β[t]
+jk + ν · (β[i],jk − β[t]
+jk).
+if Updated log-likelihood ℓ(˚β; y[˜i], X[˜i]) > c · ℓ(β[t]; y[˜i], X[˜i]). then
+Update β[t+1]
+jk
+= ˚βjk.
+Update η[i],k = η[i],k + X[i],jkβ[t+1]
+jk
+and likewise η[˜i],k.
+else
+Set β[t+1]
+jk
+= β[t]
+jk.
+end if
+end for
+end for
+Alternatively, only update coefficients βjk which lead to the greatest contribution in the next
+batch log-likelihood.
+end for
+Output: Estimates ˆβ = β[T −1]; or “samples” β[t], t = 1, . . . , T − 1; or boosting like coefficient paths
+β[t], t = 1, . . . , T − 1 if only the best working model term is updated in each batch.
+
+10
+Scalable Estimation for Structured Additive Distributional Regression
+does not perform variable selection and therefore serves as an unconstrained benchmark.
+2. Non-Cyclical Gradient Boosting (gamboostLSS). Gradient boosting for GAMLSS com-
+bines an ensemble of weak base learners. Instead of updating every distributional param-
+eter with a base learner in each iteration (cyclical), in the non-cyclical gradient boosting
+version (Thomas et al. 2018) the algorithm updates only the base learner (model term)
+which leads to the highest loss reduction over all distributional parameters in every it-
+eration. The intercepts are always updated. The optimal stopping iteration (mstop) is
+selected by five-fold CV. The non-cyclical gradient boosting algorithm is implemented
+in the R package gamboostLSS (Hofner, Mayr, Fenske, and Schmid 2022).
+3. Optimized Non-Cyclical Gradient Boosting (opt_boost). The optimized version of the
+non-cyclic gradient boosting algorithm is implemented in the R package bamlss and
+utilizes methods for large data sets, originally designed to achieve speed improvements in
+MCMC algorithms (Lang et al. 2014). Unlike the classical non-cyclic gradient boosting
+algorithm, the model intercepts count as single model terms and are not automatically
+updated. Five-fold CV is applied to find the optimal stopping iteration.
+4.2. Simulation Design
+Response Distributions
+We simulate data from the normal distribution (NO), the gamma
+distribution (GA), and the zero-adjusted Poisson distribution (ZAP). All three distributions
+are implemented in the R package gamlss.dist (Stasinopoulos and Rigby 2022). The package
+uses a specific naming convention for the parameters of the distributions, supporting up to
+four-parameter distributions. The parameters are µ, σ, ν and τ. In the simulation study, we
+let parameters µ and σ depend on covariates. Since all distributions studied in this setting
+have two parameters, no specifications for ν and τ are needed.
+Predictor Specifications
+We use the following predictors ηµ and ησ for each distribution
+ηµ = β0µ + f1(x1) + f3(x3) + f2d(lon, lat),
+ησ = β0σ + f2(x2) + f3(x3) + f4(x4),
+with model intercepts β0µ = 0, β0σ = 0 for NO, β0µ = 1, β0σ = −1 for GA and β0µ = 1,
+β0σ = −1.5 for ZAP; and
+f1(x)
+=
+x
+f2(x)
+=
+x + ((2 · x − 2)2)/5.5
+f3(x)
+=
+−x + π · sin(π · x)
+f4(x)
+=
+0.5 · x + 15 · exp
+�−2 · (x − 0.2)2�
+√
+2π
+−
+exp
+�
+−(x+0.4)2
+2
+�
+√
+2π
+f2d(z1, z2)
+=
+sin(z1) · cos(0.5 · z2).
+The simulated functions are shown in Figure 2, these are centered around zero and scaled
+so that each effect has a similar range. The link functions for the respective parameters are
+as follows: µ = ηµ, log(σ2) = ησ for NO, log(µ) = ηµ, log(σ2) = ησ for GA and log(µ2) =
+ηµ, log
+�
+σ
+1−σ
+�
+= ησ for ZAP. Finally, all covariates are drawn independently from uniform
+distributions x1, . . . , x4, lon, lat ∼ U(−2, 2).
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+11
+Figure 2:
+Functions used in the simulation study.
+Further settings
+• To investigate performance for small and large data settings alike, we simulate n =500,
+1000, 10000 and 50000 number of observations.
+• To challenge variable selection, an additional number of noise variables (denoted with
+nnoise = 0, 10, 20 in the following) is considered. Each predictor is modeled including
+all available covariates. Accordingly, for each predictor three true covariates and nnoise
+non-relevant covariates are included. Note that variables lon, lat are counted as one
+covariate.
+• In the first case the covariates are uncorrelated (ρ = 0), and in the second case correla-
+tion is introduced by the Cholesky factorization LL⊤ = Σ of the covariance matrix
+Σ =
+�
+�
+�
+�
+�
+�
+1
+ρ
+ρ2
+· · ·
+ρl−1
+ρ
+1
+ρ
+· · ·
+ρl−2
+...
+...
+...
+...
+...
+ρl−1
+ρl−2
+ρl−3
+· · ·
+1
+�
+�
+�
+�
+�
+�
+,
+where l is the number of covariates, and correlated covariates are thus generated with
+Xcorr = XL⊤ with ρ = 0.7.
+• Each scenario is replicated 100 times.
+Measures of Performance
+To evaluate the performance of the four algorithms, the MSE
+of the predictors, the MSE of the effects, the continuous ranked probability score (CRPS;
+Gneiting and Raftery 2007) and the number of falsely selected variables in each predictor
+(false positives) are calculated based on an out-of-sample validation data-set with 10000
+
+Effect of X1 on nμ
+Effect of X3 on nμ
+Spatial effect on Nμ
+2
+2
+2
+8x
+X
+0
+f3
+0
+F
+2
+2
+2
+-2
+-1
+0
+1
+2
+-2
+-1
+0
+1
+2
+-2
+-1
+0
+1
+2
+X1
+X3
+lon
+Effect of X2 on No
+Effect of X3 on no
+Effect of X4 on no
+2
+2
+2
+X4
+t2
+0
+t3
+0
+0
+乙
+-2
+-1
+0
+1
+2
+-2
+-1
+0
+1
+2
+-2
+-1
+0
+1
+2
+X2
+X3
+X412
+Scalable Estimation for Structured Additive Distributional Regression
+observations.
+The validation data-set is fixed throughout each response distribution and
+each ρ ∈ {0, 0.7}.
+We define the MSE of the predictor as the mean of the squared dif-
+ferences of the estimated additive predictors and the true additive predictors (MSEk =
+1
+n
+�
+i(ˆηi,k − ηi,k)2, for k = µ, σ).
+For the MSE of the effects we use a similar notation,
+namely the mean of the squared differences of the true effects and the estimated effects
+(MSEfk,j = 1
+n
+�
+i( ˆfi,k,j − fi,k,j)2, for k = µ, σ and j = 1, 2, 3, 4, 2d). The false positive rate is
+defined as the number of non-informative covariates which have a sufficiently large estimated
+effect f, i.e. max(f) − min(f) > threshold, with threshold = 0.1.
+Computational Details
+The simulation was run on the HPC infrastructure LEO4 of the
+University of Innsbruck. This HPC infrastructure runs on a Linux system (CentOS 7), and 50
+computing nodes with Intel Xeon (Broadwell/Skylake) processors with up to 3000 gigabyte
+(GB) available memory. Depending on the setting, the memory requirements are between 5
+and 50 GB per replication.
+4.3. Results
+Stopping and Computing Times
+Due to high computing times, we set the number of
+maximum iterations to identify the optimal stopping iteration mstop for the two boosting
+algorithms to 12000. Figure 3 shows the average mstop of all settings. For both boosting
+methods the average mstop increases with the sample size and with larger correlations be-
+tween covariates. In all but the non-correlated GA settings, opt_boost has a lower average
+of mstop than gamboostLSS. With increasing n and ρ = 0.7, the average mstop is 12000 for
+gamboostLSS, indicating that more iterations are needed. Figure 4 shows the elapsed time in
+minutes for each setting and method.
+The gamboostLSS boosting method needs around 600
+to 1100 minutes to compute a single simulation run when n = 50000 (similar to opt_boost
+which also needs several hours). Thus we deem increasing the maximum of available iterations
+as infeasible. In contrast, the batchwise backfitting method needs only 30 to 60 minutes for
+these settings.
+MSE
+A comparison of the four methods in terms of MSE is made in Figure 5 for all NO-
+settings. The MSE decreases sharply with increasing n, except for gamboostLSS in ηµ with
+ρ = 0.7, this method has a much higher MSE here. This is due to the limited number of
+stopping iterations available for gamboostLSS (note again, that the stopping iteration is set
+very large to 12000). The bamlss methods perform better in the small n settings than the
+gamboostLSS method. Remarkably, the method opt_bbfit has the smallest MSE for ηµ when
+it includes noise variables, and has basically the same performance as sam_mcmc without noise
+variables. Only in ησ and n = 500 is opt_bbfit second or third best in each case, though
+it always performs better than gamboostLSS. For larger n, the methods are very similar in
+terms of MSE. The results for the GA and ZAP distribution are qualitatively very similar and
+they can be found in the Appendix (Figures 17 and 18). For the individual effects biases, i.e.
+the MSE of the effects, we refer to the Figures 6 and 7 and the Appendix (Figures 19, 20, 21
+and 22). The overall result is that the opt_bbfit is very competitive in terms of MSE of the
+effects, in a lot of settings it performs better than the boosting methods, although the MSE
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+13
+Figure 3:
+Simulation study. Average mstop of both boosting variants. Correlation ρ = 0.7
+leads to higher mstop. For higher n and correlation the gamboostLSS variant hits the upper
+limit (horizontal dashed line at 12000) of possible stopping iterations.
+of the effects converges for all methods and effects close to zero with high enough numbers of
+observations.
+
+gamboostLSs
+Method:
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+12500
+10000
+7500
+NO
+5000
+2500
+0
+12500
+10000
+7500
+NO
+5000
+0
+2500
+0
+12500
+iteration
+10000
+7500
+GA
+5000
+0
+6uidd
+2500
+0
+12500
+sto
+10000
+7500
+II
+GA
+5000
+0
+2500
+0
+12500
+10000
+7500
+ZAI
+5000
+0
+2500
+0
+12500
+10000
+7500
+ZAI
+=
+0.7
+5000
+P
+2500
+0
+Number of observations14
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 4:
+Simulation study. Computation times for all distributions, noise variables and
+correlation settings.
+The most computational intensive settings—the two boosting vari-
+ants—depending on the number of observations require up to approximately 18 hours to
+compute. In the same settings opt_bbfit needs around 1 hour, while the MCMC method
+runs 3 hours.
+
+opt_bbfit
+sam mcmc
+Method:
+gamboostLss
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+1000
+750
+NO
+500
+0
+250
+0-
+1000
+750
+NO
+500-
+250
+0-
+1000
+ minutes
+750
+GA
+500
+II
+0
+u!
+250
+I time
+0
+Computation
+1000
+750
+=
+G
+500
+0.7
+A
+250
+0 -
+1000
+750
+ZAP
+500
+=
+0
+250
+0-
+1000
+750
+ZAP
+500-
+250-
+<0
+Number of observationsUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+15
+Figure 5:
+Simulation study. Average MSE with the NO distribution for predictor ηµ and ησ
+for different number of observations, correlation and noise variable settings.
+Predictive Accuracy
+Figure 8 shows the CRPS of the three different distributions with
+smaller values indicating higher predictive accuracy.
+The results are very similar to the
+results of the MSE. It is again noteworthy that opt_bbfit has the best performance when
+noise variables are included in the NO settings for all n, and in the other settings, when
+n ≥ 1000, the performance is almost identical to sam_mcmc and typically better than the
+boosting methods. For larger data settings the methods are very similar in terms of CRPS.
+Variable Selection
+The average false positive rates with the NO distriubtion are displayed
+in Figure 9. The false positive rate is defined as the number of non-informative covariates
+which have a sufficiently large estimated effect f, i.e. max(f) − min(f) > threshold = 0.1.
+The proposed batchwise backfitting method opt_bbfit outperforms every other method in
+terms of false positive rates. In all, except two GA distribution settings, n ≥ 5000 observations
+are always sufficient to exclude all non-informative covariates with the novel approach. In all
+
+opt_bbfit
+sam mcmc
+Method:
+gamboostLss
+opt boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.3
+0.2
+2
+0.1
+0.0-
+0.6-
+0.4 -
+=
+0.7
+0.2
+E
+0.0-
+MSI
+0.10
+0.05
+0
+0.00-
+0.20
+0.15
+0.10
+0.7
+0.05
+0.00
+Number of observations16
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 6:
+Simulation study. Average MSE of spatial effect of ηµ for all distributions, different
+number of observations, correlation and noise variables.
+settings, the true positive rates are 1 for all methods (not shown). We also evaluate the false
+positive rate with a whole range of thresholds starting very restrictive from 0.0001 up to 0.3
+for a NO-setting with different numbers of observations (n = 250, 500, 5000, 10000) and find
+that except in the n = 250 case the opt_bbfit is performing best (see Appendix Figure 25).
+The results for the GA and ZAP distribution are qualitatively the same and can be found in
+
+opt_bbfit
+sam_mcmc
+Method:
+gamboostLss
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.08
+0.06
+=d
+0.04-
+NO
+0
+0.02
+0.00.
+0.075
+L'O=d
+0.050
+NO
+0.025
+0.000
+0.02
+E Spatial effect nμ
+0
+GA
+0.01 -
+0
+0.00
+0.025
+0.020
+E
+=d
+0.015
+MSE
+GA
+0.7
+0.010
+0.005
+0.000.
+0.10
+Q
+ZAP
+0.05
+0
+0.00
+0.15
+0.10
+p= 0.7
+ZAP
+0.05
+0.00-
+Number of observationsUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+17
+Figure 7:
+Simulation study. Average MSE of f3 effect of ηµ for all distributions, different
+number of observations, correlation and noise variables.
+the Appendix (Figures 23 and 24).
+Summary
+Our batchwise backfitting algorithm has basically the same perfomance on small
+datasets (n ≤ 1000) in terms of MSE and CRPS compared to the other three methods used
+in this study, and on medium and large datasets (n ≥ 5000) it is almost consistently the best
+
+opt_bbfit
+sam_mcmc
+Method:
+gamboostLss
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.15
+0.10
+0
+NO
+"
+0
+0.05
+0.00
+0.15
+ = 0.7
+NO
+0.10
+0.05
+0.04
+- effect
+0.02
+0
+ru
+0.00
+0.06
+MSE
+0.05
+=
+0.04
+0.7
+0.03
+0.02
+0.10
+ZAP
+0.05
+0
+0.00
+0.09
+= 0.7
+ZAP
+0.06
+0.03
+Number of observations18
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 8:
+Simulation study. Average CRPS for all distributions, different number of obser-
+vations, correlation and noise variables.
+method. Compared to boosting, where computationally intensive CV (or similar) is needed
+to determine mstop batchwise backfitting does not require such additional time-consuming
+tuning. This makes our algorithm particularly convenient when applied on very large data
+sets. Our novel method is also considerably faster than both boosting variants (even with a
+determined mstop. The speed advantage ranges from around five times faster for n = 500 up
+
+opt_bbfit
+sam_mcmc
+Method:
+gamboostLss
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+1.625
+1.600
+=d
+NO
+1.575
+0
+1.550
+1.525
+1.45
+1.40-
+p = 0.7
+NO
+1.35
+1.30
+6.0
+5.8
+=d
+5.6
+0
+CRPS
+5.4 -
+4.8-
+4.6
+=d
+0.7
+4.4 
+4.2
+0.85
+=d
+ZAP
+0
+0.80-
+0.84-
+p= 0.7
+ZAP
+0.81
+0.78
+Number of observationsUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+19
+Figure 9:
+Simulation study. Average false positive rate with the NO distribution for predictor
+ηµ and ησ for different number of observations, correlation and noise variable settings.
+to 15 to 20 times faster in the large data setting with n = 50000 observations. Compared with
+the bamlss MCMC implementation, the speed advantage is evident from n = 50000 settings,
+and we expect it to increase dramatically in even larger data settings. The false positive rates
+of our batchwise backfitting method are excellent in all settings which makes this method
+also an ideal option for variable selection. Please note once more, that due to computational
+costs of benchmark methods the maximum number of observations was 50000 only. However,
+in the next Section 5 we show a model estimated with ≈ 9.1 million observations and in the
+Appendix A we exemplify that our batchwise backfitting method can easily handle up to 107
+and more observations.
+5. Application: Lightning Count Model
+Lightning is a major source of atmospheric nitrogen oxides (Schumann and Huntrieser 2007)
+which is an important greenhouse gas (Figure SPM.2 in Masson-Delmotte, Zhai, Pirani,
+Connors, Péan, Berger, Caud, Chen, Goldfarb, Gomis et al. 2021). Thus, lightning affects
+the climate. At the same time lightning is affected by climate change. This effect is subject
+to scientific debate (Murray 2018). As lightning processes cannot be resolved by numeric
+models of the atmosphere, this debate is mainly based on proxies of lightning that have
+a simple formulation and often consider only a particular aspect of the physical processes
+
+Method:
+opt_bbfit
+sam mcmc
+gamboostLSS
+opt_boost
+nμ
+nμ
+na
+na
+o=d
+p = 0.7
+p=0
+p = 0.7
+2.0
+1.5
+nnoise 
+1.0
+0.5
+0.0
+12.5
+10.0
+nnoise 
+7.5
+5.0
+0
+2.5
+0.0
+20
+nnoise = 2
+15
+10
+20
+5.
+O
+Number of observations20
+Scalable Estimation for Structured Additive Distributional Regression
+involved in lightning. Such simple formulations might be the cloud top height (Price and
+Rind 1992), iceflux in the mid atmosphere (Finney, Doherty, Wild, Huntrieser, Pumphrey,
+and Blyth 2014) or wind shear (Taszarek, Allen, Brooks, Pilguj, and Czernecki 2021), among
+others.
+As a reaction, scholars proposed to analyse lightning using machine learning (ML) approaches
+that incorporates numerous physical processes (e.g., Ukkonen and Mäkelä 2019; Simon, Mayr,
+Morgenstern, Umlauf, and Zeileis 2022).
+These are capable to process large amounts of
+data and identify most relevant variables from a pool of inputs, but focus on describing the
+occurrence of lightning via binary classification and not on the number of lightning counts
+which would be crucial to investigate the important quantity of flash rates (Cecil, Buechler,
+and Blakeslee 2014).
+The batchwise backfitting method proposed in this manuscript allows, for the first time, the
+estimation of a high-dimensional, fully probabilistic count data model, including variable
+selection, using a very large data set.
+Data
+We use high-resolution data from the Austrian Lightning Detection and Information
+System (ALDIS, Schulz, Cummins, Diendorfer, and Dorninger 2005) and explain the lightning
+counts with reanalysis data from ERA5, the fifth generation of ECMWF (European Centre
+for Medium-Range Weather Forecasts) atmospheric reanalyses of global climate (Copernicus
+Climate Change Service 2017; Hersbach and et al. 2020). ERA5 provides globally complete
+and consistent pseudo-observations of the atmosphere using the laws of physics. The horizon-
+tal resolution is approx. 32 km, while the temporal resolution is hourly and covers the years
+from 1950 to present. The model is not only interesting for a more comprehensive description
+of lightning, but also for a full reanalysis to study climate trends in lightning (Simon et al.
+2022), because homogeneous lightning observations from ALDIS are only available for the
+period in the order of a decade, here 2010–2019.
+We develop a model for the complete lightning count distribution using our proposed batch-
+wise backfitting algorithm from Section 3.1. Therefore, we aggregate the hourly lightning
+counts to the ERA5 grid cells, resulting in a final data set of ≈ 9.1 million observations. To
+estimate a well-calibrated model, we preselect 76 ERA5 covariates that are potentially good
+candidates for lightning and convective processes, such as convective available potential en-
+ergy (cape), convective precipitation (cp), cloud top height (cth), specific cloud snow water
+content between −20◦C and −40◦C (cswc2040), among others (for a detailed description of
+variables see Morgenstern, Stucke, Simon, Mayr, and Zeileis 2022). Since the distributional
+model is quite complex and very many covariates also have strong skewness, these are stan-
+dardized before estimation using the empirical cumulative distribution function estimated
+with the training data, so that all covariates are in the value range [0, 1] and thus numerical
+problems can be avoided To examine the final model performance, we split the data into a
+training and a test data set with ≈ 8.2 million (2010–2018) and ≈ 0.9 million (2019) obser-
+vations, respectively. The distribution of hourly lightning counts is shown in Figure 10 and
+indicates that the data contain a very large number of zero counts.
+Model Specification
+For this reason, in a distributional model for the number of light-
+nings, the extreme frequency of zeros must be considered. We found that the discretized
+version of the generalized Pareto distribution, DGP(ξ, σ), provides promising results (see the
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+21
+Figure 10:
+Distribution of hourly lightning counts, gray bars, along with estimated frequen-
+cies using a discretized generalized Pareto distribution, DGP(ξ, σ), blue dots and lines. Note
+the y-axis is broken because of the large number of zeros in the data, 97.4%.
+first row of Figure 13 and the next paragraph). For details on construction of the DGP, and
+discrete distributions in general we refer to Subrata (2015); Krishna and Singh Pundir (2009).
+As a first overall check, we fitted an intercept only model using the batchwise backfitting
+algorithm to assess the goodness of fit of the unconditional distributional model with DGP.
+The model estimates the two parameters with a batchsize of 50000 and 1000 batches within
+about 5 minutes on a conventional laptop with Intel(R) Core(TM) i7-8550U CPU 1.80GHz
+processor. This fitted DGP density is shown in Figure 10 by the blue dots and lines and indicates
+that the model follows the observed relative frequencies well. However, some probabilities are
+overestimated, e.g., for one and two lightnings, which is due to the fact that the model does
+not yet include covariates.
+Thus, we consider the following prediction model counts ∼ DGP(log(ξ) = ηξ, log(σ) = ησ) and
+additive predictors
+ηk = f1k(doy) + f2k(hour) + f3k(lon, lat) + f4k(cape) + . . . + f80k(mcc),
+where covariate doy is the day of the year, hour the hour of the day and model term
+f3k(lon, lat) specifies a spatial effect of longitude and latitude coordiantes. Model terms
+f4k(·), . . . , f80k(·) represent the effects of further ERA5 covariates, such as convective avail-
+able potential energy (cape) or the medium cloud cover (mcc). For the scope of simplicity,
+we do not elaborate on these covariates in this manuscript; we refer the reader to Copernicus
+Climate Change Service (2017); Hersbach and et al. (2020) for details.
+Model Fitting
+For fitting this model we proceed as follows. We use the boosting variant
+of the batchwise backfitting algorithm to select the most suitable of the 80 model terms. We
+use the AIC for selecting suitable covariates with 200 batches of size 50000. The estimation
+time is about 12 hours, which is not very long considering the huge data set and the very
+
+2.0
+%
+5.
+Observed frequencies
+Fitted DGP(≤, o) distribution
+0.5
+0.4%
+0.0
+0
+2
+6
+7
+8
+9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+>19
+Lightning counts22
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 11:
+Batchwise backfitting log-likelihood contributions for parameters ξ and σ of
+selected covariates.
+Figure 12:
+DGP lightning model. Selection of estimated smooth effects of the final model
+for parameter ξ, top row, and parameter σ, bottom row. The gray shaded areas show the
+variation of estimates in the resampling variant of the batchwise backfitting algorithm.
+large number of covariates.
+In Figure 11 the log-likelihood contributions for the selected
+covariates are shown indicating that the algorithm converged running 200 iterations/batches.
+Note that using the AIC in the batchwise backfitting algorithm results in a rather sparse
+
+S3
+mstop = 200
+mstop = 200
+s(cape)
+s(cp)
+400
+300
+LogLik contribution
+LogLik contribution
+100
+s(cswc2040)
+200
+s(cth)
+s(cape)
+s(cswc2040)
+100
+s(hh)
+s(cth)
+s(cp)
+s(mcc)
+s(hh),s(viwvd),s(mcc)
+0
+0
+1
+50
+100
+150
+200
+1
+50
+100
+150
+200
+Iteration
+Iteration0.4
+0.4
+0.4
+0.4
+0.2
+s(cswc2040).xi
+0.2
+0.2
+s(cape).xi
+0.0
+2
+?
+O-
+S
+4.
+4
+4
+0.2 
+0.4
+0.6
+0.8
+1.0
+0.00.2
+0.40.6
+0.8
+1.0
+0.2
+0.4
+0.6
+0.8
+1.0
+0
+5
+10
+15
+3
+3
+3
+3
+s(cswc2040).sigma
+2
+2
+2
+2
+ s(cape).sigma
+s(cth).sigma
+(hh).sigm
+0
+L-
+-1
+2
+2
+2
+2
+3
+?
+一
+一
+0.2
+0.4
+0.6
+0.8
+1.0
+0.0 0.2 0.4 0.6
+60.81.0
+0.20.4
+0.6
+0.81.0
+0
+5
+101520
+cape
+cswc2040
+cth
+hhUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+23
+model that selects only the most relevant variables, and that the final selected covariates are
+consistent with the study of Simon et al. (2022) which use binary classification only. This
+fact is noteworthy because variable selection is done for the entire data set and in one run
+of the batchwise backfitting algorithm, as opposed, e.g., to the costly CV commonly used
+in boosting such models. In a second step, the model is refitted with the selected variables
+using the resampling variant of the batchwise backfitting algorithm to improve the predictive
+performance. We again use 200 batches of size 50000, not using the first 100 iterations as
+burn-in. The estimation time is approximately 35 minutes using the training data with ≈ 8.2
+million observations. The reason why the resampling variant is so much faster is mainly due
+the very sparse model and the use of slice sampling of the smoothing variances under the
+“out-of-sample” AIC (see Section 3.4).
+Results
+The estimated smooth effects of the final model are shown in Figure 12. The effects
+show that some of the covariates could be modeled by linear functions, such as the effects for
+the variables cape and cswc2040 for the parameter ξ. Instead, others, such as the effect for
+hh for both ξ and σ, are nonlinear. The estimated effects appear plausible, e.g., an increase
+in cape for the location parameter ξ increases the number of lightning counts, shifting the
+probability mass of the DGP distribution to larger counts. Similarly, for the scale parameter σ,
+increasing cape also results in a shift in the probability mass towards larger lightning counts.
+The effects for hh also show that higher counts can be expected in the afternoon, when the
+ground air temperature reaches its maximum.
+In the first row of Figure 13, a worm plot is shown along with a probability integral transform
+(PIT) histogram of the quantile residuals calculated using the test data (year 2019). Both
+plots show that the model is quite well calibrated, only for the very large count observations
+(about 2% in the worm plot) the model does not seem to be optimally balanced. The reason
+for this is certainly the extremely low number of cases for large lightning counts, these are
+simply extremely difficult to model as a result. In the second row of Figure 13 we show the
+prediction from the DGP model together with the observed lightning counts for two days and
+locations in the test data set. The predictions show well that the model is indeed able to
+reflect the observed lightning activity. In addition, we also show in the plot for comparison
+the prediction from a logistic model for lightning yes/no (using the same selected covariates),
+marked by the black dashed line. It can be seen that the DGP model and the binomial model
+give basically the same point predictions, however the DGP model is much more informative
+as it allows to to derive prediction probabilities at different thresholds rather just a binary
+decision rule yes/no.
+These promising results show that the proposed method is capable to process large amounts
+of data, select the most relevant covariates and explain full probability distributions. This
+scalable method promises that distributional regression can be applied to large data sets
+such as satellite observations (for new developments see, e.g., Holmlund, Grandell, Schmetz,
+Stuhlmann, Bojkov, Munro, Lekouara, Coppens, Viticchie, August, Theodore, Watts, Dob-
+ber, Fowler, Bojinski, Schmid, Salonen, Tjemkes, Aminou, and Blythe 2021), which will
+enable better descriptions of flash rates across Europe and Africa (for a recent climatology
+see, e.g., Chakraborty, Menghal, Harshitha, and Sodunke 2022).
+
+24
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 13:
+DGP lightning model. The top left panel shows a worm plot of the out-of-sample
+randomized quantile residuals. The top right panel the corresponding probability integral
+transform (PIT) histogram. Out-of-sample predictions from the DGP lightning model for two
+locations and dates are shown in the second row. Observed lightning counts are represented
+by the black dot line, predicted probabilities are shown in the background in heat colors.
+Predictions for lighting yes/no from a logistic model are shown by the black dashed lines.
+Prediction location is shown by the red cross in the map of Austria.
+6. Summary
+This paper presents a novel algorithm for batchwise backfitting with structured additive distri-
+butional regression models, which is applicable to a much broader class of models as compared
+to the approach of Li and Wood (2020). The algorithm combines traditional backfitting with
+the ideas of SGD algorithms developed for very large data sets. It converges extremely fast
+due to an adaptive learning rate vector employing readily available unbiased estimates of the
+Hessian, similar to natural gradients. In combination with the flat file data format, it is thus
+
+Worm plot
+PIT histogram
+0.6
+1.0
+0.4
+0.8
+0.2
+Deviation
+Density
+0.6
+0.0
+-0.2
+-0.4
+-0.6 
+0.0
+1
+-4
+-2 
+0
+2
+4
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Unit normal quantile
+Probability integral transform
+2019-07-26
+2019-08-05
+5
+0.
+5
+P(counts > 0)
+Logistic
+P(counts > 0)
+Logistic
+P(counts >= 10)
+P(counts > 0)
+P(counts >= 10)
+P(counts > 0)
+P(counts >= 20)
+0.8
+4
+P(counts >= 20)
+0.8
+Lightning counts
+Lightning counts
+0.6
+Probability
+Probability
+0.4
+0
+0
+Q000000001
+0
+0
+0
+00:00
+05:00
+10:00
+15:00
+20:00
+00:00
+05:00
+10:00
+15:00
+20:00
+Hour
+HourUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+25
+possible to estimate virtually arbitrarily large models on a conventional laptop, e.g., with 107
+observations and more.
+Moreover, depending on the hyperparameter settings, smoothing parameter and variable se-
+lection is performed on-the-fly without requiring further computations on additional valida-
+tion data. This is, to the best of our knowledge, novel and has never been presented before
+in structured additive distributional regression. Besides an extensive simulation study, the
+advantages of the new algorithm are demonstrated using complex distributional regression
+models on a huge data set for lightning count prediction.
+In terms of extensions to the presented framework, the confidence intervals that are not yet
+available should be mentioned. Therefore, for the future we plan to extend the algorithm
+towards Bayesian estimation.
+Acknowledgments
+This project was partially funded by the Austrian Science Fund (FWF) grant num-
+ber 33941, and FWF grant number 31836 (Thorsten Simon). We are grateful for data sup-
+port by Gerhard Diendorfer and Wolfgang Schulz from OVE-ALDIS. The computational
+results presented here have been achieved (in part) using the LEO HPC infrastructure of
+the University of Innsbruck. Nadja Klein was supported by the Deutsche Forschungsge-
+meinschaft (DFG, German Research Foundation) through the Emmy Noether grant KL
+3037/1-1.
+References
+Adler D, Gläser C, Nenadic O, Oehlschlägel J, Schuemie M, Zucchini W (2022). ff: Memory-
+Efficient Storage of Large Data on Disk and Fast Access Functions. R package version 4.0.7,
+URL https://CRAN.R-project.org/package=ff.
+Amari S (1998). “Natural Gradient Works Efficiently in Learning.” Neural Computation,
+10(2), 251–276. doi:10.1162/089976698300017746.
+Belitz C, Lang S (2008). “Simultaneous Selection of Variables and Smoothing Parameters in
+Structured Additive Regression Models.” Computational Statistics & Data Analysis, 53,
+61–81. doi:10.1016/j.csda.2008.05.032.
+Bottou L (2012). “Stochastic Gradient Descent Tricks.” In G Montavon, GB Orr, KR Müller
+(eds.), Neural Networks: Tricks of the Trade, 2nd edition, pp. 421–436. Springer, Berlin,
+Heidelberg. ISBN 978-3-642-35289-8. doi:10.1007/978-3-642-35289-8_25.
+Cecil DJ, Buechler DE, Blakeslee RJ (2014). “Gridded Lightning Climatology from TRMM-
+LIS and OTD: Dataset Description.” Atmospheric Research, 135, 404–414. doi:10.1016/
+j.atmosres.2012.06.028.
+
+26
+Scalable Estimation for Structured Additive Distributional Regression
+Chakraborty R, Menghal PS, Harshitha M, Sodunke MA (2022). “Climatology of Lightning
+Activities Across the Equatorial African Region.” In 2022 3rd URSI Atlantic and Asia Pa-
+cific Radio Science Meeting (AT-AP-RASC), pp. 1–4. doi:10.23919/AT-AP-RASC54737.
+2022.9814276.
+Copernicus Climate Change Service (2017). “ERA5: Fifth Generation of ECMWF Atmo-
+spheric Reanalyses of the Global Climate.” Copernicus Climate Change Service Climate
+Date Store (CDS). Date of access: June 2019, https://cds.climate.copernicus.eu/
+cdsapp#!/home.
+Duan T, Anand A, Ding DY, Thai KK, Basu S, Ng A, Schuler A (2020). “NGBoost: Natural
+Gradient Boosting for Probabilistic Prediction.” In HD III, A Singh (eds.), Proceedings
+of the 37th International Conference on Machine Learning, volume 119 of Proceedings of
+Machine Learning Research, pp. 2690–2700. PMLR.
+URL https://proceedings.mlr.
+press/v119/duan20a.html.
+Efron B, Tibshirani RJ (1993). An Introduction to the Bootstrap. Number 57 in Monographs
+on Statistics and Applied Probability. Chapman & Hall/CRC, Boca Raton, Florida, USA.
+Eilers PHC, Marx BD (1996). “Flexible Smoothing Using B-Splines and Penalized Likelihood.”
+Statistical Science, 11, 89–121. doi:10.1214/ss/1038425655.
+Fahrmeir L, Kneib T, Lang S (2004).
+“Penalized Structured Additive Regression for
+Space Time Data:
+A Bayesian Perspective.”
+Statistica Sinica, 14, 731–761.
+doi:
+10.1007/978-3-642-34333-9_9.
+Fahrmeir L, Kneib T, Lang S, Marx B (2013). Regression – Models, Methods and Applications.
+Springer-Verlag, Berlin.
+Finney DL, Doherty RM, Wild O, Huntrieser H, Pumphrey HC, Blyth AM (2014). “Using
+Cloud Ice Flux to Parametrise Large-Scale Lightning.” Atmospheric Chemistry and Physics,
+14(23), 12665–12682. doi:10.5194/acp-14-12665-2014.
+Gamerman D (1997). “Sampling from the Posterior Distribution in Generalized Linear Mixed
+Models.” Statistics and Computing, 7(1), 57–68. doi:10.1023/a:1018509429360.
+Gneiting T, Raftery AE (2007).
+“Strictly Proper Scoring Rules, Prediction, and Esti-
+mation.”
+Journal of the American Statistical Association, 102(477), 359–378.
+doi:
+10.1198/016214506000001437.
+Groll A, Hambuckers J, Kneib T, Umlauf N (2019). “LASSO-Type Penalization in the Frame-
+work of Generalized Additive Models for Location, Scale and Shape.” Computational Statis-
+tics & Data Analysis, 140, 59–74. doi:10.1016/j.csda.2019.06.005.
+Hastie T, Tibshirani R (1990). Generalized Additive Models. Chapman & Hall/CRC, New
+York.
+Hersbach H, et al (2020). “The ERA5 Global Reanalysis.” Quarterly Journal of the Royal
+Meteorological Society, 146(730), 1999–2049. doi:10.1002/qj.3803.
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+27
+Hofner B, Mayr A, Fenske N, Schmid M (2022).
+gamboostLSS: Boosting Methods for
+GAMLSS Models. R package version 2.0-6, URL https://CRAN.R-project.org/package=
+gamboostLSS.
+Holmlund K, Grandell J, Schmetz J, Stuhlmann R, Bojkov B, Munro R, Lekouara M, Coppens
+D, Viticchie B, August T, Theodore B, Watts P, Dobber M, Fowler G, Bojinski S, Schmid A,
+Salonen K, Tjemkes S, Aminou D, Blythe P (2021). “Meteosat Third Generation (MTG):
+Continuation and Innovation of Observations from Geostationary Orbit.” Bulletin of the
+American Meteorological Society, 102(5), 990–1015. doi:10.1175/BAMS-D-19-0304.1.
+Klein N, Kneib T, Klasen S, Lang S (2015a). “Bayesian Structured Additive Distributional
+Regression for Multivariate Responses.”
+Journal of the Royal Statistical Society C, 64,
+569–591. doi:10.1111/rssc.12090.
+Klein N, Kneib T, Lang S (2015b). “Bayesian Generalized Additive Models for Location,
+Scale and Shape for Zero-Inflated and Overdispersed Count Data.” Journal of the American
+Statistical Association, 110(509), 405–419. doi:10.1080/01621459.2014.912955.
+Klein N, Kneib T, Lang S, Sohn A (2015c). “Bayesian Structured Additive Distributional
+Regression with an Application to Regional Income Inequality in Germany.” Annals of
+Applied Statistics, 9, 1024–1052. doi:10.1214/15-aoas823.
+Krishna H, Singh Pundir P (2009). “Discrete Burr and discrete Pareto Distributions.” Sta-
+tistical Methodology, 6(2), 177–188. doi:10.1016/j.stamet.2008.07.001.
+Lang S, Umlauf N, Wechselberger P, Harttgen K, Kneib T (2014).
+“Multilevel Struc-
+tured Additive Regression.”
+Statistics and Computing, 24(2), 223–238.
+doi:10.1007/
+s11222-012-9366-0.
+Li Z, Wood SN (2020). “Faster Model Matrix Crossproducts for Large Generalized Linear
+Models With Discretized Covariates.” Statistics and Computing, 30(1), 19–25. doi:10.
+1007/s11222-019-09864-2.
+Marx BD (1996). “Iteratively Reweighted Partial Least Squares Estimation for Generalized
+Linear Regression.” Technometrics, 38(4), 374–381. URL http://www.jstor.org/stable/
+1271308.
+Masson-Delmotte V, Zhai P, Pirani A, Connors SL, Péan C, Berger S, Caud N, Chen Y,
+Goldfarb L, Gomis M, et al. (2021). “Climate Change 2021: The Physical Science Basis.”
+Contribution of working group I to the sixth assessment report of the intergovernmental
+panel on climate change, pp. 3–32.
+Mayr A, Fenske N, Hofner B, Kneib T, Schmid M (2012). “Generalized Additive Models
+for Location, Scale and Shape for High Dimensional Data: A Flexible Approach Based on
+Boosting.” Journal of the Royal Statistical Society C, 61(3), 403–427. doi:10.1111/j.
+1467-9876.2011.01033.x.
+Morgenstern D, Stucke I, Simon T, Mayr GJ, Zeileis A (2022). “Differentiating Lightning in
+Winter and Summer With Characteristics of the Wind Field and Mass Field: Supplemen-
+tary Material.” doi:10.5281/zenodo.5851700. Funding: Austrian Research Promotion
+Agency (FFG), project no. 872656.
+
+28
+Scalable Estimation for Structured Additive Distributional Regression
+Murray LT (2018).
+“An Uncertain Future for Lightning.”
+Nature Climate Change, 8(3),
+191–192. doi:10.1038/s41558-018-0094-0.
+Neal RM (2003). “Slice Sampling.” The Annals of Statistics, 31(3), 705–767. doi:10.1214/
+aos/1056562461.
+Oelker MR, Tutz G (2017).
+“A Uniform Framework for the Combination of Penalties in
+Generalized Structured Models.” Advances in Data Analysis and Classification, 11(1), 97–
+120. doi:10.1007/s11634-015-0205-y.
+Price C, Rind D (1992). “A Simple Lightning Parameterization for Calculating Global Light-
+ning Distributions.” Journal of Geophysical Research: Atmospheres, 97(D9), 9919–9933.
+doi:10.1029/92JD00719.
+Rigby RA, Stasinopoulos DM (2005).
+“Generalized Additive Models for Location, Scale
+and Shape.” Journal of the Royal Statistical Society C, 54(3), 507–554. doi:10.1111/j.
+1467-9876.2005.00510.x.
+Robbins H, Monro S (1951). “A Stochastic Approximation Method.” The Annals of Mathe-
+matical Statistics, 22(3), 400–407. doi:10.1214/aoms/1177729586.
+Schulz W, Cummins K, Diendorfer G, Dorninger M (2005).
+“Cloud-to-Ground Lightning
+in Austria: A 10-Year Study Using Data from a Lightning Location System.” Journal of
+Geophysical Research: Atmospheres, 110(D9). doi:10.1029/2004JD005332.
+Schumann U, Huntrieser H (2007). “The Global Lightning-Induced Nitrogen Oxides Source.”
+Atmospheric Chemistry and Physics, 7(14), 3823–3907. doi:10.5194/acp-7-3823-2007.
+URL https://acp.copernicus.org/articles/7/3823/2007/.
+Simon T, Mayr GJ, Morgenstern D, Umlauf N, Zeileis A (2022). “Amplification of Annual
+and Diurnal Cycles of Alpine Lightning.” Preprint, Research Square. doi:10.21203/rs.
+3.rs-965951/v3.
+Stasinopoulos DM, Rigby RA (2022).
+gamlss.dist: Distributions for Generalized Additive
+Models for Location, Scale and Shape.
+R package version 6.0-5, URL https://CRAN.
+R-project.org/package=gamlss.dist.
+Subrata C (2015). “Generating Discrete Analogues of Continuous Probability Distributions:
+A Survey of Methods and Constructions.” Journal of Statistical Distributions and Applica-
+tions, 2(6). doi:10.1186/s40488-015-0028-6.
+Taszarek M, Allen JT, Brooks HE, Pilguj N, Czernecki B (2021). “Differing Trends in United
+States and European Severe Thunderstorm Environments in a Warming Climate.” Bulletin
+of the American Meteorological Society, 102(2), 296–322. doi:10.1175/BAMS-D-20-0004.
+1.
+Thomas J, Mayr A, Bischl B, Schmid M, Smith A, Hofner B (2018). “Gradient boosting
+for distributional regression - faster tuning and improved variable selection via noncyclical
+updates.” Statistics and Computing, 28(3), 673–687. doi:10.1007/s11222-017-9754-6.
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+29
+Tibshirani R, Saunders M, Rosset S, Zhu J, Knight K (2005). “Sparsity and Smoothness via
+the Fused Lasso.” Journal of the Royal Statistical Society: Series B (Statistical Methodol-
+ogy), 67(1), 91–108. doi:10.1111/j.1467-9868.2005.00490.x.
+Ukkonen P, Mäkelä A (2019). “Evaluation of Machine Learning Classifiers for Predicting Deep
+Convection.” J. Adv. Model. Earth Sy., 11(6), 1784–1802. doi:10.1029/2018MS001561.
+Umlauf N, Klein N, Simon T, Zeileis A (2021). “bamlss: A Lego Toolbox for Flexible Bayesian
+Regression (and Beyond).” Journal of Statistical Software, 100(4), 1–53. doi:10.18637/
+jss.v100.i04.
+Umlauf N, Klein N, Zeileis A (2018). “BAMLSS: Bayesian Additive Models for Location,
+Scale, and Shape (and Beyond).” Journal of Computational and Graphical Statistics, 27(3),
+612–627. doi:10.1080/10618600.2017.1407325.
+Umlauf N, Klein N, Zeileis A, Köhler M (2022). bamlss: Bayesian Additive Models for Location
+Scale and Shape (and Beyond). R package version 1.1-9, URL http://CRAN.R-project.
+org/package=bamlss.
+Wood SN (2003). “Thin Plate Regression Splines.” Journal of the Royal Statistical Society:
+Series B (Statistical Methodology), 65(1), 95–114. doi:10.1111/1467-9868.00374.
+Wood SN (2017). Generalized Additive Models: An Introduction with R. 2nd edition. Chapman
+& Hall/CRC, Boca Raton.
+Wood SN (2022).
+mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness
+Estimation. R package version 1.8-41, URL https://CRAN.R-project.org/package=mgcv.
+Wood SN, Li Z, Shaddick G, Augustin NH (2017). “Generalized Additive Models for Gigadata:
+Modelling the UK Black Smoke Network Daily Data.” Journal of the American Statistical
+Association, 112(519), 1199–1210. doi:10.1080/01621459.2016.1195744.
+Zhang B, Hepp T, Greven S, Bergherr E (2022). “Adaptive Step-Length Selection in Gradient
+Boosting for Gaussian Location Scale Models.” Computational Statistics. doi:10.1007/
+s00180-022-01199-3.
+
+30
+Scalable Estimation for Structured Additive Distributional Regression
+A. Batchwise Backfitting in bamlss
+This section provides introductory examples on how to fit distributional regression models for
+very large data sets with the bamlss package and the new batchwise backfitting algorithm.
+After loading the package with
+R> library("bamlss")
+we simulate a data set with 107 observations using the GAMart() function with
+R> set.seed(123)
+R> d <- GAMart(n = 1e+07, sd = -1)
+Then we save the data as a .csv file and remove the R data frame from the global environment.
+R> write.csv(d, file = "d.csv", row.names = FALSE)
+R> rm(d)
+To design the scenario very realistic with respect to a very large data set, we read the data
+back into R as a flat file data frame.
+R> library("ff")
+R> dff <- read.csv.ffdf(file = "d.csv", header = TRUE)
+The GAMart() function with sd = -1 simulates Gaussian data with y ∼ N(µ = ηµ, log(σ) =
+ησ) and predictors given by
+ηµ
+=
+f1(x1) + f2(x3) + f2d(lon, lat)
+ησ
+=
+f3(x2) + f2(x3) + f4(x4).
+Here functions f1(·), . . . , f4(·) represent univariate smooth functions and function f2d(·) a
+smooth two dimensional effect of coordinates lon and lat. Note that the data set contains
+additional noise variables x5 and x6.
+A.1. Boosting Variant
+We first illustrate the usage of the new model fitting engine using the boosting variant of
+the batchwise backfitting algorithm, see Section 3.1. Therefore, we set up a list of model
+formulae, where each formula includes all covariates.
+R> f <- ~ s(x1) + s(x2) + s(x3) + s(x4) + s(x5) + s(x6) + s(lon, lat)
+R> f <- list(update(f, y ~ .), f)
+Before estimation can be started, batch indices can be specified with
+R> set.seed(456)
+R> n <- nrow(dff)
+R> batch_ids <- lapply(1:400, function(...) sample(n, size = 10000))
+
+Umlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+31
+I.e., we use 400 batches with batchsize of 10000 such that the algorithm can practically see
+the entire data once. Then, the model is estimated with
+R> b <- bamlss(f, data = dff, family = "gaussian",
++
+sampler = FALSE, optimizer = opt_bbfit,
++
+nu = 0.1, always = FALSE, AIC = TRUE, eps_loglik = 0.0001,
++
+batch_ids = batch_ids, select = TRUE,
++
+ff_name = "ff_simdata", delete = FALSE, overwrite = FALSE,
++
+light = TRUE)
+Note that the data frame dff is an "ffdf" data frame.
+For processing all the design
+matrices for estimating the model, we therefore specify a directory name with ff_name =
+"ff_simdata", where all matrices can be stored as ff objects. The directory ff_simdata is
+created in the current working directory and will not be deleted after estimation if delete
+= FALSE. This has the advantage, that the ff matrices can be reused for other models, e.g.,
+using a different distribution, i.e., setting up more models will be much faster. If overwrite =
+FALSE, the directory for storing the ff objects will not be overwritten when calling bamlss().
+Moreover, option light = TRUE can be used to reduce the memory footprint of the final
+returned object even more. Here, we need to set sampler = FALSE in order to switch off sub-
+sequent MCMC sampling. The opt_bbfit() optimizer function is used as the model fitting
+engine, for which we specify the step length control parameter nu = 0.1. Argument always =
+FALSE causes model terms to be updated only if the relative improvement of the out-of-sample
+log-likelihood (on the next batch) is larger than 0.0001 (controlled by argument eps_loglik).
+By setting AIC = TRUE the smoothing variances are selected by the out-of-sample AIC, oth-
+erwise the out-of-sample log-likelihood is used. As we are interested in the boosting variant
+of the batchwise backfitting algorithm in this case, we need to set argument select = TRUE,
+i.e., only the model term with the largest contribution to the log-likelihood in the next batch
+will be updated. On a Linux system with Intel(R) Core(TM) i7-8550U CPU 1.80GHz pro-
+cessors, the estimation time is about 55 minutes, which is considerably fast for such a large
+data set. Selection frequencies of the 400 boosting iterations and individual log-likelihood
+contributions can be shown with
+R> contribplot(b)
+mu
+Sel. freq.
+s.s(x1)
+0.116
+s.s(x3)
+0.116
+s.s(lon,lat)
+0.112
+p
+0.004
+s.s(x2)
+0.000
+s.s(x4)
+0.000
+s.s(x5)
+0.000
+s.s(x6)
+0.000
+sigma
+Sel. freq.
+
+32
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 14:
+Log-likelihood contribution paths for selected terms of the Gaussian model.
+p
+0.220
+s.s(x3)
+0.156
+s.s(x4)
+0.140
+s.s(x2)
+0.136
+s.s(x1)
+0.000
+s.s(x5)
+0.000
+s.s(x6)
+0.000
+s.s(lon,lat)
+0.000
+The selection frequencies reveal that the boosting variant of the batchwise backfitting algo-
+rithm selected the correct model terms, the corresponding contribution paths are shown in
+Figure 14. The paths also show the convergence of the algorithm already at about iteration
+200.
+A.2. Resampling
+This section demonstrates the resampling variant with slice sampling of smoothing variances
+of the batchwise backfitting algorithm.
+From the selected model terms we set up a new
+formula
+R> f <- list(
++
+y ~ s(x1) + s(x3) + s(lon, lat),
++
+~ s(x2) + s(x3) + s(x4)
++
+)
+and only slightly modify the arguments supplied to the main model fitting function bamlss()
+
+μ
+mstop = 400
+mstop = 400
+009
+s(x2)
+s(x3),s(x1),s(lon,lat
+500
+6008001000
+s(x4)
+LogLik contribution 
+LogLik contribution
+s(x3)
+400
+300
+200
+400
+100
+200
+0
+0
+1
+100
+200
+300
+400
+1
+100
+200
+300
+400
+Iteration
+IterationUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+33
+R> m <- bamlss(f, data = dff, family = "gaussian",
++
+sampler = FALSE, optimizer = opt_bbfitp,
++
+AIC = TRUE, slice = TRUE, batch_ids = batch_ids,
++
+ff_name = "ff_simdata", delete = FALSE, overwrite = FALSE,
++
+light = TRUE)
+Estimation takes about 24 minuts. Note that we use a wrapper version opt_bbfitp() for esti-
+mating the model. The only difference is that the parameters are stored as "mcmc" “samples”
+in the returned object, so all extractor functions such as predict(), residuals(), etc., can
+be used similarly to estimating full Bayesian models with MCMC. For details on using bamlss,
+see Umlauf, Klein, Simon, and Zeileis (2021) and the project website http://bamlss.org/.
+A major advantage of the new infrastructures, including the ff package, is that all design
+matrices can be reused and do not need to be recomputed, saving large amounts of run-
+time. To use this feature, all that is required is careful handling of the ff_name, delete and
+overwrite arguments (use as described in the last section). By setting slice = TRUE, slice
+sampling of smoothing parameters in combination with the resampling variant with nu = 1,
+eps_loglik = -Inf and always = TRUE is used for batchwise backfitting, i.e., updates are
+always accepted. Convergence of the algorithm can be inspected by, e.g., coefficient paths of
+the parameters.
+
+34
+Scalable Estimation for Structured Additive Distributional Regression
+B. Simulation Results
+In this section we show all the results of the simulation study presented in Section 4.
+Figure 15:
+Functions used in the simulation study. Green lines correspond to the estimated
+effects of the opt_bbfit model of the 100 replications in the simulation setting: normal
+distribution NO, observations n = 5000, noise variables nnoise = 10 and correlation rho =
+0.
+Figure 16:
+Spatial effect used in the simulation study. Spatial effects correspond to the
+estimated two-dimensional effects of the method opt_bbfit in the 100 replications of the
+simulation setting: normal distribution NO, observations n = 5000, noise variables nnoise =
+10 and correlation rho = 0. The mean was calculated over the 100 different estimates of the
+two-dimensional effect.
+
+Effect of X1 on nμ
+Effect of X3 on nμ
+Effect of X2 on no
+Estimates
+2
+Truth
+2
+2
+8x
+X
+0
+f3
+0
+f2
+0
+F
+乙
+2
+-2
+-1
+0
+1
+2
+-2
+-1
+0
+1
+2
+-2
+-1
+0
+1
+2
+X1
+X3
+X2
+Effect of X3 on no
+Effect of X4 on no
+2
+2
+X4
+t3
+0
+-
+乙
+-2
+-1
+0
+1
+2
+-2 
+-1
+0
+1
+2
+X3
+X4True spatial effect
+Mean spatial effect
+2
+2
+0
+2
+2
+-2
+0
+2
+-2
+-1
+0
+-1
+2
+lon
+lonUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+35
+Figure 17:
+Simulation study. Average MSE with the GA distribution for predictor ηµ and ησ
+for different number of observations, correlation and noise variable settings.
+
+opt_bbfit
+sam mcmc
+Method:
+gamboostLss
+！
+opt_ boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.09
+0.06
+=
+2
+0
+0.03
+0.00
+0.20
+0.15
+2
+0.10
+0.7
+0.05
+E
+MSI
+0.00
+0.3
+0.2
+0
+0.1 
+0.0 -
+0.20
+0.15
+=
+0.10
+0.7
+0.05
+0.00
+Number of observations36
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 18:
+Simulation study. Average MSE with the ZAP distribution for predictor ηµ and
+ησ for different number of observations, correlation and noise variable settings.
+
+opt_ bbfit
+sam mcmc
+Method:
+gamboostLSs
+opt boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.15
+0.10
+0
+0.05
+0.00-
+0.15
+0.10
+=
+0.7
+0.05
+E
+0.00
+MSI
+2.0
+1.5-
+1.0-
+0
+0.5-
+0.0-
+2.5 -
+2.0-
+=d
+1.5-
+0.7
+1.0
+0.5
+0.0
+Number of observationsUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+37
+Figure 19:
+Simulation study. Average MSE of f1 effect of ηµ for all distributions, different
+number of observations, correlation and noise variables.
+
+opt_bbfit
+sam mcmc
+Method:
+gamboostLSs
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.05
+0.04
+0.03
+0
+NO
+"
+0.02
+0
+0.01
+0.00
+0.15
+0.10
+p = 0.7
+NO
+0.05
+0.00-
+0.006
+0.004
+ effect
+0
+0.002
+ru
+0.000-
+0.025
+fl
+0.020
+MSE
+=d
+0.015
+GA
+0.010
+0.7
+0.005
+0.000
+0.06
+0.04
+ZAP
+0
+0.02
+0.00
+0.075
+0.050-
+ = 0.7
+ZAP
+0.025
+0.000-
+Number of observations38
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 20:
+Simulation study. Average MSE of f2 effect of ησ for all distributions, different
+number of observations, correlation and noise variables.
+
+opt_bbfit
+sam_mcmc
+Method:
+gamboostLSs
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.05
+0.04
+0.03
+0
+NO
+"
+0.02
+0
+0.01
+0.00-
+0.125
+0.100
+p = 0.7
+0.075
+NO
+0.050.
+0.025
+0.06
+0.04
+ - effect
+0.02
+na
+0.00.
+0.16
+MSE
+=d
+0.12
+GA
+0.7
+0.08
+0.20
+0.15
+ZAP
+0.10-
+0
+0.05
+0.00
+0.3
+0.2-
+ = 0.7
+ZAP
+0.1 -
+Number of observationsUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+39
+Figure 21:
+Simulation study. Average MSE of f3 effect of ησ for all distributions, different
+number of observations, correlation and noise variables.
+
+opt_bbfit
+sam_mcmc
+Method:
+gamboostLss
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.075
+0
+0.050-
+NO
+"
+0
+0.025
+0.000
+0.12
+0.09-
+p = 0.7
+NO
+0.06
+0.03
+0.2
+ - effect
+0.1
+0
+na
+0.0-
+0.20-
+MSE
+0.15
+=d
+GA
+0.10-
+0.7
+0.05
+0.4
+0.3-
+ZAP
+0.2 -
+0
+0.1 -
+0.0 -
+0.6
+p = 0.7
+0.4 -
+ZAP
+0.2-
+0.0 -
+Number of observations40
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 22:
+Simulation study. Average MSE of f4 effect of ησ for all distributions, different
+number of observations, correlation and noise variables.
+
+opt_bbfit
+sam_mcmc
+Method:
+gamboostLss
+opt_boost
+nnoise = 0
+nnoise = 10
+nnoise = 20
+0.06
+0.04 -
+=d
+NO
+0
+0.02
+0.00.
+0.100
+0.075
+L'O=d
+NO
+0.050-
+0.025
+0.000-
+0.20-
+0.15
+=d
+ - effect
+GA
+0.10
+0
+0.05
+ou
+0.00-
+MSE
+0.10
+=d
+GA
+0.7
+0.05
+0.00
+0.3
+0.2
+=d
+ZAP
+0.1 -
+0
+0.0 -
+0.4 -
+0.3
+p= 0.7
+ZAP
+0.2
+0.1 
+0.0-
+Number of observationsUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+41
+Figure 23:
+Simulation study. Average false positive rate of the GA distribution for predictor
+ηµ and ησ for different number of observations, correlation and noise variable settings.
+
+Method:
+opt_ bbfit
+sam_mcmc
+gamboostLss
+opt_boost
+nμ
+nμ
+na
+na
+p=0
+p = 0.7
+0=d
+p = 0.7
+2.0
+1.5
+nnoise 
+1.0
+0.5
+0.0
+12.5
+10.0
+nnoise
+7.5
+5.0
+2.5
+0.0
+20
+nnoise = 
+15
+10
+5
+0-
+Number of observations42
+Scalable Estimation for Structured Additive Distributional Regression
+Figure 24:
+Simulation study. Average false positive rate of the ZAP distribution for predictor
+ηµ and ησ for different number of observations, correlation and noise variable settings.
+Figure 25:
+Simulation study. Average false positive rate of 10 replications per setting for
+different threshold values. Setting: Number of observations varies, NO, ρ = 0.7 and nnoise
+= 10. For n ≥ 500 the method opt_bbfit is the best in terms of excluding non-informative
+variables.
+
+Method:
+opt_ bbfit
+sam mcmc
+gamboostLSs
+opt_boost
+nμ
+nμ
+na
+na
+p=0
+p = 0.7
+0=d
+p = 0.7
+2.0
+1.5
+nnoise 
+1.0
+=
+0.5
+0.0
+12.5
+10.0
+nnoise
+7.5
+5.0
+=
+2.5
+0.0
+20
+nnoise =
+15
+10.
+5.
+01
+Number of observationsMethod:
+opt bbfit
+sam mcmc
+gamboostLSS
+opt boost
+n = 250
+n = 500
+n = 5000
+n = 10000
+12.5
+10.0
+7.5
+rate
+5.0
+2.5
+12.9
+10.0
+7.5
+5.0
+2.5
+0.0-
+1
+入
+3
+O:
+O:
+2
+0.0
+2
+ThresholdUmlauf N., Seiler J., Wetscher M., Simon T., Lang S., Klein N.
+43
+Affiliation:
+Nikolaus Umlauf, Johannes Seiler, Mattias Wetscher, Thorsten Simon, Stefan Lang
+Department of Statistics
+Faculty of Economics and Statistics
+Universität Innsbruck
+Universitätsstr. 15
+6020 Innsbruck, Austria
+E-mail: Nikolaus.Umlauf@uibk.ac.at,
+Johannes.Seiler@uibk.ac.at,
+Mattias.Wetscher@uibk.ac.at,
+Thorsten.Simon@uibk.ac.at,
+Stefan.Lang@uibk.ac.at
+URL: https://eeecon.uibk.ac.at/~umlauf/,
+https://www.uibk.ac.at/statistics/personal/lang/
+Nadja Klein
+Chair of Uncertainty Quantification and Statistical Learning
+Research Center Trustworthy Data Science and Security (UA Ruhr)
+Department of Statistics (Technische Universität Dortmund)
+Joseph-von-Fraunhofer-Str. 25
+44227 Dortmund, Germany
+E-mail: nadja.klein@statistik.tu-dortmund.de
+URL: https://rc-trust.ai/klein/
+
diff --git a/T9E5T4oBgHgl3EQfbA-t/content/tmp_files/load_file.txt b/T9E5T4oBgHgl3EQfbA-t/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a6212d8bf494ff8eba53f1d6389e21d05dc6a00e
--- /dev/null
+++ b/T9E5T4oBgHgl3EQfbA-t/content/tmp_files/load_file.txt
@@ -0,0 +1,1640 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf,len=1639
+page_content='Scalable Estimation for Structured Additive  Distributional Regression  Nikolaus Umlauf  Universität Innsbruck  Johannes Seiler  Universität Innsbruck  Mattias Wetscher  Universität Innsbruck  Thorsten Simon  Universität Innsbruck  Stefan Lang  Universität Innsbruck  Nadja Klein  Technische Universität Dortmund  Abstract  Recently, fitting probabilistic models have gained importance in many areas but es-  timation of such distributional models with very large data sets is a difficult task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In  particular, the use of rather complex models can easily lead to memory-related efficiency  problems that can make estimation infeasible even on high-performance computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' We  therefore propose a novel backfitting algorithm, which is based on the ideas of stochastic  gradient descent and can deal virtually with any amount of data on a conventional laptop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The algorithm performs automatic selection of variables and smoothing parameters, and  its performance is in most cases superior or at least equivalent to other implementations  for structured additive distributional regression, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', gradient boosting, while maintain-  ing low computation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Performance is evaluated using an extensive simulation study  and an exceptionally challenging and unique example of lightning count prediction over  Austria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' A very large dataset with over 9 million observations and 80 covariates is used,  so that a prediction model cannot be estimated with standard distributional regression  methods but with our new approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Keywords: Generalized additive models for location, scale and shape;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' gradient descent;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' itera-  tively weighted least squares;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Introduction  Fitting distributional regression models of high complexity to large data is challenging with  respect to storage and computational feasibility due to data volume or very high-dimensional  vectors of model parameters required to define sufficiently flexible models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Moreover, in many  applications, solving the problem also requires automatic selection of variables since manual  or stepwise searches in such model spaces are impossible to be conducted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In recent years,  techniques have already been developed to efficiently estimate generalized additive models  (GAM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Hastie and Tibshirani 1990;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Fahrmeir, Kneib, and Lang 2004) and generalized additive  models for location scale and shape (GAMLSS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Rigby and Stasinopoulos 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Klein, Kneib,  and Lang 2015b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For example, Wood, Li, Shaddick, and Augustin (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Li and Wood (2020)  show how to decompose the iterative estimation algorithm for GAMs to be able to compute  models for large data and gigadata with coefficients up to 104 and up to 108 observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05593v1  [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='CO]  13 Jan 2023  2  Scalable Estimation for Structured Additive Distributional Regression  Lang, Umlauf, Wechselberger, Harttgen, and Kneib (2014) present efficient algorithms for  Bayesian multilevel models for example by, discretization and indexing to significantly reduce  the number of floating point operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' These ideas are carried over to estimate fully Bayesian  structured additive distributional regression models (Klein, Kneib, Lang, and Sohn 2015c),  the Bayesian version of GAMLSS, such that e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' modelling the precipitation climatology  across Austria with over 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2 million daily observations is possible (Umlauf, Klein, and Zeileis  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' While in principle being easily trainable in terms of data size with the approach of Li  and Wood (2020), GAMs are not suited here given the censored nature of the response daily  precipitation with a spike at zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Nevertheless, for more complicated probabilistic models  or larger n, techniques such as Umlauf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' (2018) also reach their limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' On the one hand,  such models can no longer be computed on conventional computers since there is simply a  lack of random-access memory (RAM);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' on the other hand, the computing time increases so  much that modeling with many variables is not possible in a foreseeable time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  To break down these barriers in structured additive distributional regression models, we  propose a novel estimation algorithm, which we call batchwise backfitting and which combines  the ideas of the classic backfitting optimization with stochastic gradient descent (SGD), an  efficient algorithm based on a stochastic approximation to gradient descent for finding local  maxima of an objective function J(θ) of a parameter vector θ ∈ Rp (Robbins and Monro  1951).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Compared to costly gradient descent methods, which involve updates of the form  θ = θ − η∇θJ(θ) based on the whole data set, SGD replaces the gradient ∇θJ(θ) by a noisy  (yet unbiased) estimate thereof, thus being much faster to compute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' However, convergence  to a local optimum, which is theoretically guaranteed as long as the learning rate vector η  fulfils the Robbins-Monroe conditions (Robbins and Monro 1951) can be extremely slow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  We show that our batchwise backfitting algorithm induces a learning rate that can be de-  composed into the product of a scalar step length ν and an adaptive learning rate vector δ  based on second order information of the objective function through an unbiased estimate  of the Hessian, similar to the concept of natural gradients motivated from information the-  ory (Amari 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Duan, Anand, Ding, Thai, Basu, Ng, and Schuler 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The result is  an algorithm that requires little manual tuning and ensures fast convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Depending on  the choice of ν we show that our algorithm closely mimics special cases such as resampling  or gradient boosting (Efron and Tibshirani 1993;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Mayr, Fenske, Hofner, Kneib, and Schmid  2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In addition, we demonstrate that our new algorithm does not only significantly reduce  computation time and requires extremely little memory, it also has excellent properties in  terms of variable selection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' thus markedly contributing to a wider applicability of structured  additive distributional regression to big data and highly parameterized models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The remainder of the paper is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In Section 2, structured additive distri-  butional regression models are briefly reviewed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In Section 3, the new batchwise backfitting  algorithm and its implementation for distributional regression models is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In an  extensive simulation study in Section 4, the performance of the algorithm is investigated,  whereas in Section 5 we further highlight the usefulness of the algorithm developing a distri-  butional model for lightning count forecasting using a very large data set with ≈ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1 million  observations and 80 covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The final Section 6 concludes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Additional details on how to  use our software implementation and further simulation results are contained in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Structured Additive Distributional Regression Models  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Model Specification  The idea in structured additive distributional regression (or GAMLSS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Rigby and Stasinopou-  los 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Klein, Kneib, Klasen, and Lang 2015a) is to model all distributional parameters  of an arbitrary parametric response distribution (rather than just the mean) through co-  variates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Based on data (Yi, xi) of responses Yi (possibly non-continuous or multivariate,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Yi = Y i ∈ RD, D > 1) and available covariate information xi, for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , n ob-  servations, we assume conditional independence of individual response observations given  covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Specifically  Y |x ∼ DY  �  θ1(x)) = h−1  1 (η1(x)), θ2(x)) = h−1  2 (η2(x)), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' θK(x)) = h−1  K (ηK(x))  �  where DY denotes a parametric distribution with K parameters θk ≡ θk(x), k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , K,  and parametric density dY (·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' θ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , θK).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Each parameter θk is linked to an additive predictor  ηk ≡ ηk(x) using known monotonic and twice differentiable functions hk(·) (with inverses h−1  k  also known as link- and response functions) to ensure potential parameter space restrictions  on θk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The additive predictor for the k-th parameter is modeled as  ηk = ηk(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' βk) = f1k(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' β1k) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' + fJkk(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' βJkk),  (1)  based on j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , Jk unspecified (possibly non-linear) functions fjk(·), applied to a subset  of x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For a data set of i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , n observations, let X be the covariate matrix with rows xi,  and ηk = (η1,k, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , ηn,k)⊤ be the corresponding n dimensional vector of predictors each entry  containing the sum of evaluations of fjk(·) at xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The parameters βk = (β1k, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , βJkk)⊤ are  the regression coefficients and we denote furthermore Xk = (X1k, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , XJkk) the predictor  specific design matrices, whose structure only depend on the type of covariate(s) and as-  sumptions about fjk(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For the models discussed here, matrices Xjk are typically based on a  basis function approach, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', using B-spline basis functions (Eilers and Marx 1996) or thin-  plate splines (Wood 2003) for modeling smooth effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Therefore, each function fjk(·) may  be represented by the linear combination fjk(Xjk, βjk) = Xjkβjk which leads to so-called  GAM-type or structured additive predictors ηk (STAR, Fahrmeir et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Penalized Likelihood Estimation  Likelihood-based estimation in this flexible model class is typically based on the penalized  log-likelihood function  ℓpen(β, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y, X) = ℓ(β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y, X) +  K  �  k=1  Jk  �  j=1  Pjk(βjk, τ jk),  (2)  where ℓ(β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y, X) is log-likelihood function  ℓ(β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y, X) =  n  �  i=1  log dY (yi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' θi,1 = h−1  1 (η1(xi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' β1)), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , θi,K = h−1  K (ηK(xi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' βK))),  θk = (θ1,k, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , θn,k)⊤ are the parameter vectors and β = (β⊤  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , β⊤  K)⊤ the stacked vector  of regression coefficients to be estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The overall design matrix is X = (X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , XK),  4  Scalable Estimation for Structured Additive Distributional Regression  where each Xk consists of rows xi,k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' To avoid the problem of overfitting, each function fjk(·)  is regularized through the penalty terms Pjk(βjk, τ jk), where τ jk controls the amount of  smoothness and Pjk(·) is specific to fjk(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In general, the penalty terms are assumed to be  of the following quadratic form  Pjk(βjk, τ jk) = β⊤  jkKjk(τ jk)βjk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  (3)  For instance, when using P-splines, Pjk(·) is computed by a penalty matrix τ jkKjk formed  by the cross-product of difference matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This then penalizes too abrupt jumps of neigh-  boring coefficients to achieve a smooth functional form (a similar penalty structure results  from, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', thin-plate splines or tensor splines;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Fahrmeir, Kneib, Lang, and Marx 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Wood  2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Groll, Hambuckers, Kneib, and Umlauf (2019) extend the classical smoothing penalty  for GAMLSS to (fused) LASSO-type penalties Pjk(βjk, τ jk) = β⊤  jkKjk(τ jk)βjk, where the  penalty Kjk(·) is also a function of the regression coefficients accounting for (approximate) L1-  regularization (Tibshirani, Saunders, Rosset, Zhu, and Knight 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Oelker and Tutz 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  In the following, we will describe the algorithms with the “classic” penalization (3) for the  sake of simplicity, but more complex penalties can be implemented just as straightforwardly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Backfitting  To maximize (2), Rigby and Stasinopoulos (2005) proposed a modified backfitting algorithm  based on iteratively reweighted (penalized) least squares (IRPLS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Marx 1996), which similar  to the backfitting algorithm of Umlauf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' (2018) employs updates based on iteratively  weighted least squares (IWLS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Gamerman 1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The updating equation for the jk-th model  term of (1) is given by  β[t+1]  jk  = (X⊤  jkWkkXjk + Kjk(τ jk))−1X⊤  jkWkk(zk − η[t+1]  k,−j ),  (4)  with vector of working observations zk = η[t]  k + W−1  kk uk, score vectors uk = ∂ℓ(β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y, X)/∂ηk  and working weights Wkk = −diag(∂2ℓ(β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y, X)∂ηk∂η⊤  k ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Here, ηk,−j represents the pre-  dictor without the j-th model term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The backfitting iterations at (4) are computed until a  certain termination criterion is met, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', when the relative change of the coefficients becomes  very small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The optimal smoothing parameters can be estimated using e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' stepwise selection  (Belitz and Lang 2008), where in each updating step at (4) each τ jk = (τ1jk, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , τLjkjk)⊤ is  optimized one after the other using adaptive search intervals, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', using the Akaike (AIC)  or Bayesian information criterion (BIC), noting that in many cases, τ jk is just a scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For  a detailed description of the algorithm see Umlauf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Moreover, for numerical  reasons it is oftentimes better to replace the Hessian by the expected Fisher information with  weights Wkk = −diag(E(∂2ℓ(β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y, X)/∂ηk∂η⊤  k )) (Klein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2015b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' To reduce computation  times, the design matrix Xjk can be modified by using only the unique values of the covariate  data, which in many cases have much less observations than the number of observations in  the whole data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This leads to an updating step with reduced working observations and  weights, which can be calculated quickly via a simple sum with indices of the unique values  (Lang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Although this method can save quite a bit of computing time, memory  issues can still occur very quickly in the GAMLSS model class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Scalable Estimation  As a solution to large-scale data, we present our batchwise backfitting algorithm as part of  this section first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Then we discuss some interesting properties of our algorithm depending on  the step length choice but also further computational details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Batchwise Backfitting  Instead of using all observations of the data, we replace score vector and Hessian in (4)  through unbiased estimates thereof, which are readily available based on a random batch of  the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' That is, we use a randomly chosen subset denoted by the subindex [i] ⊆ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , n}  to arrive at a stochastic updating step of the form  β[t+1]  jk  =  (1 − ν) · β[t]  jk +  (5)  ν · (X⊤  [i],jkW[i],kkX[i],jk + Kjk(τ jk))−1X⊤  [i],jkW[i],kk(z[i],k − η[t+1]  [i],k,−j)  =  (1 − ν) · β[t]  jk + ν · β[i],jk  and introduce a step length control parameter ν (or learning rate) specifying the amount of  which β[t]  jk is updated to β[t+1]  jk  in the direction of the new estimate β[i],jk on batch [i].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In  each iteration, (5) is evaluated on exactly one batch [i], such that computational burden can  be reduced considerably .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' As mentioned in the introduction,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' this mimics a second order SGD  algorithm (Bottou 2012) since  β[t+1]  jk  = β[t]  jk + ν · (β[i],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='jk − β[t]  jk) = β[t]  jk + ν · δ[t]  jk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  (6)  where the difference δ[t]  jk between parameter updates from iteration t and batch [i] is a de-  composition of first and second order derivative information with  δ[t]  jk  =  β[i],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='jk − β[t]  jk  =  �  β[t]  jk − H[i],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='kk  �  β[t]  jk  �−1 s[i]  �  β[t]  jk  ��  − β[t]  jk  =  −H[i],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='kk  �  β[t]  jk  �−1 s[i]  �  β[t]  jk  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  where s[i](·) and H[i],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='kk(·) are unbiased estimates of the score and Hessian (see also Umlauf  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2018) evaluated on batch [i]  s[i](βjk)  =  ∂ℓpen(β, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y[i], X[i])  ∂βjk  = ∂ℓ(β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y[i], X[i])  ∂βjk  +  K  �  k=1  Jk  �  j=1  �  ∂P(βjk, τ jk)  ∂βjk  �  ,  H[i],kk(βjk)  =  ∂s[i](βjk)  ∂β⊤  jk  = ∂2ℓpen(β, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y[i], X[i])  ∂βjk∂β⊤  jk  =  ∂2ℓ(β, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y[i], X[i])  ∂βjk∂β⊤  jk  +  K  �  k=1  Jk  �  j=1  �  ∂P(βjk, τ jk)  ∂βjk∂β⊤  jk  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Using second order information can speed up convergence considerably and our updating  rule resembles that of natural gradients (Amari 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In each iteration of the batchwise  6  Scalable Estimation for Structured Additive Distributional Regression  backfitting algorithm the update step length is adaptive, because of the curvature information  provided in δ[t]  jk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The working weights W[i],kk, the working responses z[i],k and the predictors η[i],k are computed  based on the current states β[t]  k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For each batch [i], the algorithm subsequently cycles over  all parameters of the response distribution, the outer loop, and all model terms, the inner  loop, in the typical backfitting manner, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', the predictors η[i],k and model terms fjk(·)  are updated instantly within the inner loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' By iteration through the batches the batchwise  backfitting algorithm updates in a memory efficient manner from batch to batch either until all  observations are included once, or the algorithm runs through the data a prespecified number  of epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This design principle makes the batchwise backfitting optimizer computationally  simple and thus scaleable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Choosing the Batch Size  The size of the batches is application specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In general, a good strategy is to first estimate  intercept only models, with ηk = β0k, using batchwise backfitting and small batches, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=',  about 1000 observations, and then inspect the coefficient paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' If these are stationary after  a certain runtime, the batch size is sufficient and if not it should be increased successively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For  examples of coefficient paths that are stationary after a certain “burn-in” phase, see Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  This approach has proven successful, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', in the application Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Choosing the Step Length  Our default batchwise backfitting works with a fixed step length ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1, which is a good  compromise between fast updates and numerical stability and has also been shown to be  very robust in simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In addition, we consider the following two variants of the basic  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Resampling Variant  If ν = 1, the algorithm can be interpreted as a resampling method  and each update β[t+1]  jk  resembles a “sample” of the “distribution” of βjk, and convergence is  achieved in distribution, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', once the estimates are fluctuating around a certain level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The  final estimate ˆβ is then computed by taking the means or medians of the resulting coefficient  paths after convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Boosting Variant  In addition, (6) can also be utilized to enforce complete variable selection  in a boosting type algorithm when only the model term with the best improvement in the out-  of-sample log-likelihood is updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' An important innovation of this variant over classical  gradient boosting for GAMLSS is that the smoothing parameters τ jk are also updated in  each iteration (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', the last iteration already leads to the final model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In  contrast, in classical boosting for GAMLSS the optimal stopping iteration is crucial and  has to be determined separately (commonly based on costly cross validation (CV);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=',  Mayr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Thomas, Mayr, Bischl, Schmid, Smith, and Hofner 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The costly  CV makes boosting GAMLSS infeasible for big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' A further considerable advantage of  our algorithm is that it makes the selection of the best model term relatively fair, unlike  boosting variants with fixed prechosen degrees of freedom for fjk(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For example, with more  complicated distributions, it can easily happen that certain parameters are never selected  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  7  Figure 1:  Examples of coefficient paths for βjk of a spline model term fjk(·) using the three  different variants of the batchwise backfitting algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  because of too large differences in the gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Zhang, Hepp, Greven, and Bergherr (2022)  try to circumvent this problem by adaptive step length selection for ν in the linear normal  location-scale model, however, for the general class of GAMLSS this procedure seems to be  difficult or even impossible to implement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Graphical Illustration  The three different variants of the algorithm are illustrated in  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Here, the coefficient paths are shown for a model term estimated with a thin-plate  spline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The left plot shows coefficient paths of the batchwise backfitting with ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1, it  takes approximately 50 iterations for the coefficients to reach a steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The middle plot  illustrates coefficients paths for the boosting version with ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1 of the algorithm and possible  updating only if the relative improvement of the log-likelihood on the next batch [˜i] is larger  than a prespecified constant c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In the first few iterations, the model term is not selected, all  coefficients are zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Around iteration 10, coefficients start to deviate from zero and converge  to a steady state shortly after iteration 150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' After that, the coefficients are no longer updated,  as indicated by the strict horizontal movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The right plot shows coefficient paths if the  step length is set to ν = 1 and updates are always allowed in combination with slice sampling  of the smoothing parameters τ jk under the AIC using the next batch [˜i].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Similar to the basic  batchwise backfitting algorithm, the coefficients require about 50 iterations to reach a steady  state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' randomly from a proposal density and an acceptance step is not required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Estimation of Hyperparameters  As described in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2, the smoothness of fjk(·) is controlled by parameters τ jk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In the  proposed implementation these parameters are either estimated according to an information  criterion like the AIC or BIC, which is computed on an out-of-sample batch [˜i], or by slice  Classic SGD  Boosting  Resampling  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  Coefficients  Coefficients  Coefficients  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  5  5  1  50  100  150  200  1  50  100  150  200  50  100  150  200  Iteration  Iteration  Iteration8  Scalable Estimation for Structured Additive Distributional Regression  sampling under the information criterion (Neal 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Using the out-of-sample batch for  selection is a novelty, aiming to improve the predictive performance of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Moreover,  in addition to commonly used penalties in Pjk(·), complete model term selection can also be  incorporated by an additional LASSO-type penalty for coefficients βjk (Groll et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Computational Details and Implementation  The complete algorithm is described in pseudo code in Algorithm 1 and is implemented in  the R package bamlss (Umlauf, Klein, Zeileis, and Köhler 2022) within the optimizer function  opt_bbfit().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' It supports all commonly used model terms for GAMs, as implemented in  the mgcv package (Wood 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In addition, to overcome memory issues with very large  data, the bamlss package now supports the binary flat file format for data frames, which is  implemented in the ff package (Adler, Gläser, Nenadic, Oehlschlägel, Schuemie, and Zucchini  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  By processing data and design matrices with ff, the usual memory limitations of  the R ecosystem are circumvented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This is achieved by loading the data sequentially, using  chunks that fit in memory, so that the complete data is never in the RAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This means  that the batchwise backfitting optimizer opt_bbfit() can work directly with ff objects, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=',  the batches are loaded directly by the ff infrastructure, which usually means only very little  additional processing time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This makes it possible to use almost arbitrarily large data sets  for the estimation of structured additive distributional regression models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In Appendix A, we  give detailed examples on how to fit models with the new optimizer function and its handling  within the bamlss framework using simulated data with 107 observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Simulation Study  To investigate the performance of the proposed batchwise backfitting algorithm in terms  of variable selection, mean squared error (MSE), prediction and runtimes, we conduct a  benchmark study against classical Markov chain Monte Carlo (MCMC) and gradient boosting  algorithms for GAMLSS for which we give details next before describing the simulation design  and results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Estimation Approaches  In the following, we refer to our proposed approach of batchwise backfitting throughout as  opt_bbfit (as the model fitting function is called in the bamlss package).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Our batchwise  backfitting combines the boosting and the resampling variant as described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The boosting step is run for 400 iterations including all possible covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This first step is  used to preselect the covariates, and only covariates that are updated at least once are included  in the subsequent resampling variant of the algorithm, which is run for 1500 iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The  batch indices are drawn randomly, for the very small datasets of 500 observations we use a  batchsize of 400, for larger datasets up to 10000 observations the batchsize is 63% of the data,  for settings with ≥ 10000 observations, the batchsize is fixed constant at 10000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  We investigate the performance of our batchwise backfitting opt_bbfit approach compared  to the following very popular methods in distributional regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' MCMC (sam_mcmc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The default MCMC implementation of the bamlss package (Um-  lauf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2022) in R based on IWLS proposals is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Note that the sam_mcmc method  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  9  Algorithm 1 Batchwise backfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Input: y, X, α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Set: Step length ν ∈ [0, 1], batch index B = (b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , bT )⊤, goodness-of-fit criterion C,  scaling constant c ∈ R, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Initialize: β, τ, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', β = 0, τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='001 · 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  for t in 1 to number of batches T − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' do  Set current batch index i = bt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Set next batch index, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', with ˜i = bt+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  for k = 1 to K do  Initialize η[i],k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  for j = 1 to Jk do  Compute state η[i],k = η[i],k + X[i],jkβ[t]  jk on current batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  end for  end for  Likewise compute η[˜i],k on next batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  for k = 1 to K do  for j = 1 to Jk do  Compute old log-likelihood on next batch ℓ(β[t];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y[˜i], X[˜i]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Set the working response z[i],k = η[i],k + W−1  [i],kku[i],k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  IWLS step  β[i],jk = (X⊤  [i],jkW[i],kkX[i],jk + Kjk))−1X⊤  [i],jkW[i],kk(z[i],k − η[i],−j,k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Therefore find new τ [t+1]  jk  on next batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  for l = 1 to Ljk do  Set search interval for τ [t+1]  ljk  , e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Iljk = [τ [t]  ljk · 10−1, τ [t]  ljk · 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Find τ [t+1]  ljk  ← arg min  τ ⋆  ljk∈Iljk  C(β[i],jk, τ ⋆  ljk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y[˜i], X[˜i]), or slice sample under C(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  end for  Now set ˚βjk = β[t]  jk + ν · (β[i],jk − β[t]  jk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  if Updated log-likelihood ℓ(˚β;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y[˜i], X[˜i]) > c · ℓ(β[t];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' y[˜i], X[˜i]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' then  Update β[t+1]  jk  = ˚βjk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Update η[i],k = η[i],k + X[i],jkβ[t+1]  jk  and likewise η[˜i],k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  else  Set β[t+1]  jk  = β[t]  jk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  end if  end for  end for  Alternatively, only update coefficients βjk which lead to the greatest contribution in the next  batch log-likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  end for  Output: Estimates ˆβ = β[T −1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' or “samples” β[t], t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , T − 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' or boosting like coefficient paths  β[t], t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , T − 1 if only the best working model term is updated in each batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  10  Scalable Estimation for Structured Additive Distributional Regression  does not perform variable selection and therefore serves as an unconstrained benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Non-Cyclical Gradient Boosting (gamboostLSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Gradient boosting for GAMLSS com-  bines an ensemble of weak base learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Instead of updating every distributional param-  eter with a base learner in each iteration (cyclical), in the non-cyclical gradient boosting  version (Thomas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2018) the algorithm updates only the base learner (model term)  which leads to the highest loss reduction over all distributional parameters in every it-  eration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The intercepts are always updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The optimal stopping iteration (mstop) is  selected by five-fold CV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The non-cyclical gradient boosting algorithm is implemented  in the R package gamboostLSS (Hofner, Mayr, Fenske, and Schmid 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Optimized Non-Cyclical Gradient Boosting (opt_boost).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The optimized version of the  non-cyclic gradient boosting algorithm is implemented in the R package bamlss and  utilizes methods for large data sets, originally designed to achieve speed improvements in  MCMC algorithms (Lang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Unlike the classical non-cyclic gradient boosting  algorithm, the model intercepts count as single model terms and are not automatically  updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Five-fold CV is applied to find the optimal stopping iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Simulation Design  Response Distributions  We simulate data from the normal distribution (NO), the gamma  distribution (GA), and the zero-adjusted Poisson distribution (ZAP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' All three distributions  are implemented in the R package gamlss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='dist (Stasinopoulos and Rigby 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The package  uses a specific naming convention for the parameters of the distributions, supporting up to  four-parameter distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The parameters are µ, σ, ν and τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In the simulation study, we  let parameters µ and σ depend on covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Since all distributions studied in this setting  have two parameters, no specifications for ν and τ are needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Predictor Specifications  We use the following predictors ηµ and ησ for each distribution  ηµ = β0µ + f1(x1) + f3(x3) + f2d(lon, lat),  ησ = β0σ + f2(x2) + f3(x3) + f4(x4),  with model intercepts β0µ = 0, β0σ = 0 for NO, β0µ = 1, β0σ = −1 for GA and β0µ = 1,  β0σ = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5 for ZAP;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' and  f1(x)  =  x  f2(x)  =  x + ((2 · x − 2)2)/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  f3(x)  =  −x + π · sin(π · x)  f4(x)  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5 · x + 15 · exp  �−2 · (x − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2)2�  √  2π  −  exp  �  −(x+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4)2  2  �  √  2π  f2d(z1, z2)  =  sin(z1) · cos(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5 · z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The simulated functions are shown in Figure 2, these are centered around zero and scaled  so that each effect has a similar range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The link functions for the respective parameters are  as follows: µ = ηµ, log(σ2) = ησ for NO, log(µ) = ηµ, log(σ2) = ησ for GA and log(µ2) =  ηµ, log  �  σ  1−σ  �  = ησ for ZAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Finally, all covariates are drawn independently from uniform  distributions x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , x4, lon, lat ∼ U(−2, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  11  Figure 2:  Functions used in the simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Further settings  To investigate performance for small and large data settings alike, we simulate n =500,  1000, 10000 and 50000 number of observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  To challenge variable selection, an additional number of noise variables (denoted with  nnoise = 0, 10, 20 in the following) is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Each predictor is modeled including  all available covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Accordingly, for each predictor three true covariates and nnoise  non-relevant covariates are included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Note that variables lon, lat are counted as one  covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  In the first case the covariates are uncorrelated (ρ = 0), and in the second case correla-  tion is introduced by the Cholesky factorization LL⊤ = Σ of the covariance matrix  Σ =  �  �  �  �  �  �  1  ρ  ρ2  · ·  ρl−1  ρ  1  ρ  · ·  ρl−2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  ρl−1  ρl−2  ρl−3  · ·  1  �  �  �  �  �  �  ,  where l is the number of covariates, and correlated covariates are thus generated with  Xcorr = XL⊤ with ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Each scenario is replicated 100 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Measures of Performance  To evaluate the performance of the four algorithms, the MSE  of the predictors, the MSE of the effects, the continuous ranked probability score (CRPS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='Gneiting and Raftery 2007) and the number of falsely selected variables in each predictor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='(false positives) are calculated based on an out-of-sample validation data-set with 10000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='Effect of X1 on nμ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='Effect of X3 on nμ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='Spatial effect on Nμ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='X412  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='Scalable Estimation for Structured Additive Distributional Regression  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The validation data-set is fixed throughout each response distribution and  each ρ ∈ {0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  We define the MSE of the predictor as the mean of the squared dif-  ferences of the estimated additive predictors and the true additive predictors (MSEk =  1  n  �  i(ˆηi,k − ηi,k)2, for k = µ, σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  For the MSE of the effects we use a similar notation,  namely the mean of the squared differences of the true effects and the estimated effects  (MSEfk,j = 1  n  �  i( ˆfi,k,j − fi,k,j)2, for k = µ, σ and j = 1, 2, 3, 4, 2d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The false positive rate is  defined as the number of non-informative covariates which have a sufficiently large estimated  effect f, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' max(f) − min(f) > threshold, with threshold = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Computational Details  The simulation was run on the HPC infrastructure LEO4 of the  University of Innsbruck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This HPC infrastructure runs on a Linux system (CentOS 7), and 50  computing nodes with Intel Xeon (Broadwell/Skylake) processors with up to 3000 gigabyte  (GB) available memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Depending on the setting, the memory requirements are between 5  and 50 GB per replication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Results  Stopping and Computing Times  Due to high computing times, we set the number of  maximum iterations to identify the optimal stopping iteration mstop for the two boosting  algorithms to 12000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Figure 3 shows the average mstop of all settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For both boosting  methods the average mstop increases with the sample size and with larger correlations be-  tween covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In all but the non-correlated GA settings, opt_boost has a lower average  of mstop than gamboostLSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' With increasing n and ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7, the average mstop is 12000 for  gamboostLSS, indicating that more iterations are needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Figure 4 shows the elapsed time in  minutes for each setting and method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The gamboostLSS boosting method needs around 600  to 1100 minutes to compute a single simulation run when n = 50000 (similar to opt_boost  which also needs several hours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Thus we deem increasing the maximum of available iterations  as infeasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In contrast, the batchwise backfitting method needs only 30 to 60 minutes for  these settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  MSE  A comparison of the four methods in terms of MSE is made in Figure 5 for all NO-  settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The MSE decreases sharply with increasing n, except for gamboostLSS in ηµ with  ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7, this method has a much higher MSE here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This is due to the limited number of  stopping iterations available for gamboostLSS (note again, that the stopping iteration is set  very large to 12000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The bamlss methods perform better in the small n settings than the  gamboostLSS method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Remarkably, the method opt_bbfit has the smallest MSE for ηµ when  it includes noise variables, and has basically the same performance as sam_mcmc without noise  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Only in ησ and n = 500 is opt_bbfit second or third best in each case, though  it always performs better than gamboostLSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For larger n, the methods are very similar in  terms of MSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The results for the GA and ZAP distribution are qualitatively very similar and  they can be found in the Appendix (Figures 17 and 18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For the individual effects biases, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  the MSE of the effects, we refer to the Figures 6 and 7 and the Appendix (Figures 19, 20, 21  and 22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The overall result is that the opt_bbfit is very competitive in terms of MSE of the  effects, in a lot of settings it performs better than the boosting methods, although the MSE  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  13  Figure 3:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average mstop of both boosting variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Correlation ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  leads to higher mstop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For higher n and correlation the gamboostLSS variant hits the upper  limit (horizontal dashed line at 12000) of possible stopping iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  of the effects converges for all methods and effects close to zero with high enough numbers of  observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  gamboostLSs  Method:  opt_boost  nnoise = 0  nnoise = 10  nnoise = 20  12500  10000  7500  NO  5000  2500  0  12500  10000  7500  NO  5000  0  2500  0  12500  iteration  10000  7500  GA  5000  0  6uidd  2500  0  12500  sto  10000  7500  II  GA  5000  0  2500  0  12500  10000  7500  ZAI  5000  0  2500  0  12500  10000  7500  ZAI  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  5000  P  2500  0  Number of observations14  Scalable Estimation for Structured Additive Distributional Regression  Figure 4:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Computation times for all distributions, noise variables and  correlation settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The most computational intensive settings—the two boosting vari-  ants—depending on the number of observations require up to approximately 18 hours to  compute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In the same settings opt_bbfit needs around 1 hour, while the MCMC method  runs 3 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  opt_bbfit  sam mcmc  Method:  gamboostLss  opt_boost  nnoise = 0  nnoise = 10  nnoise = 20  1000  750  NO  500  0  250  0-  1000  750  NO  500-  250  0-  1000  minutes  750  GA  500  II  0  u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  250  I time  0  Computation  1000  750  =  G  500  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  A  250  0 -  1000  750  ZAP  500  =  0  250  0-  1000  750  ZAP  500-  250-  <0  Number of observationsUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  15  Figure 5:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average MSE with the NO distribution for predictor ηµ and ησ  for different number of observations, correlation and noise variable settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Predictive Accuracy  Figure 8 shows the CRPS of the three different distributions with  smaller values indicating higher predictive accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The results are very similar to the  results of the MSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' It is again noteworthy that opt_bbfit has the best performance when  noise variables are included in the NO settings for all n, and in the other settings, when  n ≥ 1000, the performance is almost identical to sam_mcmc and typically better than the  boosting methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For larger data settings the methods are very similar in terms of CRPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Variable Selection  The average false positive rates with the NO distriubtion are displayed  in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The false positive rate is defined as the number of non-informative covariates  which have a sufficiently large estimated effect f, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' max(f) − min(f) > threshold = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The proposed batchwise backfitting method opt_bbfit outperforms every other method in  terms of false positive rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In all, except two GA distribution settings, n ≥ 5000 observations  are always sufficient to exclude all non-informative covariates with the novel approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In all  opt_bbfit  sam mcmc  Method:  gamboostLss  opt boost  nnoise = 0  nnoise = 10  nnoise = 20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4 -  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0-  MSI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00  Number of observations16  Scalable Estimation for Structured Additive Distributional Regression  Figure 6:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average MSE of spatial effect of ηµ for all distributions, different  number of observations, correlation and noise variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  settings, the true positive rates are 1 for all methods (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' We also evaluate the false  positive rate with a whole range of thresholds starting very restrictive from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0001 up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='3  for a NO-setting with different numbers of observations (n = 250, 500, 5000, 10000) and find  that except in the n = 250 case the opt_bbfit is performing best (see Appendix Figure 25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The results for the GA and ZAP distribution are qualitatively the same and can be found in  opt_bbfit  sam_mcmc  Method:  gamboostLss  opt_boost  nnoise = 0  nnoise = 10  nnoise = 20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='06  =d  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='04-  NO  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content="075  L'O=d  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='050  NO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='02  E Spatial effect nμ  0  GA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='01 -  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='020  E  =d  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='015  MSE  GA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='10  Q  ZAP  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='10  p= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  ZAP  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00-  Number of observationsUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  17  Figure 7:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average MSE of f3 effect of ηµ for all distributions, different  number of observations, correlation and noise variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  the Appendix (Figures 23 and 24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Summary  Our batchwise backfitting algorithm has basically the same perfomance on small  datasets (n ≤ 1000) in terms of MSE and CRPS compared to the other three methods used  in this study, and on medium and large datasets (n ≥ 5000) it is almost consistently the best  opt_bbfit  sam_mcmc  Method:  gamboostLss  opt_boost  nnoise = 0  nnoise = 10  nnoise = 20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='10  0  NO  "  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='15  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  NO  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='04  effect  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='02  0  ru  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='06  MSE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='10  ZAP  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='09  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  ZAP  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='03  Number of observations18  Scalable Estimation for Structured Additive Distributional Regression  Figure 8:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average CRPS for all distributions, different number of obser-  vations, correlation and noise variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Compared to boosting, where computationally intensive CV (or similar) is needed  to determine mstop batchwise backfitting does not require such additional time-consuming  tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This makes our algorithm particularly convenient when applied on very large data  sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Our novel method is also considerably faster than both boosting variants (even with a  determined mstop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The speed advantage ranges from around five times faster for n = 500 up  opt_bbfit  sam_mcmc  Method:  gamboostLss  opt_boost  nnoise = 0  nnoise = 10  nnoise = 20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='625  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='600  =d  NO  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='575  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='550  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='525  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='45  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='40-  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  NO  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='35  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='30  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='8  =d  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  0  CRPS  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4 -  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='8-  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  =d  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='85  =d  ZAP  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='80-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='84-  p= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  ZAP  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='81  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='78  Number of observationsUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  19  Figure 9:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average false positive rate with the NO distribution for predictor  ηµ and ησ for different number of observations, correlation and noise variable settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  to 15 to 20 times faster in the large data setting with n = 50000 observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Compared with  the bamlss MCMC implementation, the speed advantage is evident from n = 50000 settings,  and we expect it to increase dramatically in even larger data settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The false positive rates  of our batchwise backfitting method are excellent in all settings which makes this method  also an ideal option for variable selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Please note once more, that due to computational  costs of benchmark methods the maximum number of observations was 50000 only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' However,  in the next Section 5 we show a model estimated with ≈ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1 million observations and in the  Appendix A we exemplify that our batchwise backfitting method can easily handle up to 107  and more observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Application: Lightning Count Model  Lightning is a major source of atmospheric nitrogen oxides (Schumann and Huntrieser 2007)  which is an important greenhouse gas (Figure SPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2 in Masson-Delmotte, Zhai, Pirani,  Connors, Péan, Berger, Caud, Chen, Goldfarb, Gomis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Thus, lightning affects  the climate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' At the same time lightning is affected by climate change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This effect is subject  to scientific debate (Murray 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' As lightning processes cannot be resolved by numeric  models of the atmosphere, this debate is mainly based on proxies of lightning that have  a simple formulation and often consider only a particular aspect of the physical processes  Method:  opt_bbfit  sam mcmc  gamboostLSS  opt_boost  nμ  nμ  na  na  o=d  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  p=0  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  nnoise  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  nnoise  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  20  nnoise = 2  15  10  20  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  O  Number of observations20  Scalable Estimation for Structured Additive Distributional Regression  involved in lightning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Such simple formulations might be the cloud top height (Price and  Rind 1992), iceflux in the mid atmosphere (Finney, Doherty, Wild, Huntrieser, Pumphrey,  and Blyth 2014) or wind shear (Taszarek, Allen, Brooks, Pilguj, and Czernecki 2021), among  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  As a reaction, scholars proposed to analyse lightning using machine learning (ML) approaches  that incorporates numerous physical processes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Ukkonen and Mäkelä 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Simon, Mayr,  Morgenstern, Umlauf, and Zeileis 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  These are capable to process large amounts of  data and identify most relevant variables from a pool of inputs, but focus on describing the  occurrence of lightning via binary classification and not on the number of lightning counts  which would be crucial to investigate the important quantity of flash rates (Cecil, Buechler,  and Blakeslee 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The batchwise backfitting method proposed in this manuscript allows, for the first time, the  estimation of a high-dimensional, fully probabilistic count data model, including variable  selection, using a very large data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Data  We use high-resolution data from the Austrian Lightning Detection and Information  System (ALDIS, Schulz, Cummins, Diendorfer, and Dorninger 2005) and explain the lightning  counts with reanalysis data from ERA5, the fifth generation of ECMWF (European Centre  for Medium-Range Weather Forecasts) atmospheric reanalyses of global climate (Copernicus  Climate Change Service 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Hersbach and et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' ERA5 provides globally complete  and consistent pseudo-observations of the atmosphere using the laws of physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The horizon-  tal resolution is approx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 32 km, while the temporal resolution is hourly and covers the years  from 1950 to present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The model is not only interesting for a more comprehensive description  of lightning, but also for a full reanalysis to study climate trends in lightning (Simon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  2022), because homogeneous lightning observations from ALDIS are only available for the  period in the order of a decade, here 2010–2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  We develop a model for the complete lightning count distribution using our proposed batch-  wise backfitting algorithm from Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Therefore, we aggregate the hourly lightning  counts to the ERA5 grid cells, resulting in a final data set of ≈ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1 million observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' To  estimate a well-calibrated model, we preselect 76 ERA5 covariates that are potentially good  candidates for lightning and convective processes, such as convective available potential en-  ergy (cape), convective precipitation (cp), cloud top height (cth), specific cloud snow water  content between −20◦C and −40◦C (cswc2040), among others (for a detailed description of  variables see Morgenstern, Stucke, Simon, Mayr, and Zeileis 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Since the distributional  model is quite complex and very many covariates also have strong skewness, these are stan-  dardized before estimation using the empirical cumulative distribution function estimated  with the training data, so that all covariates are in the value range [0, 1] and thus numerical  problems can be avoided To examine the final model performance, we split the data into a  training and a test data set with ≈ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2 million (2010–2018) and ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='9 million (2019) obser-  vations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The distribution of hourly lightning counts is shown in Figure 10 and  indicates that the data contain a very large number of zero counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Model Specification  For this reason, in a distributional model for the number of light-  nings, the extreme frequency of zeros must be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' We found that the discretized  version of the generalized Pareto distribution, DGP(ξ, σ), provides promising results (see the  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  21  Figure 10:  Distribution of hourly lightning counts, gray bars, along with estimated frequen-  cies using a discretized generalized Pareto distribution, DGP(ξ, σ), blue dots and lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Note  the y-axis is broken because of the large number of zeros in the data, 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  first row of Figure 13 and the next paragraph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For details on construction of the DGP, and  discrete distributions in general we refer to Subrata (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Krishna and Singh Pundir (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  As a first overall check, we fitted an intercept only model using the batchwise backfitting  algorithm to assess the goodness of fit of the unconditional distributional model with DGP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The model estimates the two parameters with a batchsize of 50000 and 1000 batches within  about 5 minutes on a conventional laptop with Intel(R) Core(TM) i7-8550U CPU 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='80GHz  processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This fitted DGP density is shown in Figure 10 by the blue dots and lines and indicates  that the model follows the observed relative frequencies well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' However, some probabilities are  overestimated, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', for one and two lightnings, which is due to the fact that the model does  not yet include covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Thus, we consider the following prediction model counts ∼ DGP(log(ξ) = ηξ, log(σ) = ησ) and  additive predictors  ηk = f1k(doy) + f2k(hour) + f3k(lon, lat) + f4k(cape) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' + f80k(mcc),  where covariate doy is the day of the year, hour the hour of the day and model term  f3k(lon, lat) specifies a spatial effect of longitude and latitude coordiantes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Model terms  f4k(·), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , f80k(·) represent the effects of further ERA5 covariates, such as convective avail-  able potential energy (cape) or the medium cloud cover (mcc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For the scope of simplicity,  we do not elaborate on these covariates in this manuscript;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' we refer the reader to Copernicus  Climate Change Service (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Hersbach and et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' (2020) for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Model Fitting  For fitting this model we proceed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' We use the boosting variant  of the batchwise backfitting algorithm to select the most suitable of the 80 model terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' We  use the AIC for selecting suitable covariates with 200 batches of size 50000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The estimation  time is about 12 hours, which is not very long considering the huge data set and the very  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  %  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Observed frequencies  Fitted DGP(≤, o) distribution  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4%  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0  2  6  7  8  9  10  11  12  13  14  15  16  17  18  19  >19  Lightning counts22  Scalable Estimation for Structured Additive Distributional Regression  Figure 11:  Batchwise backfitting log-likelihood contributions for parameters ξ and σ of  selected covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Figure 12:  DGP lightning model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Selection of estimated smooth effects of the final model  for parameter ξ, top row, and parameter σ, bottom row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The gray shaded areas show the  variation of estimates in the resampling variant of the batchwise backfitting algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  large number of covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  In Figure 11 the log-likelihood contributions for the selected  covariates are shown indicating that the algorithm converged running 200 iterations/batches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Note that using the AIC in the batchwise backfitting algorithm results in a rather sparse  S3  mstop = 200  mstop = 200  s(cape)  s(cp)  400  300  LogLik contribution  LogLik contribution  100  s(cswc2040)  200  s(cth)  s(cape)  s(cswc2040)  100  s(hh)  s(cth)  s(cp)  s(mcc)  s(hh),s(viwvd),s(mcc)  0  0  1  50  100  150  200  1  50  100  150  200  Iteration  Iteration0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  s(cswc2040).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='xi  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  s(cape).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='xi  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  O-  S  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  4  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0  5  10  15  3  3  3  3  s(cswc2040).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='sigma  2  2  2  2  s(cape).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='sigma  s(cth).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='sigma  (hh).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='sigm  0  L-  1  2  2  2  2  3  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  一  一  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0  5  101520  cape  cswc2040  cth  hhUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  23  model that selects only the most relevant variables, and that the final selected covariates are  consistent with the study of Simon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' (2022) which use binary classification only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This  fact is noteworthy because variable selection is done for the entire data set and in one run  of the batchwise backfitting algorithm, as opposed, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', to the costly CV commonly used  in boosting such models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In a second step, the model is refitted with the selected variables  using the resampling variant of the batchwise backfitting algorithm to improve the predictive  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' We again use 200 batches of size 50000, not using the first 100 iterations as  burn-in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The estimation time is approximately 35 minutes using the training data with ≈ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  million observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The reason why the resampling variant is so much faster is mainly due  the very sparse model and the use of slice sampling of the smoothing variances under the  “out-of-sample” AIC (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Results  The estimated smooth effects of the final model are shown in Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The effects  show that some of the covariates could be modeled by linear functions, such as the effects for  the variables cape and cswc2040 for the parameter ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Instead, others, such as the effect for  hh for both ξ and σ, are nonlinear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The estimated effects appear plausible, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', an increase  in cape for the location parameter ξ increases the number of lightning counts, shifting the  probability mass of the DGP distribution to larger counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Similarly, for the scale parameter σ,  increasing cape also results in a shift in the probability mass towards larger lightning counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  The effects for hh also show that higher counts can be expected in the afternoon, when the  ground air temperature reaches its maximum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  In the first row of Figure 13, a worm plot is shown along with a probability integral transform  (PIT) histogram of the quantile residuals calculated using the test data (year 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Both  plots show that the model is quite well calibrated, only for the very large count observations  (about 2% in the worm plot) the model does not seem to be optimally balanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The reason  for this is certainly the extremely low number of cases for large lightning counts, these are  simply extremely difficult to model as a result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In the second row of Figure 13 we show the  prediction from the DGP model together with the observed lightning counts for two days and  locations in the test data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The predictions show well that the model is indeed able to  reflect the observed lightning activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In addition, we also show in the plot for comparison  the prediction from a logistic model for lightning yes/no (using the same selected covariates),  marked by the black dashed line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' It can be seen that the DGP model and the binomial model  give basically the same point predictions, however the DGP model is much more informative  as it allows to to derive prediction probabilities at different thresholds rather just a binary  decision rule yes/no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  These promising results show that the proposed method is capable to process large amounts  of data, select the most relevant covariates and explain full probability distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This  scalable method promises that distributional regression can be applied to large data sets  such as satellite observations (for new developments see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Holmlund, Grandell, Schmetz,  Stuhlmann, Bojkov, Munro, Lekouara, Coppens, Viticchie, August, Theodore, Watts, Dob-  ber, Fowler, Bojinski, Schmid, Salonen, Tjemkes, Aminou, and Blythe 2021), which will  enable better descriptions of flash rates across Europe and Africa (for a recent climatology  see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Chakraborty, Menghal, Harshitha, and Sodunke 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  24  Scalable Estimation for Structured Additive Distributional Regression  Figure 13:  DGP lightning model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The top left panel shows a worm plot of the out-of-sample  randomized quantile residuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The top right panel the corresponding probability integral  transform (PIT) histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Out-of-sample predictions from the DGP lightning model for two  locations and dates are shown in the second row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Observed lightning counts are represented  by the black dot line, predicted probabilities are shown in the background in heat colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Predictions for lighting yes/no from a logistic model are shown by the black dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Prediction location is shown by the red cross in the map of Austria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Summary  This paper presents a novel algorithm for batchwise backfitting with structured additive distri-  butional regression models, which is applicable to a much broader class of models as compared  to the approach of Li and Wood (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The algorithm combines traditional backfitting with  the ideas of SGD algorithms developed for very large data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' It converges extremely fast  due to an adaptive learning rate vector employing readily available unbiased estimates of the  Hessian, similar to natural gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' In combination with the flat file data format, it is thus  Worm plot  PIT histogram  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  Deviation  Density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  1  4  2  0  2  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  Unit normal quantile  Probability integral transform  2019-07-26  2019-08-05  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  5  P(counts > 0)  Logistic  P(counts > 0)  Logistic  P(counts >= 10)  P(counts > 0)  P(counts >= 10)  P(counts > 0)  P(counts >= 20)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='8  4  P(counts >= 20)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='8  Lightning counts  Lightning counts  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='6  Probability  Probability  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='4  0  0  Q000000001  0  0  0  00:00  05:00  10:00  15:00  20:00  00:00  05:00  10:00  15:00  20:00  Hour  HourUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  25  possible to estimate virtually arbitrarily large models on a conventional laptop, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', with 107  observations and more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Moreover, depending on the hyperparameter settings, smoothing parameter and variable se-  lection is performed on-the-fly without requiring further computations on additional valida-  tion data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This is, to the best of our knowledge, novel and has never been presented before  in structured additive distributional regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Besides an extensive simulation study, the  advantages of the new algorithm are demonstrated using complex distributional regression  models on a huge data set for lightning count prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  In terms of extensions to the presented framework, the confidence intervals that are not yet  available should be mentioned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Therefore, for the future we plan to extend the algorithm  towards Bayesian estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Acknowledgments  This project was partially funded by the Austrian Science Fund (FWF) grant num-  ber 33941, and FWF grant number 31836 (Thorsten Simon).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' We are grateful for data sup-  port by Gerhard Diendorfer and Wolfgang Schulz from OVE-ALDIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The computational  results presented here have been achieved (in part) using the LEO HPC infrastructure of  the University of Innsbruck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Nadja Klein was supported by the Deutsche Forschungsge-  meinschaft (DFG, German Research Foundation) through the Emmy Noether grant KL  3037/1-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  References  Adler D, Gläser C, Nenadic O, Oehlschlägel J, Schuemie M, Zucchini W (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' ff: Memory-  Efficient Storage of Large Data on Disk and Fast Access Functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' R package version 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7,  URL https://CRAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='R-project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='org/package=ff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Amari S (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Natural Gradient Works Efficiently in Learning.” Neural Computation,  10(2), 251–276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1162/089976698300017746.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Belitz C, Lang S (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Simultaneous Selection of Variables and Smoothing Parameters in  Structured Additive Regression Models.” Computational Statistics & Data Analysis, 53,  61–81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='csda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='032.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Bottou L (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Stochastic Gradient Descent Tricks.” In G Montavon, GB Orr, KR Müller  (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' ), Neural Networks: Tricks of the Trade, 2nd edition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 421–436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Springer, Berlin,  Heidelberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' ISBN 978-3-642-35289-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1007/978-3-642-35289-8_25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Cecil DJ, Buechler DE, Blakeslee RJ (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Gridded Lightning Climatology from TRMM-  LIS and OTD: Dataset Description.” Atmospheric Research, 135, 404–414.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1016/  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='atmosres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  26  Scalable Estimation for Structured Additive Distributional Regression  Chakraborty R, Menghal PS, Harshitha M, Sodunke MA (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Climatology of Lightning  Activities Across the Equatorial African Region.” In 2022 3rd URSI Atlantic and Asia Pa-  cific Radio Science Meeting (AT-AP-RASC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='23919/AT-AP-RASC54737.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='9814276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Copernicus Climate Change Service (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “ERA5: Fifth Generation of ECMWF Atmo-  spheric Reanalyses of the Global Climate.” Copernicus Climate Change Service Climate  Date Store (CDS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Date of access: June 2019, https://cds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='climate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='copernicus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='/home.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Duan T, Anand A, Ding DY, Thai KK, Basu S, Ng A, Schuler A (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “NGBoost: Natural  Gradient Boosting for Probabilistic Prediction.” In HD III, A Singh (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' ), Proceedings  of the 37th International Conference on Machine Learning, volume 119 of Proceedings of  Machine Learning Research, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 2690–2700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  URL https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='mlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  press/v119/duan20a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Efron B, Tibshirani RJ (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' An Introduction to the Bootstrap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Number 57 in Monographs  on Statistics and Applied Probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Chapman & Hall/CRC, Boca Raton, Florida, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Eilers PHC, Marx BD (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Flexible Smoothing Using B-Splines and Penalized Likelihood.”  Statistical Science, 11, 89–121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1214/ss/1038425655.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Fahrmeir L, Kneib T, Lang S (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  “Penalized Structured Additive Regression for  Space Time Data:  A Bayesian Perspective.”  Statistica Sinica, 14, 731–761.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1007/978-3-642-34333-9_9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Fahrmeir L, Kneib T, Lang S, Marx B (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Regression – Models, Methods and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Springer-Verlag, Berlin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Finney DL, Doherty RM, Wild O, Huntrieser H, Pumphrey HC, Blyth AM (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Using  Cloud Ice Flux to Parametrise Large-Scale Lightning.” Atmospheric Chemistry and Physics,  14(23), 12665–12682.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5194/acp-14-12665-2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Gamerman D (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Sampling from the Posterior Distribution in Generalized Linear Mixed  Models.” Statistics and Computing, 7(1), 57–68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1023/a:1018509429360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Gneiting T, Raftery AE (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  “Strictly Proper Scoring Rules, Prediction, and Esti-  mation.”  Journal of the American Statistical Association, 102(477), 359–378.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  Groll A, Hambuckers J, Kneib T, Umlauf N (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “LASSO-Type Penalization in the Frame-  work of Generalized Additive Models for Location, Scale and Shape.” Computational Statis-  tics & Data Analysis, 140, 59–74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='csda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Hastie T, Tibshirani R (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Generalized Additive Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Chapman & Hall/CRC, New  York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Hersbach H, et al (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “The ERA5 Global Reanalysis.” Quarterly Journal of the Royal  Meteorological Society, 146(730), 1999–2049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  27  Hofner B, Mayr A, Fenske N, Schmid M (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  gamboostLSS: Boosting Methods for  GAMLSS Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  Holmlund K, Grandell J, Schmetz J, Stuhlmann R, Bojkov B, Munro R, Lekouara M, Coppens  D, Viticchie B, August T, Theodore B, Watts P, Dobber M, Fowler G, Bojinski S, Schmid A,  Salonen K, Tjemkes S, Aminou D, Blythe P (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Meteosat Third Generation (MTG):  Continuation and Innovation of Observations from Geostationary Orbit.” Bulletin of the  American Meteorological Society, 102(5), 990–1015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Klein N, Kneib T, Klasen S, Lang S (2015a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Bayesian Structured Additive Distributional  Regression for Multivariate Responses.”  Journal of the Royal Statistical Society C, 64,  569–591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  Klein N, Kneib T, Lang S (2015b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Bayesian Generalized Additive Models for Location,  Scale and Shape for Zero-Inflated and Overdispersed Count Data.” Journal of the American  Statistical Association, 110(509), 405–419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1080/01621459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='912955.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Klein N, Kneib T, Lang S, Sohn A (2015c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Bayesian Structured Additive Distributional  Regression with an Application to Regional Income Inequality in Germany.” Annals of  Applied Statistics, 9, 1024–1052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  Krishna H, Singh Pundir P (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Discrete Burr and discrete Pareto Distributions.” Sta-  tistical Methodology, 6(2), 177–188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='stamet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Lang S, Umlauf N, Wechselberger P, Harttgen K, Kneib T (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  “Multilevel Struc-  tured Additive Regression.”  Statistics and Computing, 24(2), 223–238.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1007/  s11222-012-9366-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Li Z, Wood SN (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Faster Model Matrix Crossproducts for Large Generalized Linear  Models With Discretized Covariates.” Statistics and Computing, 30(1), 19–25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  1007/s11222-019-09864-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Marx BD (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Iteratively Reweighted Partial Least Squares Estimation for Generalized  Linear Regression.” Technometrics, 38(4), 374–381.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='jstor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='org/stable/  1271308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Masson-Delmotte V, Zhai P, Pirani A, Connors SL, Péan C, Berger S, Caud N, Chen Y,  Goldfarb L, Gomis M, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Climate Change 2021: The Physical Science Basis.”  Contribution of working group I to the sixth assessment report of the intergovernmental  panel on climate change, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 3–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Mayr A, Fenske N, Hofner B, Kneib T, Schmid M (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Generalized Additive Models  for Location, Scale and Shape for High Dimensional Data: A Flexible Approach Based on  Boosting.” Journal of the Royal Statistical Society C, 61(3), 403–427.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  1467-9876.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='01033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  Morgenstern D, Stucke I, Simon T, Mayr GJ, Zeileis A (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Differentiating Lightning in  Winter and Summer With Characteristics of the Wind Field and Mass Field: Supplemen-  tary Material.” doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content=' Funding: Austrian Research Promotion  Agency (FFG), project no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 872656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  28  Scalable Estimation for Structured Additive Distributional Regression  Murray LT (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  “An Uncertain Future for Lightning.”  Nature Climate Change, 8(3),  191–192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1038/s41558-018-0094-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Neal RM (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Slice Sampling.” The Annals of Statistics, 31(3), 705–767.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1214/  aos/1056562461.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Oelker MR, Tutz G (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  “A Uniform Framework for the Combination of Penalties in  Generalized Structured Models.” Advances in Data Analysis and Classification, 11(1), 97–  120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1007/s11634-015-0205-y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Price C, Rind D (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “A Simple Lightning Parameterization for Calculating Global Light-  ning Distributions.” Journal of Geophysical Research: Atmospheres, 97(D9), 9919–9933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1029/92JD00719.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Rigby RA, Stasinopoulos DM (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  “Generalized Additive Models for Location, Scale  and Shape.” Journal of the Royal Statistical Society C, 54(3), 507–554.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  Robbins H, Monro S (1951).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “A Stochastic Approximation Method.” The Annals of Mathe-  matical Statistics, 22(3), 400–407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='  29  Tibshirani R, Saunders M, Rosset S, Zhu J, Knight K (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content=' “Evaluation of Machine Learning Classifiers for Predicting Deep  Convection.” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content=' Earth Sy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', 11(6), 1784–1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='1195744.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Zhang B, Hepp T, Greven S, Bergherr E (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' “Adaptive Step-Length Selection in Gradient  Boosting for Gaussian Location Scale Models.” Computational Statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1007/  s00180-022-01199-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  30  Scalable Estimation for Structured Additive Distributional Regression  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Batchwise Backfitting in bamlss  This section provides introductory examples on how to fit distributional regression models for  very large data sets with the bamlss package and the new batchwise backfitting algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  After loading the package with  R> library("bamlss")  we simulate a data set with 107 observations using the GAMart() function with  R> set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='seed(123)  R> d <- GAMart(n = 1e+07, sd = -1)  Then we save the data as a .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='csv file and remove the R data frame from the global environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  R> write.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='csv(d, file = "d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='csv", row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='names = FALSE)  R> rm(d)  To design the scenario very realistic with respect to a very large data set, we read the data  back into R as a flat file data frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  R> library("ff")  R> dff <- read.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='csv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='ffdf(file = "d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='csv", header = TRUE)  The GAMart() function with sd = -1 simulates Gaussian data with y ∼ N(µ = ηµ, log(σ) =  ησ) and predictors given by  ηµ  =  f1(x1) + f2(x3) + f2d(lon, lat)  ησ  =  f3(x2) + f2(x3) + f4(x4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Here functions f1(·), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' , f4(·) represent univariate smooth functions and function f2d(·) a  smooth two dimensional effect of coordinates lon and lat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Note that the data set contains  additional noise variables x5 and x6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Boosting Variant  We first illustrate the usage of the new model fitting engine using the boosting variant of  the batchwise backfitting algorithm, see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Therefore, we set up a list of model  formulae, where each formula includes all covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  R> f <- ~ s(x1) + s(x2) + s(x3) + s(x4) + s(x5) + s(x6) + s(lon, lat)  R> f <- list(update(f, y ~ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' ), f)  Before estimation can be started, batch indices can be specified with  R> set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='seed(456)  R> n <- nrow(dff)  R> batch_ids <- lapply(1:400, function(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=') sample(n, size = 10000))  Umlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  31  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', we use 400 batches with batchsize of 10000 such that the algorithm can practically see  the entire data once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Then, the model is estimated with  R> b <- bamlss(f, data = dff, family = "gaussian",  +  sampler = FALSE, optimizer = opt_bbfit,  +  nu = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1, always = FALSE, AIC = TRUE, eps_loglik = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0001,  +  batch_ids = batch_ids, select = TRUE,  +  ff_name = "ff_simdata", delete = FALSE, overwrite = FALSE,  +  light = TRUE)  Note that the data frame dff is an "ffdf" data frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  For processing all the design  matrices for estimating the model, we therefore specify a directory name with ff_name =  "ff_simdata", where all matrices can be stored as ff objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The directory ff_simdata is  created in the current working directory and will not be deleted after estimation if delete  = FALSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' This has the advantage, that the ff matrices can be reused for other models, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=',  using a different distribution, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', setting up more models will be much faster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' If overwrite =  FALSE, the directory for storing the ff objects will not be overwritten when calling bamlss().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Moreover, option light = TRUE can be used to reduce the memory footprint of the final  returned object even more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Here, we need to set sampler = FALSE in order to switch off sub-  sequent MCMC sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The opt_bbfit() optimizer function is used as the model fitting  engine, for which we specify the step length control parameter nu = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Argument always =  FALSE causes model terms to be updated only if the relative improvement of the out-of-sample  log-likelihood (on the next batch) is larger than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0001 (controlled by argument eps_loglik).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  By setting AIC = TRUE the smoothing variances are selected by the out-of-sample AIC, oth-  erwise the out-of-sample log-likelihood is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' As we are interested in the boosting variant  of the batchwise backfitting algorithm in this case, we need to set argument select = TRUE,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', only the model term with the largest contribution to the log-likelihood in the next batch  will be updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' On a Linux system with Intel(R) Core(TM) i7-8550U CPU 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='80GHz pro-  cessors, the estimation time is about 55 minutes, which is considerably fast for such a large  data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Selection frequencies of the 400 boosting iterations and individual log-likelihood  contributions can be shown with  R> contribplot(b)  mu  Sel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' freq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='116  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='116  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='s(lon,lat)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='112  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='004  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='s(x2)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='000  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='s(x5)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='000  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='s(x6)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='000  sigma  Sel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' freq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  32  Scalable Estimation for Structured Additive Distributional Regression  Figure 14:  Log-likelihood contribution paths for selected terms of the Gaussian model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  p  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='220  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='140  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='s(x6)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='000  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='s(lon,lat)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='000  The selection frequencies reveal that the boosting variant of the batchwise backfitting algo-  rithm selected the correct model terms, the corresponding contribution paths are shown in  Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The paths also show the convergence of the algorithm already at about iteration  200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Resampling  This section demonstrates the resampling variant with slice sampling of smoothing variances  of the batchwise backfitting algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  From the selected model terms we set up a new  formula  R> f <- list(  +  y ~ s(x1) + s(x3) + s(lon, lat),  +  ~ s(x2) + s(x3) + s(x4)  +  )  and only slightly modify the arguments supplied to the main model fitting function bamlss()  μ  mstop = 400  mstop = 400  009  s(x2)  s(x3),s(x1),s(lon,lat  500  6008001000  s(x4)  LogLik contribution  LogLik contribution  s(x3)  400  300  200  400  100  200  0  0  1  100  200  300  400  1  100  200  300  400  Iteration  IterationUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  33  R> m <- bamlss(f, data = dff, family = "gaussian",  +  sampler = FALSE, optimizer = opt_bbfitp,  +  AIC = TRUE, slice = TRUE, batch_ids = batch_ids,  +  ff_name = "ff_simdata", delete = FALSE, overwrite = FALSE,  +  light = TRUE)  Estimation takes about 24 minuts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Note that we use a wrapper version opt_bbfitp() for esti-  mating the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The only difference is that the parameters are stored as "mcmc" “samples”  in the returned object, so all extractor functions such as predict(), residuals(), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', can  be used similarly to estimating full Bayesian models with MCMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For details on using bamlss,  see Umlauf, Klein, Simon, and Zeileis (2021) and the project website http://bamlss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='org/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  A major advantage of the new infrastructures, including the ff package, is that all design  matrices can be reused and do not need to be recomputed, saving large amounts of run-  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' To use this feature, all that is required is careful handling of the ff_name, delete and  overwrite arguments (use as described in the last section).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' By setting slice = TRUE, slice  sampling of smoothing parameters in combination with the resampling variant with nu = 1,  eps_loglik = -Inf and always = TRUE is used for batchwise backfitting, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', updates are  always accepted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Convergence of the algorithm can be inspected by, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', coefficient paths of  the parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  34  Scalable Estimation for Structured Additive Distributional Regression  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Simulation Results  In this section we show all the results of the simulation study presented in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Figure 15:  Functions used in the simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Green lines correspond to the estimated  effects of the opt_bbfit model of the 100 replications in the simulation setting: normal  distribution NO, observations n = 5000, noise variables nnoise = 10 and correlation rho =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Figure 16:  Spatial effect used in the simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Spatial effects correspond to the  estimated two-dimensional effects of the method opt_bbfit in the 100 replications of the  simulation setting: normal distribution NO, observations n = 5000, noise variables nnoise =  10 and correlation rho = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' The mean was calculated over the 100 different estimates of the  two-dimensional effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Effect of X1 on nμ  Effect of X3 on nμ  Effect of X2 on no  Estimates  2  Truth  2  2  8x  X  0  f3  0  f2  0  F  乙  2  2  1  0  1  2  2  1  0  1  2  2  1  0  1  2  X1  X3  X2  Effect of X3 on no  Effect of X4 on no  2  2  X4  t3  0 乙  2  1  0  1  2  2  1  0  1  2  X3  X4True spatial effect  Mean spatial effect  2  2  0  2  2  2  0  2  2  1  0  1  2  lon  lonUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  35  Figure 17:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average MSE with the GA distribution for predictor ηµ and ησ  for different number of observations, correlation and noise variable settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  opt_bbfit  sam mcmc  Method:  gamboostLss  ！' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  opt_ boost  nnoise = 0  nnoise = 10  nnoise = 20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='06  =  2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='05  E  MSI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='15  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='00  Number of observations36  Scalable Estimation for Structured Additive Distributional Regression  Figure 18:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average MSE with the ZAP distribution for predictor ηµ and  ησ for different number of observations, correlation and noise variable settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  opt_ bbfit  sam mcmc  Method:  gamboostLSs  opt boost  nnoise = 0  nnoise = 10  nnoise = 20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='00  MSI  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='0-  =d  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='0  Number of observationsUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  37  Figure 19:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average MSE of f1 effect of ηµ for all distributions, different  number of observations, correlation and noise variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  opt_bbfit  sam mcmc  Method:  gamboostLSs  opt_boost  nnoise = 0  nnoise = 10  nnoise = 20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  41  Figure 23:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average false positive rate of the GA distribution for predictor  ηµ and ησ for different number of observations, correlation and noise variable settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Method:  opt_ bbfit  sam_mcmc  gamboostLss  opt_boost  nμ  nμ  na  na  p=0  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  0=d  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='5  nnoise  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  nnoise  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  20  nnoise =  15  10  5  0-  Number of observations42  Scalable Estimation for Structured Additive Distributional Regression  Figure 24:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average false positive rate of the ZAP distribution for predictor  ηµ and ησ for different number of observations, correlation and noise variable settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Figure 25:  Simulation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Average false positive rate of 10 replications per setting for  different threshold values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' Setting: Number of observations varies, NO, ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7 and nnoise  = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' For n ≥ 500 the method opt_bbfit is the best in terms of excluding non-informative  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  Method:  opt_ bbfit  sam mcmc  gamboostLSs  opt_boost  nμ  nμ  na  na  p=0  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  0=d  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  nnoise  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  nnoise  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  =  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  20  nnoise =  15  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  01  Number of observationsMethod:  opt bbfit  sam mcmc  gamboostLSS  opt boost  n = 250  n = 500  n = 5000  n = 10000  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='5  rate  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='9  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='0  2  ThresholdUmlauf N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Seiler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Wetscher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Simon T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=', Klein N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='  43  Affiliation:  Nikolaus Umlauf, Johannes Seiler, Mattias Wetscher, Thorsten Simon, Stefan Lang  Department of Statistics  Faculty of Economics and Statistics  Universität Innsbruck  Universitätsstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 15  6020 Innsbruck, Austria  E-mail: Nikolaus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='Umlauf@uibk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='at,  Thorsten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='Lang@uibk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='at  URL: https://eeecon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='at/~umlauf/,  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='at/statistics/personal/lang/  Nadja Klein  Chair of Uncertainty Quantification and Statistical Learning  Research Center Trustworthy Data Science and Security (UA Ruhr)  Department of Statistics (Technische Universität Dortmund)  Joseph-von-Fraunhofer-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content=' 25  44227 Dortmund, Germany  E-mail: nadja.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='klein@statistik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='tu-dortmund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
+page_content='de  URL: https://rc-trust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E5T4oBgHgl3EQfbA-t/content/2301.05593v1.pdf'}
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diff --git a/VNFJT4oBgHgl3EQfOCw1/content/tmp_files/2301.11480v1.pdf.txt b/VNFJT4oBgHgl3EQfOCw1/content/tmp_files/2301.11480v1.pdf.txt
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+Analog Schwarzschild black holes of Bose-Einstein condensates in a cavity:
+Quasinormal modes and quasibound states
+H. S. Vieira1,2,3, Kyriakos Destounis4,5 and Kostas D. Kokkotas2
+1Department of Physics, Institute of Natural Sciences,
+Federal University of Lavras, 37200-000 Lavras, Brazil
+2Theoretical Astrophysics, Institute for Astronomy and Astrophysics,
+University of T¨ubingen, 72076 T¨ubingen, Germany
+3S˜ao Carlos Institute of Physics, University of S˜ao Paulo, 13560-970 S˜ao Carlos, Brazil
+4Dipartimento di Fisica, Sapienza Universit`a di Roma, Piazzale Aldo Moro 5, 00185, Roma, Italy and
+5INFN, Sezione di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy
+Analog models of black holes have unequivocally proven to be extremely beneficial in providing
+critical information regarding black hole spectroscopy, superradiance, quantum phenomena and most
+importantly Hawking radiation and black hole evaporation; topics that have either recently begun
+to bloom through gravitational wave observations or have not yet been investigated in astrophysical
+setups. Black hole analog experiments have made astonishing steps toward the aforementioned direc-
+tions and are paramount in understanding the quantum nature of the gravitational field. Recently,
+a tabletop analog Schwarzschild black hole has been proposed by placing Bose-Einstein condensates
+of photons inside a mirror’s cavity, leading to a sink with a radial vortex that represents a velocity
+singularity. Here, we provide an extensive spectral analysis of both the tabletop acoustic black hole
+and its higher-dimensional gravitational analog. We find that quasinormal modes and quasibound
+states share qualitative similarities in both systems and show that the eikonal quasinormal modes
+of the analog acoustic black hole have a photon-sphere-like interpretation, which points to the ex-
+istence of a phonon sphere in the analog black hole. Our results, complemented with the recently
+calculated graybody factors and Hawking radiation of the acoustic analog, can provide a theoretical
+test bed for future tabletop experiments with condensates of light in a mirror’s cavity and provide
+significant insights regarding classical and quantum phenomena in higher-dimensional black holes.
+I.
+INTRODUCTION
+The emission and detection of gravitational waves
+(GWs) from the binary coalescence of black holes (BHs)
+[1–7] and compact objects [8] have established the field of
+experimental gravitation and continue to provide insights
+into the strong field regime towards the search for an ul-
+timate theory of gravitation. General relativity (GR) is
+currently been tested meticulously [9–12] and has proven
+to be the most successful to date.
+GWs carry unparalleled information during all stages
+of the binary’s evolution as it undergoes the inspiral,
+merger and ringdown stage. During these phases, GWs
+bear the externally observable properties of the binary’s
+components and the eventual compact object’s parame-
+ters that forms after ringdown, described by quasinormal
+modes (QNMs) [13–15].
+BHs undergo surprising phe-
+nomena, such as Hawking radiation when semiclassical
+effects are taken into account [16], they superradiate [17]
+under the expense of the BH’s spin [18] or charge [19–
+23], and when perturbed, they vibrate according to their
+characteristic spectra.
+The BH spectroscopy program is currently aiming to-
+wards an ultimate understanding of QNMs, how to detect
+them properly from GW data [24–26], and if nonlinear-
+ities [27–30], as well as spectral instabilities [31–38] can
+interfere with QNM extraction. Nevertheless, superra-
+diance and Hawking radiation have not been detected
+experimentally. To this end, different models are being
+used in an effort to mimic BHs and recreate such pro-
+cesses in controlled laboratory experiments.
+Analog gravity [39, 40] has the potential to provide a
+better understanding regarding phenomena that would
+otherwise elude observation in the strong field regime
+and when quantum effects become significant.
+Unruh
+pioneered the first theoretical BH analog [41], which can
+be envisioned through a fluid which on its surface, sound
+excitations are mapped to perturbation equations that
+are typically found and utilized in classical and quantum
+gravity investigations. The surface fluctuations endure
+an effective spacetime geometry that is determined by
+the propagation speed of these excitations and their rel-
+ative speed with respect to the fluid, which enables the
+construction of an acoustic BH analog. Tuning the veloc-
+ity of the fluid leads to the formation of an acoustic event
+horizon analog, beyond which sound fluctuations cannot
+escape the dumb hole, in analogy to infalling particles
+into a BH event horizon which are causally disconnected
+with spatial infinity.
+Currently, there is an abundance in analog grav-
+ity experiments that function with fluids and superflu-
+ids [42–49], Bose-Einstein condensates (BECs) [50–53]
+and optical media [54].
+Through these analog experi-
+ments, Hawking radiation [42, 51, 52, 55], superradiance
+[43–45, 56, 57], QNMs and quasibound states (QBSs)
+[46, 48, 49] have been experimentally observed. These ex-
+periments are not only successful scientific achievements
+but also can provide unmatched insights into the future
+of gravitational physics.
+Very recently, a novel tabletop experimental three-
+arXiv:2301.11480v1  [gr-qc]  27 Jan 2023
+
+2
+dimensional analog of a Schwarzschild BH was proposed
+with BECs of light placed in a mirror’s cavity [58] which
+leads to a sink with a radial vortex pointing towards the
+central velocity singularity, that was missing in other ex-
+periments with BECs where the analog BH horizons had
+a one-dimensional flow pattern that smoothly interpo-
+lates between a velocity below the speed of sound and
+thus did not possess a singular velocity profile. The novel
+proposal in [58] serves as an analog of a rotationally-
+symmetric five-dimentional Schwarzschild BH with a
+sonic event horizon and a velocity singularity due to the
+radial vortex, thus can shed light on the properties close
+to the region of the singularity.
+In Ref.
+[58], the authors have calculated the gray-
+body factors and Hawking radiation of the proposed ex-
+perimental setup in an attempt to provide data for fu-
+ture experiments.
+In our analysis we complete their
+study by calculating the QNMs and QBSs for the three-
+dimensional BEC of light in a cavity and revisit the spec-
+trum of five-dimensional Schwarzschild BH. We find that
+QNMs and QBSs share qualitative similarities in both
+the gravitational and the BEC analog system, thus giv-
+ing more legitimacy to the analogy, and identify that
+the photon sphere interpretation of eikonal QNMs of the
+gravitational BH is shared in the analog system. Thus,
+the newly proposed three-dimensional acoustic BH ana-
+log possesses a phonon sphere which properties are in-
+trinsically connected to the eikonal QNMs of phase fluc-
+tuations.
+II.
+HIGHER-DIMENSIONAL SCHWARZSCHILD
+BLACK HOLES
+The standard four-dimensional Schwarzschild solution
+was generalized to higher dimensions by Tangherlini in
+[59]. The higher-dimensional action, which is a general-
+ization of the Einstein-Hilbert action, is given by
+S =
+1
+16πGD
+�
+dDx√−gR,
+(1)
+where g ≡ det(gµν), and GD is the D-dimensional grav-
+itational constant.
+In what follows, for simplicity and
+without loss of generality, we adopt the natural units
+where GD = c = ℏ = 1. By varying the action with re-
+spect to the spacetime metric gµν, we obtain the Einstein
+equations in higher dimensions
+Rµν − 1
+2Rgµν = 0,
+(2)
+where Rµν and R are the Ricci tensor and Ricci scalar, re-
+spectively. A static, asymptotically flat and spherically-
+symmetric vacuum solution of Eq. (2), which generalizes
+the Schwarzschild BH solution in D-dimensions, has the
+form
+ds2 = −f(r)dt2 + f(r)−1dr2 + r2dΩ2
+D−2,
+(3)
+where the metric function, f(r), and the solid angle ele-
+ment, dΩ2
+D−2, are given by
+f(r) = 1 −
+M
+rD−3 ,
+(4)
+and
+dΩ2
+D−2 = dθ2
+1 + sin2 θ1dθ2
+2 + sin2 θ1 sin2 θ2dθ2
+2 + · · ·
++
+�
+�
+�
+�
+D−2
+�
+j=1
+sin2 θj
+�
+� dθ2
+D−1
+�
+� .
+(5)
+The parameter M is related to the BH mass M through
+the relation
+M =
+16πM
+(D − 2)ΩD−2
+, ΩD−2 = 2π
+D−1
+2
+Γ( D−1
+2 ),
+(6)
+where ΩD−2 is the volume of the (D − 2)-dimensional
+unit sphere and Γ(x) is the gamma function.
+Note that the solution (3) simplifies to the standard
+Schwarzschild metric when D = 4. In addition, we ob-
+serve that when the spacetime is higher-dimensional, the
+asymptotic fall-off term in the metric function f(r) be-
+comes steeper.
+This metric is Ricci flat and is called
+either the Schwarzschild-Tangherlini solution or simply
+the D-dimensional Schwarzschild BH spacetime. In this
+work, we will focus on the five-dimensional Schwarzschild
+BH, due to the explicit analogy between BECs of light
+in a cavity that form a three-dimensional Schwarzschild
+analog, as discussed in the introduction.
+The explicit line element (3) for D = 5 reads
+ds2 = − f(r)dt2 + f(r)−1dr2
++ r2 �
+dθ2 + sin2 θ
+�
+dφ2 + sin2 φ dχ2��
+,
+(7)
+with
+f(r) = 1 − M
+r2 ,
+M = 8M
+3π ,
+ΩD−2 = 2π2,
+(8)
+where θ, φ run over the range 0 to π, and χ from 0 to
+2π. The causal structure of spacetime can be identified
+from the equation
+f(r) = 0 = (r − r1)(r − r2),
+(9)
+whose solutions are the event horizon, r1 =
+√
+M, and a
+negative non-physical solution, r2 = −
+√
+M.
+A.
+Scalar wave equation
+We consider a minimally-coupled massless scalar per-
+turbation Ψ = Ψ(t, r, θ, φ, χ), whose equation of motion
+is given by the Klein-Gordon equation
+�
+1
+√−g ∂µ
+�
+gµν√−g∂ν
+��
+Ψ = 0.
+(10)
+
+3
+0.2
+0.4
+0.6
+0.8
+1.0
+1
+2
+3
+4
+5
+6
+7
+ℳ
+Re(ωnν)
+ω00
+ω01
+ω02
+ω03
+0.2
+0.4
+0.6
+0.8
+1.0
+-1.2
+-1.0
+-0.8
+-0.6
+-0.4
+ℳ
+Im(ωnν)
+ω00
+ω01
+ω02
+ω03
+0.2
+0.4
+0.6
+0.8
+1.0
+1
+2
+3
+4
+5
+6
+ℳ
+Re(ωnν)
+ω10
+ω11
+ω12
+ω13
+0.2
+0.4
+0.6
+0.8
+1.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+-1.5
+-1.0
+ℳ
+Im(ωnν)
+ω10
+ω11
+ω12
+ω13
+FIG. 1. Top panel: Real (left) and imaginary (right) part of the fundamental massless scalar QNMs ω0ν of a five-dimensional
+Schwarzschild black hole with respect to M and varying ν. Bottom panel: Real and imaginary part of the first overtone of
+massless scalar QNMs ω1ν of a five-dimensional Schwarzschild black hole with respect to M and varying ν.
+Under symmetry assumptions we choose an ansatz
+Ψ(t, r, θ, φ, χ) = e−iωtU(r)P(θ, φ, χ),
+(11)
+where ω is the frequency of the scalar field, U(r) =
+R(r)/r3/2 is the radial function and P(θ, φ, χ) is an an-
+gular function.
+By utilizing the spacetime metric (7),
+Eq. (10) can be separated into an angular and a radial
+equation as
+�
+1
+sin2 θ
+∂
+∂θ
+�
+sin2 θ ∂
+∂θ
+�
++ λ −
+1
+sin2 θ
+�
+1
+sin φ
+∂
+∂φ
+�
+sin φ ∂
+∂φ
+�
++¯λ +
+1
+sin2 φ
+∂2
+∂χ2
+��
+P(θ, φ) = 0,
+(12)
+and
+R′′(r) + f ′(r)
+f(r) R′(r)
++
+� ω2
+f 2(r) − 4λ + 3f(r) + 6rf ′(r)
+4r2f(r)
+�
+R(r) = 0.
+(13)
+Here, λ and ¯λ are the separation constants to be deter-
+mined, and the primes generally denote differentiation
+with respect to r.
+The general exact solution of the angular equation
+(12) is given by P(θ, φ, χ) = P l
+ν,4(cos θ)Ylm(φ, χ), where
+P l
+ν,4(cos θ) are the associated Legendre functions in four-
+dimensions [60–62] with arbitrary degree ν ∈ C and order
+l such that λ = ν(ν + 2), and Ylm(φ, χ) are the spherical
+harmonics with l and m being the angular and magnetic
+quantum numbers, respectively, such that ¯λ = l(l + 1).
+In what follows, we will revisit the QNMs of five-
+dimensional Schwarzschild BHs and calculate analyti-
+cally the corresponding QBSs.
+B.
+Quasinormal modes
+Equation (13) can be recast into a Schr¨odinger-like
+equation by multiplying it with f 2(r) and utilizing the
+tortoise coordinate r∗, with dr/dr∗ = f(r), to obtain
+d2R(r)
+dr2∗
++
+�
+ω2 − VBH
+�
+R(r) = 0,
+(14)
+
+4
+where the effective potential VBH is
+VBH ≡ f(r)
+�ν(ν + 2)
+r2
++ 3f(r)
+4r2
++ 3f ′(r)
+2r
+�
+.
+(15)
+QNMs ωnν are a discrete set of mode solutions of the ra-
+dial equation (14) with purely ingoing (outgoing) bound-
+ary conditions at the event horizon (infinity), such that
+R(r) ∼ e−iωr∗, r → r1,
+R(r) ∼ eiωr∗, r → ∞,
+(16)
+where n is the overtone number of the frequencies. In
+what follows, we present some typical scalar QNMs of
+a five-dimensional Schwarzschild BH. We have employed
+three different methods, namely a pseudospectral method
+[63], a matrix method [64, 65] and the Wentzel-Kramers-
+Brillouin (WKB) method [66, 67]. We have found con-
+vergence between the pseudospectral and matrix method
+QNMs up to at least six digits (convergence can reach
+even to 20 digits when more grid points are utilized) and
+confirmed the validity of eikonal QNMs with the WKB
+approximation finding similar precision. Our results also
+are in perfect agreement with those reported in [68].
+Figure 1 demonstrates the typical behavior of five-
+dimensional Schwarzschild scalar QNMs, i.e. the incre-
+ment of the BH’s mass term decreases the oscillation fre-
+quency and increases the perturbation’s lifetime.
+Fur-
+thermore, the increment of the angular number ν in-
+creases the real part of QNMs while the imaginary part
+is also increased (in absolute value) as expected from the
+eikonal limit which probes the photon sphere of the BH,
+where photons occupy unstable circular geodesics [69].
+There, the angular frequency of null geodesics is propor-
+tional to the real part of the eikonal QNM and their in-
+stability timescale is proportional to the imaginary part
+of QNMs with large ν. Therefore, the BH QNMs in study
+have a typical photon sphere interpretation [69] which we
+will further discuss in the upcoming sections. For a nu-
+merical presentation of some QNMs we refer the reader
+to Table I and Ref. [68].
+5D Scwarzschild BH
+ν
+n = 0
+n = 1
+1 1.0160 - 0.3623 i 0.8564 - 1.1576 i
+2 1.5106 - 0.3575 i 1.3927 - 1.1046 i
+10 5.5028 - 0.3539 i 5.4689 - 1.0639 i
+TABLE I. Massless scalar QNMs of the five-dimensional (5D)
+Schwarzschild BH with M = 1.
+C.
+Quasibound states
+In what follows, we will analytically solve the radial
+equation (13) for a five-dimensional Schwarzschild BH.
+QBSs are solutions to (13) with purely ingoing boundary
+conditions at the event horizon (same as QNMs) and de-
+caying boundary conditions at infinity. Since both QNMs
+and QBSs are mode solutions to the same eigenvalue
+problem, though with different asymptotic behavior, we
+will also refer to QBSs as ωnν. We will see that the fact
+that at infinity QBSs decay exponentially enables an an-
+alytic evaluation. To find their analytic expression, we
+apply the VBK approach [70, 71] in order to write the
+radial equation (13) as a Heun-type differential equation
+[72].
+We define a new radial coordinate, x, and a new pa-
+rameter, x1, as
+x = r − r2
+−r2
+,
+(17)
+and
+x1 = r1 − r2
+−r2
+,
+(18)
+such that the three original singularities (r2, 0, r1) are
+moved to the points (0, 1, x1), while maintaining a regular
+singularity at spatial infinity.
+In addition, the regular
+singular point at x = x1 is always located outside the
+unit circle |x1| > 1. The final step is to perform an F-
+homotopic transformation R(x) �→ y(x) given by
+R(x) = xA0(x − 1)A1(x − x1)Ax1 y(x),
+(19)
+where the coefficients A0, A1, and Ax1 are given by
+A0 = −
+iω
+r1 − r2
+,
+(20)
+A1 = 1
+2 − 1
+r1
+�
+r1
+�
+r1 + λ
+r2
+�
+,
+(21)
+Ax1 = −
+iω
+r1 − r2
+.
+(22)
+Thus, by substituting Eqs. (17)-(22) into Eq. (13), we
+obtain
+y′′(x) +
+�1 + 2A0
+x
++ 2A1
+x − 1 + 1 + 2Ax1
+x − x1
+�
+y′(x)
++
+A3x + A4
+x(x − 1)(x − x1)y(x) = 0,
+(23)
+where the coefficients A3, and A4 are given by
+A3 = −3 + Ax1 + 2A1(1 + Ax1) + A0(1 + 2A1 + 2Ax1)
+− (x1 − 1)(x2
+1λ − 2ω2 + 2x1ω2)
+r2
+1x2
+1
+,
+(24)
+A4 = −A0 − Ax1 − 2A0Ax1 + 3x1
+2
+− A1x1 − 2A0A1x1
++ (x1 − 1)2(x2
+1λ + 2ω2)
+r2
+1x2
+1
+.
+(25)
+The radial equation (23) has the form of a general Heun
+equation [72]. Therefore, the exact solution for the radial
+part of the Klein-Gordon equation can be written as
+Rj(x) =x
+1
+2 (γ−1)(x − 1)
+1
+2 δ(x − x1)
+1
+2 (ϵ−1)
+[C1,j y1,j(x) + C2,j y2,j(x)],
+(26)
+
+5
+where C1,j and C2,j are constants to be determined, and
+j = {0, 1, x1, ∞} labels the solution at each singular
+point, which are given as follows. The pair of linearly
+independent solutions at x = 0 (r = r2) is given by
+y1,0 = HeunG(x1, q; α, β, γ, δ; x),
+(27)
+y2,0 = x1−γHeunG(x1, (x1δ + ϵ)(1 − γ) + q;
+α + 1 − γ, β + 1 − γ, 2 − γ, δ; x),
+(28)
+where HeunG(x1, q; α, β, γ, δ; x) denotes a general Heun
+function, which is analytic in the disk |x| < 1, and has a
+Maclaurin expansion given by
+HeunG(x1, q; α, β, γ, δ; x) =
+∞
+�
+n=0
+cnxn,
+(29)
+with
+−qc0 + x1γc1 = 0
+(c0 = 1), (30)
+Pncn−1 − (Qn + q)cn + Xncn+1 = 0
+(n ≥ 1), (31)
+and
+Pn = (n − 1 + α)(n − 1 + β),
+Qn = n[(n − 1 + γ)(1 + x1) + x1δ + ϵ],
+(32)
+Xn = (n + 1)(n + γ)x1.
+The pair of linearly independent solutions at x = 1 (r =
+0) is given by
+y1,1 = HeunG(1 − x1, αβ − q; α, β, δ, γ; 1 − x),
+(33)
+y2,1 = (1 − x)1−δHeunG(1 − x1, ((1 − x1)γ + ϵ)(1 − δ)
++ αβ − q; α + 1 − δ, β + 1 − δ, 2 − δ, γ; 1 − x). (34)
+The pair of linearly independent solutions at x = x1 (r =
+r1) is given by
+y1,x1 = HeunG
+�
+x1
+x1 − 1, αβx1 − q
+x1 − 1 ; α, β, ϵ, δ; x1 − x
+x1 − 1
+�
+,
+(35)
+y2,x1 =
+�x1 − x
+x1 − 1
+�1−ϵ
+HeunG
+�
+x1
+x1 − 1,
+(x1(δ + γ) − γ)(1 − ϵ)
+x1 − 1
++ αβx1 − q
+x1 − 1 ; α + 1 − ϵ,
+β + 1 − ϵ, 2 − ϵ, δ; x1 − x
+x1 − 1
+�
+.
+(36)
+The pair of linearly independent solutions at x = ∞ (r =
+∞) is given by
+y1,∞ = x−αHeunG
+� 1
+x1
+, α(β − ϵ) + α
+x1
+(β − δ)
+− q
+x1
+; α, α − γ + 1, α − β + 1, δ; 1
+x
+�
+,
+(37)
+y2,∞ = x−βHeunG
+� 1
+x1
+, β(α − ϵ) + β
+x1
+(α − δ)
+− q
+x1
+; β, β − γ + 1, β − α + 1, δ; 1
+x
+�
+.
+(38)
+In these solutions, the parameters α, β, γ, δ, ϵ, and q are
+given by
+α =
+1
+r1 − r2
+�
+3r1 −
+�
+r1
+�
+r1 + λ
+r2
+�
++r2
+��
+1 +
+λ
+r1r2
+− 3
+�
+− 2iω
+�
+,
+(39)
+β = −
+1
+r1 − r2
+�
+r1 +
+�
+r1
+�
+r1 + λ
+r2
+�
+−r2
+��
+1 +
+λ
+r1r2
++ 1
+�
++ 2iω
+�
+,
+(40)
+γ = 1 −
+2iω
+r1 − r2
+,
+(41)
+δ = 1 − 2
+r1
+�
+r2
+1 + λr1
+r2
+,
+(42)
+ϵ = 1 −
+2iω
+r1 − r2
+,
+(43)
+q = r1
+r2
+− λ
+r2
+2
+− 1 + 1
+r2
+��
+r2
+1 + λr1
+r2
++ iω
+�
+− (r2 + 2iω)
+r1r2
+�
+r2
+1 + λr1
+r2
+− 2i(r1 − r2 − 2iω)ω
+(r1 − r2)2
+.
+(44)
+The first boundary condition related to QBSs (and
+QNMs) requires that the radial solution is purely ingoing
+at the event horizon, i.e. to impose r → r1 (or x → x1)
+on the radial solution given by Eq. (26). To do this, we
+use Eqs. (35) and (36) to get the following asymptotic
+behavior
+lim
+r→r1 Rx1(r) ∼ C1,x1 (r−r1)
+1
+2 (ϵ−1)+C2,x1 (r−r1)− 1
+2 (ϵ−1),
+(45)
+where all the remaining constants were included in C1,x1
+and C2,x1, which will be determined afterwards. Thus,
+from Eq. (43), we can write
+lim
+r→r1 Rx1(r) ∼ C1,x1 Ψin,x1 + C2,x1 Ψout,x1,
+(46)
+where Ψin,x1 and Ψout,x1 are the ingoing and outgoing
+scalar wave solutions, respectively, given by
+Ψin,x1(r > r1) = e−iωt(r − r1)− iω
+2κ1 ,
+(47)
+Ψout,x1(r > r1) = e−iωt(r − r1)+ iω
+2κ1 ,
+(48)
+with the surface gravity of the event horizon, κ1, being
+defined as
+κ1 = 1
+2
+df(r)
+dr
+����
+r=r1
+= r1 − r2
+2
+.
+(49)
+The ingoing boundary condition is satisfied when C2,x1 =
+0 in Eq. (46) and Eq. (26). Thus, we have
+lim
+r→r1 Rx1(r) ∼ C1,x1 Ψin,x1.
+(50)
+
+6
+0.2
+0.4
+0.6
+0.8
+1.0
+-4
+-3
+-2
+-1
+0
+ℳ
+Re(ωnν)
+ω00
+ω01
+ω02
+ω03
+0.2
+0.4
+0.6
+0.8
+1.0
+-3.0
+-2.5
+-2.0
+-1.5
+-1.0
+-0.5
+ℳ
+Im(ωnℓ)
+ω00
+ω01
+ω02
+ω03
+0.2
+0.4
+0.6
+0.8
+1.0
+-4
+-3
+-2
+-1
+0
+ℳ
+Re(ωnℓ)
+ω10
+ω11
+ω12
+ω13
+0.2
+0.4
+0.6
+0.8
+1.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+-1.5
+-1.0
+-0.5
+ℳ
+Im(ωnℓ)
+ω10
+ω11
+ω12
+ω13
+FIG. 2. Top panel: Real (left) and imaginary (right) part of the fundamental massless scalar QBSs ω0ν of a five-dimensional
+Schwarzschild black hole with respect to M and varying ν. Bottom panel: Real and imaginary part of the first overtone of
+massless scalar QBSs ω1ν of a five-dimensional Schwarzschild black hole with respect to M and varying ν.
+The second boundary condition related to the QBSs
+(that differs from that of QNMs) is to require that the
+radial solution vanishes at asymptotic infinity, i.e.
+to
+impose a decaying boundary condition at the limit r →
+∞ (or x → ∞) on the radial solution given by Eq. (26).
+Thus, we use Eqs. (37) and (38) to obtain the following
+asymptotic behavior
+lim
+r→∞ R∞(r) ∼ C1,∞
+1
+rσ ,
+(51)
+where we have imposed that C2,∞ = 0. The parameter
+σ is given by
+σ = α − A0 − A1 − Ax1.
+(52)
+The sign of the real part of σ determines the asymptotic
+behavior of the radial scalar wave function as r → ∞:
+if Re[σ] > 0, the radial solution tends to zero at spatial
+infinity and then it fully satisfies the second boundary
+condition for QBSs; if Re[σ] < 0, the radial solution di-
+verges at spatial infinity.
+The final asymptotic behavior of the radial scalar wave
+solution at spatial infinity will be determined when we
+know the values of the coefficients Aj, as well as the fre-
+quencies ω, and the parameter α. Those will be obtained
+by the VBK approach.
+The general Heun functions become (class I) polyno-
+mials of degree n (≥ 0) if and only if they satisfy two
+conditions [72], namely,
+α + n = 0,
+(53)
+cn+1(q) = 0,
+(54)
+where the accessory parameter q is given by Eq. (44).
+The first condition, given by Eq. (53), is called the α-
+condition, which is used to find the frequency eigenvalues.
+The second condition, given by Eq. (54), determines the
+value of the separation constant λ for each value of n,
+which is used to find the eigenvalues ν and both the radial
+and angular wave eigenfunctions. It is worth emphasizing
+that the two polynomial conditions could be applied in
+any order we wish, that is, the first condition could give
+the values of the separation constant, and the second
+condition could give the frequency eigenvalues. Thus, by
+imposing Eq. (53), we obtain the exact spectrum of QBSs
+
+7
+given by
+ωnν = −i(
+√
+M(n + 3) −
+√
+M − λ),
+(55)
+where we have used the explicit expressions of the event
+horizon.
+Here, the separation constant is, again, λ =
+ν(ν + 2), and n is the overtone number, which can be,
+without loss of generality, called the principal quantum
+number. On the other hand, by substituting Eqs. (20),
+(21), (22), (53) and (55) into Eq. (52), we get
+σ = 4,
+(56)
+which means that the parameter σ is a real, positive
+number for any value of the principal quantum num-
+ber n, as well as for any value of the separation con-
+stant λ, and hence the frequency eigenvalues given by
+Eq. (55) represent QBSs for massless scalar fields in the
+five-dimensional Schwarzschild spacetime.
+In addition,
+by substituting these equations into Eq. (44), it is pos-
+sible to obtain a nonlinear equation for q = q(λ) and
+then impose the second polynomial condition given by
+Eq. (54) to obtain the angular eigenvalues λ.
+Now, let us discuss a very important case of these
+QBSs: the fundamental mode, where n = 0.
+In this
+case, we have
+ω0ν = −i(3
+√
+M −
+√
+M − λ),
+(57)
+where
+the
+second
+polynomial
+condition,
+given
+by
+Eq. (54), is automatically satisfied, since it leads to
+cn+1(q)
+����
+n=0
+= q = n(4 + n)
+����
+n=0
+= 0.
+(58)
+This means that there is no restriction on the value of the
+separation constant λ = ν(ν + 2), with ν = 0, 1, 2, . . . .
+In particular, the ground state (n, ν) = (0, 0) of QBSs
+is given by ω00 = −2i
+√
+M.
+This is a very important
+result because it designates the absence of bound states
+when the angular number is null. These solution are not
+oscillatory but only decay in time therefore no bound
+state can be formed in this particular case, and the BH
+only oscillates in accord to QNMs.
+In Fig. 2 we show the behavior of massless scalar QBSs
+in the the BH under study. The real part for the QBS ω00
+is always zero since it does not depend on M and cor-
+roborates the aforementioned discussion. When ν ̸= 0
+QBSs exist; the mass parameter acts in the opposite way
+with respect to that of QNMs, namely their real parts
+increase with M while their lifetime decreases. The an-
+gular number ν has a somewhat similar effect to that of
+QNMs, that is its increment increases (in absolute value)
+the oscillation frequency of QBSs and quickly drives the
+imaginary parts to their asymptotic, large ν, value. Of
+course, since these modes have different boundary con-
+ditions they have no connection to null geodesics in the
+photon sphere at the eikonal limit.
+III.
+ANALOG BLACK HOLES: BOSE-EINSTEIN
+CONDENSATES OF LIGHT IN A CAVITY
+In this section, we begin by considering the general
+acoustic BH solution in Minkowski spacetime obtained
+by Unruh [41] (see also Refs. [39, 40]), and then show
+how to properly choose the sound velocity in order to
+obtain a Schwarzschild BH in BECs of photons trapped
+in a mirror cavity [58, 73].
+The fundamental equations of motion for an irrota-
+tional fluid are given by
+∇ × v = 0,
+(59)
+∂tρ + ∇ · (ρv) = 0,
+(60)
+ρdv
+dt ≡ ρ[∂tv + (v · ∇)v] = −∇p,
+(61)
+where v, ρ, and p are the velocity, density, and pressure
+of the fluid, respectively. Next, we introduce the velocity
+potential Ψ, such that v = −∇Ψ, and assume the fluid
+as barotropic, which means that ρ = ρ(p).
+Then, by
+linearizing these equations of motion around some back-
+ground (ρ0, p0, Ψ0), namely,
+ρ = ρ0 + ϵρ1,
+(62)
+p = p0 + ϵp1,
+(63)
+Ψ = Ψ0 + ϵΨ1,
+(64)
+we obtain the following equation
+− ∂t
+�∂ρ
+∂pρ0(∂tΨ1 + v0 · ∇Ψ1)
+�
++
+∇ ·
+�
+ρ0∇Ψ1 − ∂ρ
+∂pρ0v0(∂tΨ1 + v0 · ∇Ψ1)
+�
+= 0,
+(65)
+where the local speed of sound, cs, is defined by
+c−2
+s
+≡ ∂ρ
+∂p.
+(66)
+Equation (65) describes the propagation of the linearized
+scalar potential Ψ1, that is, it governs the propagation of
+the phase fluctuations as weak excitations in a homoge-
+neous stationary condensate, which can be rewritten as
+a wave equation in an analog curved spacetime as
+1
+√−g ∂µ(gµν√−g∂νΨ1) = 0.
+(67)
+Note that Eq.
+(67) is similar to the covariant Klein-
+Gordon equation (10), where the acoustic line element
+can be written as
+ds2 = ρ0
+cs
+[−c2
+sdt2 + (dxi − vi
+0dt)δij(dxj − vj
+0dt)].
+(68)
+Now, let us revisit how the (1 + 2)-dimensional acous-
+tic BH was set up in Ref. [58]. Firstly, we can assume
+that the fluid is a static spherically-symmetric conser-
+vation flow, with a polar angle θ = π/2, which implies
+
+8
+that dθ = 0.
+Next, we define the speed of sound as
+cs ≡
+�
+kn0/µ, where k is the strength of the effective
+contact interaction, n0 is the condensate density, and µ
+is the effective mass of the photon gas. Then, the velocity
+of the fluid v is the flow rate along the radial direction
+(representing the radial vortex), that is it points to the
+center of the acoustic BH towards the velocity singular-
+ity, given by
+v0 = −ℏc0
+µr ˆr = −ξcs
+c0
+r ˆr,
+(69)
+where ξ(= ℏ/µcs) is the correlation length, and c0(> 0) is
+a constant related to the acoustic horizon’s radius. Thus,
+the acoustic line element resulting by Eq. (68) can be
+written as
+ds2 = −
+�
+1 − c2
+0
+r2
+�
+dt2 + 2c0
+r drdt + dr2 + r2dφ2.
+(70)
+With the coordinate transformation
+dt → dt −
+c0
+r(1 − c2
+0/r2)dr,
+(71)
+we can write the line element of an acoustic (1 + 2)-
+dimensional BEC of light in a cavity as
+ds2 = −f(r)dt2 + f(r)−1dr2 + r2dφ2,
+(72)
+where the warp factor f(r) has the form
+f(r) = 1 − c2
+0
+r2 .
+(73)
+The radial vortex exists in a spatially (1+2)-dimensional
+BEC, therefore since the warp factor (73) is identical to
+the metric function (8), under the identification M = c2
+0,
+then this model is an analog of a (1 + 4)-dimensional
+Schwarzschild BH. This is a consequence of the fact that
+the metric of the BEC does not obey Einstein’s field equa-
+tions, but rather it is determined by pure hydrodynamics
+[58].
+The causal structure of the particular analog BH is
+strikingly similar to that presented in Sec. II. The warp
+factor equation
+f(r) = 0 = (r − r1)(r − r2),
+(74)
+has two solutions, an acoustic horizon r1 = c0, which is
+the outermost marginally trapped surface for outgoing
+phonons, and an unphysical negative solution r2 = −c0.
+The exterior acoustic event horizon is where the velocity
+of the fluid reaches the sound velocity. The central point
+of the acoustic BH can be regarded as a sink that leads to
+the higher-dimensional space from which the fluid flows
+to the three-dimensional space.
+It is worth noting that one can also obtain this effec-
+tive metric, given by Eq. (72), by using the approach
+developed in [74], which is based on the Gross-Pitaevskii
+theory [75, 76] that describes a nonlinear complex scalar
+field propagating in a curved spacetime background. In
+this approach, we simply require a fluid flow with velocity
+given by Eq. (69) in a flat Minkowski spacetime.
+In what follows, we will calculate, for the first time, the
+QNMs and QBSs of the analog BH proposed in Ref. [58],
+by using the same methods used for the five-dimensional
+Schwarzschild BH analysis in Sec. II.
+A.
+Scalar wave equation
+In order to solve the equation of motion given by
+Eq. (67), for the acoustic metric Eq. (72), we will use a
+similar separation ansatz for the phase fluctuation wave
+function
+Ψ1(t, r, φ) = e−i˜ωtU(r)eimφ,
+(75)
+where ˜ω is the frequency of phase fluctuations, U(r) =
+R(r)/r1/2 is the radial function, and m is the magnetic
+quantum number. Thus, by substituting Eqs. (72) and
+(75) into Eq. (67), we obtain
+R′′(r) + f ′(r)
+f(r) R′(r)
++
+� ˜ω2
+f 2(r) − 4m2 − f(r) + 2rf ′(r)
+4r2f(r)
+�
+R(r) = 0.
+(76)
+B.
+Quasinormal modes
+Equation (76) can be recast into a Schr¨odinger-like
+equation by multiplying with f 2(r) and utilizing the tor-
+toise coordinate r∗, with dr/dr∗ = f(r), to obtain
+d2R(r)
+dr2∗
++
+�
+˜ω2 − VBEC
+�
+R(r) = 0,
+(77)
+where the effective potential VBEC is
+VBEC ≡ f(r)
+�m2
+r2 − f(r)
+4r2 + f ′(r)
+2r
+�
+.
+(78)
+QNMs ˜ωnm, similarly, form a discrete set of mode so-
+lutions to the radial equation (77) with purely ingoing
+(outgoing) boundary conditions at the acoustic horizon
+(infinity), such that
+R(r) ∼ e−i˜ωr∗, r → r1,
+R(r) ∼ ei˜ωr∗, r → ∞.
+(79)
+In what follows, we present the QNMs of the three-
+dimensional BH analog of BECs in a cavity, where we
+have employed the same methods to numerically obtain
+and benchmark our results.
+Figure 3 demonstrates the behavior of the BEC BH
+analog’s QNMs. The increment of the vortex radius c0
+decreases the oscillation frequency and increases the per-
+turbation’s lifetime. The increment of m increases the
+
+9
+0.2
+0.4
+0.6
+0.8
+1.0
+0
+2
+4
+6
+8
+10
+12
+14
+c0
+Re(ω
+nm)
+ω
+00
+ω
+01
+ω
+02
+ω
+03
+0.2
+0.4
+0.6
+0.8
+1.0
+-7
+-6
+-5
+-4
+-3
+-2
+-1
+c0
+Im(ω
+nm)
+ω
+00
+ω
+01
+ω
+02
+ω
+03
+0.2
+0.4
+0.6
+0.8
+1.0
+0
+2
+4
+6
+8
+10
+12
+14
+c0
+Re(ω
+nm)
+ω
+10
+ω
+11
+ω
+12
+ω
+13
+0.2
+0.4
+0.6
+0.8
+1.0
+-16
+-14
+-12
+-10
+-8
+-6
+-4
+-2
+c0
+Im(ω
+nm)
+ω
+10
+ω
+11
+ω
+12
+ω
+13
+FIG. 3. Top panel: Real (left) and imaginary (right) part of the fundamental QNMs ˜ω0m of a three-dimensional acoustic
+Schwarzschild black hole with respect to c0 and varying m. Bottom panel: Real and imaginary part of the first overtone of
+QNMs ˜ω1m of the same system with respect to c0 and varying m.
+real part of QNMs while the imaginary part is also in-
+creased (in absolute value) as expected from the eikonal
+limit which probes, as we will show in the following sec-
+tion, the instability timescale of phase fluctuations at a
+critical radius where phonons are trapped in unstable
+curcular orbits around the acoustic BH. For some typical
+QNMs we refer the reader to Table II.
+3D BEC analog
+m
+n = 0
+n = 1
+1 0.4068 - 0.3412 i 0.1968 - 1.2341 i
+2 0.9527 - 0.3507 i 0.7856 - 0.2234 i
+10 4.9906 - 0.3535 i 4.9532 - 1.1248 i
+TABLE II. QNMs of the three-dimensional (3D) BEC acous-
+tic BH with c0 = 1.
+1.
+Eikonal quasinormal mode interpretation
+We are already aware that the real and imaginary part
+of eikonal QNMs are intrinsically connected to the angu-
+lar frequency and instability timescale of null geodesics,
+respectively, at the photon sphere of a vast variety of
+BH geometries [69, 77–82]. Our calculations demonstrate
+that the same behavior occurs for the acoustic BEC BH,
+which means that the system, though hydrodynamic in
+nature, has an analog photon sphere, i.e.
+a phonon
+sphere. By calculating the QNMs for large m and com-
+paring with those of the five-dimensional BH for large ν
+we find that both asymptote to the same value.
+Specifically, the QNMs of the acoustic BH in the
+eikonal limit are related to the Lyapunov exponent λ0 of
+phase fluctuations at a critical radius where phonons are
+trapped in unstable circular orbits. The Lyapunov expo-
+nent is inversely-proportional to the instability timescale
+of phonon orbits there, i.e. [69]
+˜ωWKB = mΩph − i
+�
+n + 1
+2
+�
+|λ0|,
+(80)
+
+10
+0
+20
+40
+60
+80
+100
+-0.365
+-0.360
+-0.355
+-0.350
+-0.345
+-0.340
+ν,m
+Im(ω0 ν)
+Im(ω
+0 m)
+FIG. 4.
+Imaginary parts of fundamental QNMs of a five-
+dimensional Schwarzschild black hole, Im(ω0ν) (purple dots),
+with M = 1 and increasing ν, and of the acoustic analog
+Schwarzschild black hole in a cavity, Im(˜ω0m) (orange dots),
+with c0 = 1 and increasing m. The dashed horizontal line
+designates the WKB prediction at the eikonal limit.
+where
+Ωph =
+�
+f(rph)
+r2
+ph
+,
+(81)
+is the angular frequency of phonons at the phonon sphere
+r = rph and
+|λ0| =
+�
+−1
+2
+r2
+ph
+f(rph)
+� d2
+dr2∗
+f(r)
+r2
+������
+r=rph
+(82)
+is the Lyapunov exponent or instability timescale of
+phonons.
+Figure 4 shows that both the BH and the acoustic BEC
+analog reach the same decay timescale of QNMs rapidly
+as ν and m become arbitrarily large. The asymptotic val-
+ues of eikonal QNMs extracted with the numerical meth-
+ods utilized above agree perfectly with those obtained by
+Eq. (80) for large m. The fact that both the gravita-
+tional and acoustic BH asymptote to the same eikonal
+QNMs is routed to the form of their effective potentials.
+Equations (15) and (78) are both dominated by ν and
+m when those constants acquire large values, hence the
+effective potentials practically coincide and lead to the
+same mode solutions.
+A peculiar, though not necessarily important, aspect
+of the convergence of the imaginary part of QNMs is that
+when m increases the trend of convergence to the WKB
+prediction (shown with a dashed horizontal black line in
+Fig. 4) is opposite to that of the BH when ν asymptotes
+to infinity.
+C.
+Quasibound states
+The exact solution for the radial part of the mass-
+less Klein-Gordon equation, in the acoustic BH system,
+can be written through Eqs.
+(26)-(38), with the new
+radial coordinate, x, the new parameter, x1, and the
+F-homotopic transformation, R(x) �→ y(x), defined by
+Eqs. (17), (18), and (19), respectively. However, in the
+present case, the coefficients A0, A1, Ax1, A3, and A4 are
+given by
+A0 = − i˜ω
+2c0
+,
+(83)
+A1 = 1
+2 − im
+c0
+,
+(84)
+Ax1 = − i˜ω
+2c0
+,
+(85)
+A3 = −(m + ˜ω)(2ic0 + m + ˜ω)
+c2
+0
+,
+(86)
+A4 = (m + ˜ω)(2ic0 + m + ˜ω)
+c2
+0
+,
+(87)
+such that the parameters α, β, γ, δ, ϵ, and q are given
+by
+α = 2 − i(m + ˜ω)
+c0
+,
+(88)
+β = −i(m + ˜ω)
+c0
+,
+(89)
+γ = 1 − i˜ω
+c0
+,
+(90)
+δ = 1 − 2im
+c0
+,
+(91)
+ϵ = 1 − i˜ω
+c0
+,
+(92)
+q = −(m + ˜ω)(2ic0 + m + ˜ω)
+c2
+0
+.
+(93)
+Similarly to Sec. II C, by imposing ingoing boundary
+conditions at the acoustic horizon, decay at infinity, and
+the resulting α-condition given by Eq. (53), we obtain the
+exact spectrum of QBSs ˜ωnm in the BEC Schwarzschild
+analog
+˜ωnm = −m − ic0(2 + n).
+(94)
+Furthermore, from Eqs. (83)-(94), we get
+σ = i(m + ic0n + ˜ωnm)
+c0
+= 2,
+(95)
+which means that the parameter σ is a real, positive
+(constant) number for any value of the overtone num-
+ber n, as well as for any value of the magnetic quantum
+number m, and hence the frequency eigenvalues given
+by Eq. (94) represent QBSs for phase fluctuations in the
+acoustic BEC BH studied here.
+
+11
+0.2
+0.4
+0.6
+0.8
+1.0
+-3
+-2
+-1
+0
+c0
+Re(ω
+nm)
+ω
+00
+ω
+01
+ω
+02
+ω
+03
+0.2
+0.4
+0.6
+0.8
+1.0
+-2.0
+-1.5
+-1.0
+-0.5
+0.0
+c0
+Im(ω
+nm)
+ω
+00
+ω
+01
+ω
+02
+ω
+03
+0.2
+0.4
+0.6
+0.8
+1.0
+-3
+-2
+-1
+0
+c0
+Re(ω
+nm)
+ω
+10
+ω
+11
+ω
+12
+ω
+13
+0.2
+0.4
+0.6
+0.8
+1.0
+-3.0
+-2.5
+-2.0
+-1.5
+-1.0
+-0.5
+0.0
+c0
+Im(ω
+nm)
+ω
+10
+ω
+11
+ω
+12
+ω
+13
+FIG. 5.
+Top panel: Real (left) and imaginary (right) part of the fundamental QBSs ˜ω0m of a three-dimensional acoustic
+Schwarzschild black hole with respect to the vortex radius c0 and varying m. Bottom panel: Real and imaginary part of the
+first overtone of QBSs ˜ω1m of the same system with respect to c0 and varying m.
+By focusing on the fundamental mode (n = 0) we ob-
+tain
+˜ω0m = −m − 2ic0,
+(96)
+where
+the
+second
+polynomial
+condition,
+given
+by
+Eq. (54), is automatically satisfied, since it leads to
+cn+1(q)
+����
+n=0
+= q = n(2 + n)
+����
+n=0
+= 0.
+(97)
+This means that there is no restriction on the value of
+the magnetic quantum number m; we can consider it as
+m = −∞, . . . , 0, . . . , +∞. It is noteworthy to point that
+as in the BH case, the QBSs of the acoustic BH do not
+exist when m = 0 since the real part is zero and the
+modes only decay in time, i.e. ˜ω00 = −2ic0.
+Fig. 5 demonstrates the behavior of QBSs in the ana-
+log BEC BH. Surprisingly, they have almost identical ten-
+dencies as those found for five-dimensional Schwarzschild
+BHs which further supports the analogy between them.
+Most surprisingly, the imaginary parts depend linearly
+on the vortex radius c0, which is a much more simplified
+version of what occurs in the BH case.
+IV.
+CONCLUSIONS
+In this study, we have calculated the QNMs and QBSs
+of five-dimensional Schwarzschild BHs which are analog
+models of BECs of light in a mirror cavity; an experiment
+recently proposed in [58]. We found that the spectra for
+both systems share striking qualitative similarities with
+respect to their tuning parameters, i.e.
+the BH mass
+and the cavity’s radius. Most importantly, our investi-
+gation provides proof of a phonon-sphere interpretation
+of the acoustic BEC BH since the imaginary part of the
+eikonal QNMs asymptotes to the instability timescale of
+phonons at the phonon sphere in accord to the WKB
+prediction. Our results are timely, and together with the
+recent investigation of the graybody factors and Hawk-
+ing radiation of the analog proposed in [58], can prescribe
+numerical data for actual experimental devices that may
+be constructed based on such proposal.
+In fact, although a multitude of BH analog experiments
+have taken place and made significant breakthroughs so
+far, the proposal in [58] is quite simple and elegant, in-
+cludes a velocity singularity at the center of the vor-
+
+12
+tex (aspect that other BEC-based experiments lack), has
+tabletop dimensions and can provide intuition regarding
+classical and quantum aspects of the singularity, as well
+as a better understanding of higher-dimensional BH ge-
+ometries and their properties.
+An interesting extension of the analog [58] can be the
+manipulation of the nonlinear coupling of the BECs of
+light in order to obtain a massive Klein-Gordon-like equa-
+tion for phase fluctuations through the underlying hy-
+drodynamic equations of motion [57] and study classical
+and quantum phenomena. Most importantly, a general-
+ization of the model in [58] onto a rotating BEC acoustic
+BH analog should be of utmost importance in order to
+simulate phenomena that astrophysical BHs experience.
+We leave these directions of research for the future.
+ACKNOWLEDGMENTS
+H.S.V. is partially supported by the Alexander von
+Humboldt-Stiftung/Foundation (Grant No.
+1209836).
+This study was financed in part by the Conselho Na-
+cional de Desenvolvimento Cient´ıfico e Tecnol´ogico –
+Brasil (CNPq) – Research Project No.
+150410/2022-
+0.
+It is a great pleasure to thank the Theoretical As-
+trophysics at T¨ubingen (TAT Group) for its hospitality
+and technical support. K.D. acknowledges financial sup-
+port provided under the European Union’s H2020 ERC,
+Starting Grant agreement no. DarkGRA–757480 and the
+MIUR PRIN and FARE programmes (GW-NEXT, CUP:
+B84I20000100001).
+[1] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev.
+Lett. 116, 061102 (2016), arXiv:1602.03837 [gr-qc].
+[2] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev.
+Lett. 116, 221101 (2016), [Erratum: Phys.Rev.Lett. 121,
+129902 (2018)], arXiv:1602.03841 [gr-qc].
+[3] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev.
+Lett. 119, 141101 (2017), arXiv:1709.09660 [gr-qc].
+[4] R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev.
+Lett. 125, 101102 (2020), arXiv:2009.01075 [gr-qc].
+[5] R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. D
+102, 043015 (2020), arXiv:2004.08342 [astro-ph.HE].
+[6] R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. D
+103, 122002 (2021), arXiv:2010.14529 [gr-qc].
+[7] R. Abbott et al. (LIGO Scientific, VIRGO, KAGRA),
+(2021), arXiv:2111.03606 [gr-qc].
+[8] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev.
+Lett. 119, 161101 (2017), arXiv:1710.05832 [gr-qc].
+[9] E. Berti et al., Class. Quant. Grav. 32, 243001 (2015),
+arXiv:1501.07274 [gr-qc].
+[10] L. Barack et al., Class. Quant. Grav. 36, 143001 (2019),
+arXiv:1806.05195 [gr-qc].
+[11] K. Destounis, A. G. Suvorov, and K. D. Kokkotas, Phys.
+Rev. D 102, 064041 (2020), arXiv:2009.00028 [gr-qc].
+[12] K. Destounis, A. G. Suvorov, and K. D. Kokkotas, Phys.
+Rev. Lett. 126, 141102 (2021), arXiv:2103.05643 [gr-qc].
+[13] K. D. Kokkotas and B. G. Schmidt, Living Rev. Rel. 2,
+2 (1999), arXiv:gr-qc/9909058.
+[14] E. Berti, V. Cardoso, and A. O. Starinets, Class. Quant.
+Grav. 26, 163001 (2009), arXiv:0905.2975 [gr-qc].
+[15] R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys. 83,
+793 (2011), arXiv:1102.4014 [gr-qc].
+[16] S. W. Hawking, Commun. Math. Phys. 43, 199 (1975),
+[Erratum: Commun.Math.Phys. 46, 206 (1976)].
+[17] R. Brito, V. Cardoso,
+and P. Pani, Lect. Notes Phys.
+906, pp.1 (2015), arXiv:1501.06570 [gr-qc].
+[18] R. Penrose and R. M. Floyd, Nature 229, 177 (1971).
+[19] J. D. Bekenstein, Phys. Rev. D 7, 949 (1973).
+[20] V. Cardoso,
+J. L. Costa,
+K. Destounis,
+P. Hintz,
+and A. Jansen, Phys. Rev. D 98, 104007 (2018),
+arXiv:1808.03631 [gr-qc].
+[21] K.
+Destounis,
+Phys.
+Rev.
+D
+100,
+044054
+(2019),
+arXiv:1908.06117 [gr-qc].
+[22] G. Mascher, K. Destounis,
+and K. D. Kokkotas, Phys.
+Rev. D 105, 084052 (2022), arXiv:2204.05335 [gr-qc].
+[23] K. Destounis, G. Mascher,
+and K. D. Kokkotas, Phys.
+Rev. D 105, 124058 (2022), arXiv:2206.07794 [gr-qc].
+[24] M. Isi, M. Giesler, W. M. Farr, M. A. Scheel,
+and
+S. A. Teukolsky, Phys. Rev. Lett. 123, 111102 (2019),
+arXiv:1905.00869 [gr-qc].
+[25] M. Giesler, M. Isi, M. A. Scheel, and S. Teukolsky, Phys.
+Rev. X 9, 041060 (2019), arXiv:1903.08284 [gr-qc].
+[26] R. Cotesta, G. Carullo, E. Berti, and V. Cardoso, Phys.
+Rev. Lett. 129, 111102 (2022), arXiv:2201.00822 [gr-qc].
+[27] M. H.-Y. Cheung et al., (2022), arXiv:2208.07374 [gr-qc].
+[28] M. Lagos and L. Hui, (2022), arXiv:2208.07379 [gr-qc].
+[29] K. Mitman et al., (2022), arXiv:2208.07380 [gr-qc].
+[30] A. Kehagias, D. Perrone, A. Riotto, and F. Riva, (2023),
+arXiv:2301.09345 [gr-qc].
+[31] J. L. Jaramillo, R. Panosso Macedo, and L. Al Sheikh,
+Phys. Rev. X 11, 031003 (2021), arXiv:2004.06434 [gr-
+qc].
+[32] J. L. Jaramillo, R. Panosso Macedo, and L. A. Sheikh,
+Phys. Rev. Lett. 128, 211102 (2022), arXiv:2105.03451
+[gr-qc].
+[33] K. Destounis, R. P. Macedo, E. Berti, V. Cardoso,
+and J. L. Jaramillo, Phys. Rev. D 104, 084091 (2021),
+arXiv:2107.09673 [gr-qc].
+[34] E. Gasperin and J. L. Jaramillo, Class. Quant. Grav. 39,
+115010 (2022), arXiv:2107.12865 [gr-qc].
+[35] V. Boyanov, K. Destounis, R. Panosso Macedo, V. Car-
+doso, and J. L. Jaramillo, (2022), arXiv:2209.12950 [gr-
+qc].
+[36] E. Berti, V. Cardoso, M. H.-Y. Cheung, F. Di Filippo,
+F. Duque, P. Martens, and S. Mukohyama, Phys. Rev.
+D 106, 084011 (2022), arXiv:2205.08547 [gr-qc].
+[37] J. L. Jaramillo, Class. Quant. Grav. 39, 217002 (2022),
+arXiv:2206.08025 [gr-qc].
+[38] R.
+A.
+Konoplya
+and
+A.
+Zhidenko,
+(2022),
+arXiv:2209.00679 [gr-qc].
+[39] M. Visser, Class. Quant. Grav. 15, 1767 (1998), arXiv:gr-
+qc/9712010.
+[40] C. Barcelo, S. Liberati, and M. Visser, Living Rev. Rel.
+
+13
+8, 12 (2005), arXiv:gr-qc/0505065.
+[41] W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981).
+[42] S. Weinfurtner, E. W. Tedford, M. C. J. Penrice, W. G.
+Unruh,
+and G. A. Lawrence, Phys. Rev. Lett. 106,
+021302 (2011), arXiv:1008.1911 [gr-qc].
+[43] M. Richartz, A. Prain, S. Liberati, and S. Weinfurtner,
+Phys. Rev. D 91, 124018 (2015), arXiv:1411.1662 [gr-qc].
+[44] V. Cardoso, A. Coutant, M. Richartz,
+and S. We-
+infurtner,
+Phys.
+Rev.
+Lett.
+117,
+271101
+(2016),
+arXiv:1607.01378 [gr-qc].
+[45] T. Torres, S. Patrick, A. Coutant, M. Richartz, E. W.
+Tedford,
+and S. Weinfurtner, Nature Phys. 13, 833
+(2017), arXiv:1612.06180 [gr-qc].
+[46] S. Patrick, A. Coutant, M. Richartz, and S. Weinfurtner,
+Phys. Rev. Lett. 121, 061101 (2018), arXiv:1801.08473
+[gr-qc].
+[47] S. Patrick, H. Goodhew, C. Gooding,
+and S. We-
+infurtner,
+Phys.
+Rev.
+Lett.
+126,
+041105
+(2021),
+arXiv:1905.03045 [gr-qc].
+[48] T. Torres, S. Patrick, M. Richartz, and S. Weinfurtner,
+Class. Quant. Grav. 36, 194002 (2019), arXiv:1905.00356
+[gr-qc].
+[49] T. Torres, S. Patrick, M. Richartz, and S. Weinfurtner,
+Phys. Rev. Lett. 125, 011301 (2020), arXiv:1811.07858
+[gr-qc].
+[50] L. J. Garay, J. R. Anglin, J. I. Cirac, and P. Zoller, Phys.
+Rev. A 63, 023611 (2001), arXiv:gr-qc/0005131.
+[51] J.
+Steinhauer,
+Nature
+Phys.
+10,
+864
+(2014),
+arXiv:1409.6550 [cond-mat.quant-gas].
+[52] J. R. Mu˜noz de Nova, K. Golubkov, V. I. Kolobov, and
+J. Steinhauer, Nature 569, 688 (2019), arXiv:1809.00913
+[gr-qc].
+[53] C. Gooding, S. Biermann, S. Erne, J. Louko, W. G. Un-
+ruh, J. Schmiedmayer,
+and S. Weinfurtner, Phys. Rev.
+Lett. 125, 213603 (2020), arXiv:2007.07160 [gr-qc].
+[54] J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg,
+and U. Leonhardt, Phys. Rev. Lett. 122, 010404 (2019),
+arXiv:1808.09244 [gr-qc].
+[55] M. Ornigotti, S. Bar-Ad, A. Szameit,
+and V. Fleu-
+rov, Phys. Rev. A 97, 013823 (2018), arXiv:1704.07609
+[physics.optics].
+[56] M. Richartz, A. Prain, S. Weinfurtner, and S. Liberati,
+Class. Quant. Grav. 30, 085009 (2013), arXiv:1208.3601
+[gr-qc].
+[57] M. Ciszak and F. Marino, Phys. Rev. D 103, 045004
+(2021), arXiv:2101.07508 [gr-qc].
+[58] L. Liao, E. C. I. van der Wurff, D. van Oosten,
+and
+H. T. C. Stoof, Phys. Rev. A 99, 023850 (2019),
+arXiv:1806.00023 [cond-mat.quant-gas].
+[59] F. R. Tangherlini, Nuovo Cim. 27, 636 (1963).
+[60] G. Torres del Castillo, Revista Mexicana de F´ısica
+(2013).
+[61] C. R. Frye and C. J. Efthimiou, (2012), arXiv:1205.3548
+[math.CA].
+[62] D. H. Hyers, The Functions of Mathematical Physics
+(Harry Hochstadt), Vol. 15 (Society for Industrial and
+Applied Mathematics, USA, 1973) p. 235–236.
+[63] A.
+Jansen,
+Eur.
+Phys.
+J.
+Plus
+132,
+546
+(2017),
+arXiv:1709.09178 [gr-qc].
+[64] K. Lin and W.-L. Qian, Class. Quant. Grav. 34, 095004
+(2017), arXiv:1610.08135 [gr-qc].
+[65] K. Lin and W.-L. Qian, Chin. Phys. C 43, 035105 (2019),
+arXiv:1902.08352 [gr-qc].
+[66] S. Iyer and C. M. Will, Phys. Rev. D 35, 3621 (1987).
+[67] S. Iyer, Phys. Rev. D 35, 3632 (1987).
+[68] V. Cardoso, J. P. S. Lemos, and S. Yoshida, Phys. Rev.
+D 69, 044004 (2004), arXiv:gr-qc/0309112.
+[69] V. Cardoso,
+A. S. Miranda,
+E. Berti,
+H. Witek,
+and V. T. Zanchin, Phys. Rev. D 79, 064016 (2009),
+arXiv:0812.1806 [hep-th].
+[70] H. S. Vieira and V. B. Bezerra, Annals Phys. 373, 28
+(2016), arXiv:1603.02233 [gr-qc].
+[71] H. S. Vieira and K. D. Kokkotas, Phys. Rev. D 104,
+024035 (2021), arXiv:2104.03938 [gr-qc].
+[72] A. Ronveaux, Heun’s Differential Equations (Oxford Uni-
+versity Press, New York, 1995).
+[73] Q.-B. Wang and X.-H. Ge, Phys. Rev. D 102, 104009
+(2020), arXiv:1912.05285 [hep-th].
+[74] X.-H. Ge, M. Nakahara, S.-J. Sin, Y. Tian,
+and S.-F.
+Wu, Phys. Rev. D 99, 104047 (2019), arXiv:1902.11126
+[hep-th].
+[75] E. P. Gross, Nuovo Cimento (Italy) Divided into Nuovo
+Cimento A and Nuovo Cimento B 10.1007/BF02731494.
+[76] L. Pitaevskii, Sov. Phys. JETP 13, 451 (1961).
+[77] V. Cardoso, J. a. L. Costa, K. Destounis, P. Hintz,
+and A. Jansen, Phys. Rev. Lett. 120, 031103 (2018),
+arXiv:1711.10502 [gr-qc].
+[78] K.
+Destounis,
+Phys.
+Lett.
+B
+795,
+211
+(2019),
+arXiv:1811.10629 [gr-qc].
+[79] H. Liu,
+Z. Tang,
+K. Destounis,
+B. Wang,
+E. Pa-
+pantonopoulos,
+and H. Zhang, JHEP 03, 187 (2019),
+arXiv:1902.01865 [gr-qc].
+[80] K. Destounis, R. D. B. Fontana, F. C. Mena, and E. Pa-
+pantonopoulos, JHEP 10, 280 (2019), arXiv:1908.09842
+[gr-qc].
+[81] K. Destounis, R. D. B. Fontana, and F. C. Mena, Phys.
+Rev. D 102, 044005 (2020), arXiv:2005.03028 [gr-qc].
+[82] K. Destounis, R. D. B. Fontana, and F. C. Mena, Phys.
+Rev. D 102, 104037 (2020), arXiv:2006.01152 [gr-qc].
+
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+page_content='  Federal University of Lavras,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 37200-000 Lavras,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
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+page_content='  University of T¨ubingen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 72076 T¨ubingen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Germany  3S˜ao Carlos Institute of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' University of S˜ao Paulo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 13560-970 S˜ao Carlos,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Brazil  4Dipartimento di Fisica,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Sapienza Universit`a di Roma,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Piazzale Aldo Moro 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 00185,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Roma,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Italy and  5INFN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Sezione di Roma,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Piazzale Aldo Moro 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 00185,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Roma,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Italy  Analog models of black holes have unequivocally proven to be extremely beneficial in providing  critical information regarding black hole spectroscopy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' superradiance,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' quantum phenomena and most  importantly Hawking radiation and black hole evaporation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' topics that have either recently begun  to bloom through gravitational wave observations or have not yet been investigated in astrophysical  setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Black hole analog experiments have made astonishing steps toward the aforementioned direc-  tions and are paramount in understanding the quantum nature of the gravitational field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Recently,  a tabletop analog Schwarzschild black hole has been proposed by placing Bose-Einstein condensates  of photons inside a mirror’s cavity, leading to a sink with a radial vortex that represents a velocity  singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Here, we provide an extensive spectral analysis of both the tabletop acoustic black hole  and its higher-dimensional gravitational analog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' We find that quasinormal modes and quasibound  states share qualitative similarities in both systems and show that the eikonal quasinormal modes  of the analog acoustic black hole have a photon-sphere-like interpretation, which points to the ex-  istence of a phonon sphere in the analog black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Our results, complemented with the recently  calculated graybody factors and Hawking radiation of the acoustic analog, can provide a theoretical  test bed for future tabletop experiments with condensates of light in a mirror’s cavity and provide  significant insights regarding classical and quantum phenomena in higher-dimensional black holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  INTRODUCTION  The emission and detection of gravitational waves  (GWs) from the binary coalescence of black holes (BHs)  [1–7] and compact objects [8] have established the field of  experimental gravitation and continue to provide insights  into the strong field regime towards the search for an ul-  timate theory of gravitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' General relativity (GR) is  currently been tested meticulously [9–12] and has proven  to be the most successful to date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  GWs carry unparalleled information during all stages  of the binary’s evolution as it undergoes the inspiral,  merger and ringdown stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' During these phases, GWs  bear the externally observable properties of the binary’s  components and the eventual compact object’s parame-  ters that forms after ringdown, described by quasinormal  modes (QNMs) [13–15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  BHs undergo surprising phe-  nomena, such as Hawking radiation when semiclassical  effects are taken into account [16], they superradiate [17]  under the expense of the BH’s spin [18] or charge [19–  23], and when perturbed, they vibrate according to their  characteristic spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The BH spectroscopy program is currently aiming to-  wards an ultimate understanding of QNMs, how to detect  them properly from GW data [24–26], and if nonlinear-  ities [27–30], as well as spectral instabilities [31–38] can  interfere with QNM extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Nevertheless, superra-  diance and Hawking radiation have not been detected  experimentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' To this end, different models are being  used in an effort to mimic BHs and recreate such pro-  cesses in controlled laboratory experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Analog gravity [39, 40] has the potential to provide a  better understanding regarding phenomena that would  otherwise elude observation in the strong field regime  and when quantum effects become significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Unruh  pioneered the first theoretical BH analog [41], which can  be envisioned through a fluid which on its surface, sound  excitations are mapped to perturbation equations that  are typically found and utilized in classical and quantum  gravity investigations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The surface fluctuations endure  an effective spacetime geometry that is determined by  the propagation speed of these excitations and their rel-  ative speed with respect to the fluid, which enables the  construction of an acoustic BH analog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Tuning the veloc-  ity of the fluid leads to the formation of an acoustic event  horizon analog, beyond which sound fluctuations cannot  escape the dumb hole, in analogy to infalling particles  into a BH event horizon which are causally disconnected  with spatial infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Currently, there is an abundance in analog grav-  ity experiments that function with fluids and superflu-  ids [42–49], Bose-Einstein condensates (BECs) [50–53]  and optical media [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Through these analog experi-  ments, Hawking radiation [42, 51, 52, 55], superradiance  [43–45, 56, 57], QNMs and quasibound states (QBSs)  [46, 48, 49] have been experimentally observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' These ex-  periments are not only successful scientific achievements  but also can provide unmatched insights into the future  of gravitational physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Very recently, a novel tabletop experimental three-  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='11480v1  [gr-qc]  27 Jan 2023  2  dimensional analog of a Schwarzschild BH was proposed  with BECs of light placed in a mirror’s cavity [58] which  leads to a sink with a radial vortex pointing towards the  central velocity singularity, that was missing in other ex-  periments with BECs where the analog BH horizons had  a one-dimensional flow pattern that smoothly interpo-  lates between a velocity below the speed of sound and  thus did not possess a singular velocity profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The novel  proposal in [58] serves as an analog of a rotationally-  symmetric five-dimentional Schwarzschild BH with a  sonic event horizon and a velocity singularity due to the  radial vortex, thus can shed light on the properties close  to the region of the singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [58], the authors have calculated the gray-  body factors and Hawking radiation of the proposed ex-  perimental setup in an attempt to provide data for fu-  ture experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In our analysis we complete their  study by calculating the QNMs and QBSs for the three-  dimensional BEC of light in a cavity and revisit the spec-  trum of five-dimensional Schwarzschild BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' We find that  QNMs and QBSs share qualitative similarities in both  the gravitational and the BEC analog system, thus giv-  ing more legitimacy to the analogy, and identify that  the photon sphere interpretation of eikonal QNMs of the  gravitational BH is shared in the analog system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Thus,  the newly proposed three-dimensional acoustic BH ana-  log possesses a phonon sphere which properties are in-  trinsically connected to the eikonal QNMs of phase fluc-  tuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  HIGHER-DIMENSIONAL SCHWARZSCHILD  BLACK HOLES  The standard four-dimensional Schwarzschild solution  was generalized to higher dimensions by Tangherlini in  [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The higher-dimensional action, which is a general-  ization of the Einstein-Hilbert action, is given by  S =  1  16πGD  �  dDx√−gR,  (1)  where g ≡ det(gµν), and GD is the D-dimensional grav-  itational constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In what follows, for simplicity and  without loss of generality, we adopt the natural units  where GD = c = ℏ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' By varying the action with re-  spect to the spacetime metric gµν, we obtain the Einstein  equations in higher dimensions  Rµν − 1  2Rgµν = 0,  (2)  where Rµν and R are the Ricci tensor and Ricci scalar, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A static, asymptotically flat and spherically-  symmetric vacuum solution of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (2), which generalizes  the Schwarzschild BH solution in D-dimensions, has the  form  ds2 = −f(r)dt2 + f(r)−1dr2 + r2dΩ2  D−2,  (3)  where the metric function, f(r), and the solid angle ele-  ment, dΩ2  D−2, are given by  f(r) = 1 −  M  rD−3 ,  (4)  and  dΩ2  D−2 = dθ2  1 + sin2 θ1dθ2  2 + sin2 θ1 sin2 θ2dθ2  2 + · · ·  +  �  �  �  �  D−2  �  j=1  sin2 θj  �  � dθ2  D−1  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (5)  The parameter M is related to the BH mass M through  the relation  M =  16πM  (D − 2)ΩD−2  , ΩD−2 = 2π  D−1  2  Γ( D−1  2 ),  (6)  where ΩD−2 is the volume of the (D − 2)-dimensional  unit sphere and Γ(x) is the gamma function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Note that the solution (3) simplifies to the standard  Schwarzschild metric when D = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' In addition, we ob-  serve that when the spacetime is higher-dimensional, the  asymptotic fall-off term in the metric function f(r) be-  comes steeper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  This metric is Ricci flat and is called  either the Schwarzschild-Tangherlini solution or simply  the D-dimensional Schwarzschild BH spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' In this  work, we will focus on the five-dimensional Schwarzschild  BH, due to the explicit analogy between BECs of light  in a cavity that form a three-dimensional Schwarzschild  analog, as discussed in the introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The explicit line element (3) for D = 5 reads  ds2 = − f(r)dt2 + f(r)−1dr2  + r2 �  dθ2 + sin2 θ  �  dφ2 + sin2 φ dχ2��  ,  (7)  with  f(r) = 1 − M  r2 ,  M = 8M  3π ,  ΩD−2 = 2π2,  (8)  where θ, φ run over the range 0 to π, and χ from 0 to  2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The causal structure of spacetime can be identified  from the equation  f(r) = 0 = (r − r1)(r − r2),  (9)  whose solutions are the event horizon, r1 =  √  M, and a  negative non-physical solution, r2 = −  √  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Scalar wave equation  We consider a minimally-coupled massless scalar per-  turbation Ψ = Ψ(t, r, θ, φ, χ), whose equation of motion  is given by the Klein-Gordon equation  �  1  √−g ∂µ  �  gµν√−g∂ν  ��  Ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (10)  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  1  2  3  4  5  6  7  ℳ  Re(ωnν)  ω00  ω01  ω02  ω03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  ℳ  Im(ωnν)  ω00  ω01  ω02  ω03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  1  2  3  4  5  6  ℳ  Re(ωnν)  ω10  ω11  ω12  ω13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  ℳ  Im(ωnν)  ω10  ω11  ω12  ω13  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Top panel: Real (left) and imaginary (right) part of the fundamental massless scalar QNMs ω0ν of a five-dimensional  Schwarzschild black hole with respect to M and varying ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Bottom panel: Real and imaginary part of the first overtone of  massless scalar QNMs ω1ν of a five-dimensional Schwarzschild black hole with respect to M and varying ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Under symmetry assumptions we choose an ansatz  Ψ(t, r, θ, φ, χ) = e−iωtU(r)P(θ, φ, χ),  (11)  where ω is the frequency of the scalar field, U(r) =  R(r)/r3/2 is the radial function and P(θ, φ, χ) is an an-  gular function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  By utilizing the spacetime metric (7),  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (10) can be separated into an angular and a radial  equation as  �  1  sin2 θ  ∂  ∂θ  �  sin2 θ ∂  ∂θ  �  + λ −  1  sin2 θ  �  1  sin φ  ∂  ∂φ  �  sin φ ∂  ∂φ  �  +¯λ +  1  sin2 φ  ∂2  ∂χ2  ��  P(θ, φ) = 0,  (12)  and  R′′(r) + f ′(r)  f(r) R′(r)  +  � ω2  f 2(r) − 4λ + 3f(r) + 6rf ′(r)  4r2f(r)  �  R(r) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (13)  Here, λ and ¯λ are the separation constants to be deter-  mined, and the primes generally denote differentiation  with respect to r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The general exact solution of the angular equation  (12) is given by P(θ, φ, χ) = P l  ν,4(cos θ)Ylm(φ, χ), where  P l  ν,4(cos θ) are the associated Legendre functions in four-  dimensions [60–62] with arbitrary degree ν ∈ C and order  l such that λ = ν(ν + 2), and Ylm(φ, χ) are the spherical  harmonics with l and m being the angular and magnetic  quantum numbers, respectively, such that ¯λ = l(l + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In what follows, we will revisit the QNMs of five-  dimensional Schwarzschild BHs and calculate analyti-  cally the corresponding QBSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Quasinormal modes  Equation (13) can be recast into a Schr¨odinger-like  equation by multiplying it with f 2(r) and utilizing the  tortoise coordinate r∗, with dr/dr∗ = f(r), to obtain  d2R(r)  dr2∗  +  �  ω2 − VBH  �  R(r) = 0,  (14)  4  where the effective potential VBH is  VBH ≡ f(r)  �ν(ν + 2)  r2  + 3f(r)  4r2  + 3f ′(r)  2r  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (15)  QNMs ωnν are a discrete set of mode solutions of the ra-  dial equation (14) with purely ingoing (outgoing) bound-  ary conditions at the event horizon (infinity), such that  R(r) ∼ e−iωr∗, r → r1,  R(r) ∼ eiωr∗, r → ∞,  (16)  where n is the overtone number of the frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' In  what follows, we present some typical scalar QNMs of  a five-dimensional Schwarzschild BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' We have employed  three different methods, namely a pseudospectral method  [63], a matrix method [64, 65] and the Wentzel-Kramers-  Brillouin (WKB) method [66, 67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' We have found con-  vergence between the pseudospectral and matrix method  QNMs up to at least six digits (convergence can reach  even to 20 digits when more grid points are utilized) and  confirmed the validity of eikonal QNMs with the WKB  approximation finding similar precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Our results also  are in perfect agreement with those reported in [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Figure 1 demonstrates the typical behavior of five-  dimensional Schwarzschild scalar QNMs, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' the incre-  ment of the BH’s mass term decreases the oscillation fre-  quency and increases the perturbation’s lifetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Fur-  thermore, the increment of the angular number ν in-  creases the real part of QNMs while the imaginary part  is also increased (in absolute value) as expected from the  eikonal limit which probes the photon sphere of the BH,  where photons occupy unstable circular geodesics [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  There, the angular frequency of null geodesics is propor-  tional to the real part of the eikonal QNM and their in-  stability timescale is proportional to the imaginary part  of QNMs with large ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Therefore, the BH QNMs in study  have a typical photon sphere interpretation [69] which we  will further discuss in the upcoming sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' For a nu-  merical presentation of some QNMs we refer the reader  to Table I and Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  5D Scwarzschild BH  ν  n = 0  n = 1  1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0160 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3623 i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8564 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1576 i  2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5106 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3575 i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3927 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1046 i  10 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5028 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3539 i 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4689 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0639 i  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Massless scalar QNMs of the five-dimensional (5D)  Schwarzschild BH with M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Quasibound states  In what follows, we will analytically solve the radial  equation (13) for a five-dimensional Schwarzschild BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  QBSs are solutions to (13) with purely ingoing boundary  conditions at the event horizon (same as QNMs) and de-  caying boundary conditions at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Since both QNMs  and QBSs are mode solutions to the same eigenvalue  problem, though with different asymptotic behavior, we  will also refer to QBSs as ωnν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' We will see that the fact  that at infinity QBSs decay exponentially enables an an-  alytic evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' To find their analytic expression, we  apply the VBK approach [70, 71] in order to write the  radial equation (13) as a Heun-type differential equation  [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  We define a new radial coordinate, x, and a new pa-  rameter, x1, as  x = r − r2  −r2  ,  (17)  and  x1 = r1 − r2  −r2  ,  (18)  such that the three original singularities (r2, 0, r1) are  moved to the points (0, 1, x1), while maintaining a regular  singularity at spatial infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In addition, the regular  singular point at x = x1 is always located outside the  unit circle |x1| > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The final step is to perform an F-  homotopic transformation R(x) �→ y(x) given by  R(x) = xA0(x − 1)A1(x − x1)Ax1 y(x),  (19)  where the coefficients A0, A1, and Ax1 are given by  A0 = −  iω  r1 − r2  ,  (20)  A1 = 1  2 − 1  r1  �  r1  �  r1 + λ  r2  �  ,  (21)  Ax1 = −  iω  r1 − r2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (22)  Thus, by substituting Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (17)-(22) into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (13), we  obtain  y′′(x) +  �1 + 2A0  x  + 2A1  x − 1 + 1 + 2Ax1  x − x1  �  y′(x)  +  A3x + A4  x(x − 1)(x − x1)y(x) = 0,  (23)  where the coefficients A3, and A4 are given by  A3 = −3 + Ax1 + 2A1(1 + Ax1) + A0(1 + 2A1 + 2Ax1)  − (x1 − 1)(x2  1λ − 2ω2 + 2x1ω2)  r2  1x2  1  ,  (24)  A4 = −A0 − Ax1 − 2A0Ax1 + 3x1  2  − A1x1 − 2A0A1x1  + (x1 − 1)2(x2  1λ + 2ω2)  r2  1x2  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (25)  The radial equation (23) has the form of a general Heun  equation [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Therefore, the exact solution for the radial  part of the Klein-Gordon equation can be written as  Rj(x) =x  1  2 (γ−1)(x − 1)  1  2 δ(x − x1)  1  2 (ϵ−1)  [C1,j y1,j(x) + C2,j y2,j(x)],  (26)  5  where C1,j and C2,j are constants to be determined, and  j = {0, 1, x1, ∞} labels the solution at each singular  point, which are given as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The pair of linearly  independent solutions at x = 0 (r = r2) is given by  y1,0 = HeunG(x1, q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' α, β, γ, δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' x),  (27)  y2,0 = x1−γHeunG(x1, (x1δ + ϵ)(1 − γ) + q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  α + 1 − γ, β + 1 − γ, 2 − γ, δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' x),  (28)  where HeunG(x1, q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' α, β, γ, δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' x) denotes a general Heun  function, which is analytic in the disk |x| < 1, and has a  Maclaurin expansion given by  HeunG(x1, q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' α, β, γ, δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' x) =  ∞  �  n=0  cnxn,  (29)  with  −qc0 + x1γc1 = 0  (c0 = 1), (30)  Pncn−1 − (Qn + q)cn + Xncn+1 = 0  (n ≥ 1), (31)  and  Pn = (n − 1 + α)(n − 1 + β),  Qn = n[(n − 1 + γ)(1 + x1) + x1δ + ϵ],  (32)  Xn = (n + 1)(n + γ)x1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The pair of linearly independent solutions at x = 1 (r =  0) is given by  y1,1 = HeunG(1 − x1, αβ − q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' α, β, δ, γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 1 − x),  (33)  y2,1 = (1 − x)1−δHeunG(1 − x1, ((1 − x1)γ + ϵ)(1 − δ)  + αβ − q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' α + 1 − δ, β + 1 − δ, 2 − δ, γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 1 − x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (34)  The pair of linearly independent solutions at x = x1 (r =  r1) is given by  y1,x1 = HeunG  �  x1  x1 − 1, αβx1 − q  x1 − 1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' α, β, ϵ, δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' x1 − x  x1 − 1  �  ,  (35)  y2,x1 =  �x1 − x  x1 − 1  �1−ϵ  HeunG  �  x1  x1 − 1,  (x1(δ + γ) − γ)(1 − ϵ)  x1 − 1  + αβx1 − q  x1 − 1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' α + 1 − ϵ,  β + 1 − ϵ, 2 − ϵ, δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' x1 − x  x1 − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (36)  The pair of linearly independent solutions at x = ∞ (r =  ∞) is given by  y1,∞ = x−αHeunG  � 1  x1  , α(β − ϵ) + α  x1  (β − δ)  − q  x1  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' α, α − γ + 1, α − β + 1, δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 1  x  �  ,  (37)  y2,∞ = x−βHeunG  � 1  x1  , β(α − ϵ) + β  x1  (α − δ)  − q  x1  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' β, β − γ + 1, β − α + 1, δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 1  x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (38)  In these solutions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' the parameters α,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' γ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' δ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' ϵ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' and q are  given by  α =  1  r1 − r2  �  3r1 −  �  r1  �  r1 + λ  r2  �  +r2  ��  1 +  λ  r1r2  − 3  �  − 2iω  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (39)  β = −  1  r1 − r2  �  r1 +  �  r1  �  r1 + λ  r2  �  −r2  ��  1 +  λ  r1r2  + 1  �  + 2iω  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (40)  γ = 1 −  2iω  r1 − r2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (41)  δ = 1 − 2  r1  �  r2  1 + λr1  r2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (42)  ϵ = 1 −  2iω  r1 − r2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (43)  q = r1  r2  − λ  r2  2  − 1 + 1  r2  ��  r2  1 + λr1  r2  + iω  �  − (r2 + 2iω)  r1r2  �  r2  1 + λr1  r2  − 2i(r1 − r2 − 2iω)ω  (r1 − r2)2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (44)  The first boundary condition related to QBSs (and  QNMs) requires that the radial solution is purely ingoing  at the event horizon, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' to impose r → r1 (or x → x1)  on the radial solution given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' To do this, we  use Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (35) and (36) to get the following asymptotic  behavior  lim  r→r1 Rx1(r) ∼ C1,x1 (r−r1)  1  2 (ϵ−1)+C2,x1 (r−r1)− 1  2 (ϵ−1),  (45)  where all the remaining constants were included in C1,x1  and C2,x1, which will be determined afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Thus,  from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (43), we can write  lim  r→r1 Rx1(r) ∼ C1,x1 Ψin,x1 + C2,x1 Ψout,x1,  (46)  where Ψin,x1 and Ψout,x1 are the ingoing and outgoing  scalar wave solutions, respectively, given by  Ψin,x1(r > r1) = e−iωt(r − r1)− iω  2κ1 ,  (47)  Ψout,x1(r > r1) = e−iωt(r − r1)+ iω  2κ1 ,  (48)  with the surface gravity of the event horizon, κ1, being  defined as  κ1 = 1  2  df(r)  dr  ����  r=r1  = r1 − r2  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (49)  The ingoing boundary condition is satisfied when C2,x1 =  0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (46) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Thus, we have  lim  r→r1 Rx1(r) ∼ C1,x1 Ψin,x1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (50)  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  4  3  2  1  0  ℳ  Re(ωnν)  ω00  ω01  ω02  ω03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  ℳ  Im(ωnℓ)  ω00  ω01  ω02  ω03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  4  3  2  1  0  ℳ  Re(ωnℓ)  ω10  ω11  ω12  ω13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='5  ℳ  Im(ωnℓ)  ω10  ω11  ω12  ω13  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Top panel: Real (left) and imaginary (right) part of the fundamental massless scalar QBSs ω0ν of a five-dimensional  Schwarzschild black hole with respect to M and varying ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Bottom panel: Real and imaginary part of the first overtone of  massless scalar QBSs ω1ν of a five-dimensional Schwarzschild black hole with respect to M and varying ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The second boundary condition related to the QBSs  (that differs from that of QNMs) is to require that the  radial solution vanishes at asymptotic infinity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  to  impose a decaying boundary condition at the limit r →  ∞ (or x → ∞) on the radial solution given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Thus, we use Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (37) and (38) to obtain the following  asymptotic behavior  lim  r→∞ R∞(r) ∼ C1,∞  1  rσ ,  (51)  where we have imposed that C2,∞ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The parameter  σ is given by  σ = α − A0 − A1 − Ax1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (52)  The sign of the real part of σ determines the asymptotic  behavior of the radial scalar wave function as r → ∞:  if Re[σ] > 0, the radial solution tends to zero at spatial  infinity and then it fully satisfies the second boundary  condition for QBSs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' if Re[σ] < 0, the radial solution di-  verges at spatial infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The final asymptotic behavior of the radial scalar wave  solution at spatial infinity will be determined when we  know the values of the coefficients Aj, as well as the fre-  quencies ω, and the parameter α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Those will be obtained  by the VBK approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The general Heun functions become (class I) polyno-  mials of degree n (≥ 0) if and only if they satisfy two  conditions [72], namely,  α + n = 0,  (53)  cn+1(q) = 0,  (54)  where the accessory parameter q is given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (44).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The first condition, given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (53), is called the α-  condition, which is used to find the frequency eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The second condition, given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (54), determines the  value of the separation constant λ for each value of n,  which is used to find the eigenvalues ν and both the radial  and angular wave eigenfunctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' It is worth emphasizing  that the two polynomial conditions could be applied in  any order we wish, that is, the first condition could give  the values of the separation constant, and the second  condition could give the frequency eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Thus, by  imposing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (53), we obtain the exact spectrum of QBSs  7  given by  ωnν = −i(  √  M(n + 3) −  √  M − λ),  (55)  where we have used the explicit expressions of the event  horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Here, the separation constant is, again, λ =  ν(ν + 2), and n is the overtone number, which can be,  without loss of generality, called the principal quantum  number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' On the other hand, by substituting Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (20),  (21), (22), (53) and (55) into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (52), we get  σ = 4,  (56)  which means that the parameter σ is a real, positive  number for any value of the principal quantum num-  ber n, as well as for any value of the separation con-  stant λ, and hence the frequency eigenvalues given by  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (55) represent QBSs for massless scalar fields in the  five-dimensional Schwarzschild spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In addition,  by substituting these equations into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (44), it is pos-  sible to obtain a nonlinear equation for q = q(λ) and  then impose the second polynomial condition given by  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (54) to obtain the angular eigenvalues λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Now, let us discuss a very important case of these  QBSs: the fundamental mode, where n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In this  case, we have  ω0ν = −i(3  √  M −  √  M − λ),  (57)  where  the  second  polynomial  condition,  given  by  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (54), is automatically satisfied, since it leads to  cn+1(q)  ����  n=0  = q = n(4 + n)  ����  n=0  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (58)  This means that there is no restriction on the value of the  separation constant λ = ν(ν + 2), with ν = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In particular, the ground state (n, ν) = (0, 0) of QBSs  is given by ω00 = −2i  √  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  This is a very important  result because it designates the absence of bound states  when the angular number is null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' These solution are not  oscillatory but only decay in time therefore no bound  state can be formed in this particular case, and the BH  only oscillates in accord to QNMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 2 we show the behavior of massless scalar QBSs  in the the BH under study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The real part for the QBS ω00  is always zero since it does not depend on M and cor-  roborates the aforementioned discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' When ν ̸= 0  QBSs exist;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' the mass parameter acts in the opposite way  with respect to that of QNMs, namely their real parts  increase with M while their lifetime decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The an-  gular number ν has a somewhat similar effect to that of  QNMs, that is its increment increases (in absolute value)  the oscillation frequency of QBSs and quickly drives the  imaginary parts to their asymptotic, large ν, value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Of  course, since these modes have different boundary con-  ditions they have no connection to null geodesics in the  photon sphere at the eikonal limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  ANALOG BLACK HOLES: BOSE-EINSTEIN  CONDENSATES OF LIGHT IN A CAVITY  In this section, we begin by considering the general  acoustic BH solution in Minkowski spacetime obtained  by Unruh [41] (see also Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' [39, 40]), and then show  how to properly choose the sound velocity in order to  obtain a Schwarzschild BH in BECs of photons trapped  in a mirror cavity [58, 73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The fundamental equations of motion for an irrota-  tional fluid are given by  ∇ × v = 0,  (59)  ∂tρ + ∇ · (ρv) = 0,  (60)  ρdv  dt ≡ ρ[∂tv + (v · ∇)v] = −∇p,  (61)  where v, ρ, and p are the velocity, density, and pressure  of the fluid, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Next, we introduce the velocity  potential Ψ, such that v = −∇Ψ, and assume the fluid  as barotropic, which means that ρ = ρ(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Then, by  linearizing these equations of motion around some back-  ground (ρ0, p0, Ψ0), namely,  ρ = ρ0 + ϵρ1,  (62)  p = p0 + ϵp1,  (63)  Ψ = Ψ0 + ϵΨ1,  (64)  we obtain the following equation  − ∂t  �∂ρ  ∂pρ0(∂tΨ1 + v0 · ∇Ψ1)  �  +  ∇ ·  �  ρ0∇Ψ1 − ∂ρ  ∂pρ0v0(∂tΨ1 + v0 · ∇Ψ1)  �  = 0,  (65)  where the local speed of sound, cs, is defined by  c−2  s  ≡ ∂ρ  ∂p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (66)  Equation (65) describes the propagation of the linearized  scalar potential Ψ1, that is, it governs the propagation of  the phase fluctuations as weak excitations in a homoge-  neous stationary condensate, which can be rewritten as  a wave equation in an analog curved spacetime as  1  √−g ∂µ(gµν√−g∂νΨ1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (67)  Note that Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (67) is similar to the covariant Klein-  Gordon equation (10), where the acoustic line element  can be written as  ds2 = ρ0  cs  [−c2  sdt2 + (dxi − vi  0dt)δij(dxj − vj  0dt)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (68)  Now, let us revisit how the (1 + 2)-dimensional acous-  tic BH was set up in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Firstly, we can assume  that the fluid is a static spherically-symmetric conser-  vation flow, with a polar angle θ = π/2, which implies  8  that dθ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Next, we define the speed of sound as  cs ≡  �  kn0/µ, where k is the strength of the effective  contact interaction, n0 is the condensate density, and µ  is the effective mass of the photon gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Then, the velocity  of the fluid v is the flow rate along the radial direction  (representing the radial vortex), that is it points to the  center of the acoustic BH towards the velocity singular-  ity, given by  v0 = −ℏc0  µr ˆr = −ξcs  c0  r ˆr,  (69)  where ξ(= ℏ/µcs) is the correlation length, and c0(> 0) is  a constant related to the acoustic horizon’s radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Thus,  the acoustic line element resulting by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (68) can be  written as  ds2 = −  �  1 − c2  0  r2  �  dt2 + 2c0  r drdt + dr2 + r2dφ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (70)  With the coordinate transformation  dt → dt −  c0  r(1 − c2  0/r2)dr,  (71)  we can write the line element of an acoustic (1 + 2)-  dimensional BEC of light in a cavity as  ds2 = −f(r)dt2 + f(r)−1dr2 + r2dφ2,  (72)  where the warp factor f(r) has the form  f(r) = 1 − c2  0  r2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (73)  The radial vortex exists in a spatially (1+2)-dimensional  BEC, therefore since the warp factor (73) is identical to  the metric function (8), under the identification M = c2  0,  then this model is an analog of a (1 + 4)-dimensional  Schwarzschild BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' This is a consequence of the fact that  the metric of the BEC does not obey Einstein’s field equa-  tions, but rather it is determined by pure hydrodynamics  [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The causal structure of the particular analog BH is  strikingly similar to that presented in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The warp  factor equation  f(r) = 0 = (r − r1)(r − r2),  (74)  has two solutions, an acoustic horizon r1 = c0, which is  the outermost marginally trapped surface for outgoing  phonons, and an unphysical negative solution r2 = −c0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  The exterior acoustic event horizon is where the velocity  of the fluid reaches the sound velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The central point  of the acoustic BH can be regarded as a sink that leads to  the higher-dimensional space from which the fluid flows  to the three-dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  It is worth noting that one can also obtain this effec-  tive metric, given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (72), by using the approach  developed in [74], which is based on the Gross-Pitaevskii  theory [75, 76] that describes a nonlinear complex scalar  field propagating in a curved spacetime background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' In  this approach, we simply require a fluid flow with velocity  given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (69) in a flat Minkowski spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In what follows, we will calculate, for the first time, the  QNMs and QBSs of the analog BH proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' [58],  by using the same methods used for the five-dimensional  Schwarzschild BH analysis in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Scalar wave equation  In order to solve the equation of motion given by  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (67), for the acoustic metric Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (72), we will use a  similar separation ansatz for the phase fluctuation wave  function  Ψ1(t, r, φ) = e−i˜ωtU(r)eimφ,  (75)  where ˜ω is the frequency of phase fluctuations, U(r) =  R(r)/r1/2 is the radial function, and m is the magnetic  quantum number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Thus, by substituting Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (72) and  (75) into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (67), we obtain  R′′(r) + f ′(r)  f(r) R′(r)  +  � ˜ω2  f 2(r) − 4m2 − f(r) + 2rf ′(r)  4r2f(r)  �  R(r) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (76)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Quasinormal modes  Equation (76) can be recast into a Schr¨odinger-like  equation by multiplying with f 2(r) and utilizing the tor-  toise coordinate r∗, with dr/dr∗ = f(r), to obtain  d2R(r)  dr2∗  +  �  ˜ω2 − VBEC  �  R(r) = 0,  (77)  where the effective potential VBEC is  VBEC ≡ f(r)  �m2  r2 − f(r)  4r2 + f ′(r)  2r  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (78)  QNMs ˜ωnm, similarly, form a discrete set of mode so-  lutions to the radial equation (77) with purely ingoing  (outgoing) boundary conditions at the acoustic horizon  (infinity), such that  R(r) ∼ e−i˜ωr∗, r → r1,  R(r) ∼ ei˜ωr∗, r → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (79)  In what follows, we present the QNMs of the three-  dimensional BH analog of BECs in a cavity, where we  have employed the same methods to numerically obtain  and benchmark our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Figure 3 demonstrates the behavior of the BEC BH  analog’s QNMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The increment of the vortex radius c0  decreases the oscillation frequency and increases the per-  turbation’s lifetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The increment of m increases the  9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  0  2  4  6  8  10  12  14  c0  Re(ω\uf02d  nm)  ω\uf02d  00  ω\uf02d  01  ω\uf02d  02  ω\uf02d  03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  7  6  5  4  3  2  1  c0  Im(ω\uf02d  nm)  ω\uf02d  00  ω\uf02d  01  ω\uf02d  02  ω\uf02d  03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  0  2  4  6  8  10  12  14  c0  Re(ω\uf02d  nm)  ω\uf02d  10  ω\uf02d  11  ω\uf02d  12  ω\uf02d  13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  16  14  12  10  8  6  4  2  c0  Im(ω\uf02d  nm)  ω\uf02d  10  ω\uf02d  11  ω\uf02d  12  ω\uf02d  13  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Top panel: Real (left) and imaginary (right) part of the fundamental QNMs ˜ω0m of a three-dimensional acoustic  Schwarzschild black hole with respect to c0 and varying m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Bottom panel: Real and imaginary part of the first overtone of  QNMs ˜ω1m of the same system with respect to c0 and varying m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  real part of QNMs while the imaginary part is also in-  creased (in absolute value) as expected from the eikonal  limit which probes, as we will show in the following sec-  tion, the instability timescale of phase fluctuations at a  critical radius where phonons are trapped in unstable  curcular orbits around the acoustic BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' For some typical  QNMs we refer the reader to Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  3D BEC analog  m  n = 0  n = 1  1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4068 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3412 i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1968 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2341 i  2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='9527 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3507 i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='7856 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2234 i  10 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='9906 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3535 i 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='9532 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1248 i  TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' QNMs of the three-dimensional (3D) BEC acous-  tic BH with c0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Eikonal quasinormal mode interpretation  We are already aware that the real and imaginary part  of eikonal QNMs are intrinsically connected to the angu-  lar frequency and instability timescale of null geodesics,  respectively, at the photon sphere of a vast variety of  BH geometries [69, 77–82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Our calculations demonstrate  that the same behavior occurs for the acoustic BEC BH,  which means that the system, though hydrodynamic in  nature, has an analog photon sphere, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  a phonon  sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' By calculating the QNMs for large m and com-  paring with those of the five-dimensional BH for large ν  we find that both asymptote to the same value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Specifically, the QNMs of the acoustic BH in the  eikonal limit are related to the Lyapunov exponent λ0 of  phase fluctuations at a critical radius where phonons are  trapped in unstable circular orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The Lyapunov expo-  nent is inversely-proportional to the instability timescale  of phonon orbits there, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' [69]  ˜ωWKB = mΩph − i  �  n + 1  2  �  |λ0|,  (80)  10  0  20  40  60  80  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='365  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='360  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='355  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='350  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='345  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='340  ν,m  Im(ω0 ν)  Im(ω\uf02d  0 m)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Imaginary parts of fundamental QNMs of a five-  dimensional Schwarzschild black hole, Im(ω0ν) (purple dots),  with M = 1 and increasing ν, and of the acoustic analog  Schwarzschild black hole in a cavity, Im(˜ω0m) (orange dots),  with c0 = 1 and increasing m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The dashed horizontal line  designates the WKB prediction at the eikonal limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  where  Ωph =  �  f(rph)  r2  ph  ,  (81)  is the angular frequency of phonons at the phonon sphere  r = rph and  |λ0| =  �  −1  2  r2  ph  f(rph)  � d2  dr2∗  f(r)  r2  ������  r=rph  (82)  is the Lyapunov exponent or instability timescale of  phonons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Figure 4 shows that both the BH and the acoustic BEC  analog reach the same decay timescale of QNMs rapidly  as ν and m become arbitrarily large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The asymptotic val-  ues of eikonal QNMs extracted with the numerical meth-  ods utilized above agree perfectly with those obtained by  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (80) for large m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' The fact that both the gravita-  tional and acoustic BH asymptote to the same eikonal  QNMs is routed to the form of their effective potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Equations (15) and (78) are both dominated by ν and  m when those constants acquire large values, hence the  effective potentials practically coincide and lead to the  same mode solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  A peculiar, though not necessarily important, aspect  of the convergence of the imaginary part of QNMs is that  when m increases the trend of convergence to the WKB  prediction (shown with a dashed horizontal black line in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 4) is opposite to that of the BH when ν asymptotes  to infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Quasibound states  The exact solution for the radial part of the mass-  less Klein-Gordon equation, in the acoustic BH system,  can be written through Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (26)-(38), with the new  radial coordinate, x, the new parameter, x1, and the  F-homotopic transformation, R(x) �→ y(x), defined by  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (17), (18), and (19), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' However, in the  present case, the coefficients A0, A1, Ax1, A3, and A4 are  given by  A0 = − i˜ω  2c0  ,  (83)  A1 = 1  2 − im  c0  ,  (84)  Ax1 = − i˜ω  2c0  ,  (85)  A3 = −(m + ˜ω)(2ic0 + m + ˜ω)  c2  0  ,  (86)  A4 = (m + ˜ω)(2ic0 + m + ˜ω)  c2  0  ,  (87)  such that the parameters α, β, γ, δ, ϵ, and q are given  by  α = 2 − i(m + ˜ω)  c0  ,  (88)  β = −i(m + ˜ω)  c0  ,  (89)  γ = 1 − i˜ω  c0  ,  (90)  δ = 1 − 2im  c0  ,  (91)  ϵ = 1 − i˜ω  c0  ,  (92)  q = −(m + ˜ω)(2ic0 + m + ˜ω)  c2  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (93)  Similarly to Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' II C, by imposing ingoing boundary  conditions at the acoustic horizon, decay at infinity, and  the resulting α-condition given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (53), we obtain the  exact spectrum of QBSs ˜ωnm in the BEC Schwarzschild  analog  ˜ωnm = −m − ic0(2 + n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (94)  Furthermore, from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (83)-(94), we get  σ = i(m + ic0n + ˜ωnm)  c0  = 2,  (95)  which means that the parameter σ is a real, positive  (constant) number for any value of the overtone num-  ber n, as well as for any value of the magnetic quantum  number m, and hence the frequency eigenvalues given  by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (94) represent QBSs for phase fluctuations in the  acoustic BEC BH studied here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
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+page_content='0  3  2  1  0  c0  Re(ω\uf02d  nm)  ω\uf02d  00  ω\uf02d  01  ω\uf02d  02  ω\uf02d  03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
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+page_content='0  c0  Im(ω\uf02d  nm)  ω\uf02d  00  ω\uf02d  01  ω\uf02d  02  ω\uf02d  03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
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+page_content='0  3  2  1  0  c0  Re(ω\uf02d  nm)  ω\uf02d  10  ω\uf02d  11  ω\uf02d  12  ω\uf02d  13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
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+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
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+page_content='0  c0  Im(ω\uf02d  nm)  ω\uf02d  10  ω\uf02d  11  ω\uf02d  12  ω\uf02d  13  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Top panel: Real (left) and imaginary (right) part of the fundamental QBSs ˜ω0m of a three-dimensional acoustic  Schwarzschild black hole with respect to the vortex radius c0 and varying m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Bottom panel: Real and imaginary part of the  first overtone of QBSs ˜ω1m of the same system with respect to c0 and varying m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  By focusing on the fundamental mode (n = 0) we ob-  tain  ˜ω0m = −m − 2ic0,  (96)  where  the  second  polynomial  condition,  given  by  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (54), is automatically satisfied, since it leads to  cn+1(q)  ����  n=0  = q = n(2 + n)  ����  n=0  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  (97)  This means that there is no restriction on the value of  the magnetic quantum number m;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' we can consider it as  m = −∞, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' , 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' , +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' It is noteworthy to point that  as in the BH case, the QBSs of the acoustic BH do not  exist when m = 0 since the real part is zero and the  modes only decay in time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' ˜ω00 = −2ic0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 5 demonstrates the behavior of QBSs in the ana-  log BEC BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Surprisingly, they have almost identical ten-  dencies as those found for five-dimensional Schwarzschild  BHs which further supports the analogy between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Most surprisingly, the imaginary parts depend linearly  on the vortex radius c0, which is a much more simplified  version of what occurs in the BH case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  CONCLUSIONS  In this study, we have calculated the QNMs and QBSs  of five-dimensional Schwarzschild BHs which are analog  models of BECs of light in a mirror cavity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' an experiment  recently proposed in [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' We found that the spectra for  both systems share striking qualitative similarities with  respect to their tuning parameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  the BH mass  and the cavity’s radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Most importantly, our investi-  gation provides proof of a phonon-sphere interpretation  of the acoustic BEC BH since the imaginary part of the  eikonal QNMs asymptotes to the instability timescale of  phonons at the phonon sphere in accord to the WKB  prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Our results are timely, and together with the  recent investigation of the graybody factors and Hawk-  ing radiation of the analog proposed in [58], can prescribe  numerical data for actual experimental devices that may  be constructed based on such proposal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  In fact, although a multitude of BH analog experiments  have taken place and made significant breakthroughs so  far, the proposal in [58] is quite simple and elegant, in-  cludes a velocity singularity at the center of the vor-  12  tex (aspect that other BEC-based experiments lack), has  tabletop dimensions and can provide intuition regarding  classical and quantum aspects of the singularity, as well  as a better understanding of higher-dimensional BH ge-  ometries and their properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  An interesting extension of the analog [58] can be the  manipulation of the nonlinear coupling of the BECs of  light in order to obtain a massive Klein-Gordon-like equa-  tion for phase fluctuations through the underlying hy-  drodynamic equations of motion [57] and study classical  and quantum phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Most importantly, a general-  ization of the model in [58] onto a rotating BEC acoustic  BH analog should be of utmost importance in order to  simulate phenomena that astrophysical BHs experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  We leave these directions of research for the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' is partially supported by the Alexander von  Humboldt-Stiftung/Foundation (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  1209836).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  This study was financed in part by the Conselho Na-  cional de Desenvolvimento Cient´ıfico e Tecnol´ogico –  Brasil (CNPq) – Research Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  150410/2022-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  It is a great pleasure to thank the Theoretical As-  trophysics at T¨ubingen (TAT Group) for its hospitality  and technical support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' acknowledges financial sup-  port provided under the European Union’s H2020 ERC,  Starting Grant agreement no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' DarkGRA–757480 and the  MIUR PRIN and FARE programmes (GW-NEXT, CUP:  B84I20000100001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (LIGO Scientific, Virgo), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 116, 061102 (2016), arXiv:1602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='03837 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [2] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (LIGO Scientific, Virgo), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 116, 221101 (2016), [Erratum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 121,  129902 (2018)], arXiv:1602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='03841 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [3] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (LIGO Scientific, Virgo), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 119, 141101 (2017), arXiv:1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='09660 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (LIGO Scientific, Virgo), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 125, 101102 (2020), arXiv:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='01075 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [5] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (LIGO Scientific, Virgo), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D  102, 043015 (2020), arXiv:2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='08342 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='HE].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [6] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (LIGO Scientific, Virgo), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D  103, 122002 (2021), arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='14529 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [7] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (LIGO Scientific, VIRGO, KAGRA),  (2021), arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='03606 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' (LIGO Scientific, Virgo), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 119, 161101 (2017), arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='05832 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [9] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Berti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=', Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 32, 243001 (2015),  arXiv:1501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07274 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Barack et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=', Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 36, 143001 (2019),  arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='05195 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [11] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Suvorov, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Kokkotas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 102, 064041 (2020), arXiv:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='00028 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [12] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Suvorov, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Kokkotas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 126, 141102 (2021), arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='05643 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Kokkotas and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Schmidt, Living Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 2,  2 (1999), arXiv:gr-qc/9909058.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [14] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Berti, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Starinets, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 26, 163001 (2009), arXiv:0905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='2975 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [15] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Konoplya and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Zhidenko, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 83,  793 (2011), arXiv:1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='4014 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Hawking, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 43, 199 (1975),  [Erratum: Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 46, 206 (1976)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Brito, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso,  and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Pani, Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Notes Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  906, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1 (2015), arXiv:1501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='06570 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Penrose and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Floyd, Nature 229, 177 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Bekenstein, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 7, 949 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [20] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Costa,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Hintz,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Jansen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 98, 104007 (2018),  arXiv:1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='03631 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [21] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Destounis,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  D  100,  044054  (2019),  arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='06117 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [22] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mascher, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis,  and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Kokkotas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 105, 084052 (2022), arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='05335 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [23] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mascher,  and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Kokkotas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 105, 124058 (2022), arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07794 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
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+page_content=' Isi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Giesler, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Farr, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Scheel,  and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Teukolsky, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 123, 111102 (2019),  arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='00869 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Giesler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Isi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Scheel, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Teukolsky, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' X 9, 041060 (2019), arXiv:1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='08284 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cotesta, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Carullo, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Berti, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 129, 111102 (2022), arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='00822 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cheung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=', (2022), arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07374 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lagos and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Hui, (2022), arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07379 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [29] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mitman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=', (2022), arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07380 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [30] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Kehagias, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Perrone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Riotto, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Riva, (2023),  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='09345 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [31] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Jaramillo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Panosso Macedo, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Al Sheikh,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' X 11, 031003 (2021), arXiv:2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='06434 [gr-  qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Jaramillo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Panosso Macedo, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Sheikh,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 128, 211102 (2022), arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='03451  [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [33] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Macedo, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Berti, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Jaramillo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 104, 084091 (2021),  arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='09673 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [34] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Gasperin and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Jaramillo, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 39,  115010 (2022), arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='12865 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [35] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Boyanov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Panosso Macedo, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Car-  doso, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Jaramillo, (2022), arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='12950 [gr-  qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [36] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Berti, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cheung, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Di Filippo,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Duque, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Martens, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mukohyama, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  D 106, 084011 (2022), arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='08547 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [37] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Jaramillo, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 39, 217002 (2022),  arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='08025 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [38] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Konoplya  and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Zhidenko,  (2022),  arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='00679 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Visser, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 15, 1767 (1998), arXiv:gr-  qc/9712010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [40] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Barcelo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Liberati, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Visser, Living Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  13  8, 12 (2005), arXiv:gr-qc/0505065.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [41] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Unruh, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 46, 1351 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [42] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Weinfurtner, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Tedford, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Penrice, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Unruh,  and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lawrence, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 106,  021302 (2011), arXiv:1008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1911 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [43] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Richartz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Prain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Liberati, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Weinfurtner,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 91, 124018 (2015), arXiv:1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1662 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [44] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Coutant, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Richartz,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' We-  infurtner,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  117,  271101  (2016),  arXiv:1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='01378 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [45] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Torres, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Patrick, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Coutant, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Richartz, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Tedford,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Weinfurtner, Nature Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 13, 833  (2017), arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='06180 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [46] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Patrick, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Coutant, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Richartz, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Weinfurtner,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 121, 061101 (2018), arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='08473  [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Patrick, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Goodhew, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Gooding,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' We-  infurtner,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  126,  041105  (2021),  arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='03045 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [48] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Torres, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Patrick, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Richartz, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Weinfurtner,  Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 36, 194002 (2019), arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='00356  [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [49] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Torres, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Patrick, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Richartz, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Weinfurtner,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 125, 011301 (2020), arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07858  [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [50] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Garay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Anglin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cirac, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Zoller, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A 63, 023611 (2001), arXiv:gr-qc/0005131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [51] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Steinhauer,  Nature  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  10,  864  (2014),  arXiv:1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='6550 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='quant-gas].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [52] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mu˜noz de Nova, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Golubkov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Kolobov, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Steinhauer, Nature 569, 688 (2019), arXiv:1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='00913  [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [53] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Gooding, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Biermann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Erne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Louko, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Un-  ruh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Schmiedmayer,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Weinfurtner, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 125, 213603 (2020), arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07160 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [54] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Drori, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rosenberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Bermudez, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Silberberg,  and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Leonhardt, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 122, 010404 (2019),  arXiv:1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='09244 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [55] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Ornigotti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Bar-Ad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Szameit,  and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Fleu-  rov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A 97, 013823 (2018), arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07609  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='optics].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [56] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Richartz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Prain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Weinfurtner, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Liberati,  Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 30, 085009 (2013), arXiv:1208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3601  [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [57] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Ciszak and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Marino, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 103, 045004  (2021), arXiv:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='07508 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [58] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Liao, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' van der Wurff, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' van Oosten,  and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Stoof, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' A 99, 023850 (2019),  arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='00023 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='quant-gas].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [59] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Tangherlini, Nuovo Cim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 27, 636 (1963).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [60] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Torres del Castillo, Revista Mexicana de F´ısica  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [61] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Frye and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Efthimiou, (2012), arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='3548  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='CA].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [62] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Hyers, The Functions of Mathematical Physics  (Harry Hochstadt), Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 15 (Society for Industrial and  Applied Mathematics, USA, 1973) p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 235–236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [63] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Jansen,  Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Plus  132,  546  (2017),  arXiv:1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='09178 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [64] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lin and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Qian, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 34, 095004  (2017), arXiv:1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='08135 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [65] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lin and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Qian, Chin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' C 43, 035105 (2019),  arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='08352 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [66] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Iyer and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Will, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 35, 3621 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [67] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Iyer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 35, 3632 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [68] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lemos, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Yoshida, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  D 69, 044004 (2004), arXiv:gr-qc/0309112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [69] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Miranda,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Berti,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Witek,  and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Zanchin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 79, 064016 (2009),  arXiv:0812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1806 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [70] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Vieira and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Bezerra, Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 373, 28  (2016), arXiv:1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='02233 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [71] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Vieira and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Kokkotas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 104,  024035 (2021), arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='03938 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [72] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Ronveaux, Heun’s Differential Equations (Oxford Uni-  versity Press, New York, 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [73] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Wang and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Ge, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 102, 104009  (2020), arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='05285 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [74] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Ge, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Nakahara, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Sin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Tian,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Wu, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 99, 104047 (2019), arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='11126  [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [75] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Gross, Nuovo Cimento (Italy) Divided into Nuovo  Cimento A and Nuovo Cimento B 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='1007/BF02731494.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [76] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Pitaevskii, Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' JETP 13, 451 (1961).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [77] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Cardoso, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Costa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Hintz,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Jansen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' 120, 031103 (2018),  arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='10502 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [78] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Destounis,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  B  795,  211  (2019),  arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='10629 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [79] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Liu,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Tang,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Wang,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Pa-  pantonopoulos,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Zhang, JHEP 03, 187 (2019),  arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='01865 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [80] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Fontana, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mena, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Pa-  pantonopoulos, JHEP 10, 280 (2019), arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='09842  [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [81] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Fontana, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mena, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 102, 044005 (2020), arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='03028 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  [82] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Destounis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Fontana, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' Mena, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content=' D 102, 104037 (2020), arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
+page_content='01152 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNFJT4oBgHgl3EQfOCw1/content/2301.11480v1.pdf'}
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+1
+Large Scale Qualitative Evaluation of Generative Image
+Model Outputs
+Yannick Assogba, Adam Pearce and Madison Elliott
+Abstract—Evaluating generative image models remains a difficult problem. This is due to the high dimensionality of the outputs, the
+challenging task of representing but not replicating training data, and the lack of metrics that fully correspond to human perception and
+capture all the properties we want these models to exhibit. Therefore, qualitative evaluation of model outputs is an important part of
+model development and research publication practice. Quantitative evaluation is currently under-served by existing tools, which do not
+easily facilitate structured exploration of a large number of examples across the latent space of the model. To address this issue, we
+present Ravel, a visual analytics system that enables qualitative evaluation of model outputs on the order of hundreds of thousands of
+images. Ravel allows users to discover phenomena such as mode collapse, and find areas of training data that the model has failed to
+capture. It allows users to evaluate both quality and diversity of generated images in comparison to real images or to the output of
+another model that serves as a baseline. Our paper describes three case studies demonstrating the key insights made possible with
+Ravel, supported by a domain expert user study.
+Index Terms—Information visualization, Picture/Image Generation, Machine learning
+!
+1
+INTRODUCTION
+Generative image models are a class of neural network
+based models that aim to produce novel, high-quality and
+diverse images that faithfully model a target image distribu-
+tion. A variety of architectures and training methods have been
+designed to learn such models, such as Generative Adversarial
+Networks (GANs) [1], Variational Auto-Encoders (VAEs) [2],
+Flow Based Models [3] and Diffusion Models [4].
+Evaluating these models remains difficult [5]. The high
+dimensionality of the output architectures used make likeli-
+hood estimates of model outputs difficult, and in some cases
+intractable. It has also been demonstrated that measures like
+average log likelihood do not always correlate with human
+perceptual judgments of sample quality [6]. Additionally, while
+we want models to capture the target distribution well, we
+do not want them to produce images that are actually in the
+training set (an issue commonly referred to as memorization).
+A number of metrics have emerged in the literature around
+generative image models [7] [8], with Fr´echet Inception Dis-
+tance (FID) [9] being the most popular. However, issues have
+been identified with FID, leading to the development of more
+granular metrics such as precision and recall [10] [11].
+Single-number metrics such as FID, while necessary for
+forward progress in the field, do not capture the full range
+of qualities desired of these models. Because of this, human
+visual inspection often plays a critical role in the evaluation
+and dissemination of advances in generative image modeling.
+However with existing evaluation tools, practitioners can typi-
+cally only look at a small fraction of the output space of these
+models, on the order of 10s to 100s of images (e.g., [12], [13],
+[14], [15], [16]).
+Our interviews with domain experts confirm that human
+evaluation is a critical part of practitioner workflows. Some ex-
+perts rely on human evaluation with crowd-sourced evaluators,
+they however recognize that these are often expensive or time
+consuming and are thus left to the final stages of evaluation
+•
+Yannick Assogba, Adam Pearce and Madison Elliot are with Google
+Research.
+E-mail: {yassogba,adampearce,madisone}@google.com
+if done at all, leaving them to primarily rely on small scale
+qualitative evaluation during the model development process.
+At the same time, experts in the field are concerned about
+cherry picking of results for publication but typically have no
+means to expansively explore model outputs in the rare occa-
+sions that these are published alongside academic manuscripts.
+To address these needs, we built a system called Ravel,
+which enables users to perform visual inspection of model
+outputs on scales up to three orders of magnitude greater that
+typical user workflows. We demonstrate usage of this system
+on datasets varying from 50k - 120k images. These dataset sizes
+are comparable to those used in standard quantitative evaluation
+of generative image models.
+Our primary contributions include:
+•
+A visual analytics system that supports multiple evalua-
+tion tasks (e.g. evaluating quality & diversity, discovering
+mode collapse or gaps in model output) for generative
+image models and is agnostic to model architecture and
+internals.
+•
+Interactive exploration of large generative image model
+datasets, facilitated by clustering and the use of fine
+grained visualization of cluster metrics to guide quali-
+tative evaluation.
+•
+A user interface that uses visual comparison driven by
+semantically meaningful embedding spaces to support
+reasoning about differences between image distributions
+and generate hypotheses about model behaviour.
+2
+BACKGROUND
+2.1
+Generative Image Models
+The capabilities of generative image models have greatly in-
+creased over the last several years. Since the original GAN
+paper [1] that broke the dam on modelling of faces, we now
+have systems like BigGAN [12], StyleGAN [13], GLOW [14],
+VQ-VAE [15], CDM [16] and many others that present a wide
+variety of model architecture and training algorithms and are
+capable of producing very realistic images in a wide variety of
+domains.
+arXiv:2301.04518v1  [cs.HC]  11 Jan 2023
+
+2
+2.2
+Quantitative Metrics for Evaluating Generative Image
+Models
+In this section, we outline the most commonly cited metrics in
+the research literature:
+•
+Fr´echet Inception Distance [9]: Uses a pre-trained In-
+ceptionV3 classifier [17] to generate embeddings for
+both real and generated images, then uses a statistical
+measure to compare the distribution of embeddings
+from the two sources. FID is the most popular metric
+in the literature. It requires a large number of samples
+to produce an accurate estimate (generally at least 50k
+generated images), and cannot detect memorization of
+the training set. Karras et al [18] point out that the
+texture bias in ImageNet based CNNs like InceptionV3
+[19] imply that metrics derived from them will not
+capture all aspects of image quality.
+•
+Inception Score [20]: Uses a pre-trained inception clas-
+sifier to measure, a) how well each generated image
+matches a single ImageNet class, and b) if the full the
+set of generated images has uniform coverage over all
+the ImageNet classes. Similar to FID, Inception Score
+requires a fairly large number of images and cannot
+be used to detect memorization. It also cannot measure
+intra-class diversity or detect mode collapse. See Barrat
+and Sharma [21] for a detailed discussion of issues
+with this metric. Both Inception Score and FID are
+scalar scores designed to capture both image quality and
+diversity, and thus cannot reveal if the model is trading
+off one of these properties for the other to achieve a
+better score.
+•
+Precision and Recall Metrics: To disentangle the mea-
+surement of image quality and diversity, Sajjadi et al
+[10] and Kynk¨a¨anniemi et al [11] propose precision and
+recall metrics to measure each independently. Broadly
+speaking, precision corresponds to the sample quality,
+whereas recall corresponds to the coverage of the sample
+distribution with respect to the target distribution - i.e.
+diversity.
+These metrics are generally computed over the entire dataset,
+and thus have low granularity. Even when they indicate that
+a model is better or worse, they don’t specify where in the
+distribution of generated images improvements or regressions
+lie. Ravel increases the granularity of these metrics, providing
+a way to find specific clusters of images that score poorly on
+some metric
+2.3
+Qualitative Evaluation / Visualization of Generative Im-
+age Model Outputs
+Due to the limitations of quantitative metrics discussed above,
+researchers also rely on visual inspection of model outputs
+to evaluate model performance. Visual inspection is typically
+performed during training, to monitor that the process has
+not immediately failed, as well as after training, to evaluate
+overall quality of the model. We validate and elaborate on
+this workflow and strategy with domain experts in Section 6.1.
+Although models often output 100s of thousands of images,
+our user study found that researchers are only able to inspect a
+small portion of images (in the 100s) during their analyses.
+Visually impressive samples are paramount for successfully
+publishing model advancements in scientific venues. Relevant
+papers in the field of generative image models typically include
+10s-100s of images [12] [13] [18] [22]. This represents a very
+limited sample of the variety of images these models are typi-
+cally trained to generate. Our user study also found that there
+is an assumption that authors ”cherry-pick” the best images
+to include in their publications. Relatively few authors have
+published large datasets of un-cherry-picked output images
+alongside their publications.
+There are currently no purpose-built interfaces that make
+these convenient to browse or examine. For example, [13] [18]
+each publish 100k output images to a publicly accessible Google
+drive. These images are organized into 1000 sub-folders to
+make the interface more usable given the large number of files.
+To view this output, users must either click through the folders
+individually, or bring their own interface to browse the images.
+3
+RELATED WORK
+Borji [7] [8] catalogues many of the metrics for automatic
+evaluation of generative models. Ravel utilizes the precision
+and recall metrics from [10] and [11], but does not propose any
+new metrics. We thus situate this work in primarily relation
+to work on qualitative evaluation and interfaces to explore
+generative model output.
+Crowd-worker Evaluation
+Denton et al. [23] use a small volunteer sample of human
+annotators to estimate quality by asking whether they can
+distinguish real from generated images. Zhou et al. [24] refine
+and scale this technique, asking crowd-sourced workers from
+Amazon’s Mechanical Turk to make psychophysical judgments
+about real vs. generated images. While these methods are
+good at scaling up evaluation to larger dataset sizes, they are
+more time-consuming and expensive than manual inspection
+by researchers. Thus they are typically reserved for later stages
+of the evaluation pipeline. They also tend to focus on measures
+that can be evaluated on individual images (e.g. image quality),
+rather that corpus level properties (such as image diversity).
+By contrast, Ravel is designed to support researcher evalu-
+ation earlier in the development pipeline before the use of external
+raters, and allows researchers to evaluate both quality and diver-
+sity in the same interface. It fits in between initial monitoring of
+training dynamics to ensure that the model is converging and
+larger scale human rater evaluation typically performed closer
+to model release.
+Explaining Model Internals
+Bau et al. [25] explore finding interpretable units (neurons)
+within GANs and visualizing the causal effects of ablating these
+neurons. Their method depends on having access to model
+internals and having a pre-trained object segmentation network
+to find objects within the scene to establish the casual relation-
+ship between neuron activation and network output. [26] Bau
+et al. use a pre-trained segmentation network to compare the
+distribution of objects found in generated images with those
+found in a set of real images. This provides a measure of
+diversity of the models outputs with respect to the objects that
+can be segmented by the pre-trained network. The authors also
+propose a method (Layer Inversion), to train networks that
+compute approximate inversions of real images into the latent
+space of the model, to see what the network generates instead
+of the missing objects.
+While these approaches are critical to better understanding
+of the internal mechanisms that drive model behavior, they
+are typically specific to a particular model architecture. Ravel
+treats models as black boxes and is thus agnostic to model
+architecture. Ravel does use pre-trained networks to compute
+vector representations of images, but is less sensitive to the
+final task the pre-trained network is trained to perform. For
+
+3
+example one could use the embeddings from the model under
+examination or any model that has learned semantically useful
+features such as InceptionV3.
+Online Exploration of Model Outputs
+White [27] explores a variety of ways to sample images from
+latent space that enable repeatable visual comparisons between
+models. They introduce a number of visualizations designed
+to examine how models perform with respect to specific input
+images that are used to test model behaviour. In a follow-
+up work White & Loh [28] introduce a novel visual interface
+based on a spreadsheet metaphor that allows users to use
+geometric operations in the latent space to interactively query
+these models and thus explore their output.
+While online methods enable users to explore specific hy-
+potheses, they generally suffer from supporting relatively small
+exploration spaces due to the slow generation of images. Ravel
+focuses on offline analysis of generated images, which allows
+examining much larger datasets and can thus complement
+online methods as means of generating hypotheses for further,
+more targeted investigation.
+Embedding Based Visualizations
+A number of works have visualized embedding spaces of
+large, high-dimensional datasets [29] [30] [31] [32].
+Liu et al. [33] present a visual analysis system which uses the
+latent space learned by the encoder of a VAE to explore variation
+in an existing image dataset. This task is conceptually similar to
+what we support in Ravel, however we do not attempt to learn
+a new latent space as we want to focus on the generator output
+and its latent space (rather than fixed input data).
+Ravel builds on these earlier works visualizing embedding
+spaces, and incorporates clustering to make navigating these
+spaces more tractable. We focus on dataset comparison as a
+way to ground exploration of the output space and cater to the
+needs of the image generation use case.
+Xiang et al. [34] present a visual analytics system for
+correcting labelling errors in large datasets. They visualize t-
+SNE projections of image embeddings color coded by label to
+highlight data points that are mislabelled. In contrast, Ravel is
+designed to support unconditional generation scenarios, where
+the generated (and ground truth images) have no labels. Thus,
+rather than relying on labels for grounding, Ravel enables com-
+parative evaluation of datasets to allow grounding evaluation
+of generated images in the distribution of real images.
+4
+APPROACH & SYSTEM DESIGN
+Ravel focuses on enabling visual inspection of model outputs
+in comparison with some baseline set of images, typically
+real ’ground truth’ images. From our interviews (section 6.1),
+we know that practitioners perform visual analysis of image
+samples coming out of models, but typically on small numbers
+of images. Our aim is to support and scale up those workflows to
+allow more systematic visual inspection from 10s or 100s of images to
+10,000s or 100,000s of images. We leverage four key concepts to
+facilitate this comparison across a large set of images:
+1)
+Image Embeddings: Neural image embeddings pro-
+vide a semantically rich vector space for images that
+allow computing similarity scores between pairs of im-
+ages [35]. They have become the standard in evaluation
+pipelines for generative image models (section 4.1.2)
+and we want to leverage the familiarity researchers
+have with embedding based metrics in Ravel. The abil-
+ity to compute semantic similarity between images al-
+lows us to group similar generated images together and
+allow comparison of those images to similar ground
+truth images. By default we compute the standard In-
+ceptionV3 embeddings used in metrics like FID, but can
+also add embeddings from other models including pre-
+trained models or from the model under examination if
+those are available.
+2)
+Clustering Images: In order to enable visual explo-
+ration of hundreds of thousands of images we need
+to group them into a smaller number of meaningful
+groups. We use unsupervised clustering of images to
+reduce the number of top-level items the user has to
+consider from e.g. 100k images to 1000, 500 or even 250
+clusters. We use k-means clustering and provide more
+details about this in the pipeline details section below
+3)
+Cluster Metrics: Once we have reduced the number of
+top-level elements to a manageable number we wish to
+provide hints to the user as to which clusters might be
+most interesting to explore first, as well as scaffold a
+repeatable workflow that can guide exploration. We
+compute metrics over each cluster that enable sorting
+clusters into predictable order. Many of the metrics we
+compute are designed to surface differences between
+the generated data and the baseline data in a cluster,
+with others show general properties of the cluster itself.
+We provide more details about the metrics we compute
+in the pipeline details section below. By sorting clusters
+by these metrics we allow discovery of outlier clusters
+as well as analyzing properties of different parts of
+the generative image space (e.g. seeing what kinds of
+output images have low precision)
+4)
+Interactive Visualization: Finally we provide respon-
+sive interactive visualization of images, clusters and
+associated cluster metrics. Because we compute all the
+data offline, the user interface is quite responsive and
+enable fast and free exploration of a large number of
+data-points.
+4.1
+Pipeline Details
+4.1.1
+Clustering
+Ravel clusters the image embeddings using the implementa-
+tion of k-means clustering from scikit-learn. k-means was an
+attractive clustering algorithm to start with because it is a well
+known algorithm that has a single easily understood hyper-
+parameter, namely the number of clusters. This allows the user
+to directly specify values for this hyper-parameter that they believe
+make sense for their dataset. In addition to this, compared to
+other algorithms with similar hyper parameter options such
+as spectral clustering, k-means scales well with the number of
+examples and number of clusters selected [36]. k-means also
+tends to produce fairly evenly sized clusters, which is helpful
+for displaying their contents in a uniform way.
+All clustering methods suffer from issues of imperfect
+cluster assignment, particularly at the boundaries of clusters.
+However, Ravel mitigates this issue somewhat by visualizing
+clusters according to their positions in latent space. This allows
+users to quickly discover and examine clusters that are near
+to each other and ascertain whether they are truly a single se-
+mantic cluster. For more details see the dimensionality reduction
+section (4.1.3) below.
+4.1.2
+Cluster Metrics
+We compute a number of metrics for each cluster. Having
+multiple metrics provides different lenses through which to
+consider the clusters. For example one might be interested in
+
+4
+Fig. 1. The Ravel interface primarily consists of: A) Dataset & view options. B) Summary charts & linked cluster plots. C) Side by side image grids
+for visual comparison of clusters. This view shows a cluster comparing real images on the left to generated images on the right.
+where recall or precision are low, or alternatively where clusters
+are tightly packed or more spread out.
+Clusters may have images from either the generated data
+or the baseline/ground truth, in the UI we refer to these data
+sources as splits and typically display the baseline data on the left,
+though the user can change this interactively. Many metrics are
+geared toward exposing differences between the two splits that
+are currently being explored.
+•
+Percent of Split 2: The percentage of images in the
+cluster that come from the split displayed on the right
+(usually the generated data).
+•
+Recall: Recall is a metric that describes what fraction
+of samples in the ground truth split have support in the
+alternate split. We compute recall as defined in [11] but
+aggregate the per-image values for each cluster. When
+comparing generated images to real ones a high recall
+implies the model is producing images as diverse as the
+real data.
+•
+Precision: Precision is an metric that describes what
+fraction of samples in the generated data have support
+in the ground truth. As above we compute precision
+as defined in [11] but aggregate the per-image values
+for each cluster. When comparing generated images to
+real ones a high precision implies better image qual-
+ity/realism.
+•
+Distance between split centroids: Measures the dis-
+tance between centroids of the samples in a cluster that
+belong to each split. Larger values suggest that the data
+from the two splits are more visually different while
+smaller values suggest that the left and right split are
+more visually similar.
+•
+Median distance to centroid: Median distance of sam-
+ples in the cluster to the centroid of that cluster. Smaller
+values here imply more compact clusters with more
+similar samples, higher values suggest the cluster has
+a greater variety of images.
+4.1.3
+Dimensionality Reduction
+In addition to visualizing clusters by the metrics described
+above, we also visualize the positions of cluster centroids in
+the embedding space itself. Since these are high dimensional
+embeddings spaces we need to use dimensionality reduction in
+order to visualize them in 2D. We use the UMAP algorithm
+[37] to do this projection. Other options for dimensionality
+reduction include PCA [38] or t-SNE [39]. Compared to t-
+SNE, UMAP has been reported to preserve more of the global
+structure of the original space and is significantly more compu-
+tationally efficient both as the number of dimensions increases
+and as the size of the dataset grows [37] [40]. The InceptionV3
+embedding we use is 2048 dimensional embedding, making a
+computationally efficient method particularly attractive. While
+not as directly interpretable as linear methods like PCA, UMAP
+is better able to capture some of the complex non-linear rela-
+tionships between images encoded in the embedding space.
+4.2
+User Interface
+The user interface is a browser-based application. We describe
+the design of the user interface and further discuss the utility
+of these affordances in the case study section.
+Figure 1 shows the Ravel interface, divided into 3 main
+sections:
+
+DATA
+EMBEDDING
+N CLUSTERS
+A
+SPLIT1
+SPLIT 2
+SAMPLE VIEW
+Update
+inception_pool_3
+500
+ImageNet 128 Eval
+BigGAN 128, 1.0 truncation
+Grid
+56 Samples
+50 Samples
+c
+Dataset Stats
+B
+Samples
+100000
+nples in ImageNet128Eval
+50000
+SamplesinBigGAN128,1.0truncation
+50000
+FrechetDistance
+8.08
+Recall
+0.378
+Precision
+0.726
+70) harvestman,_ 309) bee
+309) bee
+309) bee
+09Q (606
+320) damselly
+985) daisy
+985) daisy
+985) dalsy
+985) daisy
+As)ep (s86
+935) dalsy
+Highlight Classes
+Cluster Metrics
+PercentofSplit2(BigGAN128,1.0truncation)
+658) mitten
+658) mitten
+658) mitten
+850) teddy, teddy_985) daisy
+ks)ep (s86
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+Recall with'lmageNet 128 Eval'as ground truth
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+Asep (S85
+985) daisy
+985) daisy
+985) daisy
+985) dalsy
+As)ep (s86
+ks)ep (s86
+985) daisy
+0.2
+0.6
+0.8
+Precisionwith'imageNet128Evalasgroundtruth
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+As)ep (S86
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+0
+0.2
+0.4
+0.6
+0.8
+Median Distanceto Centroid
+985) daisy
+985) daisy
+985) daisy985) daisy
+Asep(585
+985) daisy
+XsJep (S85
+985) daisy
+985) dalsy
+985) dalisy
+sep (S86
+985) dalsy
+Distance between Split Centroids
+ClustersUMAP
+985) daisy
+Ase(s86
+985) daisy
+985) daisy
+985) daisy
+985) daisy
+sJep (S85
+ks)ep (S86
+sjep (s86
+985) daisy
+985) daisy
+ksjep (s86
+985) daisy
+As)ep (s86
+935) daisy
+985) dalsy
+Asep (s85
+985) daisy
+985) daisy
+985) daisy
+985) dalsy
+985) daisy
+985) daisy
+W
+As)ep ($86
+985) daisy985) daisy
+985) daisy985) daisy
+985) daisy
+ks)ep (s86
+985) dalsy
+985) daisy
+AsI8p (S86
+985) daisy
+Ksjep (585
+Ksep (s86
+985) dalsy
+985) dalisy
+985) daisy
+As)ep (s86
+As)ep (S85
+985) daisy5
+4.2.1
+(A): Dataset and View Controls
+The user can select which embedding to use, the number of
+clusters and which split to show on the left or right.
+4.2.2
+(B): Charts
+There are three main kinds of data display in the charts section
+of the UI.
+Summary Statistics
+First is a static table showing summary statistics and metrics
+for the dataset as a whole. These include things like the number
+of samples in the whole dataset, the number of samples in each
+split as well as dataset level metrics such as Fr´echet distance1,
+recall and precision [11].
+Cluster Metric Plots
+Below the summary charts are a series of beeswarm plots for
+the per-cluster metrics that were computed (see Cluster Metrics
+section above for details). Each beeswarm shows each cluster
+as a dot and plots the distribution of clusters over that metric.
+These charts are interactive, individual dots can be selected to
+show the images from that cluster in the sample viewer.
+Fig. 2. Beeswarm plot showing distribution of cluster precision scores.
+Each dot is a cluster which the currently selected dot shown in orange.
+A description of the metric can be accessed by clicking on the ? icon.
+A color encoding can also be applied by clicking on the
+rainbow icon toggle next to that plot. This color encoding is
+applied across all charts allowing comparison of one metric to
+another (Figure 3).
+Fig. 3. Recall and Precision beeswarm plots colored by precision score.
+High recall, low precision clusters can be identified using the position
+encoding in the recall plot and the color encoding applied from the
+precision plot. To save space in the display we do not display a legend,
+as the relationship between high-low values and hue is directly visible in
+the chart whose rainbow icon was toggled and exact values are of less
+importance than relative comparisons
+UMAP Plots
+1. When using the Inceptionv3 embedding this is Fr´echet Inception
+Distance (FID)
+Below the beeswarm plots are two plots showing 2D UMAP
+projections of: a) all the clusters and b) images from the currently
+selected cluster (See Figure 4). The Cluster UMAP view in
+particular allows browsing clusters by visual similarity rather
+than by the metric scores. Previews of individual images are
+shown on mouseover of points on the Samples UMAP plot
+Fig. 4. Top: UMAP projection of cluster centroids in embedding space.
+Bottom: UMAP projection of currently selected cluster, real samples are
+shown in blue and generated samples are show in red
+Highlight Classes
+In cases where the dataset does contain class labels, Ravel
+will display a search interface that allows users to search for
+and select any number of matching classes in the dataset.
+If one or more classes is selected Ravel will dim clusters
+that do not contain any images from those classes in the cluster
+plots (5).
+All the cluster plot interactions are linked, enabling users to
+see where a cluster falls in multiple metrics or in embedding
+space.
+Any chart can be collapsed by by clicking on its title, this
+allows making more room for the charts the user finds most
+useful for their analysis.
+4.2.3
+Sample Viewer
+To the right of the charts is the sample viewer. This consists of a
+pair of scrollable views displaying image thumbnails from the
+selected cluster divided by split. If there are classes/labels asso-
+ciated with the images they are displayed below the thumbnail
+and images from the same class are grouped together, otherwise
+they are displayed in the order they were processed by the
+pipeline (effectively random). Users can click on images to get
+a larger view of the image and see any additional metadata.
+Image thumbnails are displayed at a maximum size of
+150x150px and a minimum size of 100x100px depending on
+
+Precision with 'lmageNet 128 Eval' as ground truth
+0.2
+0.4
+0.6
+0.8Recall with 'lmageNet 128 Eval' as ground truth
+0.2
+0.4
+0.6
+0.8
+Precision with 'lmageNet 128 Eval' as ground truth
+0.2
+0.4
+0.6
+0.8Clusters UMAP
+Samples UMAP6
+Fig. 5. Clusters containing at least one image with the selected classes
+are highlighted in all cluster plots.
+how large the browser window is. On a 3840 x 2160 resolution
+display2 one can typically see 72 images per split for a total of
+144 images in a single screenful. However one clear limitation
+is that if there are more images than this in a cluster a user
+cannot see them all at once and does have to scroll through to
+get a better understanding of the cluster. One way to mitigate
+this is to use choose a higher number of clusters to view. Which
+results in smaller, more granular clusters, at the cost of having
+more to explore.
+5
+CASE STUDIES
+In this section, we illustrate how the design features of Ravel
+support user exploration in a series of case studies. These case
+studies highlight discoveries the authors made when using the
+tool. Our 3 use cases are: 1) Unconditional image generation in
+a single domain (faces), 2) Class conditioned generation on Im-
+ageNet data and 3) Analyzing downstream use of a generative
+model for another task - in this case, super-resolution.
+While Ravel supports the use of multiple embeddings for
+clustering and exploration, in this paper we focus primarily on
+the same Inceptionv3 embeddings used in FID score and other metrics,
+as they have become a de-facto standard in the generative
+model space and are publicly available.
+5.0.1
+Unconditional Image Generation
+Unconditional generation refers to situations where a trained
+model is used to generate images with no ’conditioning’ other
+than an input vector (often referred to as a ’noise’ or ’Z’ vector)
+drawn from a random distribution. In this case study, we
+generate 60k images from an implementation of the StyleGAN2
+architecture 3 [18] trained on the FFHQ dataset. The images are
+2. This resolution is the default 4K resolution which is widely avail-
+able. It is also close to the native resolution of a 2021 14 inch MacBook
+Pro (3024 x 1964)
+3. We want to make clear that we are using an independently trained
+StyleGAN2 and not the StyleGAN2 weights released by the original
+authors
+Fig. 6. The StyleGAN2-based model struggles to model images of
+faces with facepaint and other colorful accessories occluding the face, it
+instead produces these artefacts.
+generated using Z vectors drawn from a random distribution
+with a mean of zero and a standard deviation of one. We load
+those images, along with 67,542 images from the training set
+for a total of 127,542 images.
+Are there images that this model generates that are not part
+of the input distribution?
+Our analyst opens the Ravel interface in her browser and
+sets the number of clusters to 250, with images from the training
+data on the left and generated images on the right. Knowing
+that low precision generally implies less realistic images, she
+begins by exploring clusters on the low end of the precision
+chart and notes that the clusters with the 10 lowest values
+each contain generated images with visually obvious defects.
+Seeing these images contrasted with ground truth data gives
+her a sense of what the model is struggling to capture in each
+category. For example she notes that the model has a difficult
+time modeling complex backgrounds, portraits where there are
+more than one face, or portraits with occluding objects like
+hands or microphones. Another problem that stands out to her
+is the difficulty the model has generating faces with face-paint
+as in Figure 6. Seeing these corrupted images juxtaposed with
+real images from the training data allows her to hypothesize
+why the model struggles with this, in particularly she observes
+that these types of images are relatively rare in the training
+data.
+In examining 10 clusters, she has quickly scanned through
+approximately 4234 generated images and 2718 real images.
+5.0.2
+Class Conditioned Image Generation
+Class conditioned generation refers to models that have been
+trained to generate output images for a fixed set of distinct
+classes. Here, we look at directly comparing the output of two
+models trained on the same data and task: namely, generating
+images from 1000 classes of the ImageNet dataset [41] at a
+resolution of 128x128px. We use model implementations from
+Lucic et al’s ”Are GANs Created Equal? A Large-Scale Study”
+[42].
+We set up a Ravel instance with 50k images generated by
+BigGAN 128 and BigGAN-deep 128 [12], and 50k images from
+
+Highlight Classes
+Select allSelect none
+Filter Class List
+SelectedClasses
+117)chambered nautilus,pearlynautilus,nautilus
+685) odometer, hodometer,mileometer,milometer
+√715)pickelhaube
+810)spacebar
+878)typewriterkeyboard
+946)cardoon
+984) rapeseed
+Cluster Metrics
+Percent of Split2 (BigGANDeep128,1.0truncation)
+0%
+20%
+40%
+60%
+80%
+100%
+RecallwithBiqGAN 128,1.0truncation'as ground truth
+?
+0
+0.2
+0.4
+0.6 
+0.87
+the validation set for ImageNet4. Input vectors for each model
+are drawn from a random normal distribution, as described in
+[42], and no truncation is applied to the input vectors.
+Using these models demonstrates a workflow where re-
+searchers are trying to determine how one variant of a model, or
+an improved model architecture, behaves differently from some
+baseline model. This comparison is a common workflow in
+machine learning, typically achieved by reporting performance
+on key metrics such as FID. We demonstrate how Ravel can
+complement traditional metrics to find specific differences in
+model behaviour.
+Fig. 7. Mode collapse of the ”space bar” and ”typewriter keyboard”
+classes in the BigGAN-deep model. All 100 images in this cluster look
+identical as both classes have collapsed onto the same output.
+Fig. 8. Output of the ”space bar” and ”typewriter keyboard” classes in
+BigGAN show much more variety. This model does not exhibit mode
+collapse for these classes
+How does BigGAN compare to BigGAN-deep in terms of
+diversity of output
+Our analyst opens Ravel and sets the number of clusters to
+500, with the left split showing output from BigGAN, and the
+right split showing output from BigGAN-deep.
+It immediately jumps out to him that there are a number
+of clusters that have scores of 0 in the recall chart. He clicks
+4. Data retrived from https://www.tensorflow.org/datasets/ cata-
+log/imagenet2012
+on one of them and discovers it only contains images from
+BigGAN-deep. All 100 images from this model are from two
+classes, appear virtually identical, and are of low visual quality
+(see Figure 7). This is a classic case of mode collapse [43];
+the model was unable to learn the true distribution for these
+classes and has ’collapsed’ all output for these classes to a
+single image. In this case, both classes have been collapsed into
+the same output image. The analyst clicks on other clusters
+with zero recall and finds similar mode collapse in BigGAN-
+deep for the following classes: ”space bar”, ”typewriter keyboard”,
+”pickelhaube”, ”rapeseed”, ”cardoon”, ”chambered nautilus, pearly
+nautilus, nautilus”, and ”odometer”.
+Using the ”highlight classes” feature of Ravel 5, our analyst
+is able to find all clusters that contain images from these classes,
+and confirms that the BigGAN model does not show mode
+collapse for these classes (Figure 8).
+What about classes where both models do okay at gen-
+eration (i.e. neither model exhibits a pathological failure like
+mode collapse)?
+Our analyst now chooses to increase the granularity of
+clusters by setting the number of clusters to 1000. He turns
+on the color by option of the precision chart, and then looks at
+the recall chart to find clusters with high recall but relatively
+low precision (though not as low as in the previous section).
+Looking at higher recall clusters allows finding ones that have
+at least some overlap in their distribution, while keeping an
+eye on precision suggests differences in quality. These appear
+as light yellow dots on the right side of the recall chart. He
+randomly selects one, and discovers a cluster of sea urchins.
+Both generators produce high quality outputs, however visual
+inspection shows that BigGAN-deep produces more diverse
+output (Figure 9).
+Fig. 9. A cluster of sea urchin samples from two generators, both
+produce high quality images, but the generator on the right produces
+more diverse output. The images on the right show a greater variety of
+colors, textures and poses.
+A benefit of clustering by visual similarity, rather than
+grouping by label, is making it easier to discover overlap or
+leakage of visual semantics between classes. Using the same
+method as above, our analyst selects another cluster that con-
+sists of relatively realistic images of dishrags (Figure 10). He
+then highlights all clusters containing dishrags. He can now
+
+810) spacebar
+810) space bar810) space bar
+810) space bar
+810) space bar
+810) space bar878) typewriter k... 878) typewriter k.
+878) tvpewriter k... 878) typewriter k... 878) typewriter k... 878) typewriter k.810)spacebar810)spacebar
+810)spacebar
+810)spacebar
+810)spacebar
+810)spacebar
+810)spacebar
+878) typewriter k..
+878)typewriterk...878)typewriterk...878)typewriterk...878)typewriterk.SPLIT 1
+SPLIT 2
+SAMPLE VIEW
+BigGAN 128, 1.0 truncation
+BigGANDeep 128, 1.0 truncation
+Grid
+39 Samples
+45 Samples
+328) sea urchin
+328) sea urchin
+328) sea urchin328) sea urchin
+328) sea urchin
+ 328) sea urchin
+328) sea urchin328) sea urchin328) sea urchin
+328) sea urchin328) sea urchin
+ 328) sea urchin
+328) sea urchin 328) sea urchin328) sea urchin328) sea urchin
+328) sea urchin
+ 328) sea urchin
+328) sea urchin 328) sea urchin 328) sea urchin 328) sea urchin 328) sea urchin 328) sea urchin
+328) sea urchin
+328) sea urchin
+328) sea urchin328) sea urchin328) sea urchin328) sea urchin
+328) sea urchin328) sea urchin
+328) sea urchin328) sea urchin328) sea urchin
+ 328) sea urchin
+328) sea urchin  328) sea urchin  328) sea urchin  328) sea urchin  328) sea urchin  328) sea urchin
+328) sea urchin
+328) sea urchin328) sea urchin328) sea urchin
+328) sea urchin
+ 328) sea urchin
+328) sea urchin328) sea urchin328) sea urchin
+328) sea urchin328) sea urchin328) sea urchin
+328) sea urchin  328) sea urchin 
+396) lionfish
+328) sea urchin  328) sea urchin  328) sea urchin  328) sea urchin  328) sea urchin  328) sea urchin
+328) sea urchin 328) sea urchin  328) sea urchin8
+individually examine all these clusters. His findings, shown in
+(Figure 11 and Figure 12), suggests that other classes, namely
+handkerchief’ and ’doormat’, are ’leaking’ into how each gen-
+erator models dishrags.
+Fig. 10. A cluster of ’dishrag’ samples from BigGAN on the left and
+BigGAN-deep on the right, both produce somewhat realistic dishrags,
+but the generator on the right produces images with more diverse
+textures and colors.
+Fig. 11. BigGAN cluster with a few dishrags but many colorful hand-
+kerchiefs that have similar patterns to those seen in the main dishrag
+cluster. This suggests some leakage in visual representation between
+the two concepts.
+Fig. 12. BigGAN-deep cluster with a few dishrags but many doormats,
+this suggests a hypothesis for why many of the BIgGAN-deep dishrags
+have a very rough texture.
+5.0.3
+Downstream Applications of Generative Models: Super-
+Resolution
+In our final case study we consider the PULSE (Photo Upsam-
+pling via Latent Space Exploration) algorithm [22], a super-
+resolution algorithm that searches the manifold of a genera-
+tive image model (in this case StyleGAN2) to create plausible
+upsampled images corresponding to low resolution input im-
+ages. The post-publication release of this model received sharp
+critique, as users quickly discovered weaknesses in the mod-
+els ability to upsample images of people with non-caucasian
+features [44]. We use this example to illustrate how broader
+exploration of output manifolds could help researchers and
+Fig. 13. Cluster metric charts colored by cluster precision. On the left
+of the precision chart is a group of clusters with very low precision
+that are mostly composed of images only from the ground truth data,
+many of these also have low recall, suggesting the algorithm struggles
+to produce any output for them.
+practitioners who are using these kinds models in downstream
+applications to understand their weaknesses and mitigate risks
+before release.
+In this scenario, we use the original CelebA-HQ dataset
+from Karras, et al. [13]. This dataset consists 30,000 facial por-
+traits of celebrities at 1024x1024px. We take CelebA-HQ images
+at 32x32px and upsample them back to 1020x1024px using the
+PULSE algorithm5. We invoke PULSE with the default settings
+provided by the authors in their model release 6, however we
+increased the number of steps we run the algorithm from 100 to
+200 steps to increase the chances of PULSE producing a result
+for a given input.7
+We then compare the original 1024x1024px images and the
+PULSE up-sampled ones using Ravel. In total, we have 30000
+original CelebA-HQ images and 22092 images output from
+PULSE. 7908 images failed to produce any output after 200
+steps of the PULSE algorithm.
+What kinds of images does PULSE struggle to produce any
+output for?
+Our analyst sets the number of clusters to 250 and the
+original CelabA-HQ images on the left split, and immediately
+notices a group of clusters on the lowest end of the precision
+chart. She notices that many clusters also have low recall and
+are mostly composed of images only from the ground truth (see
+Figure 13). She clicks on some low-recall/low-precision clusters
+and observes a few categories where the algorithm struggles
+to produce any output. These include: people wearing hats or
+other headgear, images where the person has a a microphone or
+hand in front of them, faces with a lot of facepaint or makeup,
+and images where people are wearing sunglasses. Each of these
+clusters has between 60-120 images and a few samples are
+shown in Figure 14.
+What kinds of images does PULSE struggle to produce high
+quality output for?
+5. This scale factor (24x) is within the range of scale factors (8x-64x)
+the original authors used in evaluation
+6. https://github.com/adamian98/pulse
+7. We did this because PULSE will not always produce a result for
+an input image, and we found increasing the number of steps allowed
+substantially more input images to produce some result.
+
+SPLIT 1
+SPLIT 2
+SAMPLE
+BigGAN 128, 1.0 truncation
+BigGANDeep 128, 1.0 truncation
+Grid
+36 Samples
+48 Samples
+533) dishrag, di... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, di... 533) dishrag, dis... 533) dishrag, dis..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, di.. 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis.
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, di. 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis.
+533) dishrag, dis... 533) dishrag, di.533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, di..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, di..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis...
+533) dishrag, dis... 533) dishrag, dis. 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis..
+533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis... 533) dishrag, dis..
+533) dishrag, dis... 533) dishrag, dis... 539) doormat, w... 539) doormat, w... 735) poncho
+748) purse533) dishrag, dis...533) dishrag, dis... 549) envelope
+591)handkerchi... 591) handkerchi... 591)handkerchi..533) dishrag, dis... 539) doormat, w... 539) doormat, w... 539) doormat, w... 539) doormat, w... 539) doormat, w..Percent of Split 2 (PULSE upscaled CelebA 32px->1024px.)
+0%
+20%
+40%
+60%
+80%
+100%
+Recall with 'CelebA HQ 1024px' as ground truth
+0.2
+0.4
+0.6
+0.8
+Precision with 'CelebA HQ 1024px' as ground truth
+0
+0.2
+0.4
+0.6
+0.89
+Fig. 14. Each row contains samples from a different cluster with that only
+has images from the ground truth data and none from the algorithm out-
+put. These are examples of images the algorithm struggles to upscale.
+She continues to explore low precision clusters by scanning
+left to right along the chart. One of the lowest precision clusters
+contains ground truth images of people wearing spectacles (and
+a few wearing sunglasses), however from the algorithm output
+she sees a number of low quality (i.e. unrealistic) images that
+are likely up-scaled from ones where the subject is wearing
+sunglasses (Figure 15). She refines her hypothesis about what
+the algorithm does to portraits with sunglasses, determining
+that, ”if a person is wearing sunglasses, the algorithm often fails to
+produce any image, and when it does, it produces unrealistic output”.
+Fig. 15. Samples from a cluster of upscaled images of people wearing
+sunglasses.
+What kinds of images does PULSE do well at upsampling?
+The precision chart can also be used to look at what images
+PULSE does well at. As our analyst browses clusters on the
+right side of the distribution, she observes that a majority of
+high quality outputs seem to be of lighter skin tone faces that
+look relatively young or middle aged.
+Her manual inspection reveals some of the model’s fail-
+ure modes and strengths along demographic categories even
+though she does not have access to quantitative measures of
+performance across sensitive features such as skin tone or age.
+6
+DOMAIN EXPERT USER STUDY
+We evaluated Ravel in a two-stage study, where the first stage
+identified domain experts’ model evaluation goals, workflows
+and existing tools, and the second stage investigated the us-
+ability and utility of the Ravel UI. Participants were recruited
+from a convenience sample of full time employees as a large
+technology company, and there was a diversity in gender
+identity (nfemale = 1, nMale = 5), product area (5 different
+teams), and office location (nIsrael = 2, nUnitedStates = 4). Stage
+one (n = 4) included four expert research scientists and soft-
+ware engineers who currently work on training and evaluating
+generative models, and stage two (n = 5) included three of
+the users from stage one plus two additional users who have
+experience working with generative models. Both evaluation
+stages used remote moderated Google Meet video calls to speak
+with users and allow them to share their screen to show how
+they interacted with Ravel.
+6.1
+Stage One: The Current State of Evaluation
+Stage one aimed to understand the current state of evaluation
+for generative image model output. Semi-structured interviews
+were used, with questions about participants’ familiarity and
+day to day work with generative models, goals and motivation
+for model evaluation, as well as current workflows and prac-
+tices. All four users currently work on generative models, and
+were familiar with StyleGAN and its variants, BigGAN and
+its variants, as well as other models trained on ImageNet and
+FFHQ. There was diversity in architectures they work with and
+the tasks they apply generative models to. Here, we report the
+most common practices among users.
+6.1.1
+Evaluation Goals & Workflows
+All four participants reported that publication of model per-
+formance/improvement was a primary goal for their work. All
+four participants also expressed that evaluating output image
+quality was critical to understanding model performance.
+All four participants reported a mix of quantitative and
+qualitative evaluation methods. In general, their workflows
+could be characterized by a common pattern of: model training
+accompanied by limited visual inspection for sanity-checking
+→ examination of metrics → continued training → reexamina-
+tion of metrics until a predetermined threshold is reached →
+qualitative visual inspection of image output.
+Two participants indicated that they believed the current
+“best practice” for determining image quality was human
+qualitative evaluation, often from crowdsourced studies. Im-
+portantly, all four participants also emphasized the ubiquitous
+reliance upon and limitations of FID scores in model evaluation.
+While one user suggested that “FID scores are much better
+than inception scores and other metrics”, they also conceded
+that “there is not a gold standard for evaluation of generated
+images”. All users indicated that they were dissatisfied with
+FID score as a primary evaluation metric, and that they had
+all experienced and read cases where they felt that FID score
+did not align with human inference, a sentiment supported in
+Zhou, et al. [24].
+6.1.2
+Evaluation Tools
+All four users mentioned using TensorBoard [45] or Colab8
+(a computational notebook envrionment similar to Jupyter
+Notebook [46]) to examine model output. For Colab, the main
+strength reported was flexibility. The flexibility of Colab enables
+bespoke analyses that we elaborate on in section 6.2.5. Its main
+limitations were difficulties reusing code between projects and
+sharing results, especially with non-technical collaborators or
+stakeholders not directly involved with model training. For
+TensorBoard, the main strengths reported were ease of use
+during training to quickly visualize metrics and see sample
+output at different stages of training. The main limitations
+mentioned about TensorBoard were its latency when loading
+many images, and lack of customization compared to an open
+ended tool like Colab.
+8. https://colab.research.google.com/
+
+RUCAEN10
+6.1.3
+Qualitative Visual Evaluation Tasks
+Determining image quality was reported as the most important
+task. Determining the diversity of images was also important
+to all four users, and one user mentioned that looking for
+the occurrence of mode collapse was an explicit part of their
+evaluation workflow. All users indicated that it was important
+to do more granular and bespoke image generation, including
+looking at samples within certain classes or samples close to
+each other in embedding space. One user discussed examining
+different levels of truncation for latent vectors to make deci-
+sions about both realism and aesthetics in the output. Users
+reported viewing a small number of images. One user reported
+looking at approximately 64 images, and never more than 100
+images, per evaluation step of the model training pipeline.
+Another user explained that when they work with a team on an
+evaluation, they typically generate and inspect about 50 images.
+However, when working alone, this user said that they would
+inspect at least 200 images, noting that it was difficult to get a
+group consensus on more than 50 images at a time.
+We determined four categories of critical evaluation tasks
+from this part of the study: image diversity, image quality, mode
+collapse, and a “catch-all” category of additional explorations
+of classes and samples.
+6.2
+Stage Two: Observing how Ravel is Used
+The objective of this stage was to determine how the Ravel UI
+can be used for the critical evaluation tasks identified in stage
+one. A brief slide deck and video explaining the UI components
+was sent to users upon confirmation of their participation,
+which they were asked to review before the study session. The
+study sessions themselves lasted for one hour and consisted
+of task based user exploration of the tool and semi-structured
+interview questions.
+6.2.1
+Task one: Diversity
+The first task we asked users to attempt was to decide whether
+BigGAN or BigGAN-deep was performing better in terms of
+the diversity of sea urchin images, in a setup mirroring the
+Ravel instance described in Section 5.0.2. This instance showed
+128x128 pixel images from both models, with 50,000 images
+per model and 50 images per class from each model. The UI
+resolution was set to show the same number of images for each
+user: 5 images per row in each split.
+Users were presented with an instance of Ravel with the
+”sea urchin” class selected in the Highlighted Classes menu,
+showing results from BigGAN and BigGAN-deep in the left
+split and right split, respectively. On initial load the instance
+displayed the cluster containing most of sea urchin images
+selected: 39 (out of 50) urchins from BigGAN and 45 (out of
+50) urchins from BigGAN-deep.
+All users started by attending to images in each split. No
+users examined metrics or asked about metrics as a first step.
+This emphasizes the importance of Ravel intuitively depicting
+some of the most important information for assessing image
+diversity: a salient grid of sample images within a cluster
+of interest. Three users immediately noted the number of
+samples in each split, paying close attention to which model
+had a greater number of samples in the cluster of interest.
+The most common flow involved inspecting individual images
+and counting or “eyeballing” the number of images in each
+model with unique background colors, sea urchin poses, and
+sea urchin colors (all users mentioned these three features).
+Three users scanned the metrics charts and clicked on the
+other highlighted clusters with sea urchins. All five users made
+the determination that BigGAN-deep was performing better in
+terms of the diversity of sea urchin images, with one user ex-
+plicitly stating that this confirmed their prior expectations. This
+demonstrates consistency in how users complete this critical
+task with Ravel, and shows the potential for convergent deci-
+sion making and operationalization of workflows in qualitative
+visual evaluation. It is also notable that Ravel helped confirm
+one user’s prior expectations about BigGAN-deep’s diversity
+performance, although that could also have been a potential
+biasing factor in their evaluation process.
+6.2.2
+Task two: Quality
+For the second task, users were asked to decide whether Big-
+GAN or BigGAN-deep was performing better in terms of the
+quality of golden retriever images. Users were presented with
+the same Ravel instance as task one, but this time the ”golden
+retriever” class was selected in the Highlighted Classes menu
+and a cluster showing most of the golden retriever images was
+selected: 46 (out of 50) in the BigGAN split and 46 (out of 50) in
+the BigGAN-deep split.
+All users immediately noted many artifacts in output im-
+ages from both models. All users clicked on individual images
+and narrated particular issues, such as the shape of dogs’ noses,
+the number of legs, and the accuracy of the form and pose of the
+dogs in each sample. The most common workflow was to count
+or “eyeball” the number of artifacts in each split to make an
+initial determination, but evaluation workflows were notably
+more diverse between users for the rest of the task. Five users
+reported that this task was more difficult than the diversity
+task while one user reported that it was easier. Some users
+indicated that FID and Inception score for each model would be
+an important part of making this determination in their typical
+workflow. Four out of the five users made the determination
+that BigGAN-deep also performed better in terms of the quality
+of golden retriever images, and one user did not make an ex-
+plicit determination for this task. Once again, Ravel supported
+consistency in the primary image quality evaluation strategy
+across all users, but individual exploration varied after this
+initial decision. Some users validated their visual judgments
+by looking at recall and precision charts, but others simply
+explored the charts without forming additional opinions about
+the task.
+6.2.3
+Task three: Mode Collapse
+Following the Quality task, users were asked if they were
+familiar with the term mode collapse and if it was something
+they used to evaluate generative model output. Four out of
+five users were familiar with mode collapse and reported it as
+a useful discovery in the model evaluation process, while one
+user was unfamiliar with the term. Users who were familiar
+with mode collapse were then asked to use Ravel to determine
+whether it had occurred for either model within any class.
+Because this task was not constrained to a single class, it
+was more open-ended, and thus more challenging for users to
+make a determination about. Workflows varied widely between
+users, as they were given no guidance about how to accomplish
+the task or make a determination. Several users mentioned that
+they expected BigGAN to exhibit more mode collapse after
+observing that BigGAN-deep had better diversity in the first
+task. Four users who found concrete instances of mode collapse
+(e.g. Fig. 6) did so by selecting clusters with the smallest
+values in the Recall chart. Four out of five users viewed the
+cluster samples displayed in figure 7 at some point during
+their exploration, but one user did not identify it as mode
+collapse, and one user did not select it at all. Nevertheless,
+
+11
+this was a promising observation, and demonstrates further
+consistency of Ravel’s usability and specific utility of the recall
+visualization. There was majority agreement that the recall
+chart can be used to identify mode collapse, and it was revealed
+to occur more often in BigGAN-deep.
+6.2.4
+Task four: Additional exploration of classes, samples,
+and features
+For their final task, users were asked to view an instance
+of Ravel showing generated images from a StyleGAN2-based
+model in the right split, and images from its ground-truth
+training data, FFHQ, in the left split. Users were told they
+could freely explore the interface, either repeating the quality
+and diversity assessments or trying a new task that they might
+be interested in.
+This task was fully unguided, but most users started by
+assessing image quality for the StyleGAN2-based model. It was
+common for users to select clusters at the low and high ends
+of the Precision distribution. One user observed that clicking
+on a cluster with high precision revealed “typical FFHQ im-
+ages. . . very good images without occlusion, faces looking at
+the camera, showing people with straight hair, and the model
+output is very similar to these images.”. Four out of five users
+discovered and explicitly verbalized that StyleGAN2-based
+model struggled to generate images of people with facepaint.
+They did this by clicking on clusters with low precision and
+noticing artifacts on many of the generated images. All four
+of these users expressed surprise upon making this new dis-
+covery about the model. This demonstrates that even without
+a specific prompt, many users will make the same kinds of
+discoveries and follow the same types of evaluation processes
+with Ravel. One of our participants was on the team that had
+originally trained the StyleGAN2-based model that we used
+and discovered that the model was unable to generate faces of
+people wearing a particular style of fuzzy winter hat that was
+fairly common in the ground truth data. He remarked that he
+wasn’t aware of that inability and was pleasantly surprised to
+be able to discover it.
+The other common tasks were “semantic explorations” of
+the clusters and the embedding space. Four out of five users
+examined images in the FFHQ split to make decisions about
+whether the clusters were semantically meaningful, and to
+explore the diversity of FFHQ. Two users pondered whether
+or not the embedding space was doing a good job of capturing
+what they, as humans, would group together. These users inves-
+tigated the proximity of samples in the Samples UMAP chart
+and determined that the ImageNet feature space is not optimal
+for clustering faces, since they could not find consistent visual
+similarity between nearby samples in some of the clusters.
+6.2.5
+Discussion of Expert Feedback
+Users were overall impressed with the tool. All five users
+thought that Ravel would fit into their current evaluation
+process, and that it was especially useful for researchers who
+publish generative models. Here, we summarize additional
+feedback from the reflection portion of stage two.
+Two users reported that their exploration made them doubt
+whether the Inceptionv3 features were good for evaluating face
+portrait generation. In reflection, one of these users stated that
+Ravel could be used to learn about the feature space itself,
+which could be broadly useful in generative image model
+evaluation.
+Upon discovering mode collapse in BigGAN-deep, one user
+stated that Ravel would be useful for probing state-of-the-art
+models to learn which classes they can’t generate images for,
+which could point to systematic failure modes for researchers
+to focus on improving.
+One user noted that Ravel could help their team reach
+conclusions about model performance more quickly than using
+Colab, especially for understanding the diversity of images.
+They explained that using Colab required developing a bespoke
+visualization tool and manual calculations of FID in each clus-
+ter, whereas the same type of useful information was readily
+available in the Ravel UI. Two users emphasized that Ravel
+could help operationalize how researchers evaluate quality and
+diversity, one of which explained that Ravel could be “a forcing
+function for having a standard UI/pipeline for results”, arguing
+that this would make it “easier to share results with someone
+on another team, or someone non-technical. . . even with my
+manager who doesn’t have time to run my code”. This confirms
+for us that there is a place for bespoke purpose built interfaces
+like Ravel, that while less flexible than Colab, are more purpose
+built for common evaluation tasks that researchers perform.
+Overall, the expert feedback from stage two was positive
+and enthusiastic, with several users expressing excitement
+about continued exploration in Ravel and incorporating it into
+their own workflows.
+7
+LIMITATIONS AND FUTURE WORK
+Our qualitative user study was performed with a small, domain
+expert sample from a single company, and therefore may not be
+an externally valid representation of all researcher experiences
+with generative image models. The study sessions were also
+limited to one hour per user, with each evaluation task time-
+boxed to 15 minutes or less. Richer and more diverse interac-
+tions and discoveries could be possible with a longer duration
+of tool use.
+Two users wanted to see images at a higher resolution,
+and two other users wanted to see the original resolution of
+the images when examining them for artifacts; this is not an
+inherent issue with Ravel but is an important design affordance
+for the future. Two users wanted to be able to mark images in
+each split once they had viewed them, and enabling this would
+support the ’counting’ based workflows we saw participants
+use to complete the tasks.
+When using the class conditional model, users initially
+reported that they would prefer to see all images from a given
+class in the same view (i.e. clustering by class label) to make a
+judgement about that class. However on further exploration
+they noted it was useful to see ’outlier’ images for a given
+label in context with the other images they are most similar
+to. This suggests that both workflows are important to support
+for class conditioned models and should be supported by tools
+like Ravel.
+The authors also note a number of limitations of the system
+we observed while watching users use the tool:
+User’s cannot always interpret the ’meaning’ of clusters (i.e.,
+construct a rationale for why a set of images are clustered
+together). This is a general issue with unsupervised methods
+like clustering, but we found that users would often try to
+attach some semantically meaningful description to each cluster
+to ground their comparison.
+Exploring ways to ’describe’ clusters or summarize differ-
+ences between clusters could be important future work to aid
+user comprehension. We also think exploring other clustering
+methods, in particular hierarchical methods, could be a partic-
+ularly attractive means to produce clusters at different levels of
+granularity to help build understanding of groups within the
+dataset.
+
+12
+In describing the Sample viewer (section 4.2.3) we noted
+that one limitation is that not all of the images are visible in one
+screen if there are many images present in the cluster. While one
+mitigation is to decrease the size of clusters by increasing the
+number of clusters, we believe that future work could provide
+better ways to get the visual gestalt of the entire cluster in one
+view. Possibly adapting techniques such as those described in
+Activation Atlas [47], creating stacks of very similar images
+within a cluster, or other ways of sub-sampling or sorting to
+ensure that we are displaying the maximum variety about a
+cluster in a single screen.
+One user task that Ravel does not directly support is de-
+tecting memorization. One user commented that adding a real
+time nearest-neighbor search to the interface would likely make
+it useful for this task.
+8
+CONCLUSION
+We presented Ravel, a visual analysis tool that enables re-
+searchers to perform large scale qualitative evaluation of gen-
+erative model outputs. Our primary contributions included:
+•
+A visual analytics system that supports multiple evalua-
+tion tasks (e.g. evaluating quality & diversity, discovering
+mode collapse or gaps in model output) for generative
+image models and is agnostic to model architecture and
+internals.
+•
+Interactive exploration of large generative image model
+datasets, facilitated by clustering and the use of fine
+grained visualization of cluster metrics to guide quali-
+tative evaluation.
+•
+A user interface that uses visual comparison driven by
+semantically meaningful embedding spaces to support
+reasoning about differences between image distributions
+and generate hypotheses about model behaviour.
+The expert users in our study were able to generate consis-
+tent insights about model behaviour including identifying areas
+of the true data distribution the model was not capturing, such as
+face paint or certain kinds of headgear in the StyleGAN2-based
+model or mode collapse in BigGAN-deep. This kind of insight
+is an example of one that is not possible to get from just looking
+at quantitative metrics like FID.
+Our study participants confirmed our hypotheses that single
+number metrics are not fully sufficient measures of model
+performance. In addition to exploring metrics at greater granu-
+larity, Ravel allows users to explore metrics at finer granularity,
+revealing areas of model output where metrics like recall or
+precision do not capture problems in the generated images.
+Our users hypothesized that the underlying InceptionV3 em-
+bedding, used both in our tool and in the primarily metrics in
+the field, may not attend to certain kinds visual artefacts that
+are easily visible to humans. We believe that future work in
+this direction could enable better understanding of limits of the
+embedding spaces themselves and how they affect both metrics
+and the workflows that use them.
+ACKNOWLEDGMENTS
+The authors wish to thank Mario Lucic, Marvin Ritter, Ben
+Poole, Han Zhang, Chitwan Saharia, James Wexler and Lucas
+Dixon for their help and feedback on this work. We also thank
+our study participants for their feedback.
+REFERENCES
+[1]
+I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley,
+S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial
+Nets,” in Advances in Neural Information Processing Systems, vol. 27,
+2014. [Online]. Available: https://proceedings.neurips.cc/paper/
+2014/hash/5ca3e9b122f61f8f06494c97b1afccf3-Abstract.html
+[2]
+D. P. Kingma and M. Welling, “Auto-Encoding Variational
+Bayes,” Dec. 2013. [Online]. Available: https://arxiv.org/abs/
+1312.6114v10
+[3]
+L.
+Dinh,
+D.
+Krueger,
+and
+Y.
+Bengio,
+“NICE:
+Non-linear
+Independent Components Estimation,” arXiv:1410.8516 [cs], Apr.
+2015, arXiv: 1410.8516. [Online]. Available: http://arxiv.org/abs/
+1410.8516
+[4]
+J.
+Sohl-Dickstein,
+E.
+Weiss,
+N.
+Maheswaranathan,
+and
+S.
+Ganguli,
+“Deep
+Unsupervised
+Learning
+using
+Nonequi-
+librium
+Thermodynamics,”
+in
+Proceedings
+of
+the
+32nd
+International
+Conference
+on
+Machine
+Learning,
+Jun.
+2015,
+pp.
+2256–2265,
+iSSN:
+1938-7228.
+[Online].
+Available:
+https://proceedings.mlr.press/v37/sohl-dickstein15.html
+[5]
+A.
+Odena,
+“Open
+Questions
+about
+Generative
+Adversarial
+Networks,” Distill, vol. 4, no. 4, p. e18, Apr. 2019. [Online].
+Available: https://distill.pub/2019/gan-open-problems
+[6]
+L. Theis, A. v. d. Oord, and M. Bethge, “A note on the evaluation
+of generative models,” arXiv:1511.01844 [cs, stat], Apr. 2016, arXiv:
+1511.01844. [Online]. Available: http://arxiv.org/abs/1511.01844
+[7]
+A.
+Borji,
+“Pros
+and
+Cons
+of
+GAN
+Evaluation
+Measures,”
+arXiv:1802.03446 [cs], Oct. 2018.
+[8]
+——, “Pros and Cons of GAN Evaluation Measures: New Devel-
+opments,” arXiv:2103.09396 [cs], Mar. 2021.
+[9]
+M.
+Heusel,
+H.
+Ramsauer,
+T.
+Unterthiner,
+B.
+Nessler,
+and
+S. Hochreiter, “GANs Trained by a Two Time-Scale Update
+Rule Converge to a Local Nash Equilibrium,” in Advances
+in
+Neural
+Information
+Processing
+Systems,
+vol.
+30,
+2017.
+[Online]. Available: https://proceedings.neurips.cc/paper/2017/
+hash/8a1d694707eb0fefe65871369074926d-Abstract.html
+[10] M. S. M. Sajjadi, O. Bachem, M. Lucic, O. Bousquet, and S. Gelly,
+“Assessing Generative Models via Precision and Recall,” in
+Advances in Neural Information Processing Systems, vol. 31, 2018.
+[Online]. Available: https://proceedings.neurips.cc/paper/2018/
+hash/f7696a9b362ac5a51c3dc8f098b73923-Abstract.html
+[11] T. Kynk¨a¨anniemi, T. Karras, S. Laine, J. Lehtinen, and T. Aila,
+“Improved Precision and Recall Metric for Assessing Generative
+Models,” arXiv:1904.06991 [cs, stat], Oct. 2019, arXiv: 1904.06991.
+[Online]. Available: http://arxiv.org/abs/1904.06991
+[12] A.
+Brock,
+J.
+Donahue,
+and
+K.
+Simonyan,
+“Large
+Scale
+GAN Training for High Fidelity Natural Image Synthesis,”
+arXiv:1809.11096 [cs, stat], Feb. 2019, arXiv: 1809.11096. [Online].
+Available: http://arxiv.org/abs/1809.11096
+[13] T.
+Karras,
+S.
+Laine,
+and
+T.
+Aila,
+“A
+Style-Based
+Generator Architecture for Generative Adversarial Networks,”
+arXiv:1812.04948 [cs, stat], Mar. 2019, arXiv: 1812.04948. [Online].
+Available: http://arxiv.org/abs/1812.04948
+[14] D. P. Kingma and P. Dhariwal, “Glow: Generative Flow with
+Invertible 1x1 Convolutions,” arXiv:1807.03039 [cs, stat], Jul. 2018,
+arXiv: 1807.03039. [Online]. Available: http://arxiv.org/abs/1807.
+03039
+[15] A. v. d. Oord, O. Vinyals, and K. Kavukcuoglu, “Neural Discrete
+Representation Learning,” arXiv:1711.00937 [cs], May 2018, arXiv:
+1711.00937. [Online]. Available: http://arxiv.org/abs/1711.00937
+[16] J. Ho, C. Saharia, W. Chan, D. J. Fleet, M. Norouzi, and
+T. Salimans, “Cascaded Diffusion Models for High Fidelity Image
+Generation,” arXiv:2106.15282 [cs], Dec. 2021, arXiv: 2106.15282.
+[Online]. Available: http://arxiv.org/abs/2106.15282
+[17] C. Szegedy, V. Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna,
+“Rethinking the Inception Architecture for Computer Vision,”
+arXiv:1512.00567 [cs], Dec. 2015.
+[18] T. Karras, S. Laine, M. Aittala, J. Hellsten, J. Lehtinen, and T. Aila,
+“Analyzing and improving the image quality of stylegan,” in
+Proceedings of the IEEE/CVF conference on computer vision and pattern
+recognition, 2020, pp. 8110–8119.
+[19] R. Geirhos, P. Rubisch, C. Michaelis, M. Bethge, F. A. Wichmann,
+and W. Brendel, “ImageNet-trained CNNs are biased towards
+texture; increasing shape bias improves accuracy and robustness,”
+arXiv:1811.12231 [cs, q-bio, stat], Jan. 2019.
+[20] T. Salimans, I. Goodfellow, W. Zaremba, V. Cheung, A. Radford,
+X. Chen, and X. Chen, “Improved Techniques for Training GANs,”
+in Advances in Neural Information Processing Systems, vol. 29, 2016.
+
+13
+[Online]. Available: https://proceedings.neurips.cc/paper/2016/
+hash/8a3363abe792db2d8761d6403605aeb7-Abstract.html
+[21] S. Barratt and R. Sharma, “A Note on the Inception Score,”
+arXiv:1801.01973 [cs, stat], Jun. 2018, arXiv: 1801.01973. [Online].
+Available: http://arxiv.org/abs/1801.01973
+[22] S. Menon, A. Damian, S. Hu, N. Ravi, and C. Rudin, “PULSE:
+Self-Supervised Photo Upsampling via Latent Space Exploration
+of Generative Models,” in 2020 IEEE/CVF Conference on Computer
+Vision and Pattern Recognition (CVPR), Seattle, WA, USA, Jun. 2020,
+pp. 2434–2442.
+[23] E. Denton, S. Chintala, A. Szlam, and R. Fergus, “Deep Gener-
+ative Image Models using a Laplacian Pyramid of Adversarial
+Networks,” arXiv:1506.05751 [cs], Jun. 2015.
+[24] S. Zhou, M. Gordon, R. Krishna, A. Narcomey, L. F. Fei-Fei, and
+M. Bernstein, “HYPE: A Benchmark for Human eYe Perceptual
+Evaluation of Generative Models,” p. 13.
+[25] D. Bau, J.-Y. Zhu, H. Strobelt, B. Zhou, J. B. Tenenbaum, W. T.
+Freeman, and A. Torralba, “GAN Dissection: Visualizing and Un-
+derstanding Generative Adversarial Networks,” arXiv:1811.10597
+[cs], Dec. 2018.
+[26] D. Bau, J.-Y. Zhu, J. Wulff, W. Peebles, H. Strobelt, B. Zhou,
+and A. Torralba, “Seeing What a GAN Cannot Generate,”
+arXiv:1910.11626 [cs, eess], Oct. 2019.
+[27] T. White, “Sampling Generative Networks,” arXiv:1609.04468 [cs,
+stat], Dec. 2016.
+[28] T. White and B. Loh, “SpaceSheet: Navigating Conceptual Space
+with a Spreadsheet Interface,” p. 8.
+[29] D. Smilkov, N. Thorat, C. Nicholson, E. Reif, F. B. Vi´egas, and
+M. Wattenberg, “Embedding Projector: Interactive Visualization
+and Interpretation of Embeddings,” arXiv:1611.05469 [cs, stat],
+Nov. 2016.
+[30] K. Ho, “Font Map,” https://experiments.withgoogle.com/font-
+map.
+[31] C.
+Diagne
+and
+S.
+Doury,
+“Curator
+Table,”
+https://experiments.withgoogle.com/curator-table.
+[32] K.
+McDonald,
+M.
+Tan,
+and
+Y.
+Mann,
+“Bird
+Sounds,”
+https://experiments.withgoogle.com/bird-sounds.
+[33] Y. Liu, E. Jun, Q. Li, and J. Heer, “Latent Space Cartography: Visual
+Analysis of Vector Space Embeddings,” Computer Graphics Forum,
+vol. 38, no. 3, pp. 67–78, Jun. 2019.
+[34] S. Xiang, X. Ye, J. Xia, J. Wu, Y. Chen, and S. Liu, “Interactive
+Correction of Mislabeled Training Data,” in 2019 IEEE Conference
+on Visual Analytics Science and Technology (VAST), Oct. 2019, pp.
+57–68.
+[35] R. Zhang, P. Isola, A. A. Efros, E. Shechtman, and O. Wang,
+“The
+Unreasonable
+Effectiveness
+of
+Deep
+Features
+as
+a
+Perceptual
+Metric,”
+2018,
+pp.
+586–595.
+[Online].
+Avail-
+able:
+https://openaccess.thecvf.com/content cvpr 2018/html/
+Zhang The Unreasonable Effectiveness CVPR 2018 paper.html
+[36] “Scikit-learn
+Overview
+of
+Clustering.”
+[Online].
+Avail-
+able:
+https://scikit-learn.org/stable/modules/clustering.html#
+overview-of-clustering-methods
+[37] L. McInnes, J. Healy, N. Saul, and L. Grossberger, “Umap: Uni-
+form manifold approximation and projection,” The Journal of Open
+Source Software, vol. 3, no. 29, p. 861, 2018.
+[38] K. P. F.R.S., “Liii. on lines and planes of closest fit to systems of
+points in space,” The London, Edinburgh, and Dublin Philosophical
+Magazine and Journal of Science, vol. 2, no. 11, pp. 559–572, 1901.
+[39] L. Van der Maaten and G. Hinton, “Visualizing data using t-sne.”
+Journal of machine learning research, vol. 9, no. 11, 2008.
+[40] A. Coenen and A. Pearce, “Understanding UMAP,” 2019. [Online].
+Available: https://pair-code.github.io/understanding-umap/
+[41] O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma,
+Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, A. C. Berg, and
+L. Fei-Fei, “ImageNet Large Scale Visual Recognition Challenge,”
+International Journal of Computer Vision (IJCV), vol. 115, no. 3, pp.
+211–252, 2015.
+[42] M. Lucic, K. Kurach, M. Michalski, S. Gelly, and O. Bousquet,
+“Are
+GANs
+Created
+Equal?
+A
+Large-Scale
+Study,”
+in
+Advances
+in
+Neural
+Information
+Processing
+Systems,
+vol.
+31,
+2018. [Online]. Available: https://proceedings.neurips.cc/paper/
+2018/hash/e46de7e1bcaaced9a54f1e9d0d2f800d-Abstract.html
+[43] I. Goodfellow, “NIPS 2016 Tutorial: Generative Adversarial Net-
+works,” arXiv:1701.00160 [cs], Apr. 2017.
+[44] “Lessons
+from
+the
+PULSE
+Model
+and
+Discussion,”
+https://thegradient.pub/pulse-lessons/, Jun. 2020.
+[45] M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro,
+G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Good-
+fellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser,
+M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray,
+C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar,
+P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals,
+P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng,
+“TensorFlow: Large-Scale Machine Learning on Heterogeneous
+Distributed Systems,” arXiv:1603.04467 [cs], Mar. 2016.
+[46] T. Kluyver, B. Ragan-Kelley, F. P´erez, B. Granger, M. Bussonnier,
+J. Frederic, K. Kelley, J. Hamrick, J. Grout, S. Corlay, P. Ivanov,
+D. Avila, S. Abdalla, and C. Willing, “Jupyter notebooks – a
+publishing format for reproducible computational workflows,” in
+Positioning and Power in Academic Publishing: Players, Agents and
+Agendas, F. Loizides and B. Schmidt, Eds.
+IOS Press, 2016, pp. 87
+– 90.
+[47] S. Carter, Z. Armstrong, L. Schubert, I. Johnson, and C. Olah,
+“Activation Atlas,” Distill, vol. 4, no. 3, p. e15, Mar. 2019. [Online].
+Available: https://distill.pub/2019/activation-atlas
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf,len=1325
+page_content='1  Large Scale Qualitative Evaluation of Generative Image  Model Outputs  Yannick Assogba, Adam Pearce and Madison Elliott  Abstract—Evaluating generative image models remains a difficult problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This is due to the high dimensionality of the outputs, the  challenging task of representing but not replicating training data, and the lack of metrics that fully correspond to human perception and  capture all the properties we want these models to exhibit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Therefore, qualitative evaluation of model outputs is an important part of  model development and research publication practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Quantitative evaluation is currently under-served by existing tools, which do not  easily facilitate structured exploration of a large number of examples across the latent space of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' To address this issue, we  present Ravel, a visual analytics system that enables qualitative evaluation of model outputs on the order of hundreds of thousands of  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ravel allows users to discover phenomena such as mode collapse, and find areas of training data that the model has failed to  capture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' It allows users to evaluate both quality and diversity of generated images in comparison to real images or to the output of  another model that serves as a baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Our paper describes three case studies demonstrating the key insights made possible with  Ravel, supported by a domain expert user study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Index Terms—Information visualization, Picture/Image Generation, Machine learning  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  1  INTRODUCTION  Generative image models are a class of neural network  based models that aim to produce novel, high-quality and  diverse images that faithfully model a target image distribu-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A variety of architectures and training methods have been  designed to learn such models, such as Generative Adversarial  Networks (GANs) [1], Variational Auto-Encoders (VAEs) [2],  Flow Based Models [3] and Diffusion Models [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Evaluating these models remains difficult [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The high  dimensionality of the output architectures used make likeli-  hood estimates of model outputs difficult, and in some cases  intractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' It has also been demonstrated that measures like  average log likelihood do not always correlate with human  perceptual judgments of sample quality [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Additionally, while  we want models to capture the target distribution well, we  do not want them to produce images that are actually in the  training set (an issue commonly referred to as memorization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  A number of metrics have emerged in the literature around  generative image models [7] [8], with Fr´echet Inception Dis-  tance (FID) [9] being the most popular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' However, issues have  been identified with FID, leading to the development of more  granular metrics such as precision and recall [10] [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Single-number metrics such as FID, while necessary for  forward progress in the field, do not capture the full range  of qualities desired of these models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Because of this, human  visual inspection often plays a critical role in the evaluation  and dissemination of advances in generative image modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  However with existing evaluation tools, practitioners can typi-  cally only look at a small fraction of the output space of these  models, on the order of 10s to 100s of images (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=', [12], [13],  [14], [15], [16]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Our interviews with domain experts confirm that human  evaluation is a critical part of practitioner workflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Some ex-  perts rely on human evaluation with crowd-sourced evaluators,  they however recognize that these are often expensive or time  consuming and are thus left to the final stages of evaluation Yannick Assogba, Adam Pearce and Madison Elliot are with Google  Research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  E-mail: {yassogba,adampearce,madisone}@google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='com  if done at all, leaving them to primarily rely on small scale  qualitative evaluation during the model development process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  At the same time, experts in the field are concerned about  cherry picking of results for publication but typically have no  means to expansively explore model outputs in the rare occa-  sions that these are published alongside academic manuscripts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  To address these needs, we built a system called Ravel,  which enables users to perform visual inspection of model  outputs on scales up to three orders of magnitude greater that  typical user workflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We demonstrate usage of this system  on datasets varying from 50k - 120k images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' These dataset sizes  are comparable to those used in standard quantitative evaluation  of generative image models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Our primary contributions include: A visual analytics system that supports multiple evalua-  tion tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' evaluating quality & diversity, discovering  mode collapse or gaps in model output) for generative  image models and is agnostic to model architecture and  internals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Interactive exploration of large generative image model  datasets, facilitated by clustering and the use of fine  grained visualization of cluster metrics to guide quali-  tative evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A user interface that uses visual comparison driven by  semantically meaningful embedding spaces to support  reasoning about differences between image distributions  and generate hypotheses about model behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  2  BACKGROUND  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1  Generative Image Models  The capabilities of generative image models have greatly in-  creased over the last several years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Since the original GAN  paper [1] that broke the dam on modelling of faces, we now  have systems like BigGAN [12], StyleGAN [13], GLOW [14],  VQ-VAE [15], CDM [16] and many others that present a wide  variety of model architecture and training algorithms and are  capable of producing very realistic images in a wide variety of  domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='04518v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='HC]  11 Jan 2023  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  Quantitative Metrics for Evaluating Generative Image  Models  In this section, we outline the most commonly cited metrics in  the research literature: Fr´echet Inception Distance [9]: Uses a pre-trained In-  ceptionV3 classifier [17] to generate embeddings for  both real and generated images, then uses a statistical  measure to compare the distribution of embeddings  from the two sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' FID is the most popular metric  in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' It requires a large number of samples  to produce an accurate estimate (generally at least 50k  generated images), and cannot detect memorization of  the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Karras et al [18] point out that the  texture bias in ImageNet based CNNs like InceptionV3  [19] imply that metrics derived from them will not  capture all aspects of image quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Inception Score [20]: Uses a pre-trained inception clas-  sifier to measure, a) how well each generated image  matches a single ImageNet class, and b) if the full the  set of generated images has uniform coverage over all  the ImageNet classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Similar to FID, Inception Score  requires a fairly large number of images and cannot  be used to detect memorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' It also cannot measure  intra-class diversity or detect mode collapse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' See Barrat  and Sharma [21] for a detailed discussion of issues  with this metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Both Inception Score and FID are  scalar scores designed to capture both image quality and  diversity, and thus cannot reveal if the model is trading  off one of these properties for the other to achieve a  better score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Precision and Recall Metrics: To disentangle the mea-  surement of image quality and diversity, Sajjadi et al  [10] and Kynk¨a¨anniemi et al [11] propose precision and  recall metrics to measure each independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Broadly  speaking, precision corresponds to the sample quality,  whereas recall corresponds to the coverage of the sample  distribution with respect to the target distribution - i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  diversity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  These metrics are generally computed over the entire dataset,  and thus have low granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Even when they indicate that  a model is better or worse, they don’t specify where in the  distribution of generated images improvements or regressions  lie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ravel increases the granularity of these metrics, providing  a way to find specific clusters of images that score poorly on  some metric  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='3  Qualitative Evaluation / Visualization of Generative Im-  age Model Outputs  Due to the limitations of quantitative metrics discussed above,  researchers also rely on visual inspection of model outputs  to evaluate model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Visual inspection is typically  performed during training, to monitor that the process has  not immediately failed, as well as after training, to evaluate  overall quality of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We validate and elaborate on  this workflow and strategy with domain experts in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Although models often output 100s of thousands of images,  our user study found that researchers are only able to inspect a  small portion of images (in the 100s) during their analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Visually impressive samples are paramount for successfully  publishing model advancements in scientific venues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Relevant  papers in the field of generative image models typically include  10s-100s of images [12] [13] [18] [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This represents a very  limited sample of the variety of images these models are typi-  cally trained to generate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Our user study also found that there  is an assumption that authors ”cherry-pick” the best images  to include in their publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Relatively few authors have  published large datasets of un-cherry-picked output images  alongside their publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  There are currently no purpose-built interfaces that make  these convenient to browse or examine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' For example, [13] [18]  each publish 100k output images to a publicly accessible Google  drive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' These images are organized into 1000 sub-folders to  make the interface more usable given the large number of files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  To view this output, users must either click through the folders  individually, or bring their own interface to browse the images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  3  RELATED WORK  Borji [7] [8] catalogues many of the metrics for automatic  evaluation of generative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ravel utilizes the precision  and recall metrics from [10] and [11], but does not propose any  new metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We thus situate this work in primarily relation  to work on qualitative evaluation and interfaces to explore  generative model output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Crowd-worker Evaluation  Denton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [23] use a small volunteer sample of human  annotators to estimate quality by asking whether they can  distinguish real from generated images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [24] refine  and scale this technique, asking crowd-sourced workers from  Amazon’s Mechanical Turk to make psychophysical judgments  about real vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' generated images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' While these methods are  good at scaling up evaluation to larger dataset sizes, they are  more time-consuming and expensive than manual inspection  by researchers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Thus they are typically reserved for later stages  of the evaluation pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' They also tend to focus on measures  that can be evaluated on individual images (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' image quality),  rather that corpus level properties (such as image diversity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  By contrast, Ravel is designed to support researcher evalu-  ation earlier in the development pipeline before the use of external  raters, and allows researchers to evaluate both quality and diver-  sity in the same interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' It fits in between initial monitoring of  training dynamics to ensure that the model is converging and  larger scale human rater evaluation typically performed closer  to model release.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Explaining Model Internals  Bau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [25] explore finding interpretable units (neurons)  within GANs and visualizing the causal effects of ablating these  neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Their method depends on having access to model  internals and having a pre-trained object segmentation network  to find objects within the scene to establish the casual relation-  ship between neuron activation and network output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [26] Bau  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' use a pre-trained segmentation network to compare the  distribution of objects found in generated images with those  found in a set of real images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This provides a measure of  diversity of the models outputs with respect to the objects that  can be segmented by the pre-trained network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The authors also  propose a method (Layer Inversion), to train networks that  compute approximate inversions of real images into the latent  space of the model, to see what the network generates instead  of the missing objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  While these approaches are critical to better understanding  of the internal mechanisms that drive model behavior, they  are typically specific to a particular model architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ravel  treats models as black boxes and is thus agnostic to model  architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ravel does use pre-trained networks to compute  vector representations of images, but is less sensitive to the  final task the pre-trained network is trained to perform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' For  3  example one could use the embeddings from the model under  examination or any model that has learned semantically useful  features such as InceptionV3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Online Exploration of Model Outputs  White [27] explores a variety of ways to sample images from  latent space that enable repeatable visual comparisons between  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' They introduce a number of visualizations designed  to examine how models perform with respect to specific input  images that are used to test model behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In a follow-  up work White & Loh [28] introduce a novel visual interface  based on a spreadsheet metaphor that allows users to use  geometric operations in the latent space to interactively query  these models and thus explore their output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  While online methods enable users to explore specific hy-  potheses, they generally suffer from supporting relatively small  exploration spaces due to the slow generation of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ravel  focuses on offline analysis of generated images, which allows  examining much larger datasets and can thus complement  online methods as means of generating hypotheses for further,  more targeted investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Embedding Based Visualizations  A number of works have visualized embedding spaces of  large, high-dimensional datasets [29] [30] [31] [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [33] present a visual analysis system which uses the  latent space learned by the encoder of a VAE to explore variation  in an existing image dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This task is conceptually similar to  what we support in Ravel, however we do not attempt to learn  a new latent space as we want to focus on the generator output  and its latent space (rather than fixed input data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Ravel builds on these earlier works visualizing embedding  spaces, and incorporates clustering to make navigating these  spaces more tractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We focus on dataset comparison as a  way to ground exploration of the output space and cater to the  needs of the image generation use case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Xiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [34] present a visual analytics system for  correcting labelling errors in large datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' They visualize t-  SNE projections of image embeddings color coded by label to  highlight data points that are mislabelled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In contrast, Ravel is  designed to support unconditional generation scenarios, where  the generated (and ground truth images) have no labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Thus,  rather than relying on labels for grounding, Ravel enables com-  parative evaluation of datasets to allow grounding evaluation  of generated images in the distribution of real images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  4  APPROACH & SYSTEM DESIGN  Ravel focuses on enabling visual inspection of model outputs  in comparison with some baseline set of images, typically  real ’ground truth’ images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' From our interviews (section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1),  we know that practitioners perform visual analysis of image  samples coming out of models, but typically on small numbers  of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Our aim is to support and scale up those workflows to  allow more systematic visual inspection from 10s or 100s of images to  10,000s or 100,000s of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We leverage four key concepts to  facilitate this comparison across a large set of images:  1)  Image Embeddings: Neural image embeddings pro-  vide a semantically rich vector space for images that  allow computing similarity scores between pairs of im-  ages [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' They have become the standard in evaluation  pipelines for generative image models (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2)  and we want to leverage the familiarity researchers  have with embedding based metrics in Ravel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The abil-  ity to compute semantic similarity between images al-  lows us to group similar generated images together and  allow comparison of those images to similar ground  truth images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' By default we compute the standard In-  ceptionV3 embeddings used in metrics like FID, but can  also add embeddings from other models including pre-  trained models or from the model under examination if  those are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  2)  Clustering Images: In order to enable visual explo-  ration of hundreds of thousands of images we need  to group them into a smaller number of meaningful  groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We use unsupervised clustering of images to  reduce the number of top-level items the user has to  consider from e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 100k images to 1000, 500 or even 250  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We use k-means clustering and provide more  details about this in the pipeline details section below  3)  Cluster Metrics: Once we have reduced the number of  top-level elements to a manageable number we wish to  provide hints to the user as to which clusters might be  most interesting to explore first, as well as scaffold a  repeatable workflow that can guide exploration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We  compute metrics over each cluster that enable sorting  clusters into predictable order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Many of the metrics we  compute are designed to surface differences between  the generated data and the baseline data in a cluster,  with others show general properties of the cluster itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  We provide more details about the metrics we compute  in the pipeline details section below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' By sorting clusters  by these metrics we allow discovery of outlier clusters  as well as analyzing properties of different parts of  the generative image space (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' seeing what kinds of  output images have low precision)  4)  Interactive Visualization: Finally we provide respon-  sive interactive visualization of images, clusters and  associated cluster metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Because we compute all the  data offline, the user interface is quite responsive and  enable fast and free exploration of a large number of  data-points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1  Pipeline Details  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1  Clustering  Ravel clusters the image embeddings using the implementa-  tion of k-means clustering from scikit-learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' k-means was an  attractive clustering algorithm to start with because it is a well  known algorithm that has a single easily understood hyper-  parameter, namely the number of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This allows the user  to directly specify values for this hyper-parameter that they believe  make sense for their dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In addition to this, compared to  other algorithms with similar hyper parameter options such  as spectral clustering, k-means scales well with the number of  examples and number of clusters selected [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' k-means also  tends to produce fairly evenly sized clusters, which is helpful  for displaying their contents in a uniform way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  All clustering methods suffer from issues of imperfect  cluster assignment, particularly at the boundaries of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  However, Ravel mitigates this issue somewhat by visualizing  clusters according to their positions in latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This allows  users to quickly discover and examine clusters that are near  to each other and ascertain whether they are truly a single se-  mantic cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' For more details see the dimensionality reduction  section (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='3) below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  Cluster Metrics  We compute a number of metrics for each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Having  multiple metrics provides different lenses through which to  consider the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' For example one might be interested in  4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The Ravel interface primarily consists of: A) Dataset & view options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' B) Summary charts & linked cluster plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' C) Side by side image grids  for visual comparison of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This view shows a cluster comparing real images on the left to generated images on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  where recall or precision are low, or alternatively where clusters  are tightly packed or more spread out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Clusters may have images from either the generated data  or the baseline/ground truth, in the UI we refer to these data  sources as splits and typically display the baseline data on the left,  though the user can change this interactively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Many metrics are  geared toward exposing differences between the two splits that  are currently being explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Percent of Split 2: The percentage of images in the  cluster that come from the split displayed on the right  (usually the generated data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Recall: Recall is a metric that describes what fraction  of samples in the ground truth split have support in the  alternate split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We compute recall as defined in [11] but  aggregate the per-image values for each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' When  comparing generated images to real ones a high recall  implies the model is producing images as diverse as the  real data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Precision: Precision is an metric that describes what  fraction of samples in the generated data have support  in the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' As above we compute precision  as defined in [11] but aggregate the per-image values  for each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' When comparing generated images to  real ones a high precision implies better image qual-  ity/realism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Distance between split centroids: Measures the dis-  tance between centroids of the samples in a cluster that  belong to each split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Larger values suggest that the data  from the two splits are more visually different while  smaller values suggest that the left and right split are  more visually similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Median distance to centroid: Median distance of sam-  ples in the cluster to the centroid of that cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Smaller  values here imply more compact clusters with more  similar samples, higher values suggest the cluster has  a greater variety of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='3  Dimensionality Reduction  In addition to visualizing clusters by the metrics described  above, we also visualize the positions of cluster centroids in  the embedding space itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Since these are high dimensional  embeddings spaces we need to use dimensionality reduction in  order to visualize them in 2D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We use the UMAP algorithm  [37] to do this projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Other options for dimensionality  reduction include PCA [38] or t-SNE [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Compared to t-  SNE, UMAP has been reported to preserve more of the global  structure of the original space and is significantly more compu-  tationally efficient both as the number of dimensions increases  and as the size of the dataset grows [37] [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The InceptionV3  embedding we use is 2048 dimensional embedding, making a  computationally efficient method particularly attractive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' While  not as directly interpretable as linear methods like PCA, UMAP  is better able to capture some of the complex non-linear rela-  tionships between images encoded in the embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  User Interface  The user interface is a browser-based application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We describe  the design of the user interface and further discuss the utility  of these affordances in the case study section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Figure 1 shows the Ravel interface, divided into 3 main  sections:  DATA  EMBEDDING  N CLUSTERS  A  SPLIT1  SPLIT 2  SAMPLE VIEW  Update  inception_pool_3  500  ImageNet 128 Eval  BigGAN 128, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1  (A): Dataset and View Controls  The user can select which embedding to use, the number of  clusters and which split to show on the left or right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  (B): Charts  There are three main kinds of data display in the charts section  of the UI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Summary Statistics  First is a static table showing summary statistics and metrics  for the dataset as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' These include things like the number  of samples in the whole dataset, the number of samples in each  split as well as dataset level metrics such as Fr´echet distance1,  recall and precision [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Cluster Metric Plots  Below the summary charts are a series of beeswarm plots for  the per-cluster metrics that were computed (see Cluster Metrics  section above for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Each beeswarm shows each cluster  as a dot and plots the distribution of clusters over that metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  These charts are interactive, individual dots can be selected to  show the images from that cluster in the sample viewer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Beeswarm plot showing distribution of cluster precision scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Each dot is a cluster which the currently selected dot shown in orange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  A description of the metric can be accessed by clicking on the ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' icon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  A color encoding can also be applied by clicking on the  rainbow icon toggle next to that plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This color encoding is  applied across all charts allowing comparison of one metric to  another (Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Recall and Precision beeswarm plots colored by precision score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  High recall, low precision clusters can be identified using the position  encoding in the recall plot and the color encoding applied from the  precision plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' To save space in the display we do not display a legend,  as the relationship between high-low values and hue is directly visible in  the chart whose rainbow icon was toggled and exact values are of less  importance than relative comparisons  UMAP Plots  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' When using the Inceptionv3 embedding this is Fr´echet Inception  Distance (FID)  Below the beeswarm plots are two plots showing 2D UMAP  projections of: a) all the clusters and b) images from the currently  selected cluster (See Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The Cluster UMAP view in  particular allows browsing clusters by visual similarity rather  than by the metric scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Previews of individual images are  shown on mouseover of points on the Samples UMAP plot  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Top: UMAP projection of cluster centroids in embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Bottom: UMAP projection of currently selected cluster, real samples are  shown in blue and generated samples are show in red  Highlight Classes  In cases where the dataset does contain class labels, Ravel  will display a search interface that allows users to search for  and select any number of matching classes in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  If one or more classes is selected Ravel will dim clusters  that do not contain any images from those classes in the cluster  plots (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  All the cluster plot interactions are linked, enabling users to  see where a cluster falls in multiple metrics or in embedding  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Any chart can be collapsed by by clicking on its title, this  allows making more room for the charts the user finds most  useful for their analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='3  Sample Viewer  To the right of the charts is the sample viewer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This consists of a  pair of scrollable views displaying image thumbnails from the  selected cluster divided by split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' If there are classes/labels asso-  ciated with the images they are displayed below the thumbnail  and images from the same class are grouped together, otherwise  they are displayed in the order they were processed by the  pipeline (effectively random).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Users can click on images to get  a larger view of the image and see any additional metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content="  Image thumbnails are displayed at a maximum size of  150x150px and a minimum size of 100x100px depending on  Precision with 'lmageNet 128 Eval' as ground truth  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content="8Recall with 'lmageNet 128 Eval' as ground truth  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content="8  Precision with 'lmageNet 128 Eval' as ground truth  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='8Clusters UMAP  Samples UMAP6  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Clusters containing at least one image with the selected classes  are highlighted in all cluster plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  how large the browser window is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' On a 3840 x 2160 resolution  display2 one can typically see 72 images per split for a total of  144 images in a single screenful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' However one clear limitation  is that if there are more images than this in a cluster a user  cannot see them all at once and does have to scroll through to  get a better understanding of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' One way to mitigate  this is to use choose a higher number of clusters to view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Which  results in smaller, more granular clusters, at the cost of having  more to explore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  5  CASE STUDIES  In this section, we illustrate how the design features of Ravel  support user exploration in a series of case studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' These case  studies highlight discoveries the authors made when using the  tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Our 3 use cases are: 1) Unconditional image generation in  a single domain (faces), 2) Class conditioned generation on Im-  ageNet data and 3) Analyzing downstream use of a generative  model for another task - in this case, super-resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  While Ravel supports the use of multiple embeddings for  clustering and exploration, in this paper we focus primarily on  the same Inceptionv3 embeddings used in FID score and other metrics,  as they have become a de-facto standard in the generative  model space and are publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1  Unconditional Image Generation  Unconditional generation refers to situations where a trained  model is used to generate images with no ’conditioning’ other  than an input vector (often referred to as a ’noise’ or ’Z’ vector)  drawn from a random distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In this case study, we  generate 60k images from an implementation of the StyleGAN2  architecture 3 [18] trained on the FFHQ dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The images are  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This resolution is the default 4K resolution which is widely avail-  able.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' It is also close to the native resolution of a 2021 14 inch MacBook  Pro (3024 x 1964)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We want to make clear that we are using an independently trained  StyleGAN2 and not the StyleGAN2 weights released by the original  authors  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The StyleGAN2-based model struggles to model images of  faces with facepaint and other colorful accessories occluding the face, it  instead produces these artefacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  generated using Z vectors drawn from a random distribution  with a mean of zero and a standard deviation of one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We load  those images, along with 67,542 images from the training set  for a total of 127,542 images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Are there images that this model generates that are not part  of the input distribution?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Our analyst opens the Ravel interface in her browser and  sets the number of clusters to 250, with images from the training  data on the left and generated images on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Knowing  that low precision generally implies less realistic images, she  begins by exploring clusters on the low end of the precision  chart and notes that the clusters with the 10 lowest values  each contain generated images with visually obvious defects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Seeing these images contrasted with ground truth data gives  her a sense of what the model is struggling to capture in each  category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' For example she notes that the model has a difficult  time modeling complex backgrounds, portraits where there are  more than one face, or portraits with occluding objects like  hands or microphones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Another problem that stands out to her  is the difficulty the model has generating faces with face-paint  as in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Seeing these corrupted images juxtaposed with  real images from the training data allows her to hypothesize  why the model struggles with this, in particularly she observes  that these types of images are relatively rare in the training  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  In examining 10 clusters, she has quickly scanned through  approximately 4234 generated images and 2718 real images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  Class Conditioned Image Generation  Class conditioned generation refers to models that have been  trained to generate output images for a fixed set of distinct  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Here, we look at directly comparing the output of two  models trained on the same data and task: namely, generating  images from 1000 classes of the ImageNet dataset [41] at a  resolution of 128x128px.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We use model implementations from  Lucic et al’s ”Are GANs Created Equal?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A Large-Scale Study”  [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  We set up a Ravel instance with 50k images generated by  BigGAN 128 and BigGAN-deep 128 [12], and 50k images from  Highlight Classes  Select allSelect none  Filter Class List  SelectedClasses  117)chambered nautilus,pearlynautilus,nautilus  685) odometer, hodometer,mileometer,milometer  √715)pickelhaube  810)spacebar  878)typewriterkeyboard  946)cardoon  984) rapeseed  Cluster Metrics  Percent of Split2 (BigGANDeep128,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='0truncation)  0%  20%  40%  60%  80%  100%  RecallwithBiqGAN 128,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content="0truncation'as ground truth  ?" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='87  the validation set for ImageNet4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Input vectors for each model  are drawn from a random normal distribution, as described in  [42], and no truncation is applied to the input vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Using these models demonstrates a workflow where re-  searchers are trying to determine how one variant of a model, or  an improved model architecture, behaves differently from some  baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This comparison is a common workflow in  machine learning, typically achieved by reporting performance  on key metrics such as FID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We demonstrate how Ravel can  complement traditional metrics to find specific differences in  model behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Mode collapse of the ”space bar” and ”typewriter keyboard”  classes in the BigGAN-deep model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All 100 images in this cluster look  identical as both classes have collapsed onto the same output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Output of the ”space bar” and ”typewriter keyboard” classes in  BigGAN show much more variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This model does not exhibit mode  collapse for these classes  How does BigGAN compare to BigGAN-deep in terms of  diversity of output  Our analyst opens Ravel and sets the number of clusters to  500, with the left split showing output from BigGAN, and the  right split showing output from BigGAN-deep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  It immediately jumps out to him that there are a number  of clusters that have scores of 0 in the recall chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' He clicks  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Data retrived from https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/datasets/ cata-  log/imagenet2012  on one of them and discovers it only contains images from  BigGAN-deep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All 100 images from this model are from two  classes, appear virtually identical, and are of low visual quality  (see Figure 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This is a classic case of mode collapse [43];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  the model was unable to learn the true distribution for these  classes and has ’collapsed’ all output for these classes to a  single image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In this case, both classes have been collapsed into  the same output image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The analyst clicks on other clusters  with zero recall and finds similar mode collapse in BigGAN-  deep for the following classes: ”space bar”, ”typewriter keyboard”,  ”pickelhaube”, ”rapeseed”, ”cardoon”, ”chambered nautilus, pearly  nautilus, nautilus”, and ”odometer”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Using the ”highlight classes” feature of Ravel 5, our analyst  is able to find all clusters that contain images from these classes,  and confirms that the BigGAN model does not show mode  collapse for these classes (Figure 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  What about classes where both models do okay at gen-  eration (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' neither model exhibits a pathological failure like  mode collapse)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Our analyst now chooses to increase the granularity of  clusters by setting the number of clusters to 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' He turns  on the color by option of the precision chart, and then looks at  the recall chart to find clusters with high recall but relatively  low precision (though not as low as in the previous section).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Looking at higher recall clusters allows finding ones that have  at least some overlap in their distribution, while keeping an  eye on precision suggests differences in quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' These appear  as light yellow dots on the right side of the recall chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' He  randomly selects one, and discovers a cluster of sea urchins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Both generators produce high quality outputs, however visual  inspection shows that BigGAN-deep produces more diverse  output (Figure 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A cluster of sea urchin samples from two generators, both  produce high quality images, but the generator on the right produces  more diverse output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The images on the right show a greater variety of  colors, textures and poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  A benefit of clustering by visual similarity, rather than  grouping by label, is making it easier to discover overlap or  leakage of visual semantics between classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Using the same  method as above, our analyst selects another cluster that con-  sists of relatively realistic images of dishrags (Figure 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' He  then highlights all clusters containing dishrags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+page_content='individually examine all these clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' His findings, shown in  (Figure 11 and Figure 12), suggests that other classes, namely  handkerchief’ and ’doormat’, are ’leaking’ into how each gen-  erator models dishrags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A cluster of ’dishrag’ samples from BigGAN on the left and  BigGAN-deep on the right, both produce somewhat realistic dishrags,  but the generator on the right produces images with more diverse  textures and colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' BigGAN cluster with a few dishrags but many colorful hand-  kerchiefs that have similar patterns to those seen in the main dishrag  cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This suggests some leakage in visual representation between  the two concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' BigGAN-deep cluster with a few dishrags but many doormats,  this suggests a hypothesis for why many of the BIgGAN-deep dishrags  have a very rough texture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='3  Downstream Applications of Generative Models: Super-  Resolution  In our final case study we consider the PULSE (Photo Upsam-  pling via Latent Space Exploration) algorithm [22], a super-  resolution algorithm that searches the manifold of a genera-  tive image model (in this case StyleGAN2) to create plausible  upsampled images corresponding to low resolution input im-  ages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The post-publication release of this model received sharp  critique, as users quickly discovered weaknesses in the mod-  els ability to upsample images of people with non-caucasian  features [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We use this example to illustrate how broader  exploration of output manifolds could help researchers and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Cluster metric charts colored by cluster precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' On the left  of the precision chart is a group of clusters with very low precision  that are mostly composed of images only from the ground truth data,  many of these also have low recall, suggesting the algorithm struggles  to produce any output for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  practitioners who are using these kinds models in downstream  applications to understand their weaknesses and mitigate risks  before release.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  In this scenario, we use the original CelebA-HQ dataset  from Karras, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This dataset consists 30,000 facial por-  traits of celebrities at 1024x1024px.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We take CelebA-HQ images  at 32x32px and upsample them back to 1020x1024px using the  PULSE algorithm5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We invoke PULSE with the default settings  provided by the authors in their model release 6, however we  increased the number of steps we run the algorithm from 100 to  200 steps to increase the chances of PULSE producing a result  for a given input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='7  We then compare the original 1024x1024px images and the  PULSE up-sampled ones using Ravel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In total, we have 30000  original CelebA-HQ images and 22092 images output from  PULSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 7908 images failed to produce any output after 200  steps of the PULSE algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  What kinds of images does PULSE struggle to produce any  output for?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Our analyst sets the number of clusters to 250 and the  original CelabA-HQ images on the left split, and immediately  notices a group of clusters on the lowest end of the precision  chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' She notices that many clusters also have low recall and  are mostly composed of images only from the ground truth (see  Figure 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' She clicks on some low-recall/low-precision clusters  and observes a few categories where the algorithm struggles  to produce any output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' These include: people wearing hats or  other headgear, images where the person has a a microphone or  hand in front of them, faces with a lot of facepaint or makeup,  and images where people are wearing sunglasses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Each of these  clusters has between 60-120 images and a few samples are  shown in Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  What kinds of images does PULSE struggle to produce high  quality output for?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This scale factor (24x) is within the range of scale factors (8x-64x)  the original authors used in evaluation  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='com/adamian98/pulse  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We did this because PULSE will not always produce a result for  an input image, and we found increasing the number of steps allowed  substantially more input images to produce some result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+page_content=' 539) doormat, w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 539) doormat, w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 539) doormat, w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='.Percent of Split 2 (PULSE upscaled CelebA 32px->1024px.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=")  0%  20%  40%  60%  80%  100%  Recall with 'CelebA HQ 1024px' as ground truth  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content="8  Precision with 'CelebA HQ 1024px' as ground truth  0  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='89  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Each row contains samples from a different cluster with that only  has images from the ground truth data and none from the algorithm out-  put.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' These are examples of images the algorithm struggles to upscale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  She continues to explore low precision clusters by scanning  left to right along the chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' One of the lowest precision clusters  contains ground truth images of people wearing spectacles (and  a few wearing sunglasses), however from the algorithm output  she sees a number of low quality (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' unrealistic) images that  are likely up-scaled from ones where the subject is wearing  sunglasses (Figure 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' She refines her hypothesis about what  the algorithm does to portraits with sunglasses, determining  that, ”if a person is wearing sunglasses, the algorithm often fails to  produce any image, and when it does, it produces unrealistic output”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Samples from a cluster of upscaled images of people wearing  sunglasses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  What kinds of images does PULSE do well at upsampling?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  The precision chart can also be used to look at what images  PULSE does well at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' As our analyst browses clusters on the  right side of the distribution, she observes that a majority of  high quality outputs seem to be of lighter skin tone faces that  look relatively young or middle aged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Her manual inspection reveals some of the model’s fail-  ure modes and strengths along demographic categories even  though she does not have access to quantitative measures of  performance across sensitive features such as skin tone or age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6  DOMAIN EXPERT USER STUDY  We evaluated Ravel in a two-stage study, where the first stage  identified domain experts’ model evaluation goals, workflows  and existing tools, and the second stage investigated the us-  ability and utility of the Ravel UI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Participants were recruited  from a convenience sample of full time employees as a large  technology company, and there was a diversity in gender  identity (nfemale = 1, nMale = 5), product area (5 different  teams), and office location (nIsrael = 2, nUnitedStates = 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Stage  one (n = 4) included four expert research scientists and soft-  ware engineers who currently work on training and evaluating  generative models, and stage two (n = 5) included three of  the users from stage one plus two additional users who have  experience working with generative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Both evaluation  stages used remote moderated Google Meet video calls to speak  with users and allow them to share their screen to show how  they interacted with Ravel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1  Stage One: The Current State of Evaluation  Stage one aimed to understand the current state of evaluation  for generative image model output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Semi-structured interviews  were used, with questions about participants’ familiarity and  day to day work with generative models, goals and motivation  for model evaluation, as well as current workflows and prac-  tices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All four users currently work on generative models, and  were familiar with StyleGAN and its variants, BigGAN and  its variants, as well as other models trained on ImageNet and  FFHQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' There was diversity in architectures they work with and  the tasks they apply generative models to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Here, we report the  most common practices among users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1  Evaluation Goals & Workflows  All four participants reported that publication of model per-  formance/improvement was a primary goal for their work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All  four participants also expressed that evaluating output image  quality was critical to understanding model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  All four participants reported a mix of quantitative and  qualitative evaluation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In general, their workflows  could be characterized by a common pattern of: model training  accompanied by limited visual inspection for sanity-checking  → examination of metrics → continued training → reexamina-  tion of metrics until a predetermined threshold is reached →  qualitative visual inspection of image output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Two participants indicated that they believed the current  “best practice” for determining image quality was human  qualitative evaluation, often from crowdsourced studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Im-  portantly, all four participants also emphasized the ubiquitous  reliance upon and limitations of FID scores in model evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  While one user suggested that “FID scores are much better  than inception scores and other metrics”, they also conceded  that “there is not a gold standard for evaluation of generated  images”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All users indicated that they were dissatisfied with  FID score as a primary evaluation metric, and that they had  all experienced and read cases where they felt that FID score  did not align with human inference, a sentiment supported in  Zhou, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  Evaluation Tools  All four users mentioned using TensorBoard [45] or Colab8  (a computational notebook envrionment similar to Jupyter  Notebook [46]) to examine model output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' For Colab, the main  strength reported was flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The flexibility of Colab enables  bespoke analyses that we elaborate on in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Its main  limitations were difficulties reusing code between projects and  sharing results, especially with non-technical collaborators or  stakeholders not directly involved with model training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' For  TensorBoard, the main strengths reported were ease of use  during training to quickly visualize metrics and see sample  output at different stages of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The main limitations  mentioned about TensorBoard were its latency when loading  many images, and lack of customization compared to an open  ended tool like Colab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' https://colab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='com/  RUCAEN10  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='3  Qualitative Visual Evaluation Tasks  Determining image quality was reported as the most important  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Determining the diversity of images was also important  to all four users, and one user mentioned that looking for  the occurrence of mode collapse was an explicit part of their  evaluation workflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All users indicated that it was important  to do more granular and bespoke image generation, including  looking at samples within certain classes or samples close to  each other in embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' One user discussed examining  different levels of truncation for latent vectors to make deci-  sions about both realism and aesthetics in the output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Users  reported viewing a small number of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' One user reported  looking at approximately 64 images, and never more than 100  images, per evaluation step of the model training pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Another user explained that when they work with a team on an  evaluation, they typically generate and inspect about 50 images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  However, when working alone, this user said that they would  inspect at least 200 images, noting that it was difficult to get a  group consensus on more than 50 images at a time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  We determined four categories of critical evaluation tasks  from this part of the study: image diversity, image quality, mode  collapse, and a “catch-all” category of additional explorations  of classes and samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  Stage Two: Observing how Ravel is Used  The objective of this stage was to determine how the Ravel UI  can be used for the critical evaluation tasks identified in stage  one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A brief slide deck and video explaining the UI components  was sent to users upon confirmation of their participation,  which they were asked to review before the study session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The  study sessions themselves lasted for one hour and consisted  of task based user exploration of the tool and semi-structured  interview questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='1  Task one: Diversity  The first task we asked users to attempt was to decide whether  BigGAN or BigGAN-deep was performing better in terms of  the diversity of sea urchin images, in a setup mirroring the  Ravel instance described in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This instance showed  128x128 pixel images from both models, with 50,000 images  per model and 50 images per class from each model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The UI  resolution was set to show the same number of images for each  user: 5 images per row in each split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Users were presented with an instance of Ravel with the  ”sea urchin” class selected in the Highlighted Classes menu,  showing results from BigGAN and BigGAN-deep in the left  split and right split, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' On initial load the instance  displayed the cluster containing most of sea urchin images  selected: 39 (out of 50) urchins from BigGAN and 45 (out of  50) urchins from BigGAN-deep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  All users started by attending to images in each split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' No  users examined metrics or asked about metrics as a first step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  This emphasizes the importance of Ravel intuitively depicting  some of the most important information for assessing image  diversity: a salient grid of sample images within a cluster  of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Three users immediately noted the number of  samples in each split, paying close attention to which model  had a greater number of samples in the cluster of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  The most common flow involved inspecting individual images  and counting or “eyeballing” the number of images in each  model with unique background colors, sea urchin poses, and  sea urchin colors (all users mentioned these three features).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Three users scanned the metrics charts and clicked on the  other highlighted clusters with sea urchins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All five users made  the determination that BigGAN-deep was performing better in  terms of the diversity of sea urchin images, with one user ex-  plicitly stating that this confirmed their prior expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This  demonstrates consistency in how users complete this critical  task with Ravel, and shows the potential for convergent deci-  sion making and operationalization of workflows in qualitative  visual evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' It is also notable that Ravel helped confirm  one user’s prior expectations about BigGAN-deep’s diversity  performance, although that could also have been a potential  biasing factor in their evaluation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2  Task two: Quality  For the second task, users were asked to decide whether Big-  GAN or BigGAN-deep was performing better in terms of the  quality of golden retriever images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Users were presented with  the same Ravel instance as task one, but this time the ”golden  retriever” class was selected in the Highlighted Classes menu  and a cluster showing most of the golden retriever images was  selected: 46 (out of 50) in the BigGAN split and 46 (out of 50) in  the BigGAN-deep split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  All users immediately noted many artifacts in output im-  ages from both models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All users clicked on individual images  and narrated particular issues, such as the shape of dogs’ noses,  the number of legs, and the accuracy of the form and pose of the  dogs in each sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The most common workflow was to count  or “eyeball” the number of artifacts in each split to make an  initial determination, but evaluation workflows were notably  more diverse between users for the rest of the task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Five users  reported that this task was more difficult than the diversity  task while one user reported that it was easier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Some users  indicated that FID and Inception score for each model would be  an important part of making this determination in their typical  workflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Four out of the five users made the determination  that BigGAN-deep also performed better in terms of the quality  of golden retriever images, and one user did not make an ex-  plicit determination for this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Once again, Ravel supported  consistency in the primary image quality evaluation strategy  across all users, but individual exploration varied after this  initial decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Some users validated their visual judgments  by looking at recall and precision charts, but others simply  explored the charts without forming additional opinions about  the task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='3  Task three: Mode Collapse  Following the Quality task, users were asked if they were  familiar with the term mode collapse and if it was something  they used to evaluate generative model output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Four out of  five users were familiar with mode collapse and reported it as  a useful discovery in the model evaluation process, while one  user was unfamiliar with the term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Users who were familiar  with mode collapse were then asked to use Ravel to determine  whether it had occurred for either model within any class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Because this task was not constrained to a single class, it  was more open-ended, and thus more challenging for users to  make a determination about.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Workflows varied widely between  users, as they were given no guidance about how to accomplish  the task or make a determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Several users mentioned that  they expected BigGAN to exhibit more mode collapse after  observing that BigGAN-deep had better diversity in the first  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Four users who found concrete instances of mode collapse  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 6) did so by selecting clusters with the smallest  values in the Recall chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Four out of five users viewed the  cluster samples displayed in figure 7 at some point during  their exploration, but one user did not identify it as mode  collapse, and one user did not select it at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Nevertheless,  11  this was a promising observation, and demonstrates further  consistency of Ravel’s usability and specific utility of the recall  visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' There was majority agreement that the recall  chart can be used to identify mode collapse, and it was revealed  to occur more often in BigGAN-deep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='4  Task four: Additional exploration of classes, samples,  and features  For their final task, users were asked to view an instance  of Ravel showing generated images from a StyleGAN2-based  model in the right split, and images from its ground-truth  training data, FFHQ, in the left split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Users were told they  could freely explore the interface, either repeating the quality  and diversity assessments or trying a new task that they might  be interested in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  This task was fully unguided, but most users started by  assessing image quality for the StyleGAN2-based model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' It was  common for users to select clusters at the low and high ends  of the Precision distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' One user observed that clicking  on a cluster with high precision revealed “typical FFHQ im-  ages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' very good images without occlusion, faces looking at  the camera, showing people with straight hair, and the model  output is very similar to these images.”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Four out of five users  discovered and explicitly verbalized that StyleGAN2-based  model struggled to generate images of people with facepaint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  They did this by clicking on clusters with low precision and  noticing artifacts on many of the generated images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All four  of these users expressed surprise upon making this new dis-  covery about the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This demonstrates that even without  a specific prompt, many users will make the same kinds of  discoveries and follow the same types of evaluation processes  with Ravel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' One of our participants was on the team that had  originally trained the StyleGAN2-based model that we used  and discovered that the model was unable to generate faces of  people wearing a particular style of fuzzy winter hat that was  fairly common in the ground truth data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' He remarked that he  wasn’t aware of that inability and was pleasantly surprised to  be able to discover it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  The other common tasks were “semantic explorations” of  the clusters and the embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Four out of five users  examined images in the FFHQ split to make decisions about  whether the clusters were semantically meaningful, and to  explore the diversity of FFHQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Two users pondered whether  or not the embedding space was doing a good job of capturing  what they, as humans, would group together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' These users inves-  tigated the proximity of samples in the Samples UMAP chart  and determined that the ImageNet feature space is not optimal  for clustering faces, since they could not find consistent visual  similarity between nearby samples in some of the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='5  Discussion of Expert Feedback  Users were overall impressed with the tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' All five users  thought that Ravel would fit into their current evaluation  process, and that it was especially useful for researchers who  publish generative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Here, we summarize additional  feedback from the reflection portion of stage two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Two users reported that their exploration made them doubt  whether the Inceptionv3 features were good for evaluating face  portrait generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In reflection, one of these users stated that  Ravel could be used to learn about the feature space itself,  which could be broadly useful in generative image model  evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Upon discovering mode collapse in BigGAN-deep, one user  stated that Ravel would be useful for probing state-of-the-art  models to learn which classes they can’t generate images for,  which could point to systematic failure modes for researchers  to focus on improving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  One user noted that Ravel could help their team reach  conclusions about model performance more quickly than using  Colab, especially for understanding the diversity of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  They explained that using Colab required developing a bespoke  visualization tool and manual calculations of FID in each clus-  ter, whereas the same type of useful information was readily  available in the Ravel UI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Two users emphasized that Ravel  could help operationalize how researchers evaluate quality and  diversity, one of which explained that Ravel could be “a forcing  function for having a standard UI/pipeline for results”, arguing  that this would make it “easier to share results with someone  on another team, or someone non-technical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' even with my  manager who doesn’t have time to run my code”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This confirms  for us that there is a place for bespoke purpose built interfaces  like Ravel, that while less flexible than Colab, are more purpose  built for common evaluation tasks that researchers perform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Overall, the expert feedback from stage two was positive  and enthusiastic, with several users expressing excitement  about continued exploration in Ravel and incorporating it into  their own workflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  7  LIMITATIONS AND FUTURE WORK  Our qualitative user study was performed with a small, domain  expert sample from a single company, and therefore may not be  an externally valid representation of all researcher experiences  with generative image models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' The study sessions were also  limited to one hour per user, with each evaluation task time-  boxed to 15 minutes or less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Richer and more diverse interac-  tions and discoveries could be possible with a longer duration  of tool use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Two users wanted to see images at a higher resolution,  and two other users wanted to see the original resolution of  the images when examining them for artifacts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' this is not an  inherent issue with Ravel but is an important design affordance  for the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Two users wanted to be able to mark images in  each split once they had viewed them, and enabling this would  support the ’counting’ based workflows we saw participants  use to complete the tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  When using the class conditional model, users initially  reported that they would prefer to see all images from a given  class in the same view (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' clustering by class label) to make a  judgement about that class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' However on further exploration  they noted it was useful to see ’outlier’ images for a given  label in context with the other images they are most similar  to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This suggests that both workflows are important to support  for class conditioned models and should be supported by tools  like Ravel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  The authors also note a number of limitations of the system  we observed while watching users use the tool:  User’s cannot always interpret the ’meaning’ of clusters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=',  construct a rationale for why a set of images are clustered  together).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This is a general issue with unsupervised methods  like clustering, but we found that users would often try to  attach some semantically meaningful description to each cluster  to ground their comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Exploring ways to ’describe’ clusters or summarize differ-  ences between clusters could be important future work to aid  user comprehension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We also think exploring other clustering  methods, in particular hierarchical methods, could be a partic-  ularly attractive means to produce clusters at different levels of  granularity to help build understanding of groups within the  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  12  In describing the Sample viewer (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='3) we noted  that one limitation is that not all of the images are visible in one  screen if there are many images present in the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' While one  mitigation is to decrease the size of clusters by increasing the  number of clusters, we believe that future work could provide  better ways to get the visual gestalt of the entire cluster in one  view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Possibly adapting techniques such as those described in  Activation Atlas [47], creating stacks of very similar images  within a cluster, or other ways of sub-sampling or sorting to  ensure that we are displaying the maximum variety about a  cluster in a single screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  One user task that Ravel does not directly support is de-  tecting memorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' One user commented that adding a real  time nearest-neighbor search to the interface would likely make  it useful for this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  8  CONCLUSION  We presented Ravel, a visual analysis tool that enables re-  searchers to perform large scale qualitative evaluation of gen-  erative model outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Our primary contributions included: A visual analytics system that supports multiple evalua-  tion tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' evaluating quality & diversity, discovering  mode collapse or gaps in model output) for generative  image models and is agnostic to model architecture and  internals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Interactive exploration of large generative image model  datasets, facilitated by clustering and the use of fine  grained visualization of cluster metrics to guide quali-  tative evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A user interface that uses visual comparison driven by  semantically meaningful embedding spaces to support  reasoning about differences between image distributions  and generate hypotheses about model behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  The expert users in our study were able to generate consis-  tent insights about model behaviour including identifying areas  of the true data distribution the model was not capturing, such as  face paint or certain kinds of headgear in the StyleGAN2-based  model or mode collapse in BigGAN-deep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' This kind of insight  is an example of one that is not possible to get from just looking  at quantitative metrics like FID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Our study participants confirmed our hypotheses that single  number metrics are not fully sufficient measures of model  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' In addition to exploring metrics at greater granu-  larity, Ravel allows users to explore metrics at finer granularity,  revealing areas of model output where metrics like recall or  precision do not capture problems in the generated images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Our users hypothesized that the underlying InceptionV3 em-  bedding, used both in our tool and in the primarily metrics in  the field, may not attend to certain kinds visual artefacts that  are easily visible to humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We believe that future work in  this direction could enable better understanding of limits of the  embedding spaces themselves and how they affect both metrics  and the workflows that use them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  The authors wish to thank Mario Lucic, Marvin Ritter, Ben  Poole, Han Zhang, Chitwan Saharia, James Wexler and Lucas  Dixon for their help and feedback on this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' We also thank  our study participants for their feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  REFERENCES  [1]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Goodfellow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Pouget-Abadie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Mirza, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Warde-Farley,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ozair, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Courville, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bengio, “Generative Adversarial  Nets,” in Advances in Neural Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 27,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='cc/paper/  2014/hash/5ca3e9b122f61f8f06494c97b1afccf3-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='html  [2]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Kingma and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Welling, “Auto-Encoding Variational  Bayes,” Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/  1312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='6114v10  [3]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Dinh,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Krueger,  and  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Bengio,  “NICE:  Non-linear  Independent Components Estimation,” arXiv:1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='8516 [cs], Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  2015, arXiv: 1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='8516.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/  1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='8516  [4]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Sohl-Dickstein,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Weiss,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Maheswaranathan,  and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Ganguli,  “Deep  Unsupervised  Learning  using  Nonequi-  librium  Thermodynamics,”  in  Proceedings  of  the  32nd  International  Conference  on  Machine  Learning,  Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  2015,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  2256–2265,  iSSN:  1938-7228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Available:  https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='mlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='press/v37/sohl-dickstein15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='html  [5]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Odena,  “Open  Questions  about  Generative  Adversarial  Networks,” Distill, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' e18, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Available: https://distill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='pub/2019/gan-open-problems  [6]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Theis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Oord, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bethge, “A note on the evaluation  of generative models,” arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='01844 [cs, stat], Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2016, arXiv:  1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='01844.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='01844  [7]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Borji,  “Pros  and  Cons  of  GAN  Evaluation  Measures,”  arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='03446 [cs], Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [8]  ——, “Pros and Cons of GAN Evaluation Measures: New Devel-  opments,” arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='09396 [cs], Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [9]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Heusel,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Ramsauer,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Unterthiner,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Nessler,  and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Hochreiter, “GANs Trained by a Two Time-Scale Update  Rule Converge to a Local Nash Equilibrium,” in Advances  in  Neural  Information  Processing  Systems,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  30,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='cc/paper/2017/  hash/8a1d694707eb0fefe65871369074926d-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='html  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Sajjadi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bachem, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Lucic, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bousquet, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Gelly,  “Assessing Generative Models via Precision and Recall,” in  Advances in Neural Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='cc/paper/2018/  hash/f7696a9b362ac5a51c3dc8f098b73923-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='html  [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Kynk¨a¨anniemi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Karras, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Laine, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Lehtinen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Aila,  “Improved Precision and Recall Metric for Assessing Generative  Models,” arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='06991 [cs, stat], Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2019, arXiv: 1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='06991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='06991  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Brock,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Donahue,  and  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Simonyan,  “Large  Scale  GAN Training for High Fidelity Natural Image Synthesis,”  arXiv:1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='11096 [cs, stat], Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2019, arXiv: 1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='11096.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='11096  [13] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Karras,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Laine,  and  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Aila,  “A  Style-Based  Generator Architecture for Generative Adversarial Networks,”  arXiv:1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='04948 [cs, stat], Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2019, arXiv: 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='04948.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='04948  [14] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Kingma and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Dhariwal, “Glow: Generative Flow with  Invertible 1x1 Convolutions,” arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='03039 [cs, stat], Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2018,  arXiv: 1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='03039.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  03039  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Oord, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Vinyals, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Kavukcuoglu, “Neural Discrete  Representation Learning,” arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='00937 [cs], May 2018, arXiv:  1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='00937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='00937  [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ho, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Saharia, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Chan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Fleet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Norouzi, and  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Salimans, “Cascaded Diffusion Models for High Fidelity Image  Generation,” arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='15282 [cs], Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2021, arXiv: 2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='15282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='15282  [17] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Szegedy, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Vanhoucke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ioffe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Shlens, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Wojna,  “Rethinking the Inception Architecture for Computer Vision,”  arXiv:1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='00567 [cs], Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Karras, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Laine, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Aittala, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Hellsten, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Lehtinen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Aila,  “Analyzing and improving the image quality of stylegan,” in  Proceedings of the IEEE/CVF conference on computer vision and pattern  recognition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 8110–8119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Geirhos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Rubisch, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Michaelis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bethge, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Wichmann,  and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Brendel, “ImageNet-trained CNNs are biased towards  texture;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' increasing shape bias improves accuracy and robustness,”  arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='12231 [cs, q-bio, stat], Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [20] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Salimans, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Goodfellow, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zaremba, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Cheung, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Radford,  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Chen, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Chen, “Improved Techniques for Training GANs,”  in Advances in Neural Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 29, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  13  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='cc/paper/2016/  hash/8a3363abe792db2d8761d6403605aeb7-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='html  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Barratt and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Sharma, “A Note on the Inception Score,”  arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='01973 [cs, stat], Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2018, arXiv: 1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='01973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Available: http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/abs/1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='01973  [22] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Menon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Damian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Hu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ravi, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Rudin, “PULSE:  Self-Supervised Photo Upsampling via Latent Space Exploration  of Generative Models,” in 2020 IEEE/CVF Conference on Computer  Vision and Pattern Recognition (CVPR), Seattle, WA, USA, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2020,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2434–2442.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [23] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Denton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Chintala, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Szlam, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Fergus, “Deep Gener-  ative Image Models using a Laplacian Pyramid of Adversarial  Networks,” arXiv:1506.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='05751 [cs], Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zhou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Gordon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Krishna, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Narcomey, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Fei-Fei, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bernstein, “HYPE: A Benchmark for Human eYe Perceptual  Evaluation of Generative Models,” p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bau, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Strobelt, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Tenenbaum, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Freeman, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Torralba, “GAN Dissection: Visualizing and Un-  derstanding Generative Adversarial Networks,” arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='10597  [cs], Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [26] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bau, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zhu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Wulff, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Peebles, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Strobelt, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zhou,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Torralba, “Seeing What a GAN Cannot Generate,”  arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='11626 [cs, eess], Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [27] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' White, “Sampling Generative Networks,” arXiv:1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='04468 [cs,  stat], Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [28] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' White and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Loh, “SpaceSheet: Navigating Conceptual Space  with a Spreadsheet Interface,” p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Smilkov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Thorat, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Nicholson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Reif, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Vi´egas, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Wattenberg, “Embedding Projector: Interactive Visualization  and Interpretation of Embeddings,” arXiv:1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='05469 [cs, stat],  Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [30] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ho, “Font Map,” https://experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='withgoogle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='com/font-  map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Diagne  and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Doury,  “Curator  Table,”  https://experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='withgoogle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='com/curator-table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [32] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  McDonald,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Tan,  and  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Mann,  “Bird  Sounds,”  https://experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='withgoogle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='com/bird-sounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [33] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Liu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Jun, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Li, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Heer, “Latent Space Cartography: Visual  Analysis of Vector Space Embeddings,” Computer Graphics Forum,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 38, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 67–78, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Xiang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ye, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Xia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Chen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Liu, “Interactive  Correction of Mislabeled Training Data,” in 2019 IEEE Conference  on Visual Analytics Science and Technology (VAST), Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+page_content='  57–68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [35] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Isola, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Efros, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Shechtman, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Wang,  “The  Unreasonable  Effectiveness  of  Deep  Features  as  a  Perceptual  Metric,”  2018,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  586–595.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Avail-  able:  https://openaccess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+page_content='html  [36] “Scikit-learn  Overview  of  Clustering.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Avail-  able:  https://scikit-learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='org/stable/modules/clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='html#  overview-of-clustering-methods  [37] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' McInnes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Healy, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Saul, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Grossberger, “Umap: Uni-  form manifold approximation and projection,” The Journal of Open  Source Software, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 29, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 861, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [38] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=', “Liii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' on lines and planes of closest fit to systems of  points in space,” The London, Edinburgh, and Dublin Philosophical  Magazine and Journal of Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 559–572, 1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [39] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Van der Maaten and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Hinton, “Visualizing data using t-sne.”  Journal of machine learning research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 11, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Coenen and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Pearce, “Understanding UMAP,” 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Available: https://pair-code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='io/understanding-umap/  [41] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Russakovsky, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Deng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Su, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Krause, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Satheesh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ma,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Huang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Karpathy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Khosla, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bernstein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Berg, and  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Fei-Fei, “ImageNet Large Scale Visual Recognition Challenge,”  International Journal of Computer Vision (IJCV), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 115, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  211–252, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [42] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Lucic, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Kurach, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Michalski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Gelly, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bousquet,  “Are  GANs  Created  Equal?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  A  Large-Scale  Study,”  in  Advances  in  Neural  Information  Processing  Systems,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  31,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Available: https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='cc/paper/  2018/hash/e46de7e1bcaaced9a54f1e9d0d2f800d-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='html  [43] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Goodfellow, “NIPS 2016 Tutorial: Generative Adversarial Net-  works,” arXiv:1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='00160 [cs], Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [44] “Lessons  from  the  PULSE  Model  and  Discussion,”  https://thegradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='pub/pulse-lessons/, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [45] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Abadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Agarwal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Barham, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Brevdo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Citro,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Corrado, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Davis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Dean, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Devin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ghemawat, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Good-  fellow, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Harp, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Irving, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Isard, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Jia, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Jozefowicz, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+page_content=' Mane, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+page_content=' Shlens, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Steiner, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+page_content=' Tucker, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Vanhoucke, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Vasudevan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Viegas, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Vinyals,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Warden, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Wattenberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Wicke, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Yu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Zheng,  “TensorFlow: Large-Scale Machine Learning on Heterogeneous  Distributed Systems,” arXiv:1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='04467 [cs], Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [46] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Kluyver, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ragan-Kelley, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' P´erez, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Granger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Bussonnier,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Frederic, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Kelley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Hamrick, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Grout, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Corlay, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Ivanov,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Avila, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Abdalla, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Willing, “Jupyter notebooks – a  publishing format for reproducible computational workflows,” in  Positioning and Power in Academic Publishing: Players, Agents and  Agendas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Loizides and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Schmidt, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  IOS Press, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 87  – 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Carter, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Armstrong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Schubert, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Johnson, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' Olah,  “Activation Atlas,” Distill, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' e15, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='  Available: https://distill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
+page_content='pub/2019/activation-atlas' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XNE3T4oBgHgl3EQfbwpA/content/2301.04518v1.pdf'}
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+Condensed Matter Physics, 2022, Vol. 25, No. 4, 43701: 1–11
+DOI: 10.5488/CMP.25.43701
+http://www.icmp.lviv.ua/journal
+The antiferromagnetic phase transition in the
+layered Cu0.15Fe0.85PS3 semiconductor: experiment
+and DFT modelling
+V. Pashchenko
+1, O. Bludov
+1, D. Baltrunas
+2, K. Mazeika
+2, S. Motria3,
+K. Glukhov
+3∗, Yu. Vysochanskii
+3.
+1 B. Verkin Institute for Low Temperature Physics and Engineering of NAS of Ukraine, 47 Nauky Ave., 61103,
+Kharkiv, Ukraine
+2 Department of Nuclear Research Center for Physical Sciences and Technology, 231 Savanoriu ave., LT-02300,
+Vilnius, Lithuania
+3 Institute for Solid State Physics and Chemistry, Uzhhorod National University, 54 Voloshyn Str., 88000,
+Uzhhorod, Ukraine
+Received July 23, 2022, in final form October 15, 2022
+The experimental studies of the paramagnetic-antiferromagnetic phase transition through Mössbauer spec-
+troscopy and measurements of temperature and field dependencies of magnetic susceptibility in the layered
+Cu0.15Fe0.85PS3 crystal are presented. The peculiar behavior of the magnetization — field dependence at low-
+temperature region gives evidence of a weak ferromagnetism in the studied alloy. By the ab initio simulation of
+electronic and spin subsystems, in the framework of electron density functional theory, the peculiarities of spin
+ordering at low temperature as well as changes in interatomic interactions in the vicinity of the Cu substitutional
+atoms are analyzed. The calculated components of the electric field gradient tensor and asymmetry parameter
+for Fe ions are close to the ones found from Mössbauer spectra values. The Mulliken populations show that the
+main contribution to the ferromagnetic spin density is originated from 3𝑑-copper and 3𝑝-sulfur orbitals. The es-
+timated total magnetic moment of the unit cell (8.543 emu/mol) is in reasonable agreement with the measured
+experimental value of ∼ 9 emu/mol.
+Key words: metal phosphorus trichalcogenides, magnetic ordering, Mösbauer spectroscopy, phase transition,
+density functional theory
+1. Introduction
+Two-dimensional (2D) van der Waals (vdW) materials offer possibilities to study novel physical
+properties and explore their potential applications in electronic, optical, and spintronic devices in the
+nanoscale [1]. The realization of magnetism in easily exfoliated layered crystals provides accessibility
+to control and manipulate magnetic properties at a single atomic layer level [2–6]. The presence of
+multiferroicity in such materials, when they exhibit two or more primary ferroic properties, is important
+for potential applications in the non-volatile storage devices controlled by an external electric field.
+Recently, 2D ferroelectric polarization was found in CuInP2S6 several layers flakes and even in
+monolayers [7, 8]. On the other hand, 2D antiferromagnetism is also demonstrated for CuCrP2S6 layers [9].
+Furthermore, multiferroic material can be prepared by doping or modifying some monolayers, such as
+black phosphorus and graphene [10]. 2D materials with spontaneous ferromagnetism and ferroelectricity
+have rarely been reported. Recenrly, it was found that 2D CuCrP2S6 is multiferroic with magnetism
+and ferroelectricity stems from Cr and Cu cations, and the magnetoelectric coupling follows from
+∗Corresponding author: kglukhov@gmail.com
+This work is licensed under a Creative Commons Attribution 4.0 International License. Further distribution
+of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
+43701-1
+arXiv:2301.01338v1  [physics.comp-ph]  3 Jan 2023
+
+V. Pashchenko et al.
+the spin-orbit interaction [11]. Copper chromium thiophosphate CuCrP2S6 is an antiferromagnetic-
+antiferroelectric multiferroic involving collective ordering mechanisms of magnetic Cr3+ ions and off-
+centered Cu+ ions, respectively [12]. The indium compound CuInP2S6 belongs to the same C2/c space
+group as CuCrP2S6 at room temperature, but due to a specific second-order Jahn–Teller instability
+of Cu+, it attains a ferrielectric structure with Cc symmetry below 𝑇𝑐 ≈ 315 K. The solid solutions
+CuCr1−𝑥In𝑥P2S6 reveal disordered dipolar glass phases, because of randomness and frustration, and
+quasimolecular magnetic properties [13]. Dynamic polar clustering occurs in these solid solutions and
+superposes structural glassiness to the ferrielectric long-range Cu+ order at low temperatures.
+Transition metal phosphorus trichalcogenides MPS3 (M = Mn, Fe, Co, Ni, . . . ) have monoclinic crystal
+structure (space group of C2/m), in which the metal cations (M) are surrounded by an octahedral cage
+of (P2S6)4− bipyramids, and the neighboring metals have a 2D honeycomb lattice arrangement [5]. The
+crystal layers stack with vdW forces. Resulting from the competitions between the direct M–M exchange
+and indirect superexchange, mediated through S2− anions within each layer, as well as the interlayer
+exchange, determine antiferromagnetic (AFM) ordering temperature T𝑁 and its type — zigzag, Neel or
+stripy pattern [14].
+In 2D materials, magnetic anisotropy is also crucial in establishing a long-range correlation. For
+FePS3 compound, the trigonal distortion combined with the spin-orbit coupling yields a large single-axis
+magnetic anisotropy [15], and it can be described by the Ising model. In this compound, the long-range
+order is present in the direction perpendicular to the crystal layers, and FePS3 has a zigzag type of
+antiferromagnetic ground state.
+Incorporation of atomic defects and chemical substitutions in MPS3 2D materials could manipu-
+late and control their magnetic properties [16–18]. Distinct magnetic order, spin direction, and magnetic
+anisotropy, exotic phases and properties are expected to be revealed in solid solutions of these layered crys-
+tals. For example, spin glass behavior was found in Fe1−𝑥Mn𝑥PS3 [19, 20] and in CuCr1−𝑥In𝑥P2S6 [13].
+In this paper there are presented magnetic properties of FePS3 as a function of temperature, field
+and dilution of the magnetic atoms by means of substitution of a non-magnetic species, in this case
+copper — we studied the magnetic properties of 2D vdW layered Cu0.15Fe1.85PS3. The crystalline flakes
+with stoichiometry Cu0.15Fe1.85PS3 were grown using the gas transport method [21]. By dielectric,
+specific heat, and ultrasonic measurements the structural phase transition close to 109 K was found in
+these crystals [21]. Obviously, similarly to FePS3, it should be the antiferromagnetic phase transition. In
+this work, using the Mössbauer spectroscopy and magnetic investigations, together with first-principles
+studies, the peculiarities of magnetic ordering in the Cu0.15Fe1.85PS3 alloy are traced with the aim to
+search for a new layered multiferroic material for nanoscale devices.
+2. Mössbauer data
+Mössbauer spectra were measured using 57Co(Rh) source in the transmission geometry. The sample
+was composed of not grinded separate plates. The low-temperature spectra were obtained using the closed
+cycle He cryostat (Advanced Research Systems, Inc.). The doublet and Hamiltonian were applied to fit
+the Mössbauer spectra using WinNormos Site software [22]. Isomer shift is presented relative to 𝛼-Fe at
+room temperature.
+Mössbauer spectra displays the transition from an antiferromagnetic state to a paramagnetic state
+near the 110 K temperature (figure 1). Above the antiferromagnetic transition temperature, Mössbauer
+spectra were fitted to one doublet. On contrary, the magnetic subspectra (Hamiltonian method in Normos
+Site) should be used to fit the Mössbauer spectra below the transition temperature. Previously, the spectra
+of FePS3 were fitted using one set of hyperfine parameters (one subspectrum) [23]. We found that for
+Cu0.15Fe0.85PS3, a good quality of fitting was achieved using three subspectra described by Hamiltonian
+method (WinNormos Site) in the case of single crystal [24] except the spectra measured above 103 K
+temperature and below transition point which were broadened and needed extra subspectra to fit. These
+spectra were fitted using hyperfine field distribution. The set of Hamiltonian parameters included electric
+field gradient (EFG) asymmetry parameter 𝜂 and angles 𝜃 and 𝛽. 𝜃 is the angle between 𝑧 axis of EFG
+system and the direction of the magnetic field while 𝛽 is between 𝑧 axis of EFG system and 𝛾-ray
+direction. The isomer shift 𝛿 and quadrupole coupling constant 𝑒𝑄𝑉𝑧𝑧/2, where 𝑄 is nuclear quadrupole
+43701-2
+
+The antiferromagnetic phase transition in the layered Cu0.15Fe0.85PS3 semiconductor
+moment, 𝑉𝑧𝑧 is EFG tensor component, were the same for all three subspectra. The main area (70–75%)
+of the Mössbauer spectrum below 102 K can be attributed to two magnetically split subspectra having
+hyperfine fields 𝐵1 and 𝐵2 differing approximately by 1T (figure 2 a). However, the effective hyperfine
+field of them ⟨𝐵12⟩ was very close to that found for FePS3 [23, 25]. For these two subspectra, 𝜃 and 𝛽
+angles were fixed to zero i.e., 𝜃 = 0 and 𝛽 = 0. In this case, 𝑧 axis of EFG and the magnetization were
+normal to ab-plane similar to single-crystalline FePS3. For both subspectra, the combined quadruple and
+magnetic interactions gave two sets of overlapping four lines (figure 1). For the third subspectrum fitted to
+the experimental spectra, the angles were allowed to change and the best fits were obtained for 𝜃 ≈ 10–30◦
+and 𝛽 ≈ 20–40◦. Moreover, the asymmetry parameter 𝜂 ≈ 0.76 for the third subspectrum was larger
+than that of the first two subspectra (𝜂 = 0.23–0.28). Therefore, taking the Cu atoms distribution into
+consideration, the third subspectrum can be considered to be due to distorted iron atom sites having Cu
+atoms as first neighbours in hexagonal arrangement of metal atoms along ab-plane. Thus, the other two
+subspectra were attributed to iron sites similar to FePS3 [23, 25]. It should be noted that FePS3 undergoes
+first order phase transition at 120 K temperature. Coexistence of paramagnetic and antiferromagnetic
+phases was observed [23]. For Cu0.15Fe0.85PS3, the paramagnetic doublet starts also appear together with
+much more broadened magnetically split part of spectra above 102 K.
+0.9
+1.0
+ 
+ 
+8 K
+0.96
+0.98
+1.00
+ 
+R elative transm ission
+102 K
+0.90
+0.95
+1.00
+ 
+110 K
+-6
+-4
+-2
+0
+2
+4
+6
+0.90
+0.95
+1.00
+ 
+v, mm/s
+240 K
+0.90
+0.95
+1.00
+ 
+ 
+106 K
+Figure 1. Mössbauer spectra of Cu0.15Fe0.85PS3 measured at the indicated temperature.
+The lines of the doublet can be attributed to 𝛾-ray transitions to ±3/2 and ±1/2 excited energy
+levels of 57Fe nucleus. The line intensity ratio of 1.8–2.03 found above the phase transition temperature
+(figure 2 d) according to
+𝐼3/4/𝐼1/2 = (1 + cos2 𝛽)/(5/3 − cos2 𝛽)
+gave the angle 𝛽 = 27–32◦. Here, it is assumed that the EFG asymmetry parameter 𝜂 = 0. Quadruple
+splitting Δ = (𝑒𝑄𝑉𝑧𝑧/2) �1 + 𝜂2/3�1/2 was somewhat different below and above the antiferromagnetic
+43701-3
+
+V. Pashchenko et al.
+transition point. This can be explained by the first-order transition because the lattice undergoes some
+transformations [23], as in the case of FePS3 when 𝑉𝑧𝑧 > 0.
+0
+2
+4
+6
+8
+10
+0.90
+0.95
+1.00
+1.05
+0
+50
+100
+150
+200
+250
+300
+1.5
+1.6
+1.7
+1.8
+ B
+1
+  B
+2
+  B
+3
+ <B>
+ <B
+12
+>
+ 
+ 
+B, T
+a)
+ 
+ 
+d, m m /s
+b)
+ D
+ D
+12
+  D
+3
+ <D>
+D, m m /s
+T, K
+c)
+0
+50
+100
+150
+200
+250
+300
+1.8
+1.9
+2.0
+2.1
+ 
+I
+3/2
+/I
+1/2
+T, K
+d)
+Figure 2. Dependence of hyperfine field 𝐵 (a), isomer shift 𝛿 (b), quadrupole splitting Δ (c) and intensity
+ratio of lines of doublet (d) of Mössbauer spectra of Cu0.15Fe0.85PS3 crystal on temperature.
+3. Magnetic moment measurements
+3.1. Temperature dependence of the magnetic susceptibility
+Single crystal Cu0.15Fe0.85PS3 sample, of ∼ 3×4 mm flake-shaped (depicted in figure 3) and 1.54 mg
+was used for magnetic moment measurements. For all orientations of the external magnetic field at a
+temperature of about 108 K, a sharp change in the temperature dependence of the magnetic susceptibility
+(see figure 4) was observed, which may indicate the presence of a magnetic phase transition at this
+temperature.
+No narrow anomaly associated with 3D ordering is observed on the 𝜒(𝑇) curve in the region of
+108 K. Therefore, it is possible that the ordering can also occur at a higher temperature, and in this case,
+we are dealing with a phase transformation of a magnetically ordered phase. For 𝐻⊥ plane of crystal
+layers and 𝑇 < 108 K, as the temperature is lowered, the magnetic susceptibility 𝜒(𝑇) of the sample
+decreases significantly, which is typical when antiferromagnetic correlations are established in the spin
+system.
+In addition to the experimental curves 𝜒(𝑇) (in a constant magnetic field 𝐻 = 2000 Oe) in figure 4,
+the asterisks show several estimates of the values of the magnetic susceptibility of the Cu0.15Fe0.85PS3
+sample obtained by analyzing the linear sections of the field dependence 𝑀(𝐻) measured up to 5 T
+[see 𝑀(𝐻) in the following figures]. As seen in figure 4, the match for the orientation of the 𝐻∥ plane
+43701-4
+
+The antiferromagnetic phase transition in the layered Cu0.15Fe0.85PS3 semiconductor
+is perfect, with little deviation found between different experimental techniques for the 𝐻⊥ plane. The
+latter seems to be connected with the discovery of remanent magnetization (or a spontaneous weakly
+ferromagnetic moment in an antiferromagnet as a result of a small sublattice canting) in experiments for
+the 𝐻⊥ plane.
+Figure 3. (Colour online) The sample of Cu0.15Fe0.85PS3 crystal used for magnetic moment measure-
+ments.
+0
+50
+100
+150
+200
+250
+300
+0.00
+0.01
+0.02
+0.03
+0.04
+0.05
+0.06
+0.07
+0.08
+Cu
+0.15
+Fe
+0.85
+PS
+3
+H=2000 Oe
+c (cm
+3
+/mol)
+T (K)
+ H^ plane
+ H II plane
+ from M(H)
+ from M(H)
+Figure 4. (Colour online) Temperature dependence of the magnetic susceptibility 𝜒(𝑇) = 𝑀(𝑇)/𝐻 of a
+Cu0.15Fe0.85PS3 single crystal in magnetic field 𝐻 = 2000 Oe for two directions 𝐻⊥ plane and 𝐻∥ plane
+of crystal layers.
+3.2. Field dependence of the magnetic moment
+The field dependencies of the magnetic moment of the Cu0.15Fe0.85PS3 sample were studied at 120 K
+— above the assumed phase transition, 100 K — approximately the middle of the phase transformation,
+and 10 K — the low-temperature point, where all the magnetic transformation processes have already
+been completed based on their general form 𝜒(𝑇). All the obtained curves 𝑀(𝐻) for the 𝐻⊥ plane and
+𝐻∥ plane of crystal layers are shown in figure 5. All of them demonstrate a fairly good linear behavior of
+𝑀(𝐻) at any temperatures both above and below the assumed phase transition.
+For the 𝐻⊥ plane at 𝑇 = 10 K, extrapolation of the linear dependence (region above 2000 Oe) to
+zero magnetic fields detects the presence of a non-zero residual magnetic moment of the sample of the
+43701-5
+
+V. Pashchenko et al.
+0
+10000
+20000
+30000
+40000
+50000
+0
+500
+1000
+1500
+2000
+2500
+3000
+3500
+Cu
+0.15
+Fe
+0.85
+PS
+3
+H ^ plane
+M (emu/mol)
+H (Oe)
+ 5 K
+ 7 K
+ 10 K
+ 100 K
+ 120 K
+0
+10000
+20000
+30000
+40000
+50000
+0
+200
+400
+600
+800
+1000
+1200
+1400
+Cu
+0.15
+Fe
+0.85
+PS
+3
+H II plane
+M (emu/mol)
+H (Oe)
+ 10 K
+ 100 K
+ 120 K
+Figure 5. (Colour online) Field dependence of the magnetic moment 𝑀(𝐻) of Cu0.15Fe0.85PS3 sample
+at different temperatures for two orientations of the magnetic field: 𝐻⊥ plane (top panel) and 𝐻∥ plane
+of crystal layers (bottom panel).
+order of 9 emu/mol (dotted line in the insertion in figure 6). This may be due to the existence of a canted
+magnetic sublattice in an ordered antiferromagnetic system and, hence, to a weak ferromagnetic moment
+of the system in this direction. At the same time, such a feature in 𝑀(𝐻) is completely absent for the
+other direction of the 𝐻∥ plane. This behavior of the magnetization for the 𝐻⊥ plane can be satisfactorily
+explained within the framework of the four-sublattice model of an antiferromagnet of the flat cross-type.
+In very weak fields, the ground state will be similar to the state with latent ferromagnetism and the total
+moment of the system will be close to zero. A rapid increase in the magnetization with the increasing field
+43701-6
+
+The antiferromagnetic phase transition in the layered Cu0.15Fe0.85PS3 semiconductor
+will occur due to the orientational flip of a skewed pair with a weakly ferromagnetic moment oriented
+against the field to the direction of the skewed pair in which this moment is oriented along the field. In
+the fields above 2000 Oe, the four-sublattice system effectively turns into a simple two-sublattice system,
+in which the brace between the sublattices gives a weak moment along the field.
+0
+10000
+20000
+30000
+40000
+50000
+0
+200
+400
+600
+800
+1000
+0
+2000
+4000
+6000
+8000
+10000
+0
+20
+40
+60
+80
+ H ^ plane
+ H II plane
+Cu
+0.15
+Fe
+0.85
+PS
+3
+T=10 K
+M (emu/mol)
+H (Oe)
+ M  ( em u/m ol)
+ H (Oe)
+Figure 6. (Colour online) Field dependence of the magnetic moment of the Cu0.15Fe0.85PS3 sample at a
+temperature of 𝑇 = 10 K for 𝐻⊥ plane and 𝐻∥ plane. The insertion shows a low-field region.
+Thus, a characteristic field of about 2000 Oe can be considered as a phase transition field between
+the effective four-sublattice and two-sublattice magnetic structures for the system under study.
+4. Ab initio simulation results
+The QUANTUM ESPRESSO package [26], was used to perform calculations. They were carried out
+within the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof functional [27]
+or with the CA-PZ local functional based on the Ceperley and Alder data [28] parameterized by Perdew
+and Zunger [29]. The layered Cu0.15Fe0.85PS3 crystal possesses the so-called vdW gap between layers.
+Therefore, the DFT-D method taking into account the dispersion interaction elaborated by Grimme [30] is
+needed to calculate electronic properties of the material. The ultra-soft pseudopotential [31] was used to
+perform calculations for Fe — 3𝑑6 4𝑠2, Cu — 3𝑑10 4𝑠1, P — 3𝑠2 3𝑝3, S — 3𝑠2 3𝑝4 atomic configurations.
+The plane-wave basis set cut-off was chosen to be equal to 600 eV. The Monkhorst–Pack 𝑘-points grid [32]
+sampling was set at 12×12×3 points for the Brillouin zone. The convergence tolerance parameters were
+as follows: energy 5 · 10−6 eV, force 0.01 eV Å−1; stress 0.02 GPa; displacement 0.05 Å. The total energy
+convergence criterion was assumed to be fulfilled when the self-consistent field tolerance reaches the
+value 10−7 eV per atom. The ab initio simulation of the features of electronic and spin subsystems in the
+framework of electron density functional theory (DFT) allows us to estimate the values of spin density
+(figure 7) in the vicinity of all species’ sites present in the investigated system. The supercell of 3 × 3 × 1
+unit cells of FePS3 single-crystal was used for modelling the proper concentration of Cu substitutional
+atoms. A pair of Cu was used to preserve the symmetry of the Cu0.15Fe0.85PS3 lattice.
+Components of the EFG tensor and asymmetry parameter 𝜂 for Fe ions close to the experimental
+value for FePS3 crystal (𝜂 ≈ 0.23–0.28) were calculated for the system under study at 𝑇 = 0 K (table 1).
+43701-7
+
+V. Pashchenko et al.
+Figure 7. (Colour online) Spatial distribution of the calculated spin density of the Cu0.15Fe0.85PS3 model
+at 0 K. Red and blue regions correspond to opposite spin orientations.
+Table 1. Calculated averaged components of the EFG tensor and asymmetry parameter for
+Cu0.15Fe0.85PS3 crystal.
+Species
+⟨𝐶𝑞⟩, MHz
+⟨𝜂⟩
+Cu
+−3.1501
+0.8797
+Fe
+11.2971
+0.2911
+P
+32.7594
+0.2774
+S
+−26.1410
+0.0941
+Furthermore, analysis of the Mulliken population shows that the main contribution to the ferromag-
+netic spin density is originated from 3𝑑-copper and 3𝑝-sulfur orbitals (see table 2).
+Table 2. Decomposition of spin density (spin up – spin down) contributions over orbitals in
+Cu0.15Fe0.85PS3 crystal. The largest contributions are typed in bold.
+Species
+3𝑑
+3𝑝
+4 𝑓
+4𝑠
+Total
+Cu
+−0.248
+−0.028
+0.000
+−0.002
+−0.278
+Fe
+−0.087
+0.030
+0.010
+−0.002
+−0.049
+P
+−0.028
+−0.030
+0.000
+0.000
+−0.058
+S
+−0.072
+−0.282
+0.000
+−0.016
+−0.370
+Total
+−0.435
+−0.310
+0.010
+−0.020
+−0.755
+Thevalues of the valence charge transferandthespinpolarizationwere estimatedforthe Cu0.15Fe0.85PS3
+crystal (table 3). The presence of uncompensated spin ordering is found.
+5. Discussions
+In contrast to the expectation that Cu with spin 1
+2 will dilute the magnetic moments contributed by Fe
+with a larger spin, we found that 15% Cu doping partially keeps the effective fluctuating moment, although
+there is a long-range magnetic order partially distorted. This follows from the magnetic susceptibility
+43701-8
+
+FeThe antiferromagnetic phase transition in the layered Cu0.15Fe0.85PS3 semiconductor
+Table 3. The calculated values of the spin components of the valence charge and the spin polarization in
+Cu0.15Fe0.85PS3 crystal.
+Species
+𝑄up, e
+𝑄dw, e
+𝑄, e
+Σ𝑆, ℏ/2
+Cu
+15.31 ± 0.00
+15.45 ± 0.00
+−3.53
+−0.28
+Fe
+13.86 ± 1.36
+13.86 ± 1.37
+−27.51
+−0.07
+P
+7.16 ± 0.03
+7.16 ± 0.03
+12.22
+−0.07
+S
+7.82 ± 0.08
+7.83 ± 0.07
+18.82
+−0.35
+temperature dependence around transition from paramagnetic into antiferromagnetic phase — amplitude
+of the observed 𝜒(𝑇) anomaly is like the one observed in case of FePS3 pure crystal [23]. At Fe by Cu
+partial substitution, the temperature of 𝜒(𝑇) maximum is lowered from 120 K in FePS3 to 108 K in case
+of Cu0.15Fe0.85PS3. The jump of 𝜒(𝑇) at ferromagnetic transition is smeared by Cu dilution.
+In real crystal, the sulfur vacancies 𝑉S presence can also effectively suppress the strong intralayer
+antiferromagnetic correlation, giving rise to a weak ferromagnetic ground state, which is observed on the
+𝑀(𝐻) dependence below 10 K. The presence of 𝑉S disrupts anion-mediated AFM interactions and may
+be responsible for the suppression of long-range AFM correlations. Herein, the competing ferromagnetic
+exchange interactions can dominate at low temperatures, creating a magnetically frustrated system. The
+exchange interactions between the 𝑉S and metal ions, and with the local atomic distortion in the vicinity
+of defects, could also induce ferromagnetism.
+A canting configuration and the resulting net moments along the easy axis can also be attributed to
+atomic substitution. All these signatures exhibit the complexity of magnetic structure for the 15% Cu
+substituted sample.
+The susceptibilities of Cu0.15Fe1.85PS3 can be considered as for configurationally averaged clusters
+sum of two terms: a randomly diluted antiferromagnet susceptibility, as in pure FePS3, and a Curie
+correction arising from local fluctuations of the uncompensated spins due to the finite size of the cluster.
+For Cu0.15Fe1.85PS3 crystal, there is observed a weak paramagnetic contribution for small temperatures
+(figure 4), because many of the spins no longer belong to the infinite cluster. The uncompensated moments
+in the diluted 2D AFM can give rise to a Curie contribution into the magnetic susceptibility, and the
+presence of field dependence of the magnetization suggests that they interact ferromagnetically to give a
+spontaneous magnetization below 10 K.
+6. Conclusions
+According to the presented experimental data on Mössbauer spectroscopy and direct magnetic moment
+temperature and field dependencies measurements, it can be stated that the Cu0.15Fe0.85PS3 single-crystal
+undergoes a magnetic phase transition at the region of 102–108 K. A weak ferromagnetic moment at the
+low-temperature region (𝑇 = 10 K) was observed in the 𝐻⊥ plane direction. This correlates with ab initio
+calculated non-zero spin polarization of the considered material. Furthermore, the calculated values of
+the electric field gradient components and estimations of the total magnetic moment of the unit cell
+(0.764 ℏ/2 corresponds to 8.543 emu/mol) are in reasonable agreement with the measured experimental
+quantities of ∼ 9 emu/mol.
+The present studies of Cu0.15Fe0.85PS3 magnetic properties show that the uncompensated moments
+in the diluted 2D AFM can give rise to a Curie contribution, and the observed field dependence of the
+magnetization suggests that they do interact ferromagnetically to give a spontaneous magnetization at low
+temperatures. The relation of the magnetic ordering with structural change at antiferromagnetic phase
+transition can also be important and must be investigated further on.
+It is worth to note that the flattening of magnetic susceptibility at low temperature was also observed in
+rare-earth containing compounds caused by Kondo effect [33]. In the case of the studied Cu0.15Fe0.85PS3
+crystal, the system seems not to be such a strongly correlated material as rare earth materials but, of
+course, the proper investigation of the low temperature dependence of resistivity is needed.
+43701-9
+
+V. Pashchenko et al.
+References
+1. Chu J., Wang Y., Wang X., Hu K., Rao G., Gong C., Wu C., Hong H., Wang X., Liu K., Gao C., Xiong J.,
+Adv. Mater., 2020, 33, 2004469, doi:10.1002/adma.202004469.
+2. Hu T., Kan E., WIREs Comput. Mol. Sci., 2019, 9, e1409, doi:10.1002/wcms.1409.
+3. Liu Z., Deng L., Peng B., Nano Res., 2021, 14, 1802–1813, doi:10.1007/s12274-020-2860-3.
+4. Gong C., Kim E. M., Wang Y., Lee G., Zhang X., Nat. Commun., 2019, 10, 2657, doi:10.1038/s41467-019-
+10693-0.
+5. Wang F., Shifa T. A., Yu P., He P., Liu Y., Wang F., Wang Z., Zhan X., Lou X., Xia F., He J., Adv. Funct. Mater.,
+2018, 28, 1802151, doi:10.1002/adfm.201802151.
+6. Gong C., Li L., Li Z., Ji H., Stern A., Xia Y., Cao T., Bao W., Wang C., Wang Y., Qiu Z. Q., Cava R. J.,
+Louie S. G., Xia J., Zhang X., Nature, 2017, 546, 265–269, doi:10.1038/nature22060.
+7. Belianinov A., He Q., Dziaugys A., Maksymovych P., Eliseev E., Borisevich A., Morozovska A., Banys J.,
+Vysochanskii Yu., Kalinin S. V., Nano Lett., 2015, 15, 3808–3814, doi:10.1021/acs.nanolett.5b00491.
+8. Liu F., You L., Seyler K. L., Li X., Yu P., Lin J., Wang X., Zhou J., Wang H., He H., Pantelides S. T., Zhou W.,
+Sharma P., Xu X., Ajayan P. M., Wang J., Liu Z., Nat. Commun., 2016, 7, 12357, doi:10.1038/ncomms12357.
+9. Qi J., Wang H., Chen X., Qian X., Appl. Phys. Lett., 2018, 113, 043102, doi:10.1063/1.5038037.
+10. Osada M., Sasaki T., APL Mater., 2019, 7, 120902, doi:10.1063/1.5129447.
+11. Lai Y., Song Z., Wan Y., Xue M., Wang C., Ye Y., Dai L., Zhang Z., Yang W., Dua H., Yangace J., Nanoscale,
+2019, 11, 5163–5170, doi:10.1039/C9NR00738E.
+12. Dziaugys A., Shvartsman V. V., Macutkevic J., Banys J., Vysochanskii Yu., Kleemann W., Phys. Rev. B, 2012,
+85, 134105, doi:10.1103/PhysRevB.85.134105.
+13. Kleemann W., Shvartsman V. V., Borisov P., Banys J., Vysochanskii Yu. M., Phys. Rev. B, 2011, 84, 094411,
+doi:10.1103/PhysRevB.84.094411.
+14. Olsen T., J. Phys. D: Appl. Phys., 2021, 54, 314001, doi:10.1088/1361-6463/ac000e.
+15. Wildes A. R., Zhitomirsky M. E., Ziman T., Lançon D., Walker H. C., J. Phys. D: Appl. Phys., 2020, 127,
+223903, doi:10.1063/5.0009114.
+16. Sakai H., Yamazaki T., Machida N., Shigematsu T., Nasu S., Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A, 2000,
+341, 105–110, doi:10.1080/10587250008026125.
+17. Chandrasekharan N., Vasudevan S., Phys. Rev. B, 1996, 54, 14903, doi:10.1103/PhysRevB.54.14903.
+18. Mulders A. M., Klaasse J. C. P., Goossens D. J., Chadwick J., Hicks T. J., J. Phys.: Condens. Matter, 2002, 14,
+8697, doi:10.1088/0953-8984/14/37/306.
+19. Masubuchi T., Hoya H., Watanabe T., Takahashi Y., Ban S., Ohkubo N., Takase K., Takano Y., J. Alloys Compd.,
+2008, 460, 668–674, doi:10.1016/j.jallcom.2007.06.063.
+20. Bhutani A., Zuo J. L., McAuliffe R. D., dela Cruz C. R., Shoemaker D. P., Phys. Rev. Mater., 2020, 4, 034411,
+doi:10.1103/PhysRevMaterials.4.034411.
+21. Dziaugys A., Macutkevic J., Svirskas S., Juskenas R., Wencka M., Banys J., Motria S. F., Vysochanskii Yu.,
+J. Alloys Compd., 2015, 650, 386–392, doi:10.1016/j.jallcom.2015.07.261.
+22. WissEl, Data Evaluation Software — WissEl, Wissenschaftliche Elektronik GmbH, [Online; accessed 10-Jul-
+2022], URL http://www.wissel-gmbh.de/index.php?option=com_content&task=view&id=55&Itemid=116.
+23. Jernberg P., Bjarman S., Wäppling R., J. Magn. Magn. Mater., 1984, 46, 178–190, doi:10.1016/0304-
+8853(84)90355-X.
+24. Chen Y. L., Yang D. P., Mössbauer Effect in Lattice Dynamics: Experimental Techniques and Applications,
+Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2007.
+25. Rule K. C., Cashion J. D., Mulders A. M., Hicks T. J., Hyperfine Interact., 2002, 141, 219–222,
+doi:10.1023/A:1021286910897.
+26. Giannozzi P., Baroni S., Bonini N., Calandra M., Car R., Cavazzoni C., Ceresoli D., Chiarotti G. L., Cococ-
+cioni M., Dabo I. et al., J. Phys.: Condens. Matter, 2009, 21, 395502, doi:10.1088/0953-8984/21/39/395502.
+27. Perdew J. P., Burke K., Ernzerhof M., Phys. Rev. Lett., 1997, 78, 1396, doi:10.1103/PhysRevLett.78.1396.
+28. Ceperley D. M., Alder B. J., Phys. Rev. Lett., 1980, 45, 566, doi:10.1103/PhysRevLett.45.566.
+29. Perdew J. P., Zunger A., Phys. Rev. B, 1981, 23, 5048, doi:10.1103/PhysRevB.23.5048.
+30. Grimme S., J. Comput. Chem., 2006, 27, 1787–1799, doi:10.1002/jcc.20495.
+31. Vanderbilt D., Phys. Rev. B, 1990, 41, 7892, doi:10.1103/PhysRevB.41.7892.
+32. Monkhorst H. J., Pack J. D., Phys. Rev. B, 1976, 13, 5188, doi:10.1103/PhysRevB.13.5188.
+33. Menth A., Buehler E., Geballe T. H., Phys. Rev. Lett., 1969, 22, 295, doi:10.1103/PhysRevLett.22.295.
+43701-10
+
+The antiferromagnetic phase transition in the layered Cu0.15Fe0.85PS3 semiconductor
+Антиферомагнiтний фазовий перехiд в шаруватому
+напiвпровiднику Cu0.15Fe0.85PS3: експеримент та DFT
+моделювання
+В. Пащенко1, О. Блудов1, Д. Балтрунас2, К. Мазейка2, С. Мотря3, К. Глухов3,
+Ю. Височанський3
+1 Iнститут фiзики i технiки низьких температур iм. Б. Вєркiна НАН України, просп. Науки 47, 61103, Харкiв,
+Україна
+2 Вiддiл ядерних дослiджень Центру фiзичних наук та технологiї, просп. Саванорiу 231, LT-02300, Вiльнюс,
+Литва
+3 Iнститут фiзики i хiмiї твердого тiла, Ужгородський нацiональний унiверситет, вул. Волошина 54, 88000,
+Ужгород, Україна
+Представленi експериментальнi дослiдження парамагнiтно-антиферомагнiтного фазового переходу ме-
+тодом мессбауерiвської спектроскопiї та вимiрювання температурних i польових залежностей магнiтної
+сприйнятливостi в шаруватому кристалi Cu0.15Fe0.85PS3. Особлива поведiнка польової залежностi намаг-
+нiченостi в областi низьких температур свiдчить про слабкий феромагнетизм дослiджуваного матерiалу.
+За допомогою ab initio моделювання електронної та спiнової пiдсистем, в рамках теорiї функцiоналу
+електронної густини, проаналiзовано особливостi спiнового впорядкування при низькiй температурi, а
+також змiни мiжатомних взаємодiй поблизу атомiв замiщення Cu. Розрахованi компоненти тензора гра-
+дiєнта електричного поля та параметра асиметрiї для iонiв Fe близькi до значень знайдених з мессбау-
+ерiвських спектрiв. Маллiкенiвськi заселеностi показують, що основний внесок у феромагнiтну спiнову
+густину вносять 3𝑑 орбiталi мiдi та 3𝑝 сiрки. Розрахунковий загальний магнiтний момент елементарної
+комiрки (8.543 emu/mol) цiлком узгоджується з вимiряним експериментальним значенням ∼ 9 emu/mol.
+Ключовi слова: метал-фосфорнi трихалькогенiди, магнiтне впорядкування, мессбауерiвська
+спектроскопiя, фазовi переходи, теорiя функцiоналу електронної густини
+43701-11
+
+
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new file mode 100644
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+page_content=' Pashchenko  1, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Bludov  1, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
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+page_content=' Verkin Institute for Low Temperature Physics and Engineering of NAS of Ukraine, 47 Nauky Ave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 61103,  Kharkiv, Ukraine  2 Department of Nuclear Research Center for Physical Sciences and Technology, 231 Savanoriu ave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', LT-02300,  Vilnius, Lithuania  3 Institute for Solid State Physics and Chemistry, Uzhhorod National University, 54 Voloshyn Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 88000,  Uzhhorod, Ukraine  Received July 23, 2022, in final form October 15, 2022  The experimental studies of the paramagnetic-antiferromagnetic phase transition through Mössbauer spec-  troscopy and measurements of temperature and field dependencies of magnetic susceptibility in the layered  Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 crystal are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The peculiar behavior of the magnetization — field dependence at low-  temperature region gives evidence of a weak ferromagnetism in the studied alloy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' By the ab initio simulation of  electronic and spin subsystems, in the framework of electron density functional theory, the peculiarities of spin  ordering at low temperature as well as changes in interatomic interactions in the vicinity of the Cu substitutional  atoms are analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The calculated components of the electric field gradient tensor and asymmetry parameter  for Fe ions are close to the ones found from Mössbauer spectra values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The Mulliken populations show that the  main contribution to the ferromagnetic spin density is originated from 3𝑑-copper and 3𝑝-sulfur orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The es-  timated total magnetic moment of the unit cell (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='543 emu/mol) is in reasonable agreement with the measured  experimental value of ∼ 9 emu/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Key words: metal phosphorus trichalcogenides, magnetic ordering, Mösbauer spectroscopy, phase transition,  density functional theory  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Introduction  Two-dimensional (2D) van der Waals (vdW) materials offer possibilities to study novel physical  properties and explore their potential applications in electronic, optical, and spintronic devices in the  nanoscale [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The realization of magnetism in easily exfoliated layered crystals provides accessibility  to control and manipulate magnetic properties at a single atomic layer level [2–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The presence of  multiferroicity in such materials, when they exhibit two or more primary ferroic properties, is important  for potential applications in the non-volatile storage devices controlled by an external electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Recently, 2D ferroelectric polarization was found in CuInP2S6 several layers flakes and even in  monolayers [7, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' On the other hand, 2D antiferromagnetism is also demonstrated for CuCrP2S6 layers [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Furthermore, multiferroic material can be prepared by doping or modifying some monolayers, such as  black phosphorus and graphene [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' 2D materials with spontaneous ferromagnetism and ferroelectricity  have rarely been reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Recenrly, it was found that 2D CuCrP2S6 is multiferroic with magnetism  and ferroelectricity stems from Cr and Cu cations, and the magnetoelectric coupling follows from  ∗Corresponding author: kglukhov@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='com  This work is licensed under a Creative Commons Attribution 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='0 International License.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Further distribution  of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  43701-1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='01338v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='comp-ph]  3 Jan 2023  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Pashchenko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  the spin-orbit interaction [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Copper chromium thiophosphate CuCrP2S6 is an antiferromagnetic-  antiferroelectric multiferroic involving collective ordering mechanisms of magnetic Cr3+ ions and off-  centered Cu+ ions, respectively [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The indium compound CuInP2S6 belongs to the same C2/c space  group as CuCrP2S6 at room temperature, but due to a specific second-order Jahn–Teller instability  of Cu+, it attains a ferrielectric structure with Cc symmetry below 𝑇𝑐 ≈ 315 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The solid solutions  CuCr1−𝑥In𝑥P2S6 reveal disordered dipolar glass phases, because of randomness and frustration, and  quasimolecular magnetic properties [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Dynamic polar clustering occurs in these solid solutions and  superposes structural glassiness to the ferrielectric long-range Cu+ order at low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Transition metal phosphorus trichalcogenides MPS3 (M = Mn, Fe, Co, Ni, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' ) have monoclinic crystal  structure (space group of C2/m), in which the metal cations (M) are surrounded by an octahedral cage  of (P2S6)4− bipyramids, and the neighboring metals have a 2D honeycomb lattice arrangement [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The  crystal layers stack with vdW forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Resulting from the competitions between the direct M–M exchange  and indirect superexchange, mediated through S2− anions within each layer, as well as the interlayer  exchange, determine antiferromagnetic (AFM) ordering temperature T𝑁 and its type — zigzag, Neel or  stripy pattern [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  In 2D materials, magnetic anisotropy is also crucial in establishing a long-range correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' For  FePS3 compound, the trigonal distortion combined with the spin-orbit coupling yields a large single-axis  magnetic anisotropy [15], and it can be described by the Ising model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' In this compound, the long-range  order is present in the direction perpendicular to the crystal layers, and FePS3 has a zigzag type of  antiferromagnetic ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Incorporation of atomic defects and chemical substitutions in MPS3 2D materials could manipu-  late and control their magnetic properties [16–18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Distinct magnetic order, spin direction, and magnetic  anisotropy, exotic phases and properties are expected to be revealed in solid solutions of these layered crys-  tals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' For example, spin glass behavior was found in Fe1−𝑥Mn𝑥PS3 [19, 20] and in CuCr1−𝑥In𝑥P2S6 [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  In this paper there are presented magnetic properties of FePS3 as a function of temperature, field  and dilution of the magnetic atoms by means of substitution of a non-magnetic species, in this case  copper — we studied the magnetic properties of 2D vdW layered Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The crystalline flakes  with stoichiometry Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 were grown using the gas transport method [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' By dielectric,  specific heat, and ultrasonic measurements the structural phase transition close to 109 K was found in  these crystals [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Obviously, similarly to FePS3, it should be the antiferromagnetic phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' In  this work, using the Mössbauer spectroscopy and magnetic investigations, together with first-principles  studies, the peculiarities of magnetic ordering in the Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 alloy are traced with the aim to  search for a new layered multiferroic material for nanoscale devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Mössbauer data  Mössbauer spectra were measured using 57Co(Rh) source in the transmission geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The sample  was composed of not grinded separate plates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The low-temperature spectra were obtained using the closed  cycle He cryostat (Advanced Research Systems, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The doublet and Hamiltonian were applied to fit  the Mössbauer spectra using WinNormos Site software [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Isomer shift is presented relative to 𝛼-Fe at  room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Mössbauer spectra displays the transition from an antiferromagnetic state to a paramagnetic state  near the 110 K temperature (figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Above the antiferromagnetic transition temperature, Mössbauer  spectra were fitted to one doublet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' On contrary, the magnetic subspectra (Hamiltonian method in Normos  Site) should be used to fit the Mössbauer spectra below the transition temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Previously, the spectra  of FePS3 were fitted using one set of hyperfine parameters (one subspectrum) [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' We found that for  Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3, a good quality of fitting was achieved using three subspectra described by Hamiltonian  method (WinNormos Site) in the case of single crystal [24] except the spectra measured above 103 K  temperature and below transition point which were broadened and needed extra subspectra to fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' These  spectra were fitted using hyperfine field distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The set of Hamiltonian parameters included electric  field gradient (EFG) asymmetry parameter 𝜂 and angles 𝜃 and 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' 𝜃 is the angle between 𝑧 axis of EFG  system and the direction of the magnetic field while 𝛽 is between 𝑧 axis of EFG system and 𝛾-ray  direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The isomer shift 𝛿 and quadrupole coupling constant 𝑒𝑄𝑉𝑧𝑧/2, where 𝑄 is nuclear quadrupole  43701-2  The antiferromagnetic phase transition in the layered Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 semiconductor  moment, 𝑉𝑧𝑧 is EFG tensor component, were the same for all three subspectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The main area (70–75%)  of the Mössbauer spectrum below 102 K can be attributed to two magnetically split subspectra having  hyperfine fields 𝐵1 and 𝐵2 differing approximately by 1T (figure 2 a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' However, the effective hyperfine  field of them ⟨𝐵12⟩ was very close to that found for FePS3 [23, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' For these two subspectra, 𝜃 and 𝛽  angles were fixed to zero i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 𝜃 = 0 and 𝛽 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' In this case, 𝑧 axis of EFG and the magnetization were  normal to ab-plane similar to single-crystalline FePS3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' For both subspectra, the combined quadruple and  magnetic interactions gave two sets of overlapping four lines (figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' For the third subspectrum fitted to  the experimental spectra, the angles were allowed to change and the best fits were obtained for 𝜃 ≈ 10–30◦  and 𝛽 ≈ 20–40◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Moreover, the asymmetry parameter 𝜂 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='76 for the third subspectrum was larger  than that of the first two subspectra (𝜂 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='23–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Therefore, taking the Cu atoms distribution into  consideration, the third subspectrum can be considered to be due to distorted iron atom sites having Cu  atoms as first neighbours in hexagonal arrangement of metal atoms along ab-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Thus, the other two  subspectra were attributed to iron sites similar to FePS3 [23, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' It should be noted that FePS3 undergoes  first order phase transition at 120 K temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Coexistence of paramagnetic and antiferromagnetic  phases was observed [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' For Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3, the paramagnetic doublet starts also appear together with  much more broadened magnetically split part of spectra above 102 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='0  8 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='98  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='00  R elative transm ission  102 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='00  110 K  6  4  2  0  2  4  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='00  v, mm/s  240 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='00  106 K  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Mössbauer spectra of Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 measured at the indicated temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  The lines of the doublet can be attributed to 𝛾-ray transitions to ±3/2 and ±1/2 excited energy  levels of 57Fe nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The line intensity ratio of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='8–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='03 found above the phase transition temperature  (figure 2 d) according to  𝐼3/4/𝐼1/2 = (1 + cos2 𝛽)/(5/3 − cos2 𝛽)  gave the angle 𝛽 = 27–32◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Here, it is assumed that the EFG asymmetry parameter 𝜂 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Quadruple  splitting Δ = (𝑒𝑄𝑉𝑧𝑧/2) �1 + 𝜂2/3�1/2 was somewhat different below and above the antiferromagnetic  43701-3  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Pashchenko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  transition point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' This can be explained by the first-order transition because the lattice undergoes some  transformations [23], as in the case of FePS3 when 𝑉𝑧𝑧 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  0  2  4  6  8  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='05  0  50  100  150  200  250  300  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='8  B  1  B  2  B  3  <B>  <B  12  >  B, T  a)  d, m m /s  b)  D  D  12  D  3  <D>  D, m m /s  T, K  c)  0  50  100  150  200  250  300  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1  I  3/2  /I  1/2  T, K  d)  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Dependence of hyperfine field 𝐵 (a), isomer shift 𝛿 (b), quadrupole splitting Δ (c) and intensity  ratio of lines of doublet (d) of Mössbauer spectra of Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 crystal on temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Magnetic moment measurements  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Temperature dependence of the magnetic susceptibility  Single crystal Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 sample, of ∼ 3×4 mm flake-shaped (depicted in figure 3) and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='54 mg  was used for magnetic moment measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' For all orientations of the external magnetic field at a  temperature of about 108 K, a sharp change in the temperature dependence of the magnetic susceptibility  (see figure 4) was observed, which may indicate the presence of a magnetic phase transition at this  temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  No narrow anomaly associated with 3D ordering is observed on the 𝜒(𝑇) curve in the region of  108 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Therefore, it is possible that the ordering can also occur at a higher temperature, and in this case,  we are dealing with a phase transformation of a magnetically ordered phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' For 𝐻⊥ plane of crystal  layers and 𝑇 < 108 K, as the temperature is lowered, the magnetic susceptibility 𝜒(𝑇) of the sample  decreases significantly, which is typical when antiferromagnetic correlations are established in the spin  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  In addition to the experimental curves 𝜒(𝑇) (in a constant magnetic field 𝐻 = 2000 Oe) in figure 4,  the asterisks show several estimates of the values of the magnetic susceptibility of the Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3  sample obtained by analyzing the linear sections of the field dependence 𝑀(𝐻) measured up to 5 T  [see 𝑀(𝐻) in the following figures].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' As seen in figure 4, the match for the orientation of the 𝐻∥ plane  43701-4  The antiferromagnetic phase transition in the layered Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 semiconductor  is perfect, with little deviation found between different experimental techniques for the 𝐻⊥ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The  latter seems to be connected with the discovery of remanent magnetization (or a spontaneous weakly  ferromagnetic moment in an antiferromagnet as a result of a small sublattice canting) in experiments for  the 𝐻⊥ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' (Colour online) The sample of Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 crystal used for magnetic moment measure-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  0  50  100  150  200  250  300  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='08  Cu  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15  Fe  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85  PS  3  H=2000 Oe  c (cm  3  /mol)  T (K)  H^ plane  H II plane  from M(H)  from M(H)  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' (Colour online) Temperature dependence of the magnetic susceptibility 𝜒(𝑇) = 𝑀(𝑇)/𝐻 of a  Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 single crystal in magnetic field 𝐻 = 2000 Oe for two directions 𝐻⊥ plane and 𝐻∥ plane  of crystal layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Field dependence of the magnetic moment  The field dependencies of the magnetic moment of the Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 sample were studied at 120 K  — above the assumed phase transition, 100 K — approximately the middle of the phase transformation,  and 10 K — the low-temperature point, where all the magnetic transformation processes have already  been completed based on their general form 𝜒(𝑇).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' All the obtained curves 𝑀(𝐻) for the 𝐻⊥ plane and  𝐻∥ plane of crystal layers are shown in figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' All of them demonstrate a fairly good linear behavior of  𝑀(𝐻) at any temperatures both above and below the assumed phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  For the 𝐻⊥ plane at 𝑇 = 10 K, extrapolation of the linear dependence (region above 2000 Oe) to  zero magnetic fields detects the presence of a non-zero residual magnetic moment of the sample of the  43701-5  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Pashchenko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  0  10000  20000  30000  40000  50000  0  500  1000  1500  2000  2500  3000  3500  Cu  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15  Fe  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85  PS  3  H ^ plane  M (emu/mol)  H (Oe)  5 K  7 K  10 K  100 K  120 K  0  10000  20000  30000  40000  50000  0  200  400  600  800  1000  1200  1400  Cu  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15  Fe  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85  PS  3  H II plane  M (emu/mol)  H (Oe)  10 K  100 K  120 K  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' (Colour online) Field dependence of the magnetic moment 𝑀(𝐻) of Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 sample  at different temperatures for two orientations of the magnetic field: 𝐻⊥ plane (top panel) and 𝐻∥ plane  of crystal layers (bottom panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  order of 9 emu/mol (dotted line in the insertion in figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' This may be due to the existence of a canted  magnetic sublattice in an ordered antiferromagnetic system and, hence, to a weak ferromagnetic moment  of the system in this direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' At the same time, such a feature in 𝑀(𝐻) is completely absent for the  other direction of the 𝐻∥ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' This behavior of the magnetization for the 𝐻⊥ plane can be satisfactorily  explained within the framework of the four-sublattice model of an antiferromagnet of the flat cross-type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  In very weak fields, the ground state will be similar to the state with latent ferromagnetism and the total  moment of the system will be close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' A rapid increase in the magnetization with the increasing field  43701-6  The antiferromagnetic phase transition in the layered Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 semiconductor  will occur due to the orientational flip of a skewed pair with a weakly ferromagnetic moment oriented  against the field to the direction of the skewed pair in which this moment is oriented along the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' In  the fields above 2000 Oe, the four-sublattice system effectively turns into a simple two-sublattice system,  in which the brace between the sublattices gives a weak moment along the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  0  10000  20000  30000  40000  50000  0  200  400  600  800  1000  0  2000  4000  6000  8000  10000  0  20  40  60  80  H ^ plane  H II plane  Cu  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15  Fe  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85  PS  3  T=10 K  M (emu/mol)  H (Oe)  M  ( em u/m ol)  H (Oe)  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' (Colour online) Field dependence of the magnetic moment of the Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 sample at a  temperature of 𝑇 = 10 K for 𝐻⊥ plane and 𝐻∥ plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The insertion shows a low-field region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Thus, a characteristic field of about 2000 Oe can be considered as a phase transition field between  the effective four-sublattice and two-sublattice magnetic structures for the system under study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Ab initio simulation results  The QUANTUM ESPRESSO package [26], was used to perform calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' They were carried out  within the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof functional [27]  or with the CA-PZ local functional based on the Ceperley and Alder data [28] parameterized by Perdew  and Zunger [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The layered Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 crystal possesses the so-called vdW gap between layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Therefore, the DFT-D method taking into account the dispersion interaction elaborated by Grimme [30] is  needed to calculate electronic properties of the material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The ultra-soft pseudopotential [31] was used to  perform calculations for Fe — 3𝑑6 4𝑠2, Cu — 3𝑑10 4𝑠1, P — 3𝑠2 3𝑝3, S — 3𝑠2 3𝑝4 atomic configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  The plane-wave basis set cut-off was chosen to be equal to 600 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The Monkhorst–Pack 𝑘-points grid [32]  sampling was set at 12×12×3 points for the Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The convergence tolerance parameters were  as follows: energy 5 · 10−6 eV, force 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='01 eV Å−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' stress 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='02 GPa;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' displacement 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='05 Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The total energy  convergence criterion was assumed to be fulfilled when the self-consistent field tolerance reaches the  value 10−7 eV per atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The ab initio simulation of the features of electronic and spin subsystems in the  framework of electron density functional theory (DFT) allows us to estimate the values of spin density  (figure 7) in the vicinity of all species’ sites present in the investigated system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The supercell of 3 × 3 × 1  unit cells of FePS3 single-crystal was used for modelling the proper concentration of Cu substitutional  atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' A pair of Cu was used to preserve the symmetry of the Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Components of the EFG tensor and asymmetry parameter 𝜂 for Fe ions close to the experimental  value for FePS3 crystal (𝜂 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='23–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='28) were calculated for the system under study at 𝑇 = 0 K (table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  43701-7  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Pashchenko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' (Colour online) Spatial distribution of the calculated spin density of the Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 model  at 0 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Red and blue regions correspond to opposite spin orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Calculated averaged components of the EFG tensor and asymmetry parameter for  Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Species  ⟨𝐶𝑞⟩, MHz  ⟨𝜂⟩  Cu  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1501  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='8797  Fe  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='2971  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='2911  P  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='7594  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='2774  S  −26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1410  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='0941  Furthermore, analysis of the Mulliken population shows that the main contribution to the ferromag-  netic spin density is originated from 3𝑑-copper and 3𝑝-sulfur orbitals (see table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Decomposition of spin density (spin up – spin down) contributions over orbitals in  Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The largest contributions are typed in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Species  3𝑑  3𝑝  4 𝑓  4𝑠  Total  Cu  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='248  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='028  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='000  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='002  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='278  Fe  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='087  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='030  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='010  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='002  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='049  P  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='028  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='030  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='000  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='058  S  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='072  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='282  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='000  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='016  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='370  Total  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='435  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='310  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='010  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='020  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='755  Thevalues of the valence charge transferandthespinpolarizationwere estimatedforthe Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3  crystal (table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The presence of uncompensated spin ordering is found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Discussions  In contrast to the expectation that Cu with spin 1  2 will dilute the magnetic moments contributed by Fe  with a larger spin, we found that 15% Cu doping partially keeps the effective fluctuating moment, although  there is a long-range magnetic order partially distorted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' This follows from the magnetic susceptibility  43701-8  FeThe antiferromagnetic phase transition in the layered Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 semiconductor  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The calculated values of the spin components of the valence charge and the spin polarization in  Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Species  𝑄up, e  𝑄dw, e  𝑄, e  Σ𝑆, ℏ/2  Cu  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='00  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='00  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='53  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='28  Fe  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='86 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='36  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='86 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='37  −27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='51  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='07  P  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='03  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='03  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='22  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='07  S  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='08  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='07  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='82  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='35  temperature dependence around transition from paramagnetic into antiferromagnetic phase — amplitude  of the observed 𝜒(𝑇) anomaly is like the one observed in case of FePS3 pure crystal [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' At Fe by Cu  partial substitution, the temperature of 𝜒(𝑇) maximum is lowered from 120 K in FePS3 to 108 K in case  of Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The jump of 𝜒(𝑇) at ferromagnetic transition is smeared by Cu dilution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  In real crystal, the sulfur vacancies 𝑉S presence can also effectively suppress the strong intralayer  antiferromagnetic correlation, giving rise to a weak ferromagnetic ground state, which is observed on the  𝑀(𝐻) dependence below 10 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The presence of 𝑉S disrupts anion-mediated AFM interactions and may  be responsible for the suppression of long-range AFM correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Herein, the competing ferromagnetic  exchange interactions can dominate at low temperatures, creating a magnetically frustrated system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The  exchange interactions between the 𝑉S and metal ions, and with the local atomic distortion in the vicinity  of defects, could also induce ferromagnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  A canting configuration and the resulting net moments along the easy axis can also be attributed to  atomic substitution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' All these signatures exhibit the complexity of magnetic structure for the 15% Cu  substituted sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  The susceptibilities of Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 can be considered as for configurationally averaged clusters  sum of two terms: a randomly diluted antiferromagnet susceptibility, as in pure FePS3, and a Curie  correction arising from local fluctuations of the uncompensated spins due to the finite size of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  For Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 crystal, there is observed a weak paramagnetic contribution for small temperatures  (figure 4), because many of the spins no longer belong to the infinite cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The uncompensated moments  in the diluted 2D AFM can give rise to a Curie contribution into the magnetic susceptibility, and the  presence of field dependence of the magnetization suggests that they interact ferromagnetically to give a  spontaneous magnetization below 10 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Conclusions  According to the presented experimental data on Mössbauer spectroscopy and direct magnetic moment  temperature and field dependencies measurements, it can be stated that the Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 single-crystal  undergoes a magnetic phase transition at the region of 102–108 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' A weak ferromagnetic moment at the  low-temperature region (𝑇 = 10 K) was observed in the 𝐻⊥ plane direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' This correlates with ab initio  calculated non-zero spin polarization of the considered material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Furthermore, the calculated values of  the electric field gradient components and estimations of the total magnetic moment of the unit cell  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='764 ℏ/2 corresponds to 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='543 emu/mol) are in reasonable agreement with the measured experimental  quantities of ∼ 9 emu/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  The present studies of Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 magnetic properties show that the uncompensated moments  in the diluted 2D AFM can give rise to a Curie contribution, and the observed field dependence of the  magnetization suggests that they do interact ferromagnetically to give a spontaneous magnetization at low  temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' The relation of the magnetic ordering with structural change at antiferromagnetic phase  transition can also be important and must be investigated further on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  It is worth to note that the flattening of magnetic susceptibility at low temperature was also observed in  rare-earth containing compounds caused by Kondo effect [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' In the case of the studied Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3  crystal, the system seems not to be such a strongly correlated material as rare earth materials but, of  course, the proper investigation of the low temperature dependence of resistivity is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  43701-9  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Pashchenko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Chu J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Hu K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Rao G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Gong C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wu C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Hong H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Liu K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Gao C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Xiong J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=',  Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2020, 33, 2004469, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1002/adma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='202004469.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Hu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Kan E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', WIREs Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2019, 9, e1409, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1002/wcms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Liu Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Deng L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Peng B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Nano Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2021, 14, 1802–1813, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1007/s12274-020-2860-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Gong C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Kim E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Lee G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zhang X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2019, 10, 2657, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1038/s41467-019-  10693-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Wang F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Shifa T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Yu P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', He P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Liu Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zhan X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Lou X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Xia F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', He J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=',  2018, 28, 1802151, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
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+page_content=' Gong C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Li L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Li Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Ji H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Stern A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Xia Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Cao T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Bao W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Qiu Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Cava R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=',  Louie S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Xia J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zhang X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Nature, 2017, 546, 265–269, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
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+page_content=' Belianinov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', He Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Dziaugys A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Maksymovych P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Eliseev E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Borisevich A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Morozovska A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Banys J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=',  Vysochanskii Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Kalinin S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2015, 15, 3808–3814, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1021/acs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
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+page_content='5b00491.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Liu F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', You L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Seyler K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Li X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Yu P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Lin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zhou J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', He H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Pantelides S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zhou W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=',  Sharma P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Xu X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Ajayan P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Liu Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2016, 7, 12357, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1038/ncomms12357.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Qi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Chen X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Qian X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2018, 113, 043102, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='5038037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Osada M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Sasaki T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', APL Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2019, 7, 120902, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='5129447.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Lai Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Song Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wan Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Xue M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wang C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Ye Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Dai L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zhang Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Yang W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Dua H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Yangace J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Nanoscale,  2019, 11, 5163–5170, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
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+page_content='  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Dziaugys A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Shvartsman V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Macutkevic J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Banys J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Vysochanskii Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Kleemann W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' B, 2012,  85, 134105, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='134105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Kleemann W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Shvartsman V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Borisov P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Banys J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Vysochanskii Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' B, 2011, 84, 094411,  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='094411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Olsen T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' D: Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2021, 54, 314001, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1088/1361-6463/ac000e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
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+page_content=' Wildes A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zhitomirsky M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Ziman T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Lançon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Walker H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
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+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2020, 127,  223903, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='0009114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Sakai H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Yamazaki T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Machida N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Shigematsu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Nasu S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Cryst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Liq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Cryst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' A, 2000,  341, 105–110, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1080/10587250008026125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Chandrasekharan N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Vasudevan S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' B, 1996, 54, 14903, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='14903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
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+page_content=' Mulders A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Klaasse J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Goossens D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Chadwick J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Hicks T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' : Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Matter, 2002, 14,  8697, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1088/0953-8984/14/37/306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Masubuchi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Hoya H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Watanabe T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Takahashi Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Ban S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Ohkubo N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Takase K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Takano Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Alloys Compd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=',  2008, 460, 668–674, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='jallcom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='063.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Bhutani A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zuo J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', McAuliffe R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', dela Cruz C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Shoemaker D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2020, 4, 034411,  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevMaterials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='034411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Dziaugys A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Macutkevic J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Svirskas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Juskenas R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wencka M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Banys J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Motria S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Vysochanskii Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=',  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Alloys Compd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2015, 650, 386–392, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='jallcom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' WissEl, Data Evaluation Software — WissEl, Wissenschaftliche Elektronik GmbH, [Online;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' accessed 10-Jul-  2022], URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='wissel-gmbh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='de/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='php?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='option=com_content&task=view&id=55&Itemid=116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Jernberg P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Bjarman S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Wäppling R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 1984, 46, 178–190, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1016/0304-  8853(84)90355-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Chen Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Yang D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Mössbauer Effect in Lattice Dynamics: Experimental Techniques and Applications,  Wiley-VCH Verlag GmbH & Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' KGaA, Weinheim, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rule K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Cashion J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Mulders A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Hicks T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Hyperfine Interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2002, 141, 219–222,  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1023/A:1021286910897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Giannozzi P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Baroni S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Bonini N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Calandra M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Car R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Cavazzoni C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Ceresoli D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Chiarotti G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Cococ-  cioni M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Dabo I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' : Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Matter, 2009, 21, 395502, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1088/0953-8984/21/39/395502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Perdew J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Burke K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Ernzerhof M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 1997, 78, 1396, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1396.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Ceperley D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Alder B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 1980, 45, 566, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='566.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Perdew J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Zunger A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' B, 1981, 23, 5048, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='5048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Grimme S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 2006, 27, 1787–1799, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1002/jcc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='20495.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Vanderbilt D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' B, 1990, 41, 7892, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='7892.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Monkhorst H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Pack J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' B, 1976, 13, 5188, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='5188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Menth A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Buehler E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Geballe T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=', 1969, 22, 295, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='295.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  43701-10  The antiferromagnetic phase transition in the layered Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3 semiconductor  Антиферомагнiтний фазовий перехiд в шаруватому  напiвпровiднику Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3: експеримент та DFT  моделювання  В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Пащенко1, О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Блудов1, Д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Балтрунас2, К.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Мазейка2, С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Мотря3, К.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Глухов3,  Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Височанський3  1 Iнститут фiзики i технiки низьких температур iм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Вєркiна НАН України, просп.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Науки 47, 61103, Харкiв,  Україна  2 Вiддiл ядерних дослiджень Центру фiзичних наук та технологiї, просп.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Саванорiу 231, LT-02300, Вiльнюс,  Литва  3 Iнститут фiзики i хiмiї твердого тiла, Ужгородський нацiональний унiверситет, вул.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Волошина 54, 88000,  Ужгород, Україна  Представленi експериментальнi дослiдження парамагнiтно-антиферомагнiтного фазового переходу ме-  тодом мессбауерiвської спектроскопiї та вимiрювання температурних i польових залежностей магнiтної  сприйнятливостi в шаруватому кристалi Cu0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='15Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='85PS3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Особлива поведiнка польової залежностi намаг-  нiченостi в областi низьких температур свiдчить про слабкий феромагнетизм дослiджуваного матерiалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  За допомогою ab initio моделювання електронної та спiнової пiдсистем, в рамках теорiї функцiоналу  електронної густини, проаналiзовано особливостi спiнового впорядкування при низькiй температурi, а  також змiни мiжатомних взаємодiй поблизу атомiв замiщення Cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Розрахованi компоненти тензора гра-  дiєнта електричного поля та параметра асиметрiї для iонiв Fe близькi до значень знайдених з мессбау-  ерiвських спектрiв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Маллiкенiвськi заселеностi показують, що основний внесок у феромагнiтну спiнову  густину вносять 3𝑑 орбiталi мiдi та 3𝑝 сiрки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content=' Розрахунковий загальний магнiтний момент елементарної  комiрки (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='543 emu/mol) цiлком узгоджується з вимiряним експериментальним значенням ∼ 9 emu/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
+page_content='  Ключовi слова: метал-фосфорнi трихалькогенiди, магнiтне впорядкування, мессбауерiвська  спектроскопiя, фазовi переходи, теорiя функцiоналу електронної густини  43701-11' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/XdAzT4oBgHgl3EQfYfz7/content/2301.01338v1.pdf'}
diff --git a/_9E1T4oBgHgl3EQfowSL/content/tmp_files/2301.03324v1.pdf.txt b/_9E1T4oBgHgl3EQfowSL/content/tmp_files/2301.03324v1.pdf.txt
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+Received: Added at production
+Revised: Added at production
+Accepted: Added at production
+DOI: xxx/xxxx
+ARTICLE TYPE
+Numerical approximation of a thermodynamically complete
+rate-type model for the elastic–perfectly plastic response
+Pablo Alexei Gazca-Orozco*1,2 | Vít Průša2 | Karel Tůma2
+1Department of Mathematics, University of
+Freiburg, Ernst-Zermelo-Straße, 79104,
+Freiburg, Germany
+2Charles University, Faculty of Mathematics
+and Physics, Sokolovská 83, Praha, CZ 186
+75, Czech Republic
+Correspondence
+*Pablo Alexei Gazca–Orozco, Department
+of Mathematics, University of Freiburg,
+Ernst-Zermelo-Straße, 79104, Freiburg,
+Germany. Email:
+alexei.gazca@mathematik.uni-freiburg.de
+Abstract
+We analyse a numerical scheme for a system arising from a novel description of the
+standard elastic–perfectly plastic response. The elastic–perfectly plastic response is
+described via rate-type equations that do not make use of the standard elastic-plastic
+decomposition, and the model does not require the use of variational inequalities.
+Furthermore, the model naturally includes the evolution equation for temperature.
+We present a low order discretisation based on the finite element method. Under
+certain restrictions on the mesh we subsequently prove the existence of discrete solu-
+tions, and we discuss the stability properties of the numerical scheme. The analysis
+is supplemented with computational examples.
+KEYWORDS:
+Rate-type constitutive relations, perfect plasticity, finite element method, thermodynamically consistent
+models
+1
+INTRODUCTION
+The rate-independent hysteretic response is frequently encountered in various engineering applications such as electrical engi-
+neering, geomechanics and mechanical engineering. Each of these research communities have developed its own approaches
+to the modelling of the hysteretic response, see[31],[16] and[21] for a list of various hysteretic models and a discussion of their
+relations. In solid mechanics the prime example of a rate-independent hysteretic response is the elastic-plastic response, see for
+example[3] and[17] for comments on the historical development of plasticity theory. In the present contribution we work with a
+novel model for the standard elastic–plastic response, see[22,23] and[6], and we focus on mathematical aspects of the model. In
+particular we prove solvability of the corresponding spatially discretised system of governing partial differential equations.
+Before we proceed with the numerical analysis, let us briefly comment on the status of the considered model. Concerning
+the elastic–plastic response of metals, the predominant modelling approach is based on the concepts of the elastic–plastic
+decomposition, the flow rule and the yield condition, which in turn leads to a characterisation of the elastic–plastic response
+using the concepts of optimisation theory, see especially[29]. Concerning the elastic-plastic response of non-metallic materials
+such as soils, the situation is different, see, for example,[13, Ch. 8] for a critical review of some popular models. These materials
+typically exhibit “diffuse yielding behaviour”, see[17] and the discussion therein, which means that the transition from the elastic
+to the plastic regime is not sharp, but it progresses gradually, hence the concept of sharp yield condition must be abandoned.
+In this case the elastic–plastic response is typically modelled using rate-type equations designed in such a way that the whole
+model still predicts the rate-independent behaviour.
+We shall investigate the family of models introduced in[22]. This class of models belongs to the class of rate-type models,
+but it goes one step further. It also abandons the concept of elastic–plastic decomposition. In particular, the models do not use
+the traditional concept of strain decomposition to the elastic and plastic part, see[27] or[30] and references therein; the models
+arXiv:2301.03324v1  [math.NA]  9 Jan 2023
+
+2
+AUTHOR ONE ET AL
+stemming from[22] work with the stress and the strain only. In a one-dimensional setting the stress–strain relation is given by the
+rate-type equation
+d휎
+d푡 = E
+[
+1 − 퐻
+(
+휎 d휀
+d푡
+)
+퐻 (
+|휎| − 휎푦
+)] d휀
+d푡 ,
+(1)
+where 휎 denotes the stress, 휀 denotes the strain, 휎푦 denotes the yield stress, E denotes the Young modulus and 퐻 denotes the
+Heaviside step function (5). (Compare with the standard models that lead to optimisation problems, see[29, Ch. 1].) The rate-type
+stress–strain relation (1) is clearly rate-independent, and it leads to the standard elastic–perfectly plastic response. Indeed, if the
+yield stress is reached, |휎| = 휎푦, and if the material is being loaded, 휎 d휀
+d푡 ≥ 0, then (1) reduces to
+d휎
+d푡 = 0,
+(2)
+hence the stress 휎 remains constant and equal to the yield stress value. This is the plastic flow regime. On the other hand, if the
+stress is below the yield stress value, |휎| < 휎푦, or if the material is being unloaded, 휎 d휀
+d푡 < 0, then (1) reduces to
+d휎
+d푡 = E d휀
+d푡 .
+(3)
+This is the standard elastic response rewritten in terms of rates. Indeed, equation (3) is just the time derivative of Hooke law
+휎 = E 휀. Once we have (2) and (3), it is straightforward to see that the cyclic change of strain leads to the standard hysteretic
+behaviour.
+An important feature of the model (1) is that the second Heaviside function 퐻 (
+|휎| − 휎푦
+) can be replaced by a smoothed
+version thereof, which allows one to easily deal with the “diffuse yielding behaviour”, see[22] and for further comments also[17].
+Furthermore, the family of one-dimensional models based on the rate-type equation (1) can be extended to the fully three-
+dimensional finite deformations setting, see[23] and[6].
+Finally, the finite deformation version of the models can be shown to be thermodynamically consistent, see[6]. This implies
+that the energy conversions in the material are fully characterised. In particular, the heat generated in the inelastic processes is
+known, and the models allow one to study fully coupled thermomechanical processes in the finite strain setting. Despite their
+importance, such coupled thermomechanical processes are rarely studied, especially in the case of rate-type models for soils,
+see[12–14], and the situation is only slightly better for metals, see[25] for an early example thereof.
+In the present work, we focus on a model of type (1) that arises in the small strain approximation of a finite deformation model
+based on (1). The model is described in[6], and it focuses on the core features of elastic–plastic material response. The model is a
+simple model without additional subtleties such as the kinematic/isotropic hardening and so forth, and as such the model is perfect
+for a proof-of-concept numerical analysis of this class of models. In particular, we prove solvability of the equations arising
+from the spatial discretisation of the corresponding partial differential equations, and we also investigate stability properties of
+the corresponding numerical scheme.
+2
+MODEL DESCRIPTION
+Let the computational domain Ω—which is tantamount to the reference stress-free configuration of the body of interest—be
+an open bounded subset of R푑, with 푑 ∈ {2, 3}, whose boundary 휕Ω is Lipschitz, and it is disjointly divided into a Dirichlet
+(displacement) 휕Ω퐷 and a Neumann (traction) 휕Ω푁 component.
+As shown in[6] the standard elastic–perfectly plastic response with von Mises yield criterion in the small strain regime can be
+described by the following system of equations posed on the space-time domain 푄 ∶= (0, 푇 ) × Ω:
+휌⋆ ̇풗 − div τ = 휌⋆퐟
+in (0, 푇 ) × Ω,
+(4a)
+1
+E ((1 + 휈) ̇τ − 휈(tr ̇τ)I) = ̇ε − 퐻(τ ∶ ̇ε)퐻(|τ훿|2 − 휅2
+⋆) ̇ε
+in (0, 푇 ) × Ω,
+(4b)
+plus initial conditions 풗(0, ⋅) = 풗0(⋅) and τ(0, ⋅) = τ0, and boundary conditions 풗|휕Ω퐷 = 풗푏 and τ풏|휕Ω푁 = 퐭푏, where (휕Ω퐷) ∪
+휕Ω푁 = 휕Ω.
+Here 풖 denotes the displacement, ε = ε(풖) ∶=
+1
+2(∇풖 + ∇풖⊤) denotes the linearised strain operator (infinitesimal strain
+tensor), τ denotes the stress tensor, and A훿 ∶= A − 1
+푑 tr(A)I denotes the traceless part of the corresponding tensor A. The symbol
+
+AUTHOR ONE ET AL
+3
+(A ∶ B) ∶= tr (
+ABT) denotes the matrix scalar product. The function 퐻 is the classical Heaviside function, defined as
+퐻(푠) ∶=
+{ 1, 푠 ≥ 0,
+0, 푠 < 0.
+(5)
+All the quantities of interest are functions of the position in the reference configuration 퐗 ∈ Ω and time 푡 ∈ (0, 푇 ); the dot
+represents the time derivative
+̇A ∶= 휕
+휕푡A(푡, 퐗).
+The symbols E , 휈, 휅⋆ denote material parameters, namely Young modulus, Poisson ratio, and yield stress; the density in the
+reference configuration is denoted by 휌⋆ and we assume that 휌⋆ ≥ 휌−
+⋆, for some positive constant 휌−
+⋆.
+The first equation (4a) represents balance of momentum, and the second equation (4b) is the rate-type constitutive relation for
+the elastic–perfectly plastic response. Since in the small strain regime we have ̇ε = ε(풗), we see that the system (4) is a system
+of evolution equations for the velocity field 풗 and the stress tensor τ.
+The displacement 풖 and temperature 휃 can be computed post-hoc. Once the stress τ and the velocity 풗 fields are known, it
+remains to solve
+̇풖 = 풗
+in (0, 푇 ) × Ω,
+(6a)
+휌⋆푐푣 ̇휃 − div(휅th∇휃) = 퐻(τ ∶ ̇ε)퐻(|τ훿|2 − 휅2
+⋆)τ ∶ ̇ε
+in (0, 푇 ) × Ω,
+(6b)
+for 풖 and 휃. Here 푐푣 denotes the specific heat capacity at constant volume, and 휅th is the thermal conductivity. The boundary
+conditions for the displacement are chosen to be consistent with those of 풗; i.e. if 풖|휕Ω퐷 = 풖푏 then 풗|휕Ω퐷 = 풗푏 ∶= ̇풖푏. For the
+temperature we impose the no-flux boundary condition, that is ∇휃 ⋅ 풏|휕Ω = 0.
+One of the challenging aspects of system (4) is the presence of the Heaviside function, since then one has to deal with a
+differential equation with a discontinuous nonlinearity. To alleviate this difficulty, we will employ a non-sharp yield condition.
+(In the terminology used in[17] this is tantamount to the “diffusive yielding behaviour”.) The non-sharp yield condition means
+that the last term in (4b) is substituted by 퐻(τ ∶ ̇ε)퐻휖(|τ훿|2 −휅2
+⋆) ̇ε, where 퐻휖 is a regularised version of the Heaviside function.
+We consider three different options in this work, namely
+퐻(1)
+휖 (푠) ∶= 1
+2 + 1
+2
+푠
+휖
+√
+1 + ( 푠
+휖)2
+휖 > 0, 푠 ∈ R,
+(7a)
+퐻(2)
+휖 (푠) ∶= 1
+2 + 1
+2 tanh
+(푠
+휖
+)
+휖 > 0, 푠 ∈ R,
+(7b)
+퐻(3)
+휖 (푠) ∶= 1
+2 + 1
+휋 arctan
+(푠
+휖
+)
+휖 > 0, 푠 ∈ R,
+(7c)
+where 휖 is the regularisation parameter.
+The qualitative one-dimensional behaviour during loading and unloading, for the stress 휎 and strain 휖, that can be described by
+the non-sharp yield condition is depicted in Figure 1. (The magnitude of the regularisation parameter 휖 controls the “sharpness”
+of the corner on the loading curve.) We reiterate that the regularisation is in some physically relevant cases not artificial. In
+fact many materials exhibit such non-sharp yield conditions, see[17] and the discussion therein. The freedom to model such
+non-sharp/diffusive yield condition is an advantage of the approach presented here, in contrast with the more widely used
+rate-independent models, where modelling non-sharp yield conditions is more cumbersome, see again[17].
+3
+DISCRETE FORMULATION
+We employ the standard notation for Lebesgue spaces (퐿푝(Ω), ‖⋅‖퐿푝(Ω)) and Sobolev spaces (푊 1,푝(Ω), ‖⋅‖푊 1,푝(Ω)). Let {ℎ}ℎ>0
+be a family of shape-regular triangulations of Ω associated to a sequence of mesh sizes ℎ → 0; we assume here that Ω is a
+Lipschitz domain with polyhedral boundary, and also for simplicity we assume that the mesh is quasi-uniform, which implies
+that following inverse inequalites are available[9],
+‖∇풗‖퐿2(Ω) ≤ 푐invℎ−1‖풗‖퐿2(Ω)
+∀풗 ∈ 푉 ℎ,
+(8a)
+‖풗‖퐿2(휕Ω) ≤ 푐trℎ−1∕2‖풗‖퐿2(Ω)
+∀풗 ∈ 푉 ℎ,
+(8b)
+
+4
+AUTHOR ONE ET AL
+휀
+휎
+휅⋆
+Figure 1 Non-sharp yield condition obtained as a consequence of a regularised Heaviside function 퐻휀.
+where 푐inv, 푐tr > 0 are positive constants independent of ℎ; this quasi-uniformity assumption is not crucial, if desired one can
+apply instead local inverse inequalities.
+The finite element spaces for the stress and velocity are chosen as
+Σℎ = { ∈ 퐿∞(Ω)푑×푑
+sym ∶ |퐾 ∈ P0(퐾)푑×푑
+sym, ∀퐾 ∈ ℎ} = DG(0)푑×푑
+sym,
+푉 ℎ = {풗 ∈ 푊 1,∞(Ω)푑 ∶ 풗|퐾 ∈ P1(퐾)푑, ∀퐾 ∈ ℎ, 풗|휕Ω퐷 = ퟎ},
+that is, piecewise-linear Lagrange elements for the velocity and piecewise-constant approximations for the stress; here P푞(퐾)
+denotes the set of polynomials of degree at most 푞 on an element 퐾 ∈ ℎ. Since we are interested in approximating discontinuous
+terms, it is natural to employ lower order approximations, because higher degree polynomials could, in the absence of for
+example adaptivity, lead to unwanted oscillations.
+For later use it is convenient to define the compliance operator ∶ R푑×푑
+sym → R푑×푑
+sym as
+(σ) ∶= 1
+E ((1 + 휈)σ − 휈(tr σ)I),
+σ ∈ R푑×푑
+sym.
+(9)
+that is  = C−1, where C is the standard linear elasticity tensor. Since  is positive definite, we can use it to define a norm on
+the space of discrete stresses Σℎ:
+‖σ‖2
+ ∶= ∫
+Ω
+σ ∶ σ,
+σ ∈ Σℎ.
+(10)
+This norm is clearly equivalent to the 퐿2-norm; namely, 퐴min‖σ‖2
+퐿2(Ω) ≤ ‖σ‖2
+ ≤ 퐴max‖σ‖2
+퐿2(Ω), where 퐴min and 퐴max denote
+the minimum and maximum eigenvalues of , respectively. Similarly, we equip the velocity space 푉 ℎ with the weighted norm
+‖풗‖2
+휌⋆ ∶= ∫
+Ω
+휌⋆풗 ⋅ 풗,
+풗 ∈ 푉 ℎ.
+(11)
+The corresponding weighted spaces of square integrable functions at the continuous level will be denoted by 퐿2
+휌⋆(Ω) and 퐿2
+(Ω).
+Concerning the discretisation in time, we choose a time-step 휏 > 0, and we define a uniform time grid 푡푘 ∶= 푘휏, for 푘 ∈
+{1, … , 푇 ∕휏}. (We can without loss of generality assume that 푇 ∕휏 ∈ N.) The system of governing equations is then discretised in
+time with the implicit Euler method; given a family of functions {풗푘}푘∈{0,…,푇 ∕휏} we define the discrete time derivative operator
+(or temporal difference quotient) as
+d휏
+푡 풗푘 ∶= 풗푘 − 풗푘−1
+휏
+,
+푘 ∈ {1, … , 푇 ∕휏}.
+(12)
+Now we are in the position to formulate a time-stepping scheme. We assume that the boundary datum 풗푏 can be seen as the
+restriction of some CG(1) function on Ω, which we still denote by 풗푏, and we set τ0 ∶= τ0 and 풗0 ∶= 풗0. In the finite element
+formulation, assuming that approximations τ푘−1 ∈ Σℎ and 풗푘−1 ∈ 풗푏 + 푉 ℎ at time 푡푘−1 have already been found, we look for
+(τ푘
+ℎ,휏,휖, 풗푘
+ℎ,휏,휖) ∶= (τ푘, 풗푘) ∈ Σℎ × (풗푏 + 푉 ℎ) such that
+∫
+Ω
+(d휏
+푡 τ푘) ∶ σ − ∫
+Ω
+ε(풗푘) ∶ σ + ∫
+Ω
+퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘
+훿|2 − 휅2
+⋆)ε(풗푘) ∶ σ = 0
+∀σ ∈ Σℎ,
+∫
+Ω
+휌⋆d휏
+푡 풗푘 ⋅ 풘 + ∫
+Ω
+τ푘 ∶ ε(풘) = ∫
+Ω
+휌⋆퐟푘 ⋅ 풘 + ∫
+휕Ω푁
+퐭푘
+푏 ⋅ 풘
+∀풘 ∈ 푉 ℎ.
+(13)
+
+AUTHOR ONE ET AL
+5
+Here 퐟푘 and 퐭푘
+푏 are approximations of 퐟 and 퐭푏 at time 푡 = 푡푘, respectively. E.g. if 퐟 and 퐭 continuous, we can set 퐟푘(⋅) ∶= 퐟(푡푘, ⋅)
+and 퐭푘
+푏 (⋅) ∶= 퐭푏(푡푘, ⋅).
+The displacement and temperature problems (6) are be discretised with piecewise linear Lagrange elements, that is the spaces
+of discrete displacements 푈 ℎ and discrete temperatures Θℎ are defined as
+푈 ℎ = {풖 ∈ 푊 1,∞(Ω)푑 ∶ 풖|퐾 ∈ 푃1(퐾)푑, ∀퐾 ∈ ℎ, 풖|휕Ω퐷 = ퟎ},
+Θℎ = {휃 ∈ 푊 1,∞(Ω) ∶ 휃|퐾 ∈ 푃1(퐾), ∀퐾 ∈ ℎ} = CG(1).
+In the discrete formulation we set 풖0 ∶= 풖0 and 휃0 ∶= 휃0, and for 푘 ∈ {1, … , 푇 ∕휏}, assuming that τ푘 ∈ Σℎ, 풗푘 ∈ 풗푏 + 푉 ℎ,
+풖푘−1 ∈ 풖푏 + 푈 ℎ and 휃푘−1 ∈ Θℎ are known, we look for (풖푘, 휃푘) ∈ (풖푏 + 푈 ℎ) × Θℎ such that
+∫
+Ω
+d휏
+푡 풖푘 ⋅ 풘 − ∫
+Ω
+풗푘 ⋅ 풘 = 0
+∀풘 ∈ 푈 ℎ,
+∫
+Ω
+휌⋆푐푣d휏
+푡 휃푘휙 + ∫
+Ω
+휅th∇휃푘 ⋅ ∇휙 = ∫
+Ω
+퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘
+훿|2 − 휅2
+⋆)τ푘 ∶ ε(풗푘)휙
+∀휙 ∈ Θℎ.
+(14)
+Remark 1. Given the discontinuous nature of the stress space Σℎ, and noting that nonlinear functions of τ푘 remain piecewise
+constant, the equation for τ푘 in (13) holds pointwise,
+(d휏
+푡 τ푘) − ε(풗푘) + 퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘
+훿|2 − 휅2
+⋆)ε(풗푘) = 0
+in Ω.
+This defines (implicitly) a mapping 풗푘 → ̃τ푘(풗푘), which could be used to define a velocity-only problem
+∫
+Ω
+휌⋆d휏
+푡 풗푘 ⋅ 풘 + ∫
+Ω
+̃τ푘(풗푘) ∶ ε(풘) = ∫
+Ω
+휌⋆퐟푘 ⋅ 풘 + ∫
+휕Ω푁
+퐭푘 ⋅ 풘
+∀풘 ∈ 푉 ℎ.
+Using tools from automatic differentiation this can be solved, resulting in a strategy similar to the one employed traditionally,
+in which consistent tangents are employed in the linearisation[29, Ch. 4.3.6]. We do not pursue this further in this work.
+3.1
+Existence of discrete solutions
+The goal in this section is to prove that numerical solutions to (13) exist. To help with this, we look first at the system in which
+both Heaviside functions are regularised. (The regularisation parameters are denoted as 휂 and 휖.) For simplicity we also assume
+that 풗푏 = ퟎ. Define the function 퐹휂 ∶ Σℎ × 푉 ℎ → Σℎ × 푉 ℎ through the relation
+⟨퐹휂(τ, 풗), (σ, 풘)⟩ ∶= ∫
+Ω
+(τ) ∶ σ − 휏 ∫
+Ω
+ε(풗) ∶ σ + 휏 ∫
+Ω
+퐻휂(τ ∶ ε(풗))퐻휖(|τ훿|2 − 휅2
+⋆)ε(풗) ∶ σ
++ 휏 ∫
+Ω
+τ ∶ ε(풘) + ∫
+Ω
+휌⋆풗 ⋅ 풘 − ∫
+Ω
+(τ푘−1) ∶ σ − ∫
+Ω
+휌⋆풗푘−1 ⋅ 풘
+− 휏 ∫
+Ω
+휌⋆퐟푘 ⋅ 풘 − 휏 ∫
+휕Ω푁
+퐭푘
+푏 ⋅ 풘.
+Note that the (regularised) discrete formulation can be written simply as 퐹휂(τ, 풗) = 0; note also that the function 퐹휂 is continuous.
+If we manage to find a positive number ̂푐, such that ⟨퐹휂(τ, 풗), (τ, 풗)⟩ ≥ 0, for all (τ, 풗) ∈ Σℎ × 푉 ℎ with ‖τ‖2
+ + ‖풗‖2
+휌⋆ = ̂푐, then
+a corollary of Brouwer’s fixed point theorem will guarantee the existence of a discrete solution[11, Ch. 4, Cor. 1.1]. To this end, we
+take (σ, 풘) = (τ, 풗) in the definition of 퐹휂; this yields:
+⟨퐹휂(τ, 풗), (σ, 풘)⟩ ≥ ∫
+Ω
+(τ) ∶ τ + ∫
+Ω
+휌⋆|풗|2 − ‖τ푘−1‖‖τ‖ − ‖풗푘−1‖휌⋆‖풗‖휌⋆ − 휏‖퐟푘‖휌⋆‖풗‖휌⋆
+−
+휏푐tr
+(ℎ휌−
+⋆)1∕2 ‖퐭푘
+푏 ‖퐿2(휕Ω푁)‖풗‖휌⋆ + 휏 ∫
+Ω
+퐻휂(τ ∶ ε(풗))퐻휖(|τ훿|2 − 휅2
+⋆)ε(풗) ∶ τ
+≥ ‖τ‖2
+ + ‖풗‖2
+휌⋆ − 1
+2‖τ푘−1‖2
+ − 1
+2‖τ‖2
+ − ‖풗푘−1‖2
+휌⋆ − 1
+2‖풗‖2
+휌⋆ − 휏
+2‖풗‖2
+휌⋆ − 휏
+2‖퐟푘‖2
+휌⋆
+
+6
+AUTHOR ONE ET AL
+−
+푐2
+tr휏
+2휌−
+⋆ℎ‖풗‖2
+휌⋆ − 휏
+2‖퐭푘
+푏 ‖퐿2(휕Ω푁) −
+푐inv휏
+ℎ(퐴min휌−
+⋆)1∕2 ‖풗‖휌⋆‖τ‖
+≥ 1
+2
+(
+1 −
+푐inv
+(퐴min휌−
+⋆)1∕2
+휏
+ℎ
+)
+‖τ‖2
+ + 1
+2
+(
+1 −
+(퐴min휌−
+⋆)1∕2 + 퐴1∕2
+min푐2
+tr + 푐inv휌−
+⋆
+1∕2
+퐴1∕2
+min휌−
+⋆
+휏
+ℎ
+)
+‖풗‖2
+휌⋆
+− 1
+2‖τ푘−1‖2
+ − ‖풗푘−1‖2
+휌⋆ − 1
+2‖퐟‖2
+퐿2
+휌⋆(푄) + 1
+2‖퐭푏‖퐿2(0,푇 ;퐿2(휕Ω푁)),
+where we employed Young’s inequality, the inverse inequalites (8), and the fact that 휏‖퐟푘‖2
+휌⋆ ≤ ‖퐟‖2
+퐿2
+휌⋆(Ω). Hence, the claim
+follows if we assume that
+휏
+ℎ <
+퐴1∕2
+min휌−
+⋆
+푐inv휌−
+⋆
+1∕2 + 푐2
+tr퐴1∕2
+min + 퐴1∕2
+min휌−
+⋆
+1∕2 .
+(15)
+The same corollary to Brouwer’s fixed point theorem in addition implies that the solution is bounded,
+‖τ푘
+휂‖2
+ + ‖풗푘
+휂‖2
+휌⋆ ≤ ̂푐.
+We remark that it is likely that existence of discrete solutions can be proved without assuming a condition like (15) by relying
+on the equivalence of norms in finite dimensions and the fact that 휏 and ℎ are fixed. However, we choose to stick to the argument
+presented above, since the condition (15) will appear once again in the next section where we analyse the stability of the numerical
+scheme, for which uniform bounds are desirable.
+Now, since the bounds are independent of the regularisation parameter 휂 in the first Heaviside function 퐻휂, the Heine–
+Borel theorem implies that up to a subsequence, for every 푘 ∈ {1, … , 푇 ∕휏} the sequence of solutions τ푘
+휂 (here we make the
+휂-dependence explicit) converges as 휂 → 0,
+τ푘
+휂 → τ푘
+strongly in 퐿∞(Ω)푑×푑,
+풗푘
+휂 → 풗푘
+strongly in 푊 1,∞(Ω)푑,
+for some τ푘 ∈ Σℎ and 풗푘 ∈ 푉 ℎ. At this point we have used the fact that weak and strong convergence are equivalent in finite-
+dimensional spaces. This implies in particular that 퐻휂(τ푘
+휂 ∶ ε(풗푘
+휂)) → 퐻(τ푘 ∶ ε(풗푘)) pointwise a.e. in Ω, and so the limiting
+functions satisfy the system with the unregularised Heaviside function.
+In summary, numerical solutions are guaranteed to exist, assuming the ratio 휏
+ℎ is small enough. We note also that very similar
+arguments yield the existence of solutions for the displacement-temperature system (14).
+Remark 2. We could also consider semi-implicit discretisation schemes such as
+∫
+Ω
+(d휏
+푡 τ푘) ∶ σ − ∫
+Ω
+ε(풗푘) ∶ σ + ∫
+Ω
+퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘
+훿|2 − 휅2
+⋆)ε(풗푘) ∶ σ = 0
+∀σ ∈ Σℎ,
+∫
+Ω
+휌⋆d휏
+푡 풗푘 ⋅ 풘 + ∫
+Ω
+τ푘−1 ∶ ε(풘) = ∫
+Ω
+휌⋆퐟푘−1 ⋅ 풘 + ∫
+휕Ω푁
+퐭푘−1 ⋅ 풘
+∀풘 ∈ 푉 ℎ,
+(16)
+and a similar analysis applies. The difference in this scheme compared to (13) is that here the velocity 풗푘 is computed first using
+the information at time 푡푘−1 and the equation for τ푘 is solved afterwards. In the absence of plastic behaviour this results in a
+symplectic scheme that conserves a (modified) energy.
+Remark 3. A consequence of the fact that 햣햣햣(푉 ℎ) ⊂ Σℎ and that 푉 ℎ ⊂ 퐻1
+휕Ω퐷(Ω)푑 is that the following discrete inf-sup condition
+holds:
+inf
+풘∈푉 ℎ sup
+σ∈Σℎ
+∫Ω σ ∶ ε(풘)
+‖풘‖퐻1(Ω)‖σ‖2
+퐿2(Ω)
+≥ 훾⋆ > 0.
+(17)
+where 훾⋆ > 0 is independent of ℎ; note that the above is then simply a reformulation of Korn’s inequality. The validity of (17) is
+not essential for the analysis of the discrete problem (13), but it would be crucial if we were interested in solving the quasi-static
+problem (i.e. without the time derivative ̇풗).
+3.2
+Stability
+Now we take a more careful look at the stability of the scheme. Let us first look at the continuous system (4). First we assume
+that solutions are smooth enough so that all subsequent manipulations are well-defined in the classical sense. The multiplication
+
+AUTHOR ONE ET AL
+7
+of the first equation in system (4) by 풗, the second by τ and integrating over Ω results in the energy balance in the form
+1
+2
+d
+d푡
+⎛
+⎜
+⎜⎝∫
+Ω
+(τ) ∶ τ + 휌⋆|풗|2
+⎞
+⎟
+⎟⎠
++ ∫
+Ω
+퐻(τ ∶ ε(풗))퐻휖(|τ훿|2 − 휅2
+⋆)τ ∶ ε(풗) = ∫
+Ω
+휌⋆퐟 ⋅ 풗 + ∫
+휕Ω푁
+퐭푏 ⋅ 풗.
+(18)
+If we follow the terminology used in[29], thus, if we denote the kinetic energy by 퐸kin(풗) ∶= ∫Ω
+1
+2휌⋆|풗|2, the elastic potential
+energy by 퐸int(τ) ∶= ∫Ω
+1
+2(τ) ∶ τ, and the potential energy associated with the applied loads by 퐸ext(풖) ∶= − ∫Ω 휌⋆퐟 ⋅ 풖 −
+∫휕Ω푁 퐭푏 ⋅ 풖, then the energy balance can be rewritten as
+d
+d푡
+[퐸kin(풗) + 퐸int(τ) + 퐸ext(풖)] = − ∫
+Ω
+퐻(τ ∶ ε(풗))퐻휖(|τ훿|2 − 휅2
+⋆)τ ∶ ε(풗) ≤ 0.
+(19)
+Inspecting (19), it is clear that there is mechanical dissipation only when the material is being loaded and the yield stress has
+been reached. Moreover, if we define the thermal energy as 퐸th(휃) ∶= ∫Ω 휌⋆푐푣휃, then integrating the temperature equation (6b)
+and adding the result to (19), yields the total energy balance
+d
+d푡
+[퐸kin(풗) + 퐸int(τ) + 퐸ext(풖) + 퐸th(휃)] = 0.
+(20)
+The balance (20) highlights the fact that, as a consequence of the thermodynamically consistent derivation of the model, all
+various energy dissipation mechanisms are accounted for in the model.
+We now obtain an analogue of (19) at the discrete level. Choosing σ ∶= τ푘 and 풘 = 풗푘 in the numerical formulation (13),
+and using the elementary identity (푎 − 푏)푎 = 1
+2푎2 − 1
+2푏2 + 1
+2|푎 − 푏|2 for two numbers 푎, 푏 ∈ R, yields for all 푘 ∈ {1, … , 푇 ∕휏}
+the equality
+1
+2휏 ‖풗푘‖2
+휌⋆ − 1
+2휏 ‖풗푘−1‖2
+휌⋆ + 1
+2휏 ‖τ푘‖2
+ − 1
+2휏 ‖τ푘−1‖2
+ + 1
+2휏 ‖풗푘 − 풗푘−1‖2
+휌⋆
++ 1
+2휏 ‖τ푘 − τ푘−1‖2
+ + ∫
+Ω
+퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘
+훿|2 − 휅2
+⋆)ε(풗푘) ∶ τ푘 = ∫
+Ω
+휌⋆퐟 ⋅ 풗푘 + ∫
+휕Ω푁
+퐭푏 ⋅ 풗푘.
+Hence, if we define the numerical dissipation 푘
+휏 ∶=
+1
+2휏 ‖풗푘 − 풗푘−1‖2
+휌⋆ + 1
+2휏 ‖τ푘 − τ푘−1‖2
+, then the equality just derived above
+can be rewritten as
+d휏
+푡
+[퐸kin(풗푘) + 퐸int(τ푘)] + 퐸ext(풗푘) = −푘
+휏 − ∫
+Ω
+퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘
+훿|2 − 휅2
+⋆)ε(풗푘) ∶ τ푘 ≤ 0.
+(21)
+This equality clearly mimics the continuous energy balance (19), except for the presence of the numerical dissipation term 푘
+휏.
+Moreover, testing the temperature equation (14) with 휙 = 1 we also obtain the discrete total energy balance:
+d휏
+푡
+[퐸kin(풗푘) + 퐸int(τ푘) + 퐸th(휃푘)] + 퐸ext(풗푘) = −푘
+휏 ≤ 0,
+(22)
+which is analogous to the total energy balance (20), up to numerical dissipation.
+Remark 4. If we denote the piecewise-linear (in time) interpolant of the sequence {풗푘}푇 ∕휏
+푘=0 by ̃풗ℎ,휏 ∈ 퐶([0, 푇 ]; 푉 ℎ), then we see
+that
+1
+휏 ‖풗푘 − 풗푘−1‖2
+퐿2(Ω) = 휏
+‖‖‖‖‖
+휕 ̃풗ℎ,휏(푡푘
+−)
+휕푡
+‖‖‖‖‖
+2
+퐿2(Ω)
+,
+and so if the problem satisfies appropriate regularity properties so that the norm on the right-hand-side is bounded, then it is
+clear that the numerical dissipation term vanishes as 휏 → 0. Similar arguments apply to the stress.
+Now, let us denote the piecewise-constant (in time) interpolant associated to the sequence {풗푘}푇 ∕휏
+푘=0 by 풗ℎ,휏 ∈ 퐿∞((0, 푇 ); 푉 ℎ),
+and define τℎ,휏 analogously. Then, multiplying the discrete energy balance (22) by 2휏, using a similar argument to the one
+employed in the previous section, and summing over 푘, we obtain the stability estimate
+‖풗ℎ,휏‖2
+퐿∞(0,푇 ;퐿2
+휌⋆(Ω)) + ‖τℎ,휏‖2
+퐿∞(0,푇 ;퐿2
+(Ω)) +
+푇 ∕휏
+∑
+푘=1
+휏푘
+휏 ≤ ‖풗0‖2
+휌⋆ + ‖τ0‖2
+ + ‖퐟‖2
+퐿2
+휌⋆(푄) + ‖퐭푏‖2
+퐿2(0,푇 ;퐿2(휕Ω푁)),
+(23)
+where we assume that the condition (15) is satisfied. We remark here that analogous arguments apply to the displacement and
+the temperature system (14).
+
+8
+AUTHOR ONE ET AL
+Remark 5. From the inf-sup condition (17) we can also try to obtain a bound for the discrete velocities
+휏‖풗푘‖퐻1(Ω) ≤ 휏 sup
+σ∈Σℎ
+∫Ω ε(풗푘) ∶ σ
+‖σ‖퐿2(Ω)
+≤ 퐴−1
+min(‖τ푘‖ + ‖τ푘−1‖) + 휏‖ε(풗푘)‖퐿2(Ω).
+In the absence of plastic behaviour the last term is not present and this would imply, together with (23), that we can bound
+uniformly ‖풗ℎ,휏‖퐿2(0,푇 ;퐻1(Ω)) in terms of the data; this is what would be expected in the linear elasticity model. However, in
+general this only yields a bound for 풗ℎ,휏 in 퐿2(푄)푑, which does not improve (23). This lack of a priori boundedness of the
+velocity gradients is what results in the restriction on the ratio 휏
+ℎ.
+Remark 6. Note that
+푇 ∕휏
+∑
+푘=1
+휏푘
+휏 =
+푇 ∕휏
+∑
+푘=1
+‖풗푘 − 풗푘−1‖2
+휌⋆ + ‖τ푘 − τ푘−1‖2
+ = ‖휕푡풗ℎ,휏‖(0,푇 ;퐿2
+휌⋆(Ω)) + ‖휕푡τℎ,휏‖(0,푇 ;퐿2
+(Ω)),
+and so the discrete stability estimate (23) also yields a bound on the time derivatives of the approximate solutions; here
+(0, 푇 ; 퐿2
+휌⋆(Ω)) denotes the space of Radon measures in time with values into 퐿2
+휌⋆(Ω). (The space (0, 푇 ; 퐿2
+(Ω)) is defined
+analogously.) This is enough, for example by applying[26, Cor. 7.9]), to prove that as 휏 → 0, the solutions (τℎ,휏, 풗ℎ,휏) converge to
+functions (τℎ, 풗ℎ) that solve the system
+휌⋆ ̇풗ℎ − div τℎ = 휌⋆퐟
+in 푉 ℎ,
+( ̇τℎ) = ε(풗)ℎ − 퐻(τℎ ∶ ε(풗)ℎ)퐻휖(|(τℎ)훿|2 − 휅2
+⋆)ε(풗)ℎ
+in Σℎ.
+(24)
+Obtaining convergence as ℎ → 0 is a more delicate matter given the relatively weak bounds available to us (c.f. Remark 5). In
+fact, at this point we face the lack of analytical results for a system of partial differential equations of the rate-type (4)—it is not
+completely obvious what the proper notion of weak solution should be. Conceivably, this problem could become more tractable
+by introducing hardening into the model, and then the solutions for the perfect plasticity model would be obtained in a vanishing
+hardening limit; this will be the subject of future research.
+4
+NUMERICAL EXPERIMENTS
+We now implement the discrete formulations (13) and (14) to illustrate that they indeed capture the behaviour expected from the
+model. We first implement the problem in one spatial dimension, and we show that the mechanical response is as expected during
+one loading-unloading cycle. Subsequently we implement the problem describing a two dimensional plate with an elliptical hole.
+The nonlinear systems for the stress and velocity at each time step are handled with Newton’s method supplemented with the
+error oriented line search NLEQERR from PETSc[2]; the absolute and relative tolerances for the nonlinear solver are set to 10−6.
+The linear systems at each Newton step are solved using the LU factorisation algorithm from MUMPS[1]; the linear systems for
+the displacement and the temperature are solved in turn using MUMPS as well. Everything is implemented through the finite
+element software firedrake[24]; the code used to implement the computational experiments, including the exact components of
+firedrake that have been employed, has been archived in Zenodo (https://zenodo.org/record/7342357)[33] for reproducibility
+purposes.
+4.1
+One dimensional mechanical response
+We solve the problem on the unit interval Ω = (0, 1) and for times 푡 ∈ [0, 1]. (If not stated otherwise all physical quantities are
+given in the SI base units or use combination thereof.) We impose boundary conditions on the displacement:
+푢(푡, 0) = −푢(푡, 1) ∶=
+{
+− 1
+10푒1+
+1
+4푡(푡−1) 푡 ∈ (0, 1).
+0
+otherwise.
+(25)
+This describes loading for 푡 ∈ (1, 1
+2) s and unloading otherwise. Since the problem is one-dimensional, we denote the scalar
+displacement, stress and strain are denoted by 푢, 휎, and 휀, respectively. We set the Young modulus to E = 104 Pa. (The values
+of physical constants are in this example entirely artificial.) We employ a simple continuation algorithm with respect to 휖 to
+produce better initial guesses for Newton’s method; for instance, the problem is solved with a larger (and thus easier) value for 휖
+and the solution is used as an initial guess for the problem with regularisation parameter 휖 −훿휖 until the desired value is reached.
+
+AUTHOR ONE ET AL
+9
+(a) Stress-strain response
+(b) Maximum stress
+Figure 2 Mechanical response at 푋 = 0.75 m for the problem with 휅⋆ = 107 Pa.
+(a) Heaviside function 퐻(1)
+휖 , 휖 = 10
+(b) Heaviside function 퐻(1)
+휖 , 휖 = 200
+Figure 3 Stress-strain response at 푋 = 0.75 m for the problem with 휅⋆ = 80 Pa.
+Figure 2 shows the stress-strain response at the point 푋 = 0.75 m with a very large yield-stress 휅⋆ = 107 Pa; the problem is
+solved with 482 spatial degrees of freedom and a time step 휏 = 5 × 10−4 s; a plot of the maximum stress ‖휎‖퐿∞(Ω) with respect
+to time is also shown for reference. This is simply a sanity check to verify that the solution of our proposed numerical scheme
+behaves as expected; namely, the solution exhibits solely elastic behaviour.
+The same problem is subsequently solved for the yield stress of 휅⋆ = 80 Pa with different values of 휖; the stress-strain
+relations are shown in Figure 3. The values of the maximum stress are plotted in Figure 4 for different values of 휖 and the
+different approximations/regularisations of the Heaviside function. We observe that the numerical solutions capture the expected
+elastic–perfectly plastic behaviour during one loading-unloading cycle. We also observe for large 휖 a non-sharp yield transition;
+depending on which Heaviside approximation we employ, the computed stress can be allowed to go slightly beyond 휅⋆, but this
+effect disappears as 휖 decreases; in this regard we observe that the regularisation 퐻(2)
+휖
+based on the hyperbolic tangent is the one
+that violates the constraint the least.
+
+200
+160
+120
+b
+80
+40
+loading
+unloading
+0
+0.000
+0.004
+0.008
+0.012
+0.016
+0.020
+[3 ]200
+160
+?120
+)αT
+b
+80
+40
+loading
+unloading
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+t80
+60
+40
+20
+b
+0
+-20
+-40
+-60
+loading
+-80
+-×--
+unloading
+0.000
+0.004
+0.008
+0.012
+0.016
+0.02080
+60
+40
+20
+b
+0
+-20
+-40
+-60
+loading
+-80
+unloading
+0.000
+0.004
+0.008
+0.012
+0.016
+0.02010
+AUTHOR ONE ET AL
+(a) Heaviside function 퐻(1)
+휖 , 휖 = 10
+(b) Heaviside function 퐻(1)
+휖 , 휖 = 100
+(c) Heaviside function 퐻(2)
+휖 , 휖 = 10
+(d) Heaviside function 퐻(2)
+휖 , 휖 = 100
+(e) Heaviside function 퐻(3)
+휖 , 휖 = 10
+(f) Heaviside function 퐻(3)
+휖 , 휖 = 100
+Figure 4 Maximum stress over time for the problem with 휅⋆ = 80 Pa, and various approximations of the Heaviside function.
+
+80
+60
+()T /
+40
+b
+20
+--.--
+loading
+11×1
+unloading
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+t80
+60
+(U)αT
+40
+b
+20
+--.-- loading
+unloading
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+t80
+60
+()T /
+40
+b
+20
+--o-- loading
+unloading
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+t80
+60
+(U)αT
+40
+b
+20
+--.-- loading
+unloading
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+t80
+60
+(U)αT
+:40
+b
+20
+--.-- loading
+unloading
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+t80
+60
+()T /
+40
+b
+20
+--.-- loading
+unloading
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+tAUTHOR ONE ET AL
+11
+x
+l
+L
+2a
+2b
+P(t)
+P(t)
+y
+Figure 5 Square domain with an elliptical hole.
+4.2
+2D plate with an elliptical hole
+The problem is solved on the two-dimensional domain (− 퐿
+2 , 퐿
+2 ) × ( −푙
+2 , −푙
+2 ), in which an elliptical hole is made, with semi-minor
+and semi-major axis of lengths 푎 and 푏, respectively (see Figure 5); in the implementation we choose 퐿 = 푙 = 1 m, 푎 = 0.3 m,
+and 푏 = 0.5 m. We consider homogeneous Neumann boundary conditions for the temperature, while on the left and right
+boundaries and on the elliptical boundary we prescribe homogeneous natural boundary conditions for the mechanical problem,
+while on the top and bottom we apply a time-dependent traction 푃 (푡) in the vertical direction. This traction is meant to represent
+one loading-unloading cycle, and its magnitude taken to be a bump function
+푃 (푡) ∶=
+{
+20푒1+
+1
+4푡(푡−1) 푡 ∈ (0, 1),
+0
+otherwise.
+Concerning the initial conditions we assume that the body of interest is initially in the stress-free state and that the initial
+displacement is equal to zero. The initial temperature distribution is homogeneous in space, and in what follows we report only
+temperature changes with respect to this initial state.
+Concerning the material parameters we take the values E = 104 Pa, 휈 = 0.3, 휅⋆ = 1 Pa, 휅th = 1W ⋅ m−1 ⋅ K−1, and
+푐푣 = 1 J ⋅ kg−1 ⋅ K−1. (These parameter values are again artificial, we do not aim at a particular set of parameter values for a
+real material.) The problem is solved with a time step of 휏 = 5 × 10−4 s, 1.52 × 105 degrees of freedom for the stress-velocity
+problem (13) and 5.8 × 104 degrees of freedom for the displacement-temperature problem (14). We employ the first Heaviside
+regularisation 퐻(1)
+휖
+with the regularisation parameter fixed as 휖 = 100.
+Figure 6 shows plots of the magnitude of the deviatoric part of the stress τ훿, for the elastic problem and the problem with 휅⋆;
+the domain is deformed according to the solution for the displacement. (The deformation is magnified 15 times.) We observe
+stresses concentrating on the sides of the elliptical hole. Note that the stress reaches much higher values in the elastic case.
+Figure 7 shows the solution at the final time 푡 = 1 s; in the elastic case the strain is practically zero, while in the plastic case
+there is still a residual strain on the sides of the elliptical hole.
+The evolution of the temperature difference 휃 with respect to the initial temperature is shown in Figure 8, along with plots of
+the function 퐻휖(|τ훿|2−휅2
+⋆), which allows us to track whether the yield criterion is satisfied. In Figure 8 we observe the behaviour
+expected from the model; namely, the regions where the stress concentrates—and where the yield criterion is satisfied—act as
+a heat source for the temperature field. Note that without this heat source the temperature field would be otherwise identically
+zero, thanks to the boundary conditions. Moreover, we also see in Figure 8 (F) that at time 푡 = 0.54 s there is no longer a heat
+source for the temperature field, since at this time the loading criterion τ ∶ ε > 0 is not satisfied.
+
+12
+AUTHOR ONE ET AL
+(a) 푡 = 0 s
+(b) 푡 = 0 s
+(c) 푡 = 0.25 s
+(d) 푡 = 0.25 s
+(e) 푡 = 0.5 s
+(f) 푡 = 0.5 s
+Figure 6 Magnitude of τ훿 for the elastic problem with 휅⋆ = 107 Pa (right) and the problem with 휅⋆ = 60 Pa (left).
+
+65
+60
+55
+50
+45
+40
+35
+30
+25
+20
+15
+10
+5
+0110
+100
+06
+80
+70
+60
+. 50
+40
+.30
+20
+1065
+60
+55
+50
+45
+40
+一
+35
+一
+30
+一
+25
+20
+15
+10
+5
+0110
+100
+90
+80
+70
+60
+50
+40
+一
+30
+20
+1065
+60
+55
+50
+45
+40
+一
+35
+一
+30
+25
+20
+15
+10
+5
+0110
+100
+90
+一
+80
+70
+60
+50
+40
+一
+30
+20
+10AUTHOR ONE ET AL
+13
+(a) 휅⋆ = 60 Pa, 푡 = 1 s
+(b) 휅⋆ = 107 Pa, 푡 = 1 s
+Figure 7 Magnitude of ε at the final time near the interior hole.
+5
+CONCLUDING REMARKS
+The family of models stemming from the simple rate-type equation (1) provides a novel approach to the modelling of inelastic
+response. Starting with the introduction of the simple rate-type equation (1) in[22], several variants and generalisation of (1) have
+been investigated, see, for example,[23], and a thermodynamical framework for some of these models have been successfully
+developed even in the finite deformations setting, see[6]. (For another treatment of rate-type models from a thermodynamic point
+of view see also[10] and the discussion in[15] based on the concept of internal variables, to name a few.) Furthermore, the models
+in this class have also been employed in modelling the response of various materials, see[32],[20],[19] [28] and[4]. We have focused
+on a generalisation of (1) that describes the standard elastic–perfectly plastic response.
+In particular, we have investigated numerical schemes for the solution of the corresponding governing equations (4) and (6)
+respectively. Given the novelty of the model, the mathematical theory for the corresponding model is clearly underdeveloped
+compared to the mathematical theory for the classical models of elastic–perfectly plastic behaviour, see, for example,[8],[29]
+or[18]. From this perspective, it might seem useless to develop yet another variant of mathematical theory for the standard elastic–
+perfectly plastic response. However, our analysis serves a different purpose. We focus on a prototypical example of a rate-type
+evolution equation for a rate-independent process, and our objective is to investigate the viability of the rate-type models based
+approach. Naturally, the vision is to continue with numerical analysis of more involved models for inelastic responses that go
+beyond the standard elastic–perfectly plastic response.
+The considered model for elastic–perfectly plastic response is from the physical point of view conceptually very clean and
+simple, and this transfers to the numerical analysis as well. The model is amenable to standard discretisation techniques, and
+we show that the “straightforward” finite element discretisation of the model inherits directly the energy stability properties
+of the continuous model. Furthermore, since the model possesses a solid thermodynamical basis, we can also compute the
+evolution of the temperature field. (Concerning the temperature evolution, our model is a simple one, the thermal response related
+to the plastic deformation can be more complicated, see[25] and subsequent works.) Finally, we show that—up to numerical
+dissipation—all the energy budget of the system is accounted for. The numerical analysis is documented by an implementation
+of the proposed scheme.
+The analysis shows that the rate-type model under consideration is numerically tractable. From a broader perspective this
+suggests that the modelling of inelastic rate-independent phenomena via the rate-type models might be—from the theoretical
+numerical analysis point of view—feasible as well. In particular numerical schemes for models describing complex inelastic
+phenomena such as Mullins effect, see[7] for a general discussion and[5] for a rate-type model, might be of interest in this regard.
+
+0
+0.002
+0.004
+0.006
+0.008
+0.010
+0.002
+0.004
+0.006
+0.008
+0.0114
+AUTHOR ONE ET AL
+(a) 푡 = 0 s
+(b) 푡 = 0 s
+(c) 푡 = 0.375 s
+(d) 푡 = 0.375 s
+(e) 푡 = 0.54 s
+(f) 푡 = 0.54 s
+Figure 8 Plot of the temperature difference 휃 with respect to the initial state (right) and 퐻휖(|τ훿|2 − 휅2
+⋆) (left) for the problem
+with 휅⋆ = 60 Pa.
+
+1.0
+0.95
+0.9 
+0.85
+0.8
+0.75
+0.7
+0.65
+0.6 
+ 0.55
+ 0.5 
+0.45
+ 0.4 
+0.35
+ 0.3 
+0.25
+ 0.2
+0.15
+ 0. 1 
+0.05
+0.0-0.005
+0.0045
+0.004
+0.0035
+0.003
+0.0025
+0.002
+0.0015
+0.001
+0.00051.0
+0.95
+0.9
+0.85
+- 0.8
+0.75
+- 0.7 
+0.65
+0.6 
+0.55
+- 0.5
+ 0.45
+- 0.4
+0.35
+ 0.3 
+0.25
+ 0.2 
+ 0.15
+ 0. 1 
+0.05
+0.0-0.005
+0.0045
+0.004
+0.0035
+0.003
+0.0025
+0.002
+0.0015
+0.001
+0.0005
+01.0
+0.95
+0.9
+0.85
+- 0.8
+0.75
+- 0.7 
+0.65
+0.6 
+0.55
+- 0.5
+ 0.45
+- 0.4
+0.35
+ 0.3 
+0.25
+ 0.2 
+ 0.15
+ 0. 1 
+0.05
+0.0 0.005
+0.0045
+0.004
+0.0035
+0.003
+0.0025
+0.002
+0.0015
+.0.001
+0.0005
+0AUTHOR ONE ET AL
+15
+References
+[1] P. R. Amestoy, I. S. Duff, J. Koster, and J. Y. L’Excellent. A fully asynchronous multifrontal solver using distributed
+dynamic scheduling. SIAM J. Matrix Anal. Appl., 23(1):15–41, 2001.
+[2] S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijhout, W. D. Gropp, D. Kaushik,
+M. G. Knepley, L. C. McInnes, K. Rupp, S. Smith, B. F. Zampini, H. Zhang, and H. Zhang. PETSc users manual. Tech.
+Report ANL–95/11–Revision 3.8, Argonne National Laboratory, 2017. http://www.mcs.anl.gov/petsc.
+[3] Otto T. Bruhns. History of plasticity. In Holm Altenbach and Andreas Öchsner, editors, Encyclopedia of Continuum
+Mechanics, pages 1–61. Springer, Berlin, 2018.
+[4] R. Bustamante and K. R. Rajagopal.
+A three-dimensional implicit constitutive relation for a body exhibiting stress
+softening: Part I – theoretical underpinnings. Acta Mech., 233(7):2541–2559, 2022.
+[5] D. Cichra, P. A. Gazca-Orozco, V. Průša, and K. Tůma. A thermodynamic framework for non-isothermal phenomenolog-
+ical models of Mullins effect. ArXiv Preprint: 2209.09148, 2022.
+[6] D. Cichra and V. Průša. A thermodynamic basis for implicit rate-type constitutive relations describing the inelastic response
+of solids undergoing finite deformation. Math. Mech. Solids, 25(12):2222–2230, 2020.
+[7] Julie Diani, Bruno Fayolle, and Pierre Gilormini. A review on the Mullins effect. Eur. Polym. J., 45(3):601–612, 2009.
+[8] G. Duvaut and J. L. Lions. Inequalities in Mechanics and Physics. Springer, 1976.
+[9] A. Ern and J-L. Guermond. Finite Elements I: Approximation and Interpolation, volume 72. Springer Nature, 2021.
+[10] C. Giorgi and A. Morro. A thermodynamic approach to rate-type models of elastic-plastic materials. J. Elast., 147:113–148,
+2021.
+[11] V. Girault and P. A. Raviart. Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms. Springer
+Verlag, 1986.
+[12] K. Hashiguchi. Nonlinear continuum mechanics for finite elasticity–plasticity. Elsevier, 2020.
+[13] Koichi Hashiguchi.
+Elastoplasticity theory, volume 69 of Lecture Notes in Applied and Computational Mechanics.
+Springer, Berlin, 2nd edition, 2014.
+[14] Koichi Hashiguchi. Foundations of elastoplasticity: subloading surface model. Springer, 3rd edition, 2017.
+[15] G. T. Houlsby and A. M. Puzrin. Principles of hyperplasticity: An approach to plasticity theory based on thermodynamic
+principles. Springer, London, 2006.
+[16] M. Ismail, F. Ikhouane, and J. Rodellar. The hysteresis Bouc–Wen model – A survey. Arch. Comput. Methods Eng.,
+16(2):161–188, 2009.
+[17] D. Jarecki, A. R. Srinivasa, and N. Iyyer.
+Rate-independent elasto-plastic materials—a brief history and some new
+developments. Int. J. Adv. Eng. Sci. Appl. Math., 13(1):3–17, 2021.
+[18] Martin Kružík and Tomáš Roubíček. Mathematical methods in continuum mechanics of solids. Interaction of Mechanics
+and Mathematics. Springer, 2019.
+[19] F. Mozafari, P. Thamburaja, N. Moslemi, and A. Srinivasa.
+Finite-element simulation of multi-axial fatigue loading
+in metals based on a novel experimentally-validated microplastic hysteresis-tracking method. Finite Elem. Anal. Des.,
+187:103481, 2021.
+[20] F. Mozafari, P. Thamburaja, A.R. Srinivasa, and N. Moslemi. A rate independent inelasticity model with smooth transition
+for unifying low-cycle to high-cycle fatigue life prediction. Int. J. Mech. Sci., 159:325–335, 2019.
+
+16
+AUTHOR ONE ET AL
+[21] Jin-Song Pei, François Gay-Balmaz, Darby J Luscher, James L Beck, Michael D Todd, Joseph P Wright, Yu Qiao, Marco B
+Quadrelli, Chuck R Farrar, and Nicholas AJ Lieven. Connecting mem-models with classical theories. Nonlinear Dyn.,
+103(2):1321–1344, 2021.
+[22] K. R. Rajagopal and A. R. Srinivasa. Inelastic response of solids described by implicit constitutive relations with nonlinear
+small strain elastic response. Int. J. Plast., 71:1–9, 2015.
+[23] K. R. Rajagopal and A. R. Srinivasa. An implicit three-dimensional model for describing the inelastic response of solids
+undergoing finite deformation. Z. angew. Math. Phys., 67(4):86, 2016.
+[24] F. Rathgeber, D. A. Ham, L. Mitchell, M. Lange, F. Luporini, A. T. T. Mcrae, G-T. Bercea, G. R. Markall, and P. H. J. Kelly.
+Firedrake: automating the finite element method by composing abstractions. ACM Trans. Math. Softw., 43(3), 2016.
+[25] P. Rosakis, A.J. Rosakis, G. Ravichandran, and J. Hodowany. A thermodynamic internal variable model for the partition
+of plastic work into heat and stored energy in metals. J. Mech. Phys. Solids, 48(3):581–607, 2000.
+[26] T. Roubíček. Nonlinear Partial Differential Equations with Applications. Birkhäuser, second edition, 2013.
+[27] Souhayl Sadik and Arash Yavari. On the origins of the idea of the multiplicative decomposition of the deformation gradient.
+Math. Mech. Solids, 22(4):771–772, 2017.
+[28] U. Saravanan, K. R. Rajagopal, R. M. Tom, and K. Bharadwaj. A model for a solid undergoing rate-independent dissipative
+mechanical processes. Math. Mech. Solids, 26(2):230–243, 2021.
+[29] J. C. Simo and T.J. R. Hughes. Computational Inelasticity, volume 7. Springer Science & Business Media, 2006.
+[30] David J. Steigmann. A primer on plasticity, pages 125–153. Springer, Cham, 2020.
+[31] A. Visintin. Differential models of hysteresis, volume 111 of Applied Mathematical Sciences. Springer, Berlin, 1994.
+[32] Zhujiang Wang, Arun R. Srinivasa, K. R. Rajagopal, and J. N. Reddy. Simulation of inextensible elasto-plastic beams
+based on an implicit rate type model. Int. J. Non-Linear Mech., 99:165–172, 2018.
+[33] Software used in ‘Numerical approximation of a thermodynamically complete rate-type model for the elastic–perfectly
+plastic response’, https://zenodo.org/record/7342357, 2022.
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf,len=842
+page_content='Received: Added at production  Revised: Added at production  Accepted: Added at production  DOI: xxx/xxxx  ARTICLE TYPE  Numerical approximation of a thermodynamically complete  rate-type model for the elastic–perfectly plastic response  Pablo Alexei Gazca-Orozco*1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2 | Vít Průša2 | Karel Tůma2  1Department of Mathematics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' University of  Freiburg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Ernst-Zermelo-Straße,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 79104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Freiburg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Germany  2Charles University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Faculty of Mathematics  and Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Sokolovská 83,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Praha,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' CZ 186  75,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Czech Republic  Correspondence  Pablo Alexei Gazca–Orozco,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Department  of Mathematics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' University of Freiburg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Ernst-Zermelo-Straße,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 79104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Freiburg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Email:  alexei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='gazca@mathematik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='uni-freiburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='de  Abstract  We analyse a numerical scheme for a system arising from a novel description of the  standard elastic–perfectly plastic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The elastic–perfectly plastic response is  described via rate-type equations that do not make use of the standard elastic-plastic  decomposition, and the model does not require the use of variational inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Furthermore, the model naturally includes the evolution equation for temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  We present a low order discretisation based on the finite element method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Under  certain restrictions on the mesh we subsequently prove the existence of discrete solu-  tions, and we discuss the stability properties of the numerical scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The analysis  is supplemented with computational examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  KEYWORDS:  Rate-type constitutive relations, perfect plasticity, finite element method, thermodynamically consistent  models  1  INTRODUCTION  The rate-independent hysteretic response is frequently encountered in various engineering applications such as electrical engi-  neering, geomechanics and mechanical engineering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Each of these research communities have developed its own approaches  to the modelling of the hysteretic response, see[31],[16] and[21] for a list of various hysteretic models and a discussion of their  relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In solid mechanics the prime example of a rate-independent hysteretic response is the elastic-plastic response, see for  example[3] and[17] for comments on the historical development of plasticity theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In the present contribution we work with a  novel model for the standard elastic–plastic response, see[22,23] and[6], and we focus on mathematical aspects of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In  particular we prove solvability of the corresponding spatially discretised system of governing partial differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Before we proceed with the numerical analysis, let us briefly comment on the status of the considered model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Concerning  the elastic–plastic response of metals, the predominant modelling approach is based on the concepts of the elastic–plastic  decomposition, the flow rule and the yield condition, which in turn leads to a characterisation of the elastic–plastic response  using the concepts of optimisation theory, see especially[29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Concerning the elastic-plastic response of non-metallic materials  such as soils, the situation is different, see, for example,[13, Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 8] for a critical review of some popular models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' These materials  typically exhibit “diffuse yielding behaviour”, see[17] and the discussion therein, which means that the transition from the elastic  to the plastic regime is not sharp, but it progresses gradually, hence the concept of sharp yield condition must be abandoned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  In this case the elastic–plastic response is typically modelled using rate-type equations designed in such a way that the whole  model still predicts the rate-independent behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  We shall investigate the family of models introduced in[22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' This class of models belongs to the class of rate-type models,  but it goes one step further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' It also abandons the concept of elastic–plastic decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In particular, the models do not use  the traditional concept of strain decomposition to the elastic and plastic part, see[27] or[30] and references therein;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' the models  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='03324v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='NA]  9 Jan 2023  2  AUTHOR ONE ET AL  stemming from[22] work with the stress and the strain only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In a one-dimensional setting the stress–strain relation is given by the  rate-type equation  d휎  d푡 = E  [  1 − 퐻  (  휎 d휀  d푡  )  퐻 (  |휎| − 휎푦  )] d휀  d푡 ,  (1)  where 휎 denotes the stress, 휀 denotes the strain, 휎푦 denotes the yield stress, E denotes the Young modulus and 퐻 denotes the  Heaviside step function (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (Compare with the standard models that lead to optimisation problems, see[29, Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') The rate-type  stress–strain relation (1) is clearly rate-independent, and it leads to the standard elastic–perfectly plastic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Indeed, if the  yield stress is reached, |휎| = 휎푦, and if the material is being loaded, 휎 d휀  d푡 ≥ 0, then (1) reduces to  d휎  d푡 = 0,  (2)  hence the stress 휎 remains constant and equal to the yield stress value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' This is the plastic flow regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' On the other hand, if the  stress is below the yield stress value, |휎| < 휎푦, or if the material is being unloaded, 휎 d휀  d푡 < 0, then (1) reduces to  d휎  d푡 = E d휀  d푡 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (3)  This is the standard elastic response rewritten in terms of rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Indeed, equation (3) is just the time derivative of Hooke law  휎 = E 휀.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Once we have (2) and (3), it is straightforward to see that the cyclic change of strain leads to the standard hysteretic  behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  An important feature of the model (1) is that the second Heaviside function 퐻 (  |휎| − 휎푦  ) can be replaced by a smoothed  version thereof, which allows one to easily deal with the “diffuse yielding behaviour”, see[22] and for further comments also[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Furthermore, the family of one-dimensional models based on the rate-type equation (1) can be extended to the fully three-  dimensional finite deformations setting, see[23] and[6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Finally, the finite deformation version of the models can be shown to be thermodynamically consistent, see[6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' This implies  that the energy conversions in the material are fully characterised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In particular, the heat generated in the inelastic processes is  known, and the models allow one to study fully coupled thermomechanical processes in the finite strain setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Despite their  importance, such coupled thermomechanical processes are rarely studied, especially in the case of rate-type models for soils,  see[12–14], and the situation is only slightly better for metals, see[25] for an early example thereof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  In the present work, we focus on a model of type (1) that arises in the small strain approximation of a finite deformation model  based on (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The model is described in[6], and it focuses on the core features of elastic–plastic material response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The model is a  simple model without additional subtleties such as the kinematic/isotropic hardening and so forth, and as such the model is perfect  for a proof-of-concept numerical analysis of this class of models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In particular, we prove solvability of the equations arising  from the spatial discretisation of the corresponding partial differential equations, and we also investigate stability properties of  the corresponding numerical scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  2  MODEL DESCRIPTION  Let the computational domain Ω—which is tantamount to the reference stress-free configuration of the body of interest—be  an open bounded subset of R푑, with 푑 ∈ {2, 3}, whose boundary 휕Ω is Lipschitz, and it is disjointly divided into a Dirichlet  (displacement) 휕Ω퐷 and a Neumann (traction) 휕Ω푁 component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  As shown in[6] the standard elastic–perfectly plastic response with von Mises yield criterion in the small strain regime can be  described by the following system of equations posed on the space-time domain 푄 ∶= (0, 푇 ) × Ω:  휌⋆ ̇풗 − div τ = 휌⋆퐟  in (0, 푇 ) × Ω,  (4a)  1  E ((1 + 휈) ̇τ − 휈(tr ̇τ)I) = ̇ε − 퐻(τ ∶ ̇ε)퐻(|τ훿|2 − 휅2  ⋆) ̇ε  in (0, 푇 ) × Ω,  (4b)  plus initial conditions 풗(0, ⋅) = 풗0(⋅) and τ(0, ⋅) = τ0, and boundary conditions 풗|휕Ω퐷 = 풗푏 and τ풏|휕Ω푁 = 퐭푏, where (휕Ω퐷) ∪  휕Ω푁 = 휕Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Here 풖 denotes the displacement, ε = ε(풖) ∶=  1  2(∇풖 + ∇풖⊤) denotes the linearised strain operator (infinitesimal strain  tensor), τ denotes the stress tensor, and A훿 ∶= A − 1  푑 tr(A)I denotes the traceless part of the corresponding tensor A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The symbol  AUTHOR ONE ET AL  3  (A ∶ B) ∶= tr (  ABT) denotes the matrix scalar product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The function 퐻 is the classical Heaviside function, defined as  퐻(푠) ∶=  { 1, 푠 ≥ 0,  0, 푠 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (5)  All the quantities of interest are functions of the position in the reference configuration 퐗 ∈ Ω and time 푡 ∈ (0, 푇 );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' the dot  represents the time derivative  ̇A ∶= 휕  휕푡A(푡, 퐗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The symbols E , 휈, 휅⋆ denote material parameters, namely Young modulus, Poisson ratio, and yield stress;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' the density in the  reference configuration is denoted by 휌⋆ and we assume that 휌⋆ ≥ 휌−  ⋆, for some positive constant 휌−  ⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The first equation (4a) represents balance of momentum, and the second equation (4b) is the rate-type constitutive relation for  the elastic–perfectly plastic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Since in the small strain regime we have ̇ε = ε(풗), we see that the system (4) is a system  of evolution equations for the velocity field 풗 and the stress tensor τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The displacement 풖 and temperature 휃 can be computed post-hoc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Once the stress τ and the velocity 풗 fields are known, it  remains to solve  ̇풖 = 풗  in (0, 푇 ) × Ω,  (6a)  휌⋆푐푣 ̇휃 − div(휅th∇휃) = 퐻(τ ∶ ̇ε)퐻(|τ훿|2 − 휅2  ⋆)τ ∶ ̇ε  in (0, 푇 ) × Ω,  (6b)  for 풖 and 휃.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Here 푐푣 denotes the specific heat capacity at constant volume, and 휅th is the thermal conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The boundary  conditions for the displacement are chosen to be consistent with those of 풗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' if 풖|휕Ω퐷 = 풖푏 then 풗|휕Ω퐷 = 풗푏 ∶= ̇풖푏.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' For the  temperature we impose the no-flux boundary condition, that is ∇휃 ⋅ 풏|휕Ω = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  One of the challenging aspects of system (4) is the presence of the Heaviside function, since then one has to deal with a  differential equation with a discontinuous nonlinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' To alleviate this difficulty, we will employ a non-sharp yield condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (In the terminology used in[17] this is tantamount to the “diffusive yielding behaviour”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') The non-sharp yield condition means  that the last term in (4b) is substituted by 퐻(τ ∶ ̇ε)퐻휖(|τ훿|2 −휅2  ⋆) ̇ε, where 퐻휖 is a regularised version of the Heaviside function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  We consider three different options in this work, namely  퐻(1)  휖 (푠) ∶= 1  2 + 1  2  푠  휖  √  1 + ( 푠  휖)2  휖 > 0, 푠 ∈ R,  (7a)  퐻(2)  휖 (푠) ∶= 1  2 + 1  2 tanh  (푠  휖  )  휖 > 0, 푠 ∈ R,  (7b)  퐻(3)  휖 (푠) ∶= 1  2 + 1  휋 arctan  (푠  휖  )  휖 > 0, 푠 ∈ R,  (7c)  where 휖 is the regularisation parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The qualitative one-dimensional behaviour during loading and unloading, for the stress 휎 and strain 휖, that can be described by  the non-sharp yield condition is depicted in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (The magnitude of the regularisation parameter 휖 controls the “sharpness”  of the corner on the loading curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') We reiterate that the regularisation is in some physically relevant cases not artificial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In  fact many materials exhibit such non-sharp yield conditions, see[17] and the discussion therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The freedom to model such  non-sharp/diffusive yield condition is an advantage of the approach presented here, in contrast with the more widely used  rate-independent models, where modelling non-sharp yield conditions is more cumbersome, see again[17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  3  DISCRETE FORMULATION  We employ the standard notation for Lebesgue spaces (퐿푝(Ω), ‖⋅‖퐿푝(Ω)) and Sobolev spaces (푊 1,푝(Ω), ‖⋅‖푊 1,푝(Ω)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Let {\ue240ℎ}ℎ>0  be a family of shape-regular triangulations of Ω associated to a sequence of mesh sizes ℎ → 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' we assume here that Ω is a  Lipschitz domain with polyhedral boundary, and also for simplicity we assume that the mesh is quasi-uniform, which implies  that following inverse inequalites are available[9],  ‖∇풗‖퐿2(Ω) ≤ 푐invℎ−1‖풗‖퐿2(Ω)  ∀풗 ∈ 푉 ℎ,  (8a)  ‖풗‖퐿2(휕Ω) ≤ 푐trℎ−1∕2‖풗‖퐿2(Ω)  ∀풗 ∈ 푉 ℎ,  (8b)  4  AUTHOR ONE ET AL  휀  휎  휅⋆  Figure 1 Non-sharp yield condition obtained as a consequence of a regularised Heaviside function 퐻휀.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  where 푐inv, 푐tr > 0 are positive constants independent of ℎ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' this quasi-uniformity assumption is not crucial, if desired one can  apply instead local inverse inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The finite element spaces for the stress and velocity are chosen as  Σℎ = {\ue1a8\ue1a8\ue1a8 ∈ 퐿∞(Ω)푑×푑  sym ∶ \ue1a8\ue1a8\ue1a8|퐾 ∈ P0(퐾)푑×푑  sym, ∀퐾 ∈ \ue240ℎ} = DG(0)푑×푑  sym,  푉 ℎ = {풗 ∈ 푊 1,∞(Ω)푑 ∶ 풗|퐾 ∈ P1(퐾)푑, ∀퐾 ∈ \ue240ℎ, 풗|휕Ω퐷 = ퟎ},  that is, piecewise-linear Lagrange elements for the velocity and piecewise-constant approximations for the stress;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' here P푞(퐾)  denotes the set of polynomials of degree at most 푞 on an element 퐾 ∈ \ue240ℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Since we are interested in approximating discontinuous  terms, it is natural to employ lower order approximations, because higher degree polynomials could, in the absence of for  example adaptivity, lead to unwanted oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  For later use it is convenient to define the compliance operator \ue22d∶ R푑×푑  sym → R푑×푑  sym as  \ue22d(σ) ∶= 1  E ((1 + 휈)σ − 휈(tr σ)I),  σ ∈ R푑×푑  sym.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (9)  that is \ue22d = C−1, where C is the standard linear elasticity tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Since \ue22d is positive definite, we can use it to define a norm on  the space of discrete stresses Σℎ:  ‖σ‖2  \ue22d ∶= ∫  Ω  \ue22dσ ∶ σ,  σ ∈ Σℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (10)  This norm is clearly equivalent to the 퐿2-norm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' namely, 퐴min‖σ‖2  퐿2(Ω) ≤ ‖σ‖2  \ue22d ≤ 퐴max‖σ‖2  퐿2(Ω), where 퐴min and 퐴max denote  the minimum and maximum eigenvalues of \ue22d, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Similarly, we equip the velocity space 푉 ℎ with the weighted norm  ‖풗‖2  휌⋆ ∶= ∫  Ω  휌⋆풗 ⋅ 풗,  풗 ∈ 푉 ℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (11)  The corresponding weighted spaces of square integrable functions at the continuous level will be denoted by 퐿2  휌⋆(Ω) and 퐿2  \ue22d(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Concerning the discretisation in time, we choose a time-step 휏 > 0, and we define a uniform time grid 푡푘 ∶= 푘휏, for 푘 ∈  {1, … , 푇 ∕휏}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (We can without loss of generality assume that 푇 ∕휏 ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') The system of governing equations is then discretised in  time with the implicit Euler method;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' given a family of functions {풗푘}푘∈{0,…,푇 ∕휏} we define the discrete time derivative operator  (or temporal difference quotient) as  d휏  푡 풗푘 ∶= 풗푘 − 풗푘−1  휏  ,  푘 ∈ {1, … , 푇 ∕휏}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (12)  Now we are in the position to formulate a time-stepping scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We assume that the boundary datum 풗푏 can be seen as the  restriction of some CG(1) function on Ω, which we still denote by 풗푏, and we set τ0 ∶= τ0 and 풗0 ∶= 풗0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In the finite element  formulation, assuming that approximations τ푘−1 ∈ Σℎ and 풗푘−1 ∈ 풗푏 + 푉 ℎ at time 푡푘−1 have already been found, we look for  (τ푘  ℎ,휏,휖, 풗푘  ℎ,휏,휖) ∶= (τ푘, 풗푘) ∈ Σℎ × (풗푏 + 푉 ℎ) such that  ∫  Ω  \ue22d(d휏  푡 τ푘) ∶ σ − ∫  Ω  ε(풗푘) ∶ σ + ∫  Ω  퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘  훿|2 − 휅2  ⋆)ε(풗푘) ∶ σ = 0  ∀σ ∈ Σℎ,  ∫  Ω  휌⋆d휏  푡 풗푘 ⋅ 풘 + ∫  Ω  τ푘 ∶ ε(풘) = ∫  Ω  휌⋆퐟푘 ⋅ 풘 + ∫  휕Ω푁  퐭푘  푏 ⋅ 풘  ∀풘 ∈ 푉 ℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (13)  AUTHOR ONE ET AL  5  Here 퐟푘 and 퐭푘  푏 are approximations of 퐟 and 퐭푏 at time 푡 = 푡푘, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' if 퐟 and 퐭 continuous, we can set 퐟푘(⋅) ∶= 퐟(푡푘, ⋅)  and 퐭푘  푏 (⋅) ∶= 퐭푏(푡푘, ⋅).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The displacement and temperature problems (6) are be discretised with piecewise linear Lagrange elements, that is the spaces  of discrete displacements 푈 ℎ and discrete temperatures Θℎ are defined as  푈 ℎ = {풖 ∈ 푊 1,∞(Ω)푑 ∶ 풖|퐾 ∈ 푃1(퐾)푑, ∀퐾 ∈ \ue240ℎ, 풖|휕Ω퐷 = ퟎ},  Θℎ = {휃 ∈ 푊 1,∞(Ω) ∶ 휃|퐾 ∈ 푃1(퐾), ∀퐾 ∈ \ue240ℎ} = CG(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  In the discrete formulation we set 풖0 ∶= 풖0 and 휃0 ∶= 휃0, and for 푘 ∈ {1, … , 푇 ∕휏}, assuming that τ푘 ∈ Σℎ, 풗푘 ∈ 풗푏 + 푉 ℎ,  풖푘−1 ∈ 풖푏 + 푈 ℎ and 휃푘−1 ∈ Θℎ are known, we look for (풖푘, 휃푘) ∈ (풖푏 + 푈 ℎ) × Θℎ such that  ∫  Ω  d휏  푡 풖푘 ⋅ 풘 − ∫  Ω  풗푘 ⋅ 풘 = 0  ∀풘 ∈ 푈 ℎ,  ∫  Ω  휌⋆푐푣d휏  푡 휃푘휙 + ∫  Ω  휅th∇휃푘 ⋅ ∇휙 = ∫  Ω  퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘  훿|2 − 휅2  ⋆)τ푘 ∶ ε(풗푘)휙  ∀휙 ∈ Θℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (14)  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Given the discontinuous nature of the stress space Σℎ, and noting that nonlinear functions of τ푘 remain piecewise  constant, the equation for τ푘 in (13) holds pointwise,  \ue22d(d휏  푡 τ푘) − ε(풗푘) + 퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘  훿|2 − 휅2  ⋆)ε(풗푘) = 0  in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  This defines (implicitly) a mapping 풗푘 → ̃τ푘(풗푘), which could be used to define a velocity-only problem  ∫  Ω  휌⋆d휏  푡 풗푘 ⋅ 풘 + ∫  Ω  ̃τ푘(풗푘) ∶ ε(풘) = ∫  Ω  휌⋆퐟푘 ⋅ 풘 + ∫  휕Ω푁  퐭푘 ⋅ 풘  ∀풘 ∈ 푉 ℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Using tools from automatic differentiation this can be solved, resulting in a strategy similar to the one employed traditionally,  in which consistent tangents are employed in the linearisation[29, Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We do not pursue this further in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='1  Existence of discrete solutions  The goal in this section is to prove that numerical solutions to (13) exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' To help with this, we look first at the system in which  both Heaviside functions are regularised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (The regularisation parameters are denoted as 휂 and 휖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') For simplicity we also assume  that 풗푏 = ퟎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Define the function 퐹휂 ∶ Σℎ × 푉 ℎ → Σℎ × 푉 ℎ through the relation  ⟨퐹휂(τ, 풗), (σ, 풘)⟩ ∶= ∫  Ω  \ue22d(τ) ∶ σ − 휏 ∫  Ω  ε(풗) ∶ σ + 휏 ∫  Ω  퐻휂(τ ∶ ε(풗))퐻휖(|τ훿|2 − 휅2  ⋆)ε(풗) ∶ σ  + 휏 ∫  Ω  τ ∶ ε(풘) + ∫  Ω  휌⋆풗 ⋅ 풘 − ∫  Ω  \ue22d(τ푘−1) ∶ σ − ∫  Ω  휌⋆풗푘−1 ⋅ 풘  − 휏 ∫  Ω  휌⋆퐟푘 ⋅ 풘 − 휏 ∫  휕Ω푁  퐭푘  푏 ⋅ 풘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Note that the (regularised) discrete formulation can be written simply as 퐹휂(τ, 풗) = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' note also that the function 퐹휂 is continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  If we manage to find a positive number ̂푐, such that ⟨퐹휂(τ, 풗), (τ, 풗)⟩ ≥ 0, for all (τ, 풗) ∈ Σℎ × 푉 ℎ with ‖τ‖2  \ue22d + ‖풗‖2  휌⋆ = ̂푐, then  a corollary of Brouwer’s fixed point theorem will guarantee the existence of a discrete solution[11, Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 4, Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' To this end, we  take (σ, 풘) = (τ, 풗) in the definition of 퐹휂;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' this yields:  ⟨퐹휂(τ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 풗),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (σ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 풘)⟩ ≥ ∫  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='Ω  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='\ue22d(τ) ∶ τ + ∫  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='Ω  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆|풗|2 − ‖τ푘−1‖\ue22d‖τ‖\ue22d − ‖풗푘−1‖휌⋆‖풗‖휌⋆ − 휏‖퐟푘‖휌⋆‖풗‖휌⋆  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휏푐tr  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='(ℎ휌−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='⋆)1∕2 ‖퐭푘  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='푏 ‖퐿2(휕Ω푁)‖풗‖휌⋆ + 휏 ∫  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='Ω  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐻휂(τ ∶ ε(풗))퐻휖(|τ훿|2 − 휅2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='⋆)ε(풗) ∶ τ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='≥ ‖τ‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='\ue22d + ‖풗‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆ − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖τ푘−1‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='\ue22d − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖τ‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='\ue22d − ‖풗푘−1‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆ − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖풗‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆ − 휏  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖풗‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆ − 휏  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖퐟푘‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='AUTHOR ONE ET AL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='푐2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='tr휏  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2휌−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='⋆ℎ‖풗‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆ − 휏  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖퐭푘  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='푏 ‖퐿2(휕Ω푁) −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='푐inv휏  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='ℎ(퐴min휌−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='⋆)1∕2 ‖풗‖휌⋆‖τ‖\ue22d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='≥ 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='(  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='1 −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='푐inv  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='(퐴min휌−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='⋆)1∕2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휏  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='ℎ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=')  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='‖τ‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='\ue22d + 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='(  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='1 −  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='(퐴min휌−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='⋆)1∕2 + 퐴1∕2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='min푐2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='tr + 푐inv휌−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='⋆  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='1∕2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐴1∕2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='min휌−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='⋆  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휏  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='ℎ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=')  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='‖풗‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='− 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖τ푘−1‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='\ue22d − ‖풗푘−1‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆ − 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖퐟‖2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐿2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='휌⋆(푄) + 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2‖퐭푏‖퐿2(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐿2(휕Ω푁)),  where we employed Young’s inequality, the inverse inequalites (8), and the fact that 휏‖퐟푘‖2  휌⋆ ≤ ‖퐟‖2  퐿2  휌⋆(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Hence, the claim  follows if we assume that  휏  ℎ <  퐴1∕2  min휌−  ⋆  푐inv휌−  ⋆  1∕2 + 푐2  tr퐴1∕2  min + 퐴1∕2  min휌−  ⋆  1∕2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (15)  The same corollary to Brouwer’s fixed point theorem in addition implies that the solution is bounded,  ‖τ푘  휂‖2  \ue22d + ‖풗푘  휂‖2  휌⋆ ≤ ̂푐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  We remark that it is likely that existence of discrete solutions can be proved without assuming a condition like (15) by relying  on the equivalence of norms in finite dimensions and the fact that 휏 and ℎ are fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' However, we choose to stick to the argument  presented above, since the condition (15) will appear once again in the next section where we analyse the stability of the numerical  scheme, for which uniform bounds are desirable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Now, since the bounds are independent of the regularisation parameter 휂 in the first Heaviside function 퐻휂, the Heine–  Borel theorem implies that up to a subsequence, for every 푘 ∈ {1, … , 푇 ∕휏} the sequence of solutions τ푘  휂 (here we make the  휂-dependence explicit) converges as 휂 → 0,  τ푘  휂 → τ푘  strongly in 퐿∞(Ω)푑×푑,  풗푘  휂 → 풗푘  strongly in 푊 1,∞(Ω)푑,  for some τ푘 ∈ Σℎ and 풗푘 ∈ 푉 ℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' At this point we have used the fact that weak and strong convergence are equivalent in finite-  dimensional spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' This implies in particular that 퐻휂(τ푘  휂 ∶ ε(풗푘  휂)) → 퐻(τ푘 ∶ ε(풗푘)) pointwise a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' in Ω, and so the limiting  functions satisfy the system with the unregularised Heaviside function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  In summary, numerical solutions are guaranteed to exist, assuming the ratio 휏  ℎ is small enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We note also that very similar  arguments yield the existence of solutions for the displacement-temperature system (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We could also consider semi-implicit discretisation schemes such as  ∫  Ω  \ue22d(d휏  푡 τ푘) ∶ σ − ∫  Ω  ε(풗푘) ∶ σ + ∫  Ω  퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘  훿|2 − 휅2  ⋆)ε(풗푘) ∶ σ = 0  ∀σ ∈ Σℎ,  ∫  Ω  휌⋆d휏  푡 풗푘 ⋅ 풘 + ∫  Ω  τ푘−1 ∶ ε(풘) = ∫  Ω  휌⋆퐟푘−1 ⋅ 풘 + ∫  휕Ω푁  퐭푘−1 ⋅ 풘  ∀풘 ∈ 푉 ℎ,  (16)  and a similar analysis applies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The difference in this scheme compared to (13) is that here the velocity 풗푘 is computed first using  the information at time 푡푘−1 and the equation for τ푘 is solved afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In the absence of plastic behaviour this results in a  symplectic scheme that conserves a (modified) energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A consequence of the fact that 햣햣햣(푉 ℎ) ⊂ Σℎ and that 푉 ℎ ⊂ 퐻1  휕Ω퐷(Ω)푑 is that the following discrete inf-sup condition  holds:  inf  풘∈푉 ℎ sup  σ∈Σℎ  ∫Ω σ ∶ ε(풘)  ‖풘‖퐻1(Ω)‖σ‖2  퐿2(Ω)  ≥ 훾⋆ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (17)  where 훾⋆ > 0 is independent of ℎ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' note that the above is then simply a reformulation of Korn’s inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The validity of (17) is  not essential for the analysis of the discrete problem (13), but it would be crucial if we were interested in solving the quasi-static  problem (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' without the time derivative ̇풗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2  Stability  Now we take a more careful look at the stability of the scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Let us first look at the continuous system (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' First we assume  that solutions are smooth enough so that all subsequent manipulations are well-defined in the classical sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The multiplication  AUTHOR ONE ET AL  7  of the first equation in system (4) by 풗, the second by τ and integrating over Ω results in the energy balance in the form  1  2  d  d푡  ⎛  ⎜  ⎜⎝∫  Ω  \ue22d(τ) ∶ τ + 휌⋆|풗|2  ⎞  ⎟  ⎟⎠  + ∫  Ω  퐻(τ ∶ ε(풗))퐻휖(|τ훿|2 − 휅2  ⋆)τ ∶ ε(풗) = ∫  Ω  휌⋆퐟 ⋅ 풗 + ∫  휕Ω푁  퐭푏 ⋅ 풗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (18)  If we follow the terminology used in[29], thus, if we denote the kinetic energy by 퐸kin(풗) ∶= ∫Ω  1  2휌⋆|풗|2, the elastic potential  energy by 퐸int(τ) ∶= ∫Ω  1  2\ue22d(τ) ∶ τ, and the potential energy associated with the applied loads by 퐸ext(풖) ∶= − ∫Ω 휌⋆퐟 ⋅ 풖 −  ∫휕Ω푁 퐭푏 ⋅ 풖, then the energy balance can be rewritten as  d  d푡  [퐸kin(풗) + 퐸int(τ) + 퐸ext(풖)] = − ∫  Ω  퐻(τ ∶ ε(풗))퐻휖(|τ훿|2 − 휅2  ⋆)τ ∶ ε(풗) ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (19)  Inspecting (19), it is clear that there is mechanical dissipation only when the material is being loaded and the yield stress has  been reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Moreover, if we define the thermal energy as 퐸th(휃) ∶= ∫Ω 휌⋆푐푣휃, then integrating the temperature equation (6b)  and adding the result to (19), yields the total energy balance  d  d푡  [퐸kin(풗) + 퐸int(τ) + 퐸ext(풖) + 퐸th(휃)] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (20)  The balance (20) highlights the fact that, as a consequence of the thermodynamically consistent derivation of the model, all  various energy dissipation mechanisms are accounted for in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  We now obtain an analogue of (19) at the discrete level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Choosing σ ∶= τ푘 and 풘 = 풗푘 in the numerical formulation (13),  and using the elementary identity (푎 − 푏)푎 = 1  2푎2 − 1  2푏2 + 1  2|푎 − 푏|2 for two numbers 푎, 푏 ∈ R, yields for all 푘 ∈ {1, … , 푇 ∕휏}  the equality  1  2휏 ‖풗푘‖2  휌⋆ − 1  2휏 ‖풗푘−1‖2  휌⋆ + 1  2휏 ‖τ푘‖2  \ue22d − 1  2휏 ‖τ푘−1‖2  \ue22d + 1  2휏 ‖풗푘 − 풗푘−1‖2  휌⋆  + 1  2휏 ‖τ푘 − τ푘−1‖2  \ue22d + ∫  Ω  퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘  훿|2 − 휅2  ⋆)ε(풗푘) ∶ τ푘 = ∫  Ω  휌⋆퐟 ⋅ 풗푘 + ∫  휕Ω푁  퐭푏 ⋅ 풗푘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Hence, if we define the numerical dissipation \ue230푘  휏 ∶=  1  2휏 ‖풗푘 − 풗푘−1‖2  휌⋆ + 1  2휏 ‖τ푘 − τ푘−1‖2  \ue22d, then the equality just derived above  can be rewritten as  d휏  푡  [퐸kin(풗푘) + 퐸int(τ푘)] + 퐸ext(풗푘) = −\ue230푘  휏 − ∫  Ω  퐻(τ푘 ∶ ε(풗푘))퐻휖(|τ푘  훿|2 − 휅2  ⋆)ε(풗푘) ∶ τ푘 ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (21)  This equality clearly mimics the continuous energy balance (19), except for the presence of the numerical dissipation term \ue230푘  휏.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Moreover, testing the temperature equation (14) with 휙 = 1 we also obtain the discrete total energy balance:  d휏  푡  [퐸kin(풗푘) + 퐸int(τ푘) + 퐸th(휃푘)] + 퐸ext(풗푘) = −\ue230푘  휏 ≤ 0,  (22)  which is analogous to the total energy balance (20), up to numerical dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' If we denote the piecewise-linear (in time) interpolant of the sequence {풗푘}푇 ∕휏  푘=0 by ̃풗ℎ,휏 ∈ 퐶([0, 푇 ];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 푉 ℎ), then we see  that  1  휏 ‖풗푘 − 풗푘−1‖2  퐿2(Ω) = 휏  ‖‖‖‖‖  휕 ̃풗ℎ,휏(푡푘  −)  휕푡  ‖‖‖‖‖  2  퐿2(Ω)  ,  and so if the problem satisfies appropriate regularity properties so that the norm on the right-hand-side is bounded, then it is  clear that the numerical dissipation term vanishes as 휏 → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Similar arguments apply to the stress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Now, let us denote the piecewise-constant (in time) interpolant associated to the sequence {풗푘}푇 ∕휏  푘=0 by 풗ℎ,휏 ∈ 퐿∞((0, 푇 );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 푉 ℎ),  and define τℎ,휏 analogously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Then, multiplying the discrete energy balance (22) by 2휏, using a similar argument to the one  employed in the previous section, and summing over 푘, we obtain the stability estimate  ‖풗ℎ,휏‖2  퐿∞(0,푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐿2  휌⋆(Ω)) + ‖τℎ,휏‖2  퐿∞(0,푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐿2  \ue22d(Ω)) +  푇 ∕휏  ∑  푘=1  휏\ue230푘  휏 ≤ ‖풗0‖2  휌⋆ + ‖τ0‖2  \ue22d + ‖퐟‖2  퐿2  휌⋆(푄) + ‖퐭푏‖2  퐿2(0,푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐿2(휕Ω푁)),  (23)  where we assume that the condition (15) is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We remark here that analogous arguments apply to the displacement and  the temperature system (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  8  AUTHOR ONE ET AL  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' From the inf-sup condition (17) we can also try to obtain a bound for the discrete velocities  휏‖풗푘‖퐻1(Ω) ≤ 휏 sup  σ∈Σℎ  ∫Ω ε(풗푘) ∶ σ  ‖σ‖퐿2(Ω)  ≤ 퐴−1  min(‖τ푘‖\ue22d + ‖τ푘−1‖\ue22d) + 휏‖ε(풗푘)‖퐿2(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  In the absence of plastic behaviour the last term is not present and this would imply, together with (23), that we can bound  uniformly ‖풗ℎ,휏‖퐿2(0,푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐻1(Ω)) in terms of the data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' this is what would be expected in the linear elasticity model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' However, in  general this only yields a bound for 풗ℎ,휏 in 퐿2(푄)푑, which does not improve (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' This lack of a priori boundedness of the  velocity gradients is what results in the restriction on the ratio 휏  ℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Note that  푇 ∕휏  ∑  푘=1  휏\ue230푘  휏 =  푇 ∕휏  ∑  푘=1  ‖풗푘 − 풗푘−1‖2  휌⋆ + ‖τ푘 − τ푘−1‖2  \ue22d = ‖휕푡풗ℎ,휏‖\ue239(0,푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐿2  휌⋆(Ω)) + ‖휕푡τℎ,휏‖\ue239(0,푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='퐿2  \ue22d(Ω)),  and so the discrete stability estimate (23) also yields a bound on the time derivatives of the approximate solutions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' here  \ue239(0, 푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 퐿2  휌⋆(Ω)) denotes the space of Radon measures in time with values into 퐿2  휌⋆(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (The space \ue239(0, 푇 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 퐿2  \ue22d(Ω)) is defined  analogously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') This is enough, for example by applying[26, Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='9]), to prove that as 휏 → 0, the solutions (τℎ,휏, 풗ℎ,휏) converge to  functions (τℎ, 풗ℎ) that solve the system  휌⋆ ̇풗ℎ − div τℎ = 휌⋆퐟  in 푉 ℎ,  \ue22d( ̇τℎ) = ε(풗)ℎ − 퐻(τℎ ∶ ε(풗)ℎ)퐻휖(|(τℎ)훿|2 − 휅2  ⋆)ε(풗)ℎ  in Σℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (24)  Obtaining convergence as ℎ → 0 is a more delicate matter given the relatively weak bounds available to us (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Remark 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In  fact, at this point we face the lack of analytical results for a system of partial differential equations of the rate-type (4)—it is not  completely obvious what the proper notion of weak solution should be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Conceivably, this problem could become more tractable  by introducing hardening into the model, and then the solutions for the perfect plasticity model would be obtained in a vanishing  hardening limit;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' this will be the subject of future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  4  NUMERICAL EXPERIMENTS  We now implement the discrete formulations (13) and (14) to illustrate that they indeed capture the behaviour expected from the  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We first implement the problem in one spatial dimension, and we show that the mechanical response is as expected during  one loading-unloading cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Subsequently we implement the problem describing a two dimensional plate with an elliptical hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The nonlinear systems for the stress and velocity at each time step are handled with Newton’s method supplemented with the  error oriented line search NLEQERR from PETSc[2];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' the absolute and relative tolerances for the nonlinear solver are set to 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The linear systems at each Newton step are solved using the LU factorisation algorithm from MUMPS[1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' the linear systems for  the displacement and the temperature are solved in turn using MUMPS as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Everything is implemented through the finite  element software firedrake[24];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' the code used to implement the computational experiments, including the exact components of  firedrake that have been employed, has been archived in Zenodo (https://zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='org/record/7342357)[33] for reproducibility  purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='1  One dimensional mechanical response  We solve the problem on the unit interval Ω = (0, 1) and for times 푡 ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (If not stated otherwise all physical quantities are  given in the SI base units or use combination thereof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') We impose boundary conditions on the displacement:  푢(푡, 0) = −푢(푡, 1) ∶=  {  − 1  10푒1+  1  4푡(푡−1) 푡 ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  0  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (25)  This describes loading for 푡 ∈ (1, 1  2) s and unloading otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Since the problem is one-dimensional, we denote the scalar  displacement, stress and strain are denoted by 푢, 휎, and 휀, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We set the Young modulus to E = 104 Pa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (The values  of physical constants are in this example entirely artificial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') We employ a simple continuation algorithm with respect to 휖 to  produce better initial guesses for Newton’s method;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' for instance, the problem is solved with a larger (and thus easier) value for 휖  and the solution is used as an initial guess for the problem with regularisation parameter 휖 −훿휖 until the desired value is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  AUTHOR ONE ET AL  9  (a) Stress-strain response  (b) Maximum stress  Figure 2 Mechanical response at 푋 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='75 m for the problem with 휅⋆ = 107 Pa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  (a) Heaviside function 퐻(1)  휖 , 휖 = 10  (b) Heaviside function 퐻(1)  휖 , 휖 = 200  Figure 3 Stress-strain response at 푋 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='75 m for the problem with 휅⋆ = 80 Pa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Figure 2 shows the stress-strain response at the point 푋 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='75 m with a very large yield-stress 휅⋆ = 107 Pa;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' the problem is  solved with 482 spatial degrees of freedom and a time step 휏 = 5 × 10−4 s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' a plot of the maximum stress ‖휎‖퐿∞(Ω) with respect  to time is also shown for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' This is simply a sanity check to verify that the solution of our proposed numerical scheme  behaves as expected;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' namely, the solution exhibits solely elastic behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The same problem is subsequently solved for the yield stress of 휅⋆ = 80 Pa with different values of 휖;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' the stress-strain  relations are shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The values of the maximum stress are plotted in Figure 4 for different values of 휖 and the  different approximations/regularisations of the Heaviside function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We observe that the numerical solutions capture the expected  elastic–perfectly plastic behaviour during one loading-unloading cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We also observe for large 휖 a non-sharp yield transition;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  depending on which Heaviside approximation we employ, the computed stress can be allowed to go slightly beyond 휅⋆, but this  effect disappears as 휖 decreases;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' in this regard we observe that the regularisation 퐻(2)  휖  based on the hyperbolic tangent is the one  that violates the constraint the least.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content='02010  AUTHOR ONE ET AL  (a) Heaviside function 퐻(1)  휖 , 휖 = 10  (b) Heaviside function 퐻(1)  휖 , 휖 = 100  (c) Heaviside function 퐻(2)  휖 , 휖 = 10  (d) Heaviside function 퐻(2)  휖 , 휖 = 100  (e) Heaviside function 퐻(3)  휖 , 휖 = 10  (f) Heaviside function 퐻(3)  휖 , 휖 = 100  Figure 4 Maximum stress over time for the problem with 휅⋆ = 80 Pa, and various approximations of the Heaviside function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content='0  tAUTHOR ONE ET AL  11  x  l  L  2a  2b  P(t)  P(t)  y  Figure 5 Square domain with an elliptical hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='2  2D plate with an elliptical hole  The problem is solved on the two-dimensional domain (− 퐿  2 , 퐿  2 ) × ( −푙  2 , −푙  2 ), in which an elliptical hole is made, with semi-minor  and semi-major axis of lengths 푎 and 푏, respectively (see Figure 5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' in the implementation we choose 퐿 = 푙 = 1 m, 푎 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='3 m,  and 푏 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='5 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We consider homogeneous Neumann boundary conditions for the temperature, while on the left and right  boundaries and on the elliptical boundary we prescribe homogeneous natural boundary conditions for the mechanical problem,  while on the top and bottom we apply a time-dependent traction 푃 (푡) in the vertical direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' This traction is meant to represent  one loading-unloading cycle, and its magnitude taken to be a bump function  푃 (푡) ∶=  {  20푒1+  1  4푡(푡−1) 푡 ∈ (0, 1),  0  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Concerning the initial conditions we assume that the body of interest is initially in the stress-free state and that the initial  displacement is equal to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The initial temperature distribution is homogeneous in space, and in what follows we report only  temperature changes with respect to this initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Concerning the material parameters we take the values E = 104 Pa, 휈 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='3, 휅⋆ = 1 Pa, 휅th = 1W ⋅ m−1 ⋅ K−1, and  푐푣 = 1 J ⋅ kg−1 ⋅ K−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (These parameter values are again artificial, we do not aim at a particular set of parameter values for a  real material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') The problem is solved with a time step of 휏 = 5 × 10−4 s, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='52 × 105 degrees of freedom for the stress-velocity  problem (13) and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='8 × 104 degrees of freedom for the displacement-temperature problem (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We employ the first Heaviside  regularisation 퐻(1)  휖  with the regularisation parameter fixed as 휖 = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Figure 6 shows plots of the magnitude of the deviatoric part of the stress τ훿, for the elastic problem and the problem with 휅⋆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  the domain is deformed according to the solution for the displacement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (The deformation is magnified 15 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') We observe  stresses concentrating on the sides of the elliptical hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Note that the stress reaches much higher values in the elastic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Figure 7 shows the solution at the final time 푡 = 1 s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' in the elastic case the strain is practically zero, while in the plastic case  there is still a residual strain on the sides of the elliptical hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The evolution of the temperature difference 휃 with respect to the initial temperature is shown in Figure 8, along with plots of  the function 퐻휖(|τ훿|2−휅2  ⋆), which allows us to track whether the yield criterion is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In Figure 8 we observe the behaviour  expected from the model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' namely, the regions where the stress concentrates—and where the yield criterion is satisfied—act as  a heat source for the temperature field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Note that without this heat source the temperature field would be otherwise identically  zero, thanks to the boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Moreover, we also see in Figure 8 (F) that at time 푡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='54 s there is no longer a heat  source for the temperature field, since at this time the loading criterion τ ∶ ε > 0 is not satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  12  AUTHOR ONE ET AL  (a) 푡 = 0 s  (b) 푡 = 0 s  (c) 푡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='25 s  (d) 푡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='25 s  (e) 푡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='5 s  (f) 푡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='5 s  Figure 6 Magnitude of τ훿 for the elastic problem with 휅⋆ = 107 Pa (right) and the problem with 휅⋆ = 60 Pa (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  65  60  55  50  45  40  35  30  25  20  15  10  5  0110  100  06  80  70  60  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' 50  40  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='30  20  1065  60  55  50  45  40  一  35  一  30  一  25  20  15  10  5  0110  100  90  80  70  60  50  40  一  30  20  1065  60  55  50  45  40  一  35  一  30  25  20  15  10  5  0110  100  90  一  80  70  60  50  40  一  30  20  10AUTHOR ONE ET AL  13  (a) 휅⋆ = 60 Pa, 푡 = 1 s  (b) 휅⋆ = 107 Pa, 푡 = 1 s  Figure 7 Magnitude of ε at the final time near the interior hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  5  CONCLUDING REMARKS  The family of models stemming from the simple rate-type equation (1) provides a novel approach to the modelling of inelastic  response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Starting with the introduction of the simple rate-type equation (1) in[22], several variants and generalisation of (1) have  been investigated, see, for example,[23], and a thermodynamical framework for some of these models have been successfully  developed even in the finite deformations setting, see[6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (For another treatment of rate-type models from a thermodynamic point  of view see also[10] and the discussion in[15] based on the concept of internal variables, to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') Furthermore, the models  in this class have also been employed in modelling the response of various materials, see[32],[20],[19] [28] and[4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We have focused  on a generalisation of (1) that describes the standard elastic–perfectly plastic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  In particular, we have investigated numerical schemes for the solution of the corresponding governing equations (4) and (6)  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Given the novelty of the model, the mathematical theory for the corresponding model is clearly underdeveloped  compared to the mathematical theory for the classical models of elastic–perfectly plastic behaviour, see, for example,[8],[29]  or[18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' From this perspective, it might seem useless to develop yet another variant of mathematical theory for the standard elastic–  perfectly plastic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' However, our analysis serves a different purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' We focus on a prototypical example of a rate-type  evolution equation for a rate-independent process, and our objective is to investigate the viability of the rate-type models based  approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Naturally, the vision is to continue with numerical analysis of more involved models for inelastic responses that go  beyond the standard elastic–perfectly plastic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The considered model for elastic–perfectly plastic response is from the physical point of view conceptually very clean and  simple, and this transfers to the numerical analysis as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The model is amenable to standard discretisation techniques, and  we show that the “straightforward” finite element discretisation of the model inherits directly the energy stability properties  of the continuous model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Furthermore, since the model possesses a solid thermodynamical basis, we can also compute the  evolution of the temperature field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' (Concerning the temperature evolution, our model is a simple one, the thermal response related  to the plastic deformation can be more complicated, see[25] and subsequent works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=') Finally, we show that—up to numerical  dissipation—all the energy budget of the system is accounted for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The numerical analysis is documented by an implementation  of the proposed scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  The analysis shows that the rate-type model under consideration is numerically tractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' From a broader perspective this  suggests that the modelling of inelastic rate-independent phenomena via the rate-type models might be—from the theoretical  numerical analysis point of view—feasible as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In particular numerical schemes for models describing complex inelastic  phenomena such as Mullins effect, see[7] for a general discussion and[5] for a rate-type model, might be of interest in this regard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content='0114  AUTHOR ONE ET AL  (a) 푡 = 0 s  (b) 푡 = 0 s  (c) 푡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='375 s  (d) 푡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='375 s  (e) 푡 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content='54 s  Figure 8 Plot of the temperature difference 휃 with respect to the initial state (right) and 퐻휖(|τ훿|2 − 휅2  ⋆) (left) for the problem  with 휅⋆ = 60 Pa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Duff, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' L’Excellent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A fully asynchronous multifrontal solver using distributed  dynamic scheduling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Matrix Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 23(1):15–41, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Balay, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Abhyankar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Adams, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' PETSc users manual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content='  Report ANL–95/11–Revision 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='8, Argonne National Laboratory, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' Bruhns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' History of plasticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' In Holm Altenbach and Andreas Öchsner, editors, Encyclopedia of Continuum  Mechanics, pages 1–61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content='  A three-dimensional implicit constitutive relation for a body exhibiting stress  softening: Part I – theoretical underpinnings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Acta Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 233(7):2541–2559, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' Cichra, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Gazca-Orozco, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Průša, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Tůma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A thermodynamic framework for non-isothermal phenomenolog-  ical models of Mullins effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' ArXiv Preprint: 2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='09148, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Cichra and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Průša.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A thermodynamic basis for implicit rate-type constitutive relations describing the inelastic response  of solids undergoing finite deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Solids, 25(12):2222–2230, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [7] Julie Diani, Bruno Fayolle, and Pierre Gilormini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A review on the Mullins effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Polym.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 45(3):601–612, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [8] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Duvaut and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Lions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Inequalities in Mechanics and Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Springer, 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Ern and J-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Guermond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Finite Elements I: Approximation and Interpolation, volume 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content='  [10] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Giorgi and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Morro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A thermodynamic approach to rate-type models of elastic-plastic materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Elast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 147:113–148,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [11] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Girault and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Raviart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Springer  Verlag, 1986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [12] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Hashiguchi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Nonlinear continuum mechanics for finite elasticity–plasticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Elsevier, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [13] Koichi Hashiguchi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Elastoplasticity theory, volume 69 of Lecture Notes in Applied and Computational Mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Springer, Berlin, 2nd edition, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [14] Koichi Hashiguchi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Foundations of elastoplasticity: subloading surface model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Springer, 3rd edition, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [15] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Houlsby and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Puzrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Principles of hyperplasticity: An approach to plasticity theory based on thermodynamic  principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Springer, London, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Ismail, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Ikhouane, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Rodellar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' The hysteresis Bouc–Wen model – A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Methods Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=',  16(2):161–188, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [17] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Jarecki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Srinivasa, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Iyyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
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+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 13(1):3–17, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [18] Martin Kružík and Tomáš Roubíček.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mathematical methods in continuum mechanics of solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Interaction of Mechanics  and Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Springer, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [19] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mozafari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Thamburaja, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Moslemi, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Srinivasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Finite-element simulation of multi-axial fatigue loading  in metals based on a novel experimentally-validated microplastic hysteresis-tracking method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Finite Elem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Des.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=',  187:103481, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [20] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mozafari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Thamburaja, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Srinivasa, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Moslemi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A rate independent inelasticity model with smooth transition  for unifying low-cycle to high-cycle fatigue life prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 159:325–335, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  16  AUTHOR ONE ET AL  [21] Jin-Song Pei, François Gay-Balmaz, Darby J Luscher, James L Beck, Michael D Todd, Joseph P Wright, Yu Qiao, Marco B  Quadrelli, Chuck R Farrar, and Nicholas AJ Lieven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Connecting mem-models with classical theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Nonlinear Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=',  103(2):1321–1344, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Rajagopal and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Srinivasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Inelastic response of solids described by implicit constitutive relations with nonlinear  small strain elastic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Plast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 71:1–9, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [23] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Rajagopal and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Srinivasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' An implicit three-dimensional model for describing the inelastic response of solids  undergoing finite deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 67(4):86, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [24] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Rathgeber, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Ham, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mitchell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Lange, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Luporini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mcrae, G-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Bercea, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Markall, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Kelly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Firedrake: automating the finite element method by composing abstractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Softw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 43(3), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [25] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Rosakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Rosakis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Ravichandran, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Hodowany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A thermodynamic internal variable model for the partition  of plastic work into heat and stored energy in metals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Solids, 48(3):581–607, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [26] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Roubíček.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Nonlinear Partial Differential Equations with Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Birkhäuser, second edition, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [27] Souhayl Sadik and Arash Yavari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' On the origins of the idea of the multiplicative decomposition of the deformation gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Solids, 22(4):771–772, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [28] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Saravanan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Rajagopal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Tom, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Bharadwaj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A model for a solid undergoing rate-independent dissipative  mechanical processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Solids, 26(2):230–243, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Simo and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Hughes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Computational Inelasticity, volume 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Springer Science & Business Media, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [30] David J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Steigmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' A primer on plasticity, pages 125–153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Springer, Cham, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [31] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Visintin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Differential models of hysteresis, volume 111 of Applied Mathematical Sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Springer, Berlin, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [32] Zhujiang Wang, Arun R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Srinivasa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Rajagopal, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Reddy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Simulation of inextensible elasto-plastic beams  based on an implicit rate type model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=' Non-Linear Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content=', 99:165–172, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='  [33] Software used in ‘Numerical approximation of a thermodynamically complete rate-type model for the elastic–perfectly  plastic response’, https://zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
+page_content='org/record/7342357, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E1T4oBgHgl3EQfowSL/content/2301.03324v1.pdf'}
diff --git a/_dE3T4oBgHgl3EQfTAmK/content/tmp_files/2301.04438v1.pdf.txt b/_dE3T4oBgHgl3EQfTAmK/content/tmp_files/2301.04438v1.pdf.txt
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+A 2D ferroelectric vortex lattice in twisted BaTiO3 freestanding layers 
+ 
+G. Sánchez-Santolino*,& 1, V. Rouco*,& 1, S. Puebla2, H. Aramberri3, V. Zamora1, F. A. Cuellar1, 
+C. Munuera2,4, F. Mompean2,4, M. Garcia-Hernandez 2,4, A. Castellanos-Gomez2,4, J. Íñiguez 3,5, 
+C. Leon1,4, J. Santamaria1,4&. 
+1 GFMC. Dept. Fisica de Materiales. Facultad de Fisica. Universidad Complutense. 28040 
+Madrid  
+2 Instituto de Ciencia de Materiales de Madrid ICMM-CSIC 28049 Cantoblanco. Spain 
+ 
+3 Materials Research and Technology Department, Luxembourg Institute of Science and 
+Technology (LIST), Avenue des Hauts-Fourneaux 5, L-4362 Esch/Alzette, Luxembourg. 
+4 Unidad Asociada UCM/CSIC, “Laboratorio de Heteroestructuras con aplicación en spintrónica” 
+ 
+5 Department of Physics and Materials Science, University of Luxembourg, 41 Rue du Brill, 
+L-4422 Belvaux, Luxembourg 
+ 
+&Corresponding authors: G. Sanchez-Santolino: gsanchezsantolino@ucm.es, V. Rouco: vrouco@ucm.es, 
+SANTAMARIA Jacobo:  jacsan@ucm.es 
+ 
+* Equal contributors 
+The wealth of complex polar topologies [1- 6] recently found in nanoscale ferroelectrics result from a 
+delicate balance between the materials’ intrinsic tendency to develop a homogeneous polarization 
+and the electric and mechanic boundary conditions imposed upon them. Ferroelectric–dielectric 
+interfaces are model systems where polarization curling originates from open circuit-like electric 
+boundary conditions, to avoid the build-up of polarization charges through the formation of flux-
+closure [7-10] domains that evolve into vortex-like structures at the nanoscale [11-13]. Interestingly, 
+while ferroelectricity is known to couple strongly to strain (both homogeneous [14] and 
+inhomogeneous [15, 16]), the effect of mechanical constraints [17] on thin film nanoscale 
+ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns 
+that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric 
+perovskite layers with controlled twist angles opens an unprecedented opportunity to tailor these 
+topological nanostructures in a way determined by the lateral strain modulation associated to the 
+twisting. Interestingly, we find that a peculiar pattern of polarization vortices and antivortices 
+emerges from the flexoelectric coupling of polarization to strain gradients. This finding opens exciting 
+
+opportunities to create two-dimensional high density vortex crystals that would allow us to explore 
+novel physical effects and functionalities.   
+ 
+TEXT 
+The persistence of ferroelectricity at the nanoscale hinges on the compensation of the polarization 
+bound charges and depolarizing fields building up at surfaces or interfaces. In ferroelectric films with 
+metallic electrodes the depolarizing fields can be screened by (free) charge accumulation and by the 
+formation of domains [18]. The situation is even more dramatic in nanoscale ferroelectric samples with 
+dielectric boundaries (including vacuum or insulating non-polar surface layers) where the polarization 
+can undergo a transition into vortex [11-13] or more complex [1-6] topological states, with rotational 
+polar configurations persisting to small diameters where polarization departs from the high-symmetry 
+directions favored by the lattice anisotropy [19].  
+Mechanical boundary conditions [17], as those imposed by interfacial strain, play a critical role in 
+determining the final polarization state, as they may combine with electric boundary conditions in non-
+trivial ways. Importantly, the strong coupling of ferroelectricity to both homogeneous and 
+inhomogeneous strain is at the origin of the effectiveness of mechanical boundary conditions in 
+triggering unexpected effects, such as the enhanced ferroelectricity in epitaxially strained layers [14] or 
+the polarization switching under the strain gradients created by an AFM tip pressing on the sample 
+surface [20]. As it turns out, however, access to externally tunable strain patterns is in practice very 
+limited.  
+ 
+In epitaxial thin films mechanical boundary conditions are to a large extent immovably and solely 
+determined by the atom-on-atom replication of the structure of the substrate by the growing film. 
+Hence, while the interface with the substrate is subject to in-plane strains imposed by the lattice 
+
+mismatch, the sample surface is in a zero stress state, as there are no tractions acting on it. In epitaxial 
+uniformly strained single-domain layers, internal elastic fields are homogeneous and rigidly imposed by 
+these mixed boundary conditions. Inhomogeneous strain results typically from uncontrollable strain 
+relaxation, misfit dislocations or ferroelastic domain formation [15]. The structural constraints imposed 
+by epitaxy leave little or no room to modify mechanical boundary conditions. Moreover, controllable 
+shear or inhomogeneous strain patterns are commonly out of reach. This is the reason why, although on 
+general grounds exotic ferroelectric states can be expected to result from the manipulation of 
+mechanical boundary conditions, this scenario remains mostly unexplored.  
+   
+In this paper we demonstrate a new strategy to engineer mechanical boundary conditions based on the 
+strain modulation induced at the interface between two twisted freestanding oxide layers. In layered 
+materials such as graphite [21, 22] or transition metal dichalcogenides [23-25], twisted bilayers have led 
+to the emergence of unexpected collective states [26, 27]. Interestingly, the weak van der Waals 
+interlayer interaction in such twisted bilayers leads to inhomogeneous strain patterns with deformations 
+up to 2% [28]. Extending the exploration to artificial twisted stacks of ionically bonded transition metal 
+oxides, however, has been hampered by the difficulty to isolate these systems in freestanding form. The 
+recent reports on the fabrication of freestanding single crystalline oxide thin films [29-31], which can be 
+handled in a way similar to van der Waals 2D materials, open up the possibility of stacking freestanding 
+layers with arbitrary twist angles [32, 33] and thus design completely novel strain patterns. To our 
+knowledge, this approach to induce strain landscapes spatially varying at the nanoscale in complex 
+oxides has not been reported so far. Here we show that the lateral strain modulation caused by the 
+interface matching between two twisted freestanding ferroelectric BaTiO3 layers sets a mechanical 
+boundary condition not attainable by epitaxial strain, and to a large extent controllable by the relative 
+rotation angle. The nanoscale modulated distribution of symmetric and antisymmetric shear strains 
+
+yields a surprising rotational polarization texture with alternating clockwise and counterclockwise 
+vortices and antivortices, whose distribution, spacing and size is controlled by the twist angle. First-
+principles simulations show that this complex configuration of highly localized symmetric and 
+antisymmetric shears concomitant with the ferroelectric vortex 2D crystal constitutes in fact a stable 
+equilibrium state. The coupling between shear strain gradients and complex polarization texture is 
+discussed in terms of a direct flexoelectric effect.   
+ 
+15 nm thick BaTiO3 (BTO) layers epitaxially grown on (001) SrTiO3 (STO) substrates were delaminated to 
+form twisted bilayer homojunctions with deterministic twist angles (see Figure 1a and Methods). 
+Bilayers were transferred onto holey Si3N4 membranes. To study the structural properties of individual 
+layers of the twisted bilayers we performed a depth sectioning high angle annular dark field (HAADF) 
+scanning transmission electron microscopy (STEM) experiment (see Methods). Focusing on the entrance 
+surface of the stack (defocus = 0 nm) we observe the typical structure of a BaTiO3 perovskite which 
+corresponds to the top layer. The Moiré contrast is revealed by changing the defocus to reach the 
+interface of the twisted bilayer (defocus = - 15 nm), as shown in Fig. 1b. A further increasing defocus 
+brings the bottom layer in focus, which appears rotated by the twist angle of the bilayer. Twisted 
+ferroelectric bilayers exhibit characteristic Moiré features determined by the atomic coincidence pattern 
+between the two layers (see Fig. 1c). The 10.4 º twist angle, determined from the fast Fourier transform 
+(FFT) image, is homogeneous along the fabricated sample and close to the nominal 10º rotation of the 
+films during the deterministic transfer process. The FFT shows the spots from both top and bottom 
+twisted BTO layers; for clarity we will denote the directions corresponding to the twisted layer forming 
+the Moiré pattern as (100)* and (010)*. The Moiré pattern shows two distinct (plateau-like) features at 
+the highly (atom-on-atom) coincidental regions of both layers, marked as AA and AB in Fig. 1b and on 
+the rigid atomic model shown in Fig. 1d. Around AA sites there is AA stacking (Ba on Ba, Ti on Ti and O 
+
+on O) between the top and bottom layers, while AB sites show an AB stacking (Ba on Ti and Ti on Ba) for 
+the Ba and Ti cations of the twisted layers while preserving the AA stacking for the O anions. We studied 
+Moiré structures formed in α = 3, 6, 10.4 and 50º twisted BaTiO3 bilayers; in the main text we discuss 
+data taken on the samples with 10.4° and 3° twist angles.  
+ 
+Intralayer strain was measured on the top layer using the entrance surface focused image (defocus = 0). 
+The emergence of a strongly spatially varying strain landscape with the same periodicity as the Moiré 
+ 
+Figure 1: Fabrication of twisted freestanding BaTiO3 bilayers. a) Schematic of the deterministic two steps transfer 
+process. b) Depth sectioning STEM-HAADF experiment of a twisted BaTiO3 bilayer stack focusing on the entrance surface 
+of the stack (defocus = 0 nm) and the interface (defocus = -15 nm) c) Moiré structure formed at the interface between 
+the BaTiO3 layers. A network of two distinct AA and AB motives is formed due to the twist. The image on the right shows 
+the Fast Fourier Transform noting the reflections of both the top and bottom freestanding BaTiO3 films. The scale bar is 
+2 nm d) Model of the rigid atomic structure corresponding to two BaTiO3 lattices with a twist angle of 10.4° showing Ba 
+atoms in green, Ti in blue and O in red. AA and AB sites are marked in blue and red respectively. 
+
+a)
+1stTransfer
+KI+HCI
+80°℃
+2ndTransfer
+PDMS
+PPC
+BTO
+LSMO
+80°℃
+STO
+b)
+(100)
+(100)*
+depth
+d)
+(100)
+(100)*lattice - and determined at the top layer - clearly demonstrates the strong interaction between the two 
+twisted layers. The resultant strain map shows a periodically modulated pattern of symmetric shear 
+strains (𝜀𝑥𝑦 =  
+1
+2 (
+𝜕𝑢𝑥
+𝜕𝑦 +
+𝜕𝑢𝑦
+𝜕𝑥 )) with alternating positive and negative shear strain cores (see Figs. 2b, e for 
+bilayers twisted 10.4 and 3 degrees, respectively). Strain analysis included the antisymmetric 
+components of the strain tensor (𝜔𝑥𝑦 =  
+1
+2 (
+𝜕𝑢𝑥
+𝜕𝑦 −
+𝜕𝑢𝑦
+𝜕𝑥 )) associated to local rotations of the perovskite 
+lattice (See Extended Figure S1 a and b).  Control experiments on single BTO freestanding layers show a 
+nearly homogeneous strain distribution, making it clear that the complex strain maps obtained in the 
+bilayers originate at the stacking of the twisted layers. Notice that at the AA and AB sites there is 
+maximal atom-on-atom coincidence between the twisted layers; we find very small shear strains in 
+those areas. In between the AA and AB sites of the Moiré pattern we find regions of maximum strain, 
+named S-sites hereafter, with nearly homogeneous positive and negative shears. The shear strain 
+modulation shows the same periodicity as the Moiré pattern, indicating that the strain results in fact 
+from a displacement field reconstruction in the top layer induced by the matching at the interface. An 
+important remark is that such a periodical shear strain landscape is unique, as it cannot be attained, to 
+the best of our knowledge, either by epitaxial strain or by any pattern of externally applied stresses.  
+ 
+In order to investigate how the strain modulation observed on the top layer of the twisted BTO bilayers 
+affects the ferroelectric polarization we have measured the off-centering of the B-site cations in the 
+individual unit cells (relative displacement of the B-site Ti cation from the centrosymmetric position, 
+determined with the A-site Ba cations within the same unit cell). Twisted bilayers showed net in-plane 
+polarization in the [1,1] direction of the perovskite lattice (in the pseudo-cubic reference) with a 
+superimposed polar texture. Polar displacements were obtained to be in the range of 0.15 to 0.20 Å, 
+which is consistent with what is found in bulk BaTiO3. In BaTiO3, the magnitude of the spontaneous 
+
+polarization is known to be approximately constant regardless of the orientation it may present in the 
+different ferroelectric phases this compound can adopt [34, 35]. This suggests that the polarization of 
+our layers must be largely confined to the plane, the (not measured) vertical component being very 
+small if present at all. Further, this in-plane polarization is most likely a consequence of the stacking in 
+our materials. The interfaces between layers will inevitably result in a discontinuity of the vertical 
+component of the electric displacement vector, with the concomitant occurrence of depolarizing fields. 
+In such conditions, an in-plane polarization is energetically favored, as it does not suffer from any 
+electrostatic penalty. The situation can be compared to that of layered perovskite crystals (e.g., 
+Ruddlesden-Popper phases), which typically present spontaneous polarizations perpendicular to the 
+stacking direction [36-38]. Note also that our free-standing layers are not subject to any global 
+mechanical constraints that might drive the occurrence of an in-plane polarization, further supporting its 
+electrostatic origin.  
+The net polarization pointing along the [1,1] in-plane direction indicates that our layers present the 
+orthorhombic ferroelectric phase that also occurs in the bulk material. BaTiO3 crystals present a 
+tetragonal structure at room temperature, which would suggest a polarization along [1,0] or [0,1] in our 
+layers; yet, single BTO freestanding layers (see Extended Figure S2) showed averaged polarization 
+vectors in the [1,1] direction. Given the proximity to the bulk tetragonal to orthorhombic transition 
+(which occurs at 278 K) and the fact that these two phases have very similar free energies at ambient 
+conditions, the observed orthorhombic-like state seems perfectly acceptable, as it may be stabilized by 
+any of many factors distinguishing our BaTiO3 layers from the bulk compound. 
+The complex polar texture of our layers can be better assessed by subtracting the average polarization 
+value in the image (See Extended Figure 3 for a comparison). The polarization maps in Figs. 2c, f show a 
+continuous curling of the polar displacements, forming a periodic network of non-trivial topological 
+structures with alternating polarization vortices (AA and AB sites) and antivortices (S sites of the Moiré 
+
+pattern). We can describe the topological structure in terms of a non-zero toroidal moment [11- 13] 
+parallel to the z direction defined as 𝑄 =
+1
+2𝑁 ∑ 𝑟𝑖𝑥𝑃𝑖
+𝑁
+1
+, where Pi is the local dipole moment located at ri 
+and N is the number of dipoles (cells).  
+ 
+The toroidal moment alternates sign periodically in diagonal directions of the Moiré pattern (see Figures 
+2c and 2f) in a way determined by a periodic array of alternating clockwise and counterclockwise 
+vortices in AA and AB sites, respectively. Ferroelectric vortices are topological objects characterized by a 
+ 
+Figure 2: Strain and polarization modulations at twisted BaTiO3 bilayers. a) STEM-HAADF image of a 10.4° twisted BaTiO3 bilayer stack 
+focusing on the interface of the bilayer (defocus = -15 nm). b) Shear strain (𝜀𝑥𝑦 component of the lattice strain tensor) depicting a periodic 
+strain modulation at the top BaTiO3 layer. c) Ti displacement map (black arrows) measured on the top BaTiO3 layer corresponding to the 
+same area superimposed to the toroidal moment (Q) of the ferroelectric polarization showing a network of clockwise (red) and 
+counterclockwise (blue) vortices. Ti displacements are amplified by a factor of 20 for clarity. d), e), f) show the same analysis for a 3° 
+twisted BaTiO3 bilayer. Red and blue octagons in all panels indicate sites with AA (AA-sites) and AB (AB-sites) stacking respectively. The 
+averaged polarization (modulus) is approximately 20  𝜇𝐶 𝑐𝑚−2, close to the bulk BaTiO3 value.  
+b)
+a)
+c)
+e)
+d)
+f)
+
+4
+3
+2
+1
+A2)
+0
+O
+-2
+3
+44
+2
+2
+0
+-4nm0
+-2(%)
+0
+-2nmwinding number 𝑛 =+1 (see Supplementary Note 1) regardless of their polarity (clockwise or 
+counterclockwise). Values of the toroidal moment at the vortex sites depend on the size of the vortex 
+and on the ferroelectric displacements (dipole moment). Interestingly, we obtain values similar to those 
+reported for flat epitaxial BTO nanoparticles [13]. In the Moiré pattern, vortices alternate with 
+antivortices (sitting at S-sites), which are topological structures with 𝑛 =-1 winding number and zero 
+toroidal moment. Crucially, there is a close correspondence between the vortex lattice with the 
+distribution of shear strains underlying the Moiré pattern. Clockwise or counterclockwise vortices are 
+located at AA- and AB-sites with nearly zero shear strain (albeit maximal rotational strain). On the other 
+hand, antivortices sit at the S sites with maximal shear strain (but nearly zero rotational strain).   
+ 
+To get further confirmation of this topological polar pattern, we resort to density-functional theory, 
+considering simplified (computationally tractable) simulated systems that are nevertheless relevant to 
+our problem. More precisely, we work with a periodically repeated supercell composed of 6x6x1 
+elemental BaTiO3 units and consider an initial configuration that mimics the inhomogeneous 
+polarization pattern measured in the 10 twisted layers. We then run a structural relaxation where all 
+variables can evolve to minimize the energy of the system. We obtain, as a stable solution, the 
+polarization and strain maps shown in Fig. 3, in qualitative agreement with the experimental results of 
+Fig. 2 and thus confirming the connection between the observed strain and dipole modulations. 
+According to our simulations, this topological state is 9 meV per formula unit above the homogeneous 
+orthorhombic phase with polarization along the [1,1] diagonal. This relatively small difference is in fact 
+an upper bound (see Methods) for the energy cost of deforming the trivial homogeneous state to 
+
+acquire the topological features of Figs. 2 and 3. Hence, our calculations support the notion that 
+interlayer interactions may suffice to induce the experimentally observed strain and dipole patterns. 
+ 
+ 
+Let us finally tackle this critical question: what causes the peculiar inhomogeneous polarization textures 
+in our layers? These complex quasi-periodic orders are controlled by the twist angle, which indicates 
+they are the result of interlayer interactions. Further, it is apparent that the vortex- and antivortex-like 
+dipole arrangements in Figs. 2c and 2f are correlated with the measured strain patterns of Figs. 2b and 
+2e. This suggests that, to understand these polar textures, it is reasonable to ignore the microscopic 
+details of the couplings across the twisted interface and, instead, focus on how the observed elastic 
+modulation affects the polarization. Indeed, ferroelectric perovskites like BaTiO3 present strong 
+electromechanical couplings that are potential candidates to explain our observations.  
+Let us begin by considering the simplest strain-polarization couplings. From well-established models of 
+ferroelectric perovskites like BaTiO3 [39], we know that a shear strain 𝜀𝑥𝑦 > 0 typically favors a 
+ 
+Figure 3: Density functional theory model of a ferroelectric vortex lattice in BaTiO3. a) DFT calculated model. b) Shear strain (𝜀𝑥𝑦 
+component of the lattice strain tensor) obtained from the DFT model. c) Ti displacement map (black arrows) superimposed to the 
+toroidal moment (Q) of the ferroelectric polarization obtained from the DFT model. Ti displacements are amplified by a factor of 40 for 
+clarity. Red and blue marks in all panels indicate the AA and AB stacking regions, respectively. 
+b)
+a)
+c)
+
+1
+2
+-1%
+-2polarization oriented along the [1,1] in-plane diagonal, while 𝜀𝑥𝑦 < 0 leads to polarizations along 
+[1, −1]; hence, we can expect 𝛿𝑃𝑥𝛿𝑃𝑦 ∝ 𝜀𝑥𝑦, where by (𝛿𝑃𝑥, 𝛿𝑃𝑦) we refer to the inhomogeneous part 
+of the measured polarization, as shown in Figs. 2c and 2f (and also Fig. 3c). However, it is clear from our 
+results that this relationship does not hold for the measured strains (Figs. 2b and 2e, and Fig. 3b) and 
+inhomogeneous polarizations (Figs. 2c and 2f, and also Fig. 3c), as one can e.g. find regions with 𝜀𝑥𝑦 > 0 
+and an either positive or negative 𝛿𝑃𝑥𝛿𝑃𝑦 product. A strong piezoelectric effect would also lead to 
+𝛿𝑃𝑥𝛿𝑃𝑦 ∝ 𝜀𝑥𝑦, and is not supported by our observations either. Hence, these are not the dominant 
+couplings in our samples. 
+Next, we note that our measured strain maps feature large strain gradients with maximum values 
+reaching ±4 × 107 𝑚−1, which we explicitly show in Figure 4. By virtue of the direct flexoelectric 
+coupling [38], such gradients should yield a polarization change, the expected dominant effects being 
+𝛿𝑃𝑥 ≈ 𝜇𝑥𝑦𝑥𝑦
+eff
+∂𝜖𝑥𝑦
+∂𝑦  
+(1) 
+and  
+𝛿𝑃𝑦 ≈ 𝜇𝑥𝑦𝑥𝑦
+eff
+∂𝜖𝑥𝑦
+∂𝑥  
+(2) 
+where 𝜇𝑥𝑦𝑥𝑦
+eff
+ is the effective flexoelectric coefficient active in our samples. Notably, from the measured 
+strain gradients (Figs. 2b and 2e, and Fig. 3b) and inhomogeneous polarization (Figs. 2c and 2f, and also 
+Fig. 3c), we do see direct support for this coupling in our results. In fact, we find that the regions with 
+ 
+∂𝜖𝑥𝑦
+∂𝑥  > 0, shown as red vertical fringes in Figure 4, feature positive 𝛿𝑃𝑦 > 0; conversely, the regions 
+with  
+∂𝜖𝑥𝑦
+∂𝑥  < 0,  shown as blue  vertical fringes in Figure 4, show  𝛿𝑃𝑦 < 0. A similar relation holds for 
+the 
+∂𝜖𝑥𝑦
+∂𝑦  gradients and the 𝛿𝑃𝑥 component of the polarization.  
+ 
+
+ 
+ 
+In fact, the relationship between strain and polarization patterns can be captured in a simple geometric 
+manner. As shown in Fig. 5, the symmetry breaking caused by the shear (and rotational) strain 
+modulation readily leads to the observed arrangement of polar vortices and antivortices. A local shear 
+strain 𝜖𝑥𝑦 ≠ 0 breaks the square symmetry of the cells of Fig. 5, yielding two large-angle corners and 
+two small-angle corners. In the figure, arrows (flexoelectric polarizations) are drawn assuming that the 
+cations displace towards the small-angle corners, which naturally yields an antivortex-like dipole 
+ 
+ 
+Figure 4: Shear strain gradients of twisted BaTiO3 bilayers. Derivative of the shear strain along the x axis of a 3° twisted BaTiO3 bilayer 
+(a) and a 10,4° twisted BaTiO3 bilayer (b) and a DFT calculated model corresponding to 10° twisted layers (c). Derivative of the shear 
+strain along the y axis of a 3° twisted BaTiO3 bilayer (d) and a 10.4° twisted BaTiO3 bilayer (e) and a DFT calculated model corresponding 
+to 10° twisted layers (f). Ti displacement map (black arrows) are superimposed to all images. Ti displacements are amplified for clarity 
+by a factor of 20 in (a, b, d, e) and 40 in (c, f).  
+ 
+
+a)
+b)
+c)
+0.004
+0.004
+0.004
+0.002
+0.002
+0.002
+dExy/ax (A-1)
+(t-) xe/4x3e
+(A-1)
+0.000
+0.000
+0.000
+aExy/ax
+0.002
+0.002
+0.002
+0.004
+0.004
+0.004
+d)
+e]
+f)
+0.004
+0.004
+0.004
+0.002
+0.002
+0.002
+(A-1)
+(A-1)
+0.000
+aExy/ay
+0.000
+0.000
+ejn
+30
+0.002
+0.002
+0.002
+0.004
+0.004
+0.004arrangement with zero curl of the polarization field centered at the cells with 𝜖𝑥𝑦 ≠ 0. Correspondingly, 
+polarization vortices (non-zero curl) form around the cells with 𝜖𝑥𝑦 = 0.  
+ 
+ 
+Our quantitative measurements allow us to compute strain gradients and polarization modulations and, 
+thus, estimate the effective flexoelectric coefficient 𝜇𝑥𝑦𝑥𝑦
+eff
+. We approximately have  
+ 
+ 
+Figure 5: Pictorial view of the flexoelectric couplings. Sketch of the BaTiO3 layer, showing regions of approximately constant shear strain 
+as cells of a periodic lattice. We indicate the analogues of the AA and AB sites discussed in the text. The black arrows stand for the 
+polarization induced by the flexoelectric effect; these arrows are consistent with Eqs. (1) and (2) for 𝜇𝑥𝑦𝑥𝑦
+eff
+> 0, and they present the 
+vortices and antivortices observed experimentally. Note that the flexoelectric polarization can be intuitively understood from the 
+symmetry breaking caused by the strain modulation. For example, at any given lattice point (shared by four cells, with four associated 
+cell angles), we always find an arrow pointing towards the cell with the smallest (< 90°) angle. 
+ 
+AB
+   <  
+   >  
+   =  
+   >  
+   >  
+   >  
+AB
+   =  
+AA
+   =  
+AA
+   =  
+
+𝜇𝑥𝑦𝑥𝑦
+eff
+≈ 𝛿𝑃𝑥 (
+Δ𝜖𝑥𝑦
+Δ𝑦 )
+−1
+≈
+20 𝜇𝐶 𝑐𝑚−2
+4 × 107 𝑚−1 ≈ 5 𝑛𝐶 𝑚−1, 
+which is significantly smaller than typical experimental results for bulk BaTiO3 at room temperature 
+(values between 0.15 and 3.3  𝜇𝐶 𝑚−1 have been reported [40-42]). A variety of reasons may explain 
+this difference. For example, our constrained BaTiO3 layers might be electrically stiffer than the bulk 
+material and thus present a smaller flexoelectric response. (The magnitude of the flexoelectric coupling 
+is known to be proportional to the magnitude of the dielectric response [17].) Probably most critical: a 
+linear approximation as that in Eqs. (1) and (2) may be inadequate to explain and quantify the effect of 
+the giant strain gradients in our samples. (To determine flexoelectric coefficients experimentally, the 
+considered strain gradients are intentionally small, of the order of 1 𝑚−1 [43]. Strain gradients of the 
+order of 8 × 105 𝑚−1  – as those associated to ferroelastic domains [15] – are considered to be very 
+large. The gradients in our samples are even larger, by almost two orders of magnitude.) Additionally, 
+we may have differences coming from surface contributions to the flexoelectric effect [44]; such surface 
+effects might be present in bulk measurements but seem unlikely to play a role in our case, since the 
+relevant shears and gradients do not involve any component normal to the layers. Having said this, let 
+us also note that there are theoretical predictions yielding 𝜇𝑥𝑦𝑥𝑦 values around 0.08 𝑛𝐶 𝑚−1 for BaTiO3 
+[45], i.e., a smaller effect than the one we estimate. Shedding further light into these issues would be a 
+great challenge, for both experiment and theory, and falls beyond the scope of the present work. 
+ 
+It is also interesting to note that the second derivatives of the shear strain can be used to compute the 
+expected curl of the polarization vector. In fact, from the flexoelectric coupling between strain gradients 
+and polarization (Eqs. (1) and (2)), the following relation holds: 
+𝜕𝑃𝑥
+𝜕𝑦 − 𝜕𝑃𝑦
+𝜕𝑥 = 𝜇𝑥𝑦𝑥𝑦
+eff
+(𝜕2𝜖𝑥𝑦
+𝜕𝑦2 − 𝜕2𝜖𝑥𝑦
+𝜕𝑥2 ), 
+
+closely captured by experimental results (see Extended Figures S4 showing the second derivatives of the 
+strain gradient and S5 showing the curl of the polarization).   
+In summary, we have found that the stacking of twisted free standing ferroelectric layers features a non-
+trivial ferroelectric texture driven by the mechanical boundary conditions imposed by the interface of 
+twisted freestanding layers. The ferroelectric topology consists of a 2D vortex crystal with a lattice 
+periodicity determined by the twisting angle. This opens the door to new design possibilities enabled by 
+the unique modulations that are possible in Moiré bilayers. The highly correlated topological pattern 
+with vortices and antivortices is reminiscent of the square lattice of merons, objects with n= ½ 
+topological number only existing in lattices, observed in chiral magnets with magnetic anisotropy [46, 
+47]. At variance with previous ferroelectric textures found in ferroelectric films confined in the growth 
+direction, our polar landscape is 2D and highly tunable by controlling the twisting angle of the bilayer 
+and is, thus, more amenable for applications in high density ferroelectric memories.  
+ 
+Materials and Methods: 
+Freestanding perovskite films fabrication: 
+ 
+15 nm thick BTO layers were grown onto LSMO buffered (100) SrTiO3 (STO) substrates via pure oxygen 
+sputtering technique at high pressures (3.2 mbar) [48]. This technique produces highly epitaxial growth 
+with sharp interfaces and negligible stoichiometry deviations (see Extended Figure S6). The LSMO acts as 
+a sacrificial layer that allows the release of the BTO layer upon immersion in a selective KI+HCl etchant 
+[49]. Prior to immersion, a polypropylene carbonate (PPC, Sigma Aldrich) film was spin-coated onto the 
+strained heterostructure and adhered to a commercial polydimethylsiloxane (PDMS, Gel-Film WF 4x 6.0 
+
+mil by Gel-Pak®) support. This allows the release and transfer of the entire BTO freestanding layer onto 
+holey Si3N4 membrane grids for STEM observation. After the first and prior to the second BTO transfer, 
+the membranes are dipped in acetone and isopropyl alcohol to remove the remained PPC and clean the 
+final interface. The second BTO layer is transferred onto the first one with a twisted angle which is 
+deterministically controlled by using the edges of the two BTO layers (with defined crystallographic 
+orientation imposed by the (100) STO substrate) as a reference. See sketch in Fig. 1a. After the second 
+transfer the surface of the final twisted heterostructure is cleaned as described above. 
+ 
+Scanning transmission electron microscopy (STEM): 
+STEM characterization was carried out using a JEOL JEM-ARM 200cF aberration corrected electron 
+microscope equipped with a cold field emission gun and a Gatan Quantum spectrometer, operated at 
+200 kV. Depth sectioning HAADF-STEM was performed by acquiring atomic-resolution HAADF-STEM 
+images as a function of defocus [50, 51], allowing us to probe different depths of the sample and 
+discriminate between the top and bottom layers of the stack. HAADF-STEM images were acquired using 
+a 30 mrad probe forming aperture semiangle and a HAADF detector collection semiangle of 70-200 
+mrad.  
+ 
+Determination of polarization and strain. 
+To determine the ferroelectric polarization, the atomic positions of both A-site Ba and B-site Ti cations 
+were measured on STEM-HAADF images of 3° and 10,4° twisted BaTiO3 bilayer stacks acquired focusing 
+on the entrance surface of the stack (defocus = 0 nm). In order to precisely determine the atomic 
+positions, we performed a two-dimensional gaussian fitting using Atomap [52] Polarization was 
+
+calculated from the off centering of the B-site Ti cations in the individual unit cells (relative displacement 
+of the B-site Ti cation from the centrosymmetric position, determined with the A-site Ba cations within 
+the same unit cell) [53].  
+Strain analysis was performed using the Peak Pairs Analysis (PPA) software package (HREM Research) for 
+Digital Micrograph [51]. The analysis was performed on STEM-HAADF images of 3° and 10,4° twisted 
+BaTiO3 bilayer stacks acquired focusing on the entrance surface of the stack (defocus = 0 nm). In order to 
+improve the precision of the analysis the scanning direction was rotated off the crystallographic axes of 
+BaTiO3. For the analysis we perform a Bragg filter selecting the two main reflections along the (100) and 
+(010) directions as base vectors for the analysis. The peak positions are then determined on the filtered 
+image and the relative displacements fields (𝑢𝑥, 𝑢𝑦) of the measured lattice with respect to a reference 
+lattice area are calculated. In this case we have use the whole image as reference. Finally, the 
+components of the strain tensor are calculated from the displacement fields as:   𝜀𝑥𝑥 =
+𝜕𝑢𝑥
+𝜕𝑥 , 𝜀𝑦𝑦 =
+𝜕𝑢𝑦
+𝜕𝑦 , 
+𝜀𝑥𝑦 =
+1
+2 (
+𝜕𝑢𝑥
+𝜕𝑦 +
+𝜕𝑢𝑦
+𝜕𝑥 ) and 𝜔𝑥𝑦 =
+1
+2 (
+𝜕𝑢𝑦
+𝜕𝑥 −
+𝜕𝑢𝑥
+𝜕𝑦 ) . 
+ 
+First-principles calculations: 
+ We performed density functional theory (DFT) calculations as implemented in the Vienna Ab initio 
+Simulation Package (VASP) [54, 55] . We used the Perdew-Burke-Ernzerhof formulation for solids 
+(PBEsol) [56] implementation of the generalized gradient approximation for the exchange-correlation 
+functional. The atomic cores are treated within the projector-augmented wave approach [57], 
+considering the following states explicitly: 5s, 5p and 6s for Ba; 3p, 4s and 3d for Ti; and 2s and 2p for O. 
+We employed a 500 eV energy cut-off for the plane-wave basis set. The simulation cells comprised 
+6x6x1 perovskite unit cells and were computed using a 1x1x4 Monkhorst-Pack [58] k-point grid. The 
+
+structures were fully relaxed until residual forces fell below 0.01 eV/Å and residual stresses fell below 
+0.001 GPa. 
+Let us stress that our DFT simulations correspond to the limit of very low temperature (formally, 0 K). 
+Thus, the computed energy differences – i.e., the 9 meV per formula unit separating the monodomain 
+ferroelectric state from the vortex-antivortex structure – can be taken as an upper bound for the 
+relevant free energy difference at room temperature. (In essence, the calculated energy difference 
+comes from the ferroelectric domain walls – whose energy is known to decrease upon heating – and the 
+inhomogeneous strain modulation – which is imposed by the inter-layer couplings.) Note also that in our 
+simulations we treat the monodomain and vortex-antivortex configurations as two separate cases, while 
+in experiment the topological features are a relatively small modulation of the homogeneous state. For 
+this reason too, the computed energy difference is an upper bound for the actual energy cost of 
+inducing (relatively small) topological features superimposed to the homogeneous state. All in all, our 
+DFT results strongly suggest that the experimentally observed topological structure is easily accessible 
+and physically sound. Finally, let us remark that simulating directly the perturbed homogeneous state 
+would require DFT relaxations constrained to respect the experimentally observed inhomogeneous 
+strain pattern; such calculations would involve several non-trivial assumptions and technical 
+complications, and we did not pursue them here. 
+ 
+REFERENCES  
+[1] Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198–201 (2016).  
+[2] Hsu, S.-L. et al. Emergence of the vortex state in confined ferroelectric heterostructures. Adv. Mater. 
+31, 1901014–1901022 (2019). 
+
+[3] Shafer, P. et al. Emergent chirality in the electric polarization texture of titanate superlattices. Proc. 
+Natl Acad. Sci. USA 115, 915–920 (2018).  
+[4] Gruverman, A. et al. Vortex ferroelectric domains. J. Phys. Condens. Matter 20, 4 (2008).  
+[5] Nelson, C. T. et al. Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces. Nano 
+Lett. 11, 828–834 (2011) 
+[6] S. Das et al.,  Observation of room-temperature polar skyrmions, Nature 568, 369 (2019)  
+[7] C.-L. Jia, K. W. Urban, M. Alexe, D. Hesse, and I. Vrejoiu, Science 331, 1420 (2011).  
+[8] J. Peters, G. Apachitei, R. Beanland, M. Alexe, and A. M. Sachez, Nat. Commun. 7, 13484 (2016).  
+[9]  A. Schilling, D. Byrne, G. Catalan, K. G. Webber, Y. A. Genenko, G. S. Wu, J. F. Scott, and J. M. Gregg, 
+Nano Lett. 9, 3359–3364 (2009).  
+[10] Y. L. Tang, Y. L. Zhu, X. L. Ma, A. Y. Borisevich, A. N. Morozovska, E. A. Eliseev, W. Y. Wang, Y. J. 
+Wang, Y. B. Xu, Z. D. Zhang, and S. J. Pennycook, Science 348, 547 (2015). 
+[11]  I. Naumov, L. Bellaiche, H. Fu, Nature 432, 737 (2004) 
+[12] I. Kornew, H. X. Fu, and L. Bellaiche, Phys. Rev. Lett. 93, 196104 (2004). 
+[13] I. Naumov, A. M. Bratkovsky, Phys. Rev. Lett. 101, 107601 (2008) 
+[14] Choi, K. J. et al. Enhancement of ferroelectricity in strained BaTiO3 thin films. Science 306, 1005–
+1009 (2004). 
+[15] Flexoelectric rotation of polarization in ferroelectric thin films G. Catalan, A. Lubk, A. H. G. 
+Vlooswijk, E. Snoeck, C. Magen, A. Janssens, G. Rispens , G. Rijnders , D. H. A. Blank and B. Noheda. Nat 
+Mater. 10, 963 (2011). 
+
+[16] Pavlo Zubko, Gustau Catalan and Alexander K. Tagantsev Flexoelectric Effect in Solids. Annual 
+Review of Materials Research, 43, 387 (2013) 
+[17] Pertsev, N. A., Zembilgotov, A. G. & Tagantsev, A. K. Effect of mechanical boundary conditions on 
+phase diagrams of epitaxial ferroelectric thin films. Phys. Rev. Lett. 80, 1988–1991 (1998). 
+[18] Pablo Aguado-Puente and Javier Junquera Ferromagnetic like Closure Domains in Ferroelectric 
+Ultrathin Films: First-Principles Simulations. Phys Rev. Lett.100 177601 (2008) 
+[19] Jiawang Hong et al. Topology of the polarization field in ferroelectric nanowires from first principles. 
+Phys Rev B 81, 172101 (2010)  
+[20] H Lu, C-W Bark, D Esque de los Ojos, J Alcala, C B Eom, G Catalan, A Gruverman. Mechanical writing 
+of ferroelectric polarization. Science 336, 59 (2012) 
+[21] K S Novoselov , A K Geim, S V Morozov, D Jiang, M I Katsnelson, I V Grigorieva, S V Dubonos, A A 
+Firsov Two-dimensional gas of massless Dirac fermions in graphene Nature 438, 197 (2005) 
+[22] Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S., & Geim, A. K. The electronic 
+properties of graphene. Reviews of Modern Physics, 81, 109 (2009) 
+[23] Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN, Strano MS, Electronics and optoelectronics of two-
+dimensional transition metal dichalcogenides. Nat. Nanotechnology, 7, 699 (2012) 
+[24] B Radisavljevic, A Radenovic, J Brivio, V Giacometti, A Kis, Single-layer MoS2 transistors. Nat 
+Nanotechnol 6, 147 (2011) 
+[25] Sajedeh Manzeli, Dmitry Ovchinnikov, Diego Pasquier, Oleg V. Yazyev & Andras Kis, 2D transition 
+metal dichalcogenides. Nature Reviews Materials 2, 17033 (2017) 
+
+[26] Yuan Cao, Valla Fatemi, Shiang Fang, Kenji Watanabe, Takashi Taniguchi, Efthimios Kaxiras, Pablo 
+Jarillo-Herrero Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43 
+(2018) 
+[27] Alexey I Berdyugin et al., Out-of-equilibrium criticalities in graphene superlattices Science 375, 430 
+(2022)  
+[28] Pablo San-Jose, A. Gutiérrez-Rubio, Mauricio Sturla, and Francisco Guinea, Spontaneous strains and 
+gap in graphene on boron nitride. Phys. Rev. B 90, 075428 
+[29] Lu, D., Baek, D. J., Hong, S. S., Kourkoutis, L. F., Hikita, Y., Hwang, H. Y Synthesis of freestanding 
+single-crystal perovskite films and heterostructures by etching of sacrificial water-soluble layers. Nature 
+Materials, 15, 1255 (2016) 
+[30] Hong, S. S., Gu, M., Verma, M., Harbola, V., Wang, B. Y., Lu, D., Vailionis, A., Hikita, Y., Pentcheva, R., 
+Rondinelli, J. M., Hwang, H. Y. Extreme tensile strain states in La0.7Ca0.3MnO3 membranes. Science 368, 
+71–76 (2020) 
+[31] G. Dong et al., Super-elastic ferroelectric single-crystal membrane with continuous electric dipole 
+rotation, Science 366, 475 (2019). 
+[32] J. Shen, Z. Dong, M. Qi, Y. Zhang, C. Zhu, Z. Wu, and D. Li, Observation of Moiré Patterns in Twisted 
+Stacks of Bilayer Perovskite Oxide Nanomembranes with Various Lattice Symmetries, ACS Appl. Mater. 
+Interfaces 14, 50386 (2022). 
+[33] Y. Li, C. Xiang, F. M. Chiabrera, S. Yun, H. Zhang, D. J. Kelly, R. T. Dahm, C. K. R. Kirchert, T. E. L. 
+Cozannet, F. Trier, D. V. Christensen, T. J. Booth, S. B. Simonsen, S. Kadkhodazadeh, T. S. Jespersen, and 
+N. Pryds, Stacking and Twisting of Freestanding Complex Oxide Thin Films, Adv. Mater. 34, 2203187 
+(2022). 
+
+[34] A.F. Devonshire, Phil. Mag. 40, 1040 (1949); 
+[35] J. Íñiguez, S. Ivantchev, J.M. Pérez-Mato and A. García, Phys. Rev. B 63, 144103 (2001). 
+[36] A.T. Mulder, N.A. Benedek, J.M. Rondinelli and C.J. Fennie, Adv. Func. Mats. 23, 4810 (2013) 
+[37] C. Ederer and N.A. Spaldin, Phys. Rev. B 74, 024102 (2006);  
+[38] J. López-Pérez and J. Íñiguez , Phys. Rev. B 84 , 075121 (2011). 
+[39] R.D. King-Smith and D. Vanderbilt, Phys. Rev. B 49, 5828 (1994). 
+ 
+[40] J. Harada, J.D. Axe and G. Shirane, Neutron-scattering study of soft modes in cubic BaTiO3, Phys. 
+Rev. B 4, 155 (1971). 
+ 
+  
+[41] P.V. Yudin, R. Ahluwalia and A.K. Tagantsev, Upper bounds for flexoelectric coefficients in 
+ferroelectrics, Appl. Phys. Lett. 104, 2 (2014). 
+ 
+ 
+[42] B. Wang, Y. Gu, S. Zhang and L.-Q. Chen, Flexoelectricity in solids: Progress, challenges, and 
+perspectives, Prog. Mats. Sci. 106, 100570 (2019). 
+ 
+[43] Ma, W. & Cross, L. E. Strain-gradient-induced electric polarization in lead zirconate titanate 
+ceramics. Appl. Phys. Lett. 82, 3293 3295 (2003). 
+ 
+[44] M. Stengel, Phys. Rev. B 90, 201112(R) (2014). 
+ 
+[45] Cyrus E. Dreyer, Massimiliano Stengel, and David Vanderbilt, Current-density implementation for 
+calculating flexoelectric coefficients. Phys. Rev. B 98, 075153 
+ 
+ [46] X. Z. Yu et al., Transformation between meron and skyrmion topological spin textures in a chiral 
+magnet Nature 564, 95 (2018)  
+
+[47] Yu-Tsun Shao et al. Emergent chirality in a polar meron to skyrmion phase transition. Microscopy 
+and Microanalysis, 27, Supplement S1, 348 – 350 (2021) 
+[48] Gabriel Sanchez-Santolino et al.  Resonant electron tunnelling assisted by charged domain walls in 
+multiferroic tunnel junctions. Nature Nanotechnology volume 12, pages655–662 (2017)  
+[49] D. Pesquera et al Beyond substrates: strain engineering of ferroelectric membranes Advanced 
+Materials 32 (43), 2003780  
+[50] A. Y. Borisevich, A. R. Lupini, and S. J. Pennycook, Depth sectioning with the aberration-corrected 
+scanning transmission electron microscope, Proc. Natl. Acad. Sci. U. S. A., 103, 3044 (2006) 
+ [51] R. Ishikawa, A. R. Lupini, Y. Hinuma, and S. J. Pennycook, Large-angle illumination STEM: Toward 
+three-dimensional atom-by-atom imaging, Ultramicroscopy, vol. 151, pp. 122–129, 2015, doi: 
+10.1016/j.ultramic.2014.11.009. 
+ [52] M. Nord, P. E. Vullum, I. MacLaren, T. Tybell, and R. Holmestad, “Atomap: a new software tool for 
+the automated analysis of atomic resolution images using two-dimensional Gaussian fitting,” Adv. 
+Struct. Chem. Imaging, vol. 3, no. 1, p. 9, Dec. 2017, doi: 10.1186/s40679-017-0042-5. 
+ [53] Ghosez, P., Michenaud, J. & Gonze, X. Dynamical atomic charges: the case of ABO3 compounds. 
+Phys. Rev. B 58, 6224–6240 (1998) 
+[54] Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a 
+plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996). 
+[55] Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. 
+Phys. Rev. B 59, 1758–1775 (1999). 
+
+[56] Perdew, J. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. 
+Rev. Lett. 100, 136406 (2008). 
+[57] Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994). 
+[58] Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–
+5192 (1976). 
+ 
+Acknowledgments 
+Authors acknowledge received funding from the project To2Dox of FlagERA ERA-NET Cofund in 
+Quantum Technologies implemented within the European Union’s Horizon 2020 Program. Work (JS, CL, 
+FM , M G-H)  supported by Spanish AEI through grants, PID2020-118078RB-I00 and by Regional 
+Government of Madrid CAM through SINERGICO project Y2020/NMT-6661 CAIRO-CM. G.S.-S. 
+acknowledges financial support from Spanish MCI Grant Nos. RTI2018-099054-J-I00 (MCI/AEI/FEDER, 
+UE) and IJC2018-038164-I. Work (VR) supported by the Madrid Government (Comunidad de Madrid-
+Spain) under the Multiannual Agreement with Universidad Complutense de Madrid in the line Research 
+Incentive for Young PhDs, in the context of the V PRICIT (Regional Programme of Research and 
+Technological Innovation. European Union's Horizon 2020 research and innovation program (Grant 
+Agreement No. 755655 ERC-StG 2017 project 2D-TOPSENSE, Grant Agreement No. 785219 Graphene 
+Core2-Graphene-based disruptive technologies and Grant agreement No. 881603 Graphene Core3-
+Graphene-based disruptive technologies), the EU FLAG-ERA project To2Dox (JTC-2019-009), the 
+Comunidad de Madrid through the CAIRO-CM project (Y2020/NMT-6661) and the Spanish Ministry of 
+Science and Innovation (grant PID2020-118078RB-I00 and fellowship PRE2018-084818). 
+
+Electron microscopy observations were carried out at the Centro Nacional de Microscopia Electrónica, 
+CNME-UCM. Work at LIST was supported by the Luxembourg National Research Fund through grant 
+FNR/C18/MS/12705883/REFOX. 
+ 
+ 
+Data availability statement. The data used in this paper are available from the authors upon reasonable 
+request  
+Authors contributions.  VR, VZ, SP, FAC prepared the samples with help and guidance of CM, FM, MGH 
+and ACG. GSS did the electron microscopy. GSS, VR, VZ, CL, JS analyzed the electron microscopy data. HA 
+and JI did the theory analysis. GSS, VR, HA, JI, CL and JS wrote the manuscript with inputs and help of all 
+authors.  
+Competing interests: The authors declare no competing interests. 
+ 
+
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+page_content=' Garcia-Hernandez 2,4, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Castellanos-Gomez2,4, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Íñiguez 3,5, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
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+page_content=' Santamaria1,4&.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 1 GFMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Fisica de Materiales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Facultad de Fisica.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Universidad Complutense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 28040 Madrid 2 Instituto de Ciencia de Materiales de Madrid ICMM-CSIC 28049 Cantoblanco.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Spain  3 Materials Research and Technology Department, Luxembourg Institute of Science and Technology (LIST), Avenue des Hauts-Fourneaux 5, L-4362 Esch/Alzette, Luxembourg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 4 Unidad Asociada UCM/CSIC, “Laboratorio de Heteroestructuras con aplicación en spintrónica”  5 Department of Physics and Materials Science, University of Luxembourg, 41 Rue du Brill, L-4422 Belvaux, Luxembourg  &Corresponding authors: G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Sanchez-Santolino: gsanchezsantolino@ucm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='es, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rouco: vrouco@ucm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='es, SANTAMARIA Jacobo:  jacsan@ucm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='es  Equal contributors The wealth of complex polar topologies [1  6] recently found in nanoscale ferroelectrics result from a delicate balance between the materials’ intrinsic tendency to develop a homogeneous polarization and the electric and mechanic boundary conditions imposed upon them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ferroelectric–dielectric interfaces are model systems where polarization curling originates from open circuit  like electric boundary conditions, to avoid the build  up of polarization charges through the formation of flux  closure [7  10] domains that evolve into vortex  like structures at the nanoscale [11  13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Interestingly, while ferroelectricity is known to couple strongly to strain (both homogeneous [14] and inhomogeneous [15, 16]), the effect of mechanical constraints [17] on thin film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles opens an unprecedented opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated to the twisting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Interestingly, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' This finding opens exciting  opportunities to create two-dimensional high density vortex crystals that would allow us to explore novel physical effects and functionalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  TEXT The persistence of ferroelectricity at the nanoscale hinges on the compensation of the polarization bound charges and depolarizing fields building up at surfaces or interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In ferroelectric films with metallic electrodes the depolarizing fields can be screened by (free) charge accumulation and by the formation of domains [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The situation is even more dramatic in nanoscale ferroelectric samples with dielectric boundaries (including vacuum or insulating non-polar surface layers) where the polarization can undergo a transition into vortex [11-13] or more complex [1-6] topological states, with rotational polar configurations persisting to small diameters where polarization departs from the high-symmetry directions favored by the lattice anisotropy [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mechanical boundary conditions [17], as those imposed by interfacial strain, play a critical role in determining the final polarization state, as they may combine with electric boundary conditions in non- trivial ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Importantly, the strong coupling of ferroelectricity to both homogeneous and inhomogeneous strain is at the origin of the effectiveness of mechanical boundary conditions in triggering unexpected effects, such as the enhanced ferroelectricity in epitaxially strained layers [14] or the polarization switching under the strain gradients created by an AFM tip pressing on the sample surface [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' As it turns out, however, access to externally tunable strain patterns is in practice very limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  In epitaxial thin films mechanical boundary conditions are to a large extent immovably and solely determined by the atom-on-atom replication of the structure of the substrate by the growing film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Hence, while the interface with the substrate is subject to in-plane strains imposed by the lattice  mismatch, the sample surface is in a zero stress state, as there are no tractions acting on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In epitaxial uniformly strained single-domain layers, internal elastic fields are homogeneous and rigidly imposed by these mixed boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Inhomogeneous strain results typically from uncontrollable strain relaxation, misfit dislocations or ferroelastic domain formation [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The structural constraints imposed by epitaxy leave little or no room to modify mechanical boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Moreover, controllable shear or inhomogeneous strain patterns are commonly out of reach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' This is the reason why, although on general grounds exotic ferroelectric states can be expected to result from the manipulation of mechanical boundary conditions, this scenario remains mostly unexplored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  In this paper we demonstrate a new strategy to engineer mechanical boundary conditions based on the strain modulation induced at the interface between two twisted freestanding oxide layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In layered materials such as graphite [21, 22] or transition metal dichalcogenides [23-25], twisted bilayers have led to the emergence of unexpected collective states [26, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Interestingly, the weak van der Waals interlayer interaction in such twisted bilayers leads to inhomogeneous strain patterns with deformations up to 2% [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Extending the exploration to artificial twisted stacks of ionically bonded transition metal oxides, however, has been hampered by the difficulty to isolate these systems in freestanding form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The recent reports on the fabrication of freestanding single crystalline oxide thin films [29-31], which can be handled in a way similar to van der Waals 2D materials, open up the possibility of stacking freestanding layers with arbitrary twist angles [32, 33] and thus design completely novel strain patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' To our knowledge, this approach to induce strain landscapes spatially varying at the nanoscale in complex oxides has not been reported so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Here we show that the lateral strain modulation caused by the interface matching between two twisted freestanding ferroelectric BaTiO3 layers sets a mechanical boundary condition not attainable by epitaxial strain, and to a large extent controllable by the relative rotation angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  The nanoscale modulated distribution of symmetric and antisymmetric shear strains  yields a surprising rotational polarization texture with alternating clockwise and counterclockwise vortices and antivortices, whose distribution, spacing and size is controlled by the twist angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' First- principles simulations show that this complex configuration of highly localized symmetric and antisymmetric shears concomitant with the ferroelectric vortex 2D crystal constitutes in fact a stable equilibrium state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The coupling between shear strain gradients and complex polarization texture is discussed in terms of a direct flexoelectric effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  15 nm thick BaTiO3 (BTO) layers epitaxially grown on (001) SrTiO3 (STO) substrates were delaminated to form twisted bilayer homojunctions with deterministic twist angles (see Figure 1a and Methods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Bilayers were transferred onto holey Si3N4 membranes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' To study the structural properties of individual layers of the twisted bilayers we performed a depth sectioning high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) experiment (see Methods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Focusing on the entrance surface of the stack (defocus = 0 nm) we observe the typical structure of a BaTiO3 perovskite which corresponds to the top layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The Moiré contrast is revealed by changing the defocus to reach the interface of the twisted bilayer (defocus = - 15 nm), as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 1b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A further increasing defocus brings the bottom layer in focus, which appears rotated by the twist angle of the bilayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Twisted ferroelectric bilayers exhibit characteristic Moiré features determined by the atomic coincidence pattern between the two layers (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 1c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='4 º twist angle, determined from the fast Fourier transform (FFT) image, is homogeneous along the fabricated sample and close to the nominal 10º rotation of the films during the deterministic transfer process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The FFT shows the spots from both top and bottom twisted BTO layers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' for clarity we will denote the directions corresponding to the twisted layer forming the Moiré pattern as (100)* and (010)*.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  The Moiré pattern shows two distinct (plateau-like) features at the highly (atom-on-atom) coincidental regions of both layers, marked as AA and AB in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 1b and on the rigid atomic model shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 1d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Around AA sites there is AA stacking (Ba on Ba, Ti on Ti and O  on O) between the top and bottom layers, while AB sites show an AB stacking (Ba on Ti and Ti on Ba) for the Ba and Ti cations of the twisted layers while preserving the AA stacking for the O anions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' We studied Moiré structures formed in α = 3, 6, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='4 and 50º twisted BaTiO3 bilayers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' in the main text we discuss data taken on the samples with 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='4° and 3° twist angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Intralayer strain was measured on the top layer using the entrance surface focused image (defocus = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The emergence of a strongly spatially varying strain landscape with the same periodicity as the Moiré  Figure 1: Fabrication of twisted freestanding BaTiO3 bilayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' a) Schematic of the deterministic two steps transfer process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' b) Depth sectioning STEM-HAADF experiment of a twisted BaTiO3 bilayer stack focusing on the entrance surface of the stack (defocus = 0 nm) and the interface (defocus = -15 nm) c) Moiré structure formed at the interface between the BaTiO3 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A network of two distinct AA and AB motives is formed due to the twist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The image on the right shows the Fast Fourier Transform noting the reflections of both the top and bottom freestanding BaTiO3 films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The scale bar is 2 nm d) Model of the rigid atomic structure corresponding to two BaTiO3 lattices with a twist angle of 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='4° showing Ba atoms in green, Ti in blue and O in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' AA and AB sites are marked in blue and red respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  a) 1stTransfer KI+HCI 80°℃ 2ndTransfer PDMS PPC BTO LSMO 80°℃ STO b) (100) (100)* depth d) (100) (100)*lattice - and determined at the top layer - clearly demonstrates the strong interaction between the two twisted layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The resultant strain map shows a periodically modulated pattern of symmetric shear strains (𝜀𝑥𝑦 = 1 2 ( 𝜕𝑢𝑥 𝜕𝑦 + 𝜕𝑢𝑦 𝜕𝑥 )) with alternating positive and negative shear strain cores (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2b, e for bilayers twisted 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='4 and 3 degrees, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Strain analysis included the antisymmetric components of the strain tensor (𝜔𝑥𝑦 = 1 2 ( 𝜕𝑢𝑥 𝜕𝑦 − 𝜕𝑢𝑦 𝜕𝑥 )) associated to local rotations of the perovskite lattice (See Extended Figure S1 a and b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Control experiments on single BTO freestanding layers show a nearly homogeneous strain distribution, making it clear that the complex strain maps obtained in the bilayers originate at the stacking of the twisted layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Notice that at the AA and AB sites there is maximal atom-on-atom coincidence between the twisted layers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' we find very small shear strains in those areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In between the AA and AB sites of the Moiré pattern we find regions of maximum strain, named S-sites hereafter, with nearly homogeneous positive and negative shears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The shear strain modulation shows the same periodicity as the Moiré pattern, indicating that the strain results in fact from a displacement field reconstruction in the top layer induced by the matching at the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  An important remark is that such a periodical shear strain landscape is unique, as it cannot be attained, to the best of our knowledge, either by epitaxial strain or by any pattern of externally applied stresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  In order to investigate how the strain modulation observed on the top layer of the twisted BTO bilayers affects the ferroelectric polarization we have measured the off-centering of the B-site cations in the individual unit cells (relative displacement of the B-site Ti cation from the centrosymmetric position, determined with the A-site Ba cations within the same unit cell).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Twisted bilayers showed net in-plane polarization in the [1,1] direction of the perovskite lattice (in the pseudo-cubic reference) with a superimposed polar texture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Polar displacements were obtained to be in the range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='15 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='20 Å, which is consistent with what is found in bulk BaTiO3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In BaTiO3, the magnitude of the spontaneous  polarization is known to be approximately constant regardless of the orientation it may present in the different ferroelectric phases this compound can adopt [34, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' This suggests that the polarization of our layers must be largely confined to the plane, the (not measured) vertical component being very small if present at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Further, this in-plane polarization is most likely a consequence of the stacking in our materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The interfaces between layers will inevitably result in a discontinuity of the vertical component of the electric displacement vector, with the concomitant occurrence of depolarizing fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In such conditions, an in-plane polarization is energetically favored, as it does not suffer from any electrostatic penalty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The situation can be compared to that of layered perovskite crystals (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Ruddlesden-Popper phases), which typically present spontaneous polarizations perpendicular to the stacking direction [36-38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Note also that our free-standing layers are not subject to any global mechanical constraints that might drive the occurrence of an in-plane polarization, further supporting its electrostatic origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The net polarization pointing along the [1,1] in-plane direction indicates that our layers present the orthorhombic ferroelectric phase that also occurs in the bulk material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  BaTiO3 crystals present a tetragonal structure at room temperature, which would suggest a polarization along [1,0] or [0,1] in our layers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' yet, single BTO freestanding layers (see Extended Figure S2) showed averaged polarization vectors in the [1,1] direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Given the proximity to the bulk tetragonal to orthorhombic transition (which occurs at 278 K) and the fact that these two phases have very similar free energies at ambient conditions, the observed orthorhombic-like state seems perfectly acceptable, as it may be stabilized by any of many factors distinguishing our BaTiO3 layers from the bulk compound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The complex polar texture of our layers can be better assessed by subtracting the average polarization value in the image (See Extended Figure 3 for a comparison).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The polarization maps in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2c, f show a continuous curling of the polar displacements, forming a periodic network of non-trivial topological structures with alternating polarization vortices (AA and AB sites) and antivortices (S sites of the Moiré  pattern).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' We can describe the topological structure in terms of a non-zero toroidal moment [11- 13] parallel to the z direction defined as 𝑄 = 1 2𝑁 ∑ 𝑟𝑖𝑥𝑃𝑖 𝑁 1 , where Pi is the local dipole moment located at ri and N is the number of dipoles (cells).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  The toroidal moment alternates sign periodically in diagonal directions of the Moiré pattern (see Figures 2c and 2f) in a way determined by a periodic array of alternating clockwise and counterclockwise vortices in AA and AB sites, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ferroelectric vortices are topological objects characterized by a  Figure 2: Strain and polarization modulations at twisted BaTiO3 bilayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' a) STEM-HAADF image of a 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='4° twisted BaTiO3 bilayer stack focusing on the interface of the bilayer (defocus = -15 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' b) Shear strain (𝜀𝑥𝑦 component of the lattice strain tensor) depicting a periodic strain modulation at the top BaTiO3 layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' c) Ti displacement map (black arrows) measured on the top BaTiO3 layer corresponding to the same area superimposed to the toroidal moment (Q) of the ferroelectric polarization showing a network of clockwise (red) and counterclockwise (blue) vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ti displacements are amplified by a factor of 20 for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' d), e), f) show the same analysis for a 3° twisted BaTiO3 bilayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Red and blue octagons in all panels indicate sites with AA (AA-sites) and AB (AB-sites) stacking respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The averaged polarization (modulus) is approximately 20  𝜇𝐶 𝑐𝑚−2, close to the bulk BaTiO3 value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' b) a) c) e) d) f)  4 3 2 1 A2) 0 O -2 3 44 2 2 0 -4nm0 -2(%) 0 -2nmwinding number 𝑛 =+1 (see Supplementary Note 1) regardless of their polarity (clockwise or counterclockwise).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Values of the toroidal moment at the vortex sites depend on the size of the vortex and on the ferroelectric displacements (dipole moment).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Interestingly, we obtain values similar to those reported for flat epitaxial BTO nanoparticles [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In the Moiré pattern, vortices alternate with antivortices (sitting at S-sites), which are topological structures with 𝑛 =-1 winding number and zero toroidal moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Crucially, there is a close correspondence between the vortex lattice with the distribution of shear strains underlying the Moiré pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Clockwise or counterclockwise vortices are located at AA- and AB-sites with nearly zero shear strain (albeit maximal rotational strain).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' On the other hand, antivortices sit at the S sites with maximal shear strain (but nearly zero rotational strain).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  To get further confirmation of this topological polar pattern, we resort to density-functional theory, considering simplified (computationally tractable) simulated systems that are nevertheless relevant to our problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' More precisely, we work with a periodically repeated supercell composed of 6x6x1 elemental BaTiO3 units and consider an initial configuration that mimics the inhomogeneous polarization pattern measured in the 10\uf0b0 twisted layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' We then run a structural relaxation where all variables can evolve to minimize the energy of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' We obtain, as a stable solution, the polarization and strain maps shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 3, in qualitative agreement with the experimental results of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2 and thus confirming the connection between the observed strain and dipole modulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' According to our simulations, this topological state is 9 meV per formula unit above the homogeneous orthorhombic phase with polarization along the [1,1] diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' This relatively small difference is in fact an upper bound (see Methods) for the energy cost of deforming the trivial homogeneous state to  acquire the topological features of Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Hence, our calculations support the notion that interlayer interactions may suffice to induce the experimentally observed strain and dipole patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Let us finally tackle this critical question: what causes the peculiar inhomogeneous polarization textures in our layers?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' These complex quasi-periodic orders are controlled by the twist angle, which indicates they are the result of interlayer interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Further, it is apparent that the vortex- and antivortex-like dipole arrangements in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2c and 2f are correlated with the measured strain patterns of Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2b and 2e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' This suggests that, to understand these polar textures, it is reasonable to ignore the microscopic details of the couplings across the twisted interface and, instead, focus on how the observed elastic modulation affects the polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Indeed, ferroelectric perovskites like BaTiO3 present strong electromechanical couplings that are potential candidates to explain our observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Let us begin by considering the simplest strain-polarization couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' From well-established models of ferroelectric perovskites like BaTiO3 [39], we know that a shear strain 𝜀𝑥𝑦 > 0 typically favors a  Figure 3: Density functional theory model of a ferroelectric vortex lattice in BaTiO3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' a) DFT calculated model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' b) Shear strain (𝜀𝑥𝑦 component of the lattice strain tensor) obtained from the DFT model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' c) Ti displacement map (black arrows) superimposed to the toroidal moment (Q) of the ferroelectric polarization obtained from the DFT model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ti displacements are amplified by a factor of 40 for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Red and blue marks in all panels indicate the AA and AB stacking regions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' b) a) c)  1 2 -1% -2polarization oriented along the [1,1] in-plane diagonal, while 𝜀𝑥𝑦 < 0 leads to polarizations along [1, −1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' hence, we can expect 𝛿𝑃𝑥𝛿𝑃𝑦 ∝ 𝜀𝑥𝑦, where by (𝛿𝑃𝑥, 𝛿𝑃𝑦) we refer to the inhomogeneous part of the measured polarization, as shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2c and 2f (and also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 3c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' However, it is clear from our results that this relationship does not hold for the measured strains (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2b and 2e, and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 3b) and inhomogeneous polarizations (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2c and 2f, and also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 3c), as one can e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' find regions with 𝜀𝑥𝑦 > 0 and an either positive or negative 𝛿𝑃𝑥𝛿𝑃𝑦 product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A strong piezoelectric effect would also lead to 𝛿𝑃𝑥𝛿𝑃𝑦 ∝ 𝜀𝑥𝑦, and is not supported by our observations either.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Hence, these are not the dominant couplings in our samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Next, we note that our measured strain maps feature large strain gradients with maximum values reaching ±4 × 107 𝑚−1, which we explicitly show in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' By virtue of the direct flexoelectric coupling [38], such gradients should yield a polarization change, the expected dominant effects being 𝛿𝑃𝑥 ≈ 𝜇𝑥𝑦𝑥𝑦 eff ∂𝜖𝑥𝑦 ∂𝑦 (1) and 𝛿𝑃𝑦 ≈ 𝜇𝑥𝑦𝑥𝑦 eff ∂𝜖𝑥𝑦 ∂𝑥 (2) where 𝜇𝑥𝑦𝑥𝑦 eff is the effective flexoelectric coefficient active in our samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Notably, from the measured strain gradients (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2b and 2e, and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 3b) and inhomogeneous polarization (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2c and 2f, and also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 3c), we do see direct support for this coupling in our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In fact, we find that the regions with  ∂𝜖𝑥𝑦 ∂𝑥  > 0, shown as red vertical fringes in Figure 4, feature positive 𝛿𝑃𝑦 > 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' conversely, the regions with ∂𝜖𝑥𝑦 ∂𝑥  < 0,  shown as blue  vertical fringes in Figure 4, show  𝛿𝑃𝑦 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A similar relation holds for the ∂𝜖𝑥𝑦 ∂𝑦  gradients and the 𝛿𝑃𝑥 component of the polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  In fact, the relationship between strain and polarization patterns can be captured in a simple geometric manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 5, the symmetry breaking caused by the shear (and rotational) strain modulation readily leads to the observed arrangement of polar vortices and antivortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A local shear strain 𝜖𝑥𝑦 ≠ 0 breaks the square symmetry of the cells of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 5, yielding two large-angle corners and two small-angle corners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In the figure, arrows (flexoelectric polarizations) are drawn assuming that the cations displace towards the small-angle corners, which naturally yields an antivortex-like dipole  Figure 4: Shear strain gradients of twisted BaTiO3 bilayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Derivative of the shear strain along the x axis of a 3° twisted BaTiO3 bilayer (a) and a 10,4° twisted BaTiO3 bilayer (b) and a DFT calculated model corresponding to 10° twisted layers (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Derivative of the shear strain along the y axis of a 3° twisted BaTiO3 bilayer (d) and a 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='4° twisted BaTiO3 bilayer (e) and a DFT calculated model corresponding to 10° twisted layers (f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ti displacement map (black arrows) are superimposed to all images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ti displacements are amplified for clarity by a factor of 20 in (a, b, d, e) and 40 in (c, f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  a) b) c) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
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+page_content='004arrangement with zero curl of the polarization field centered at the cells with 𝜖𝑥𝑦 ≠ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Correspondingly, polarization vortices (non-zero curl) form around the cells with 𝜖𝑥𝑦 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Our quantitative measurements allow us to compute strain gradients and polarization modulations and, thus, estimate the effective flexoelectric coefficient 𝜇𝑥𝑦𝑥𝑦 eff .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' We approximately have  Figure 5: Pictorial view of the flexoelectric couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Sketch of the BaTiO3 layer, showing regions of approximately constant shear strain as cells of a periodic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' We indicate the analogues of the AA and AB sites discussed in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The black arrows stand for the polarization induced by the flexoelectric effect;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' these arrows are consistent with Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' (1) and (2) for 𝜇𝑥𝑦𝑥𝑦 eff > 0, and they present the vortices and antivortices observed experimentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Note that the flexoelectric polarization can be intuitively understood from the symmetry breaking caused by the strain modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' For example, at any given lattice point (shared by four cells, with four associated cell angles), we always find an arrow pointing towards the cell with the smallest (< 90°) angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  AB  <  >  =  >  >  >  AB  =  AA  =  AA  =  𝜇𝑥𝑦𝑥𝑦 eff ≈ 𝛿𝑃𝑥 ( Δ𝜖𝑥𝑦 Δ𝑦 ) −1 ≈ 20 𝜇𝐶 𝑐𝑚−2 4 × 107 𝑚−1 ≈ 5 𝑛𝐶 𝑚−1, which is significantly smaller than typical experimental results for bulk BaTiO3 at room temperature (values between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='15 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='3  𝜇𝐶 𝑚−1 have been reported [40-42]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A variety of reasons may explain this difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' For example, our constrained BaTiO3 layers might be electrically stiffer than the bulk material and thus present a smaller flexoelectric response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' (The magnitude of the flexoelectric coupling is known to be proportional to the magnitude of the dielectric response [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=') Probably most critical: a linear approximation as that in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' (1) and (2) may be inadequate to explain and quantify the effect of the giant strain gradients in our samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' (To determine flexoelectric coefficients experimentally, the considered strain gradients are intentionally small, of the order of 1 𝑚−1 [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Strain gradients of the order of 8 × 105 𝑚−1  – as those associated to ferroelastic domains [15] – are considered to be very large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The gradients in our samples are even larger, by almost two orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=') Additionally, we may have differences coming from surface contributions to the flexoelectric effect [44];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' such surface effects might be present in bulk measurements but seem unlikely to play a role in our case, since the relevant shears and gradients do not involve any component normal to the layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Having said this, let us also note that there are theoretical predictions yielding 𝜇𝑥𝑦𝑥𝑦 values around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='08 𝑛𝐶 𝑚−1 for BaTiO3 [45], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', a smaller effect than the one we estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Shedding further light into these issues would be a great challenge, for both experiment and theory, and falls beyond the scope of the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  It is also interesting to note that the second derivatives of the shear strain can be used to compute the expected curl of the polarization vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In fact, from the flexoelectric coupling between strain gradients and polarization (Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' (1) and (2)), the following relation holds: 𝜕𝑃𝑥 𝜕𝑦 − 𝜕𝑃𝑦 𝜕𝑥 = 𝜇𝑥𝑦𝑥𝑦 eff (𝜕2𝜖𝑥𝑦 𝜕𝑦2 − 𝜕2𝜖𝑥𝑦 𝜕𝑥2 ),  closely captured by experimental results (see Extended Figures S4 showing the second derivatives of the strain gradient and S5 showing the curl of the polarization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In summary, we have found that the stacking of twisted free standing ferroelectric layers features a non- trivial ferroelectric texture driven by the mechanical boundary conditions imposed by the interface of twisted freestanding layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The ferroelectric topology consists of a 2D vortex crystal with a lattice periodicity determined by the twisting angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' This opens the door to new design possibilities enabled by the unique modulations that are possible in Moiré bilayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The highly correlated topological pattern with vortices and antivortices is reminiscent of the square lattice of merons, objects with n= ½ topological number only existing in lattices, observed in chiral magnets with magnetic anisotropy [46, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' At variance with previous ferroelectric textures found in ferroelectric films confined in the growth direction, our polar landscape is 2D and highly tunable by controlling the twisting angle of the bilayer and is, thus, more amenable for applications in high density ferroelectric memories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Materials and Methods:  Freestanding perovskite films fabrication:  15 nm thick BTO layers were grown onto LSMO buffered (100) SrTiO3 (STO) substrates via pure oxygen sputtering technique at high pressures (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='2 mbar) [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' This technique produces highly epitaxial growth with sharp interfaces and negligible stoichiometry deviations (see Extended Figure S6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The LSMO acts as a sacrificial layer that allows the release of the BTO layer upon immersion in a selective KI+HCl etchant [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Prior to immersion, a polypropylene carbonate (PPC, Sigma Aldrich) film was spin-coated onto the strained heterostructure and adhered to a commercial polydimethylsiloxane (PDMS, Gel-Film WF 4x 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='0  mil by Gel-Pak®) support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' This allows the release and transfer of the entire BTO freestanding layer onto holey Si3N4 membrane grids for STEM observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' After the first and prior to the second BTO transfer, the membranes are dipped in acetone and isopropyl alcohol to remove the remained PPC and clean the final interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The second BTO layer is transferred onto the first one with a twisted angle which is deterministically controlled by using the edges of the two BTO layers (with defined crystallographic orientation imposed by the (100) STO substrate) as a reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' See sketch in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 1a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' After the second transfer the surface of the final twisted heterostructure is cleaned as described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Scanning transmission electron microscopy (STEM): STEM characterization was carried out using a JEOL JEM-ARM 200cF aberration corrected electron microscope equipped with a cold field emission gun and a Gatan Quantum spectrometer, operated at 200 kV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Depth sectioning HAADF-STEM was performed by acquiring atomic-resolution HAADF-STEM images as a function of defocus [50, 51], allowing us to probe different depths of the sample and discriminate between the top and bottom layers of the stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' HAADF-STEM images were acquired using a 30 mrad probe forming aperture semiangle and a HAADF detector collection semiangle of 70-200 mrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Determination of polarization and strain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' To determine the ferroelectric polarization, the atomic positions of both A-site Ba and B-site Ti cations were measured on STEM-HAADF images of 3° and 10,4° twisted BaTiO3 bilayer stacks acquired focusing on the entrance surface of the stack (defocus = 0 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In order to precisely determine the atomic positions, we performed a two-dimensional gaussian fitting using Atomap [52] Polarization was  calculated from the off centering of the B-site Ti cations in the individual unit cells (relative displacement of the B-site Ti cation from the centrosymmetric position, determined with the A-site Ba cations within the same unit cell) [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Strain analysis was performed using the Peak Pairs Analysis (PPA) software package (HREM Research) for Digital Micrograph [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The analysis was performed on STEM-HAADF images of 3° and 10,4° twisted BaTiO3 bilayer stacks acquired focusing on the entrance surface of the stack (defocus = 0 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In order to improve the precision of the analysis the scanning direction was rotated off the crystallographic axes of BaTiO3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' For the analysis we perform a Bragg filter selecting the two main reflections along the (100) and (010) directions as base vectors for the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The peak positions are then determined on the filtered image and the relative displacements fields (𝑢𝑥, 𝑢𝑦) of the measured lattice with respect to a reference lattice area are calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' In this case we have use the whole image as reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Finally, the components of the strain tensor are calculated from the displacement fields as:   𝜀𝑥𝑥 = 𝜕𝑢𝑥 𝜕𝑥 , 𝜀𝑦𝑦 = 𝜕𝑢𝑦 𝜕𝑦 , 𝜀𝑥𝑦 = 1 2 ( 𝜕𝑢𝑥 𝜕𝑦 + 𝜕𝑢𝑦 𝜕𝑥 ) and 𝜔𝑥𝑦 = 1 2 ( 𝜕𝑢𝑦 𝜕𝑥 − 𝜕𝑢𝑥 𝜕𝑦 ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  First-principles calculations: We performed density functional theory (DFT) calculations as implemented in the Vienna Ab initio Simulation Package (VASP) [54, 55] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' We used the Perdew-Burke-Ernzerhof formulation for solids (PBEsol) [56] implementation of the generalized gradient approximation for the exchange-correlation functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The atomic cores are treated within the projector-augmented wave approach [57], considering the following states explicitly: 5s, 5p and 6s for Ba;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 3p, 4s and 3d for Ti;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' and 2s and 2p for O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' We employed a 500 eV energy cut-off for the plane-wave basis set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The simulation cells comprised 6x6x1 perovskite unit cells and were computed using a 1x1x4 Monkhorst-Pack [58] k-point grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The  structures were fully relaxed until residual forces fell below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='01 eV/Å and residual stresses fell below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='001 GPa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Let us stress that our DFT simulations correspond to the limit of very low temperature (formally, 0 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Thus, the computed energy differences – i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', the 9 meV per formula unit separating the monodomain ferroelectric state from the vortex-antivortex structure – can be taken as an upper bound for the relevant free energy difference at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' (In essence, the calculated energy difference comes from the ferroelectric domain walls – whose energy is known to decrease upon heating – and the inhomogeneous strain modulation – which is imposed by the inter-layer couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=') Note also that in our simulations we treat the monodomain and vortex-antivortex configurations as two separate cases, while in experiment the topological features are a relatively small modulation of the homogeneous state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' For this reason too, the computed energy difference is an upper bound for the actual energy cost of inducing (relatively small) topological features superimposed to the homogeneous state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' All in all, our DFT results strongly suggest that the experimentally observed topological structure is easily accessible and physically sound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Finally, let us remark that simulating directly the perturbed homogeneous state would require DFT relaxations constrained to respect the experimentally observed inhomogeneous strain pattern;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' such calculations would involve several non-trivial assumptions and technical complications, and we did not pursue them here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  REFERENCES [1] Yadav, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Observation of polar vortices in oxide superlattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nature 530, 198–201 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [2] Hsu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Emergence of the vortex state in confined ferroelectric heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 31, 1901014–1901022 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [3] Shafer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Emergent chirality in the electric polarization texture of titanate superlattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Natl Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' USA 115, 915–920 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [4] Gruverman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Vortex ferroelectric domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Matter 20, 4 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [5] Nelson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 11, 828–834 (2011) [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=',  Observation of room-temperature polar skyrmions, Nature 568, 369 (2019) [7] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Jia, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Urban, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Alexe, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Hesse, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Vrejoiu, Science 331, 1420 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Peters, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Apachitei, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Beanland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Alexe, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Sachez, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 7, 13484 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [9]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Schilling, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Byrne, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Catalan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Webber, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Genenko, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Scott, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Gregg, Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 9, 3359–3364 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [10] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Tang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Zhu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ma, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Borisevich, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Morozovska, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Eliseev, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Xu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Zhang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Pennycook, Science 348, 547 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [11]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Naumov, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Bellaiche, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Fu, Nature 432, 737 (2004) [12] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Kornew, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Fu, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Bellaiche, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 93, 196104 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [13] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Naumov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Bratkovsky, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 101, 107601 (2008) [14] Choi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Enhancement of ferroelectricity in strained BaTiO3 thin films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Science 306, 1005– 1009 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [15] Flexoelectric rotation of polarization in ferroelectric thin films G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Catalan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lubk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Vlooswijk, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Snoeck, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Magen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Janssens, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rispens , G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rijnders , D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Blank and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Noheda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nat Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 10, 963 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [16] Pavlo Zubko, Gustau Catalan and Alexander K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Tagantsev Flexoelectric Effect in Solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Annual Review of Materials Research, 43, 387 (2013) [17] Pertsev, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Zembilgotov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' & Tagantsev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 80, 1988–1991 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [18] Pablo Aguado-Puente and Javier Junquera Ferromagnetic like Closure Domains in Ferroelectric Ultrathin Films: First-Principles Simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='100 177601 (2008) [19] Jiawang Hong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Topology of the polarization field in ferroelectric nanowires from first principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys Rev B 81, 172101 (2010) [20] H Lu, C-W Bark, D Esque de los Ojos, J Alcala, C B Eom, G Catalan, A Gruverman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mechanical writing of ferroelectric polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Science 336, 59 (2012) [21] K S Novoselov , A K Geim, S V Morozov, D Jiang, M I Katsnelson, I V Grigorieva, S V Dubonos, A A Firsov Two-dimensional gas of massless Dirac fermions in graphene Nature 438, 197 (2005) [22] Castro Neto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Guinea, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Peres, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Novoselov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', & Geim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The electronic properties of graphene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Reviews of Modern Physics, 81, 109 (2009) [23] Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN, Strano MS, Electronics and optoelectronics of two- dimensional transition metal dichalcogenides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nanotechnology, 7, 699 (2012) [24] B Radisavljevic, A Radenovic, J Brivio, V Giacometti, A Kis, Single-layer MoS2 transistors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Nat Nanotechnol 6, 147 (2011) [25] Sajedeh Manzeli, Dmitry Ovchinnikov, Diego Pasquier, Oleg V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Yazyev & Andras Kis, 2D transition metal dichalcogenides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nature Reviews Materials 2, 17033 (2017)  [26] Yuan Cao, Valla Fatemi, Shiang Fang, Kenji Watanabe, Takashi Taniguchi, Efthimios Kaxiras, Pablo Jarillo-Herrero Unconventional superconductivity in magic-angle graphene superlattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nature 556, 43 (2018) [27] Alexey I Berdyugin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Out-of-equilibrium criticalities in graphene superlattices Science 375, 430 (2022) [28] Pablo San-Jose, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Gutiérrez-Rubio, Mauricio Sturla, and Francisco Guinea, Spontaneous strains and gap in graphene on boron nitride.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 90, 075428 [29] Lu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Baek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Hong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Kourkoutis, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Hikita, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Hwang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Y Synthesis of freestanding single-crystal perovskite films and heterostructures by etching of sacrificial water-soluble layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nature Materials, 15, 1255 (2016) [30] Hong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Gu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Verma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Harbola, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Lu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Vailionis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Hikita, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Pentcheva, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Rondinelli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Hwang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Extreme tensile strain states in La0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='7Ca0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='3MnO3 membranes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Science 368, 71–76 (2020) [31] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Super-elastic ferroelectric single-crystal membrane with continuous electric dipole rotation, Science 366, 475 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Shen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Dong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Qi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Wu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Li, Observation of Moiré Patterns in Twisted Stacks of Bilayer Perovskite Oxide Nanomembranes with Various Lattice Symmetries, ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Interfaces 14, 50386 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [33] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Xiang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Chiabrera, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Yun, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Kelly, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Dahm, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Kirchert, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Cozannet, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Trier, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Christensen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Booth, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Simonsen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Kadkhodazadeh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Jespersen, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Pryds, Stacking and Twisting of Freestanding Complex Oxide Thin Films, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 34, 2203187 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [34] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Devonshire, Phil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 40, 1040 (1949);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Íñiguez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ivantchev, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Pérez-Mato and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' García, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 63, 144103 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mulder, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Benedek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rondinelli and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Fennie, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Func.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 23, 4810 (2013) [37] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ederer and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Spaldin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 74, 024102 (2006);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [38] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' López-Pérez and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Íñiguez , Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 84 , 075121 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [39] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' King-Smith and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Vanderbilt, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 49, 5828 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [40] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Harada, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Axe and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Shirane, Neutron-scattering study of soft modes in cubic BaTiO3, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 4, 155 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [41] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Yudin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ahluwalia and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Tagantsev, Upper bounds for flexoelectric coefficients in ferroelectrics, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 104, 2 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [42] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Gu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Zhang and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Chen, Flexoelectricity in solids: Progress, challenges, and perspectives, Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Mats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 106, 100570 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [43] Ma, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' & Cross, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Strain-gradient-induced electric polarization in lead zirconate titanate ceramics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 82, 3293 3295 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [44] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Stengel, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 90, 201112(R) (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [45] Cyrus E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Dreyer, Massimiliano Stengel, and David Vanderbilt, Current-density implementation for calculating flexoelectric coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 98, 075153  [46] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Transformation between meron and skyrmion topological spin textures in a chiral magnet Nature 564, 95 (2018)  [47] Yu-Tsun Shao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Emergent chirality in a polar meron to skyrmion phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Microscopy and Microanalysis, 27, Supplement S1, 348 – 350 (2021) [48] Gabriel Sanchez-Santolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Resonant electron tunnelling assisted by charged domain walls in multiferroic tunnel junctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nature Nanotechnology volume 12, pages655–662 (2017) [49] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Pesquera et al Beyond substrates: strain engineering of ferroelectric membranes Advanced Materials 32 (43), 2003780 [50] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Borisevich, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lupini, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Pennycook, Depth sectioning with the aberration-corrected scanning transmission electron microscope, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', 103, 3044 (2006) [51] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Ishikawa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lupini, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Hinuma, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Pennycook, Large-angle illumination STEM: Toward three-dimensional atom-by-atom imaging, Ultramicroscopy, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 151, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 122–129, 2015, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='ultramic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [52] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Nord, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Vullum, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' MacLaren, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Tybell, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Holmestad, “Atomap: a new software tool for the automated analysis of atomic resolution images using two-dimensional Gaussian fitting,” Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Struct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Imaging, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 9, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 2017, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='1186/s40679-017-0042-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [53] Ghosez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=', Michenaud, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' & Gonze, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Dynamical atomic charges: the case of ABO3 compounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 58, 6224–6240 (1998) [54] Kresse, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' & Furthmüller, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 54, 11169–11186 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [55] Kresse, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' & Joubert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' From ultrasoft pseudopotentials to the projector augmented-wave method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 59, 1758–1775 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  [56] Perdew, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Restoring the density-gradient expansion for exchange in solids and surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 100, 136406 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [57] Blöchl, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Projector augmented-wave method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 50, 17953–17979 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' [58] Monkhorst, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' & Pack, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Special points for Brillouin-zone integrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' B 13, 5188– 5192 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Acknowledgments Authors acknowledge received funding from the project To2Dox of FlagERA ERA-NET Cofund in Quantum Technologies implemented within the European Union’s Horizon 2020 Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Work (JS, CL, FM , M G-H)  supported by Spanish AEI through grants, PID2020-118078RB-I00 and by Regional Government of Madrid CAM through SINERGICO project Y2020/NMT-6661 CAIRO-CM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' acknowledges financial support from Spanish MCI Grant Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' RTI2018-099054-J-I00 (MCI/AEI/FEDER, UE) and IJC2018-038164-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Work (VR) supported by the Madrid Government (Comunidad de Madrid- Spain) under the Multiannual Agreement with Universidad Complutense de Madrid in the line Research Incentive for Young PhDs, in the context of the V PRICIT (Regional Programme of Research and Technological Innovation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=" European Union's Horizon 2020 research and innovation program (Grant Agreement No." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 755655 ERC-StG 2017 project 2D-TOPSENSE, Grant Agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 785219 Graphene Core2-Graphene-based disruptive technologies and Grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' 881603 Graphene Core3- Graphene-based disruptive technologies), the EU FLAG-ERA project To2Dox (JTC-2019-009), the Comunidad de Madrid through the CAIRO-CM project (Y2020/NMT-6661) and the Spanish Ministry of Science and Innovation (grant PID2020-118078RB-I00 and fellowship PRE2018-084818).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Electron microscopy observations were carried out at the Centro Nacional de Microscopia Electrónica, CNME-UCM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Work at LIST was supported by the Luxembourg National Research Fund through grant FNR/C18/MS/12705883/REFOX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content='  Data availability statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' The data used in this paper are available from the authors upon reasonable request Authors contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' VR, VZ, SP, FAC prepared the samples with help and guidance of CM, FM, MGH and ACG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' GSS did the electron microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' GSS, VR, VZ, CL, JS analyzed the electron microscopy data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' HA and JI did the theory analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' GSS, VR, HA, JI, CL and JS wrote the manuscript with inputs and help of all authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
+page_content=' Competing interests: The authors declare no competing interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dE3T4oBgHgl3EQfTAmK/content/2301.04438v1.pdf'}
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+arXiv:2301.03775v1  [cs.IT]  10 Jan 2023
+1
+Secure Communication for Spatially Correlated Massive
+MIMO with Low-Resolution DACs
+Dan Yang, Student Member, IEEE, Jindan Xu, Member, IEEE, Wei Xu, Senior Member, IEEE,
+Ning Wang, Member, IEEE, Bin Sheng, Member, IEEE, and A. Lee Swindlehurst, Fellow, IEEE
+Abstract—In this paper, the performance of a secure massive
+multiple-input multiple-output (MIMO) system adopting low-
+resolution digital-to-analog converters (DACs) is analyzed over
+spatially correlated wireless channels. A tight lower bound for
+the achievable secrecy rate is derived with artificial noise (AN)
+transmitted in the null space of the user channels. Using the
+analytical results, the impact of spatial correlation on the secrecy
+rate is explicitly evaluated in the presence of low-resolution DACs.
+The analytical observations reveal that using low-resolution DACs
+can be beneficial to the secrecy performance compared with ideal
+DACs, when the channels are strongly correlated and optimal
+power allocation is not employed.
+Index Terms—Physical layer security, massive MIMO, spatial
+correlation, digital-to-analog converters (DACs)
+I. INTRODUCTION
+P
+HYSICAL layer security (PLS) has become an emerging
+technology for securing wireless communication without
+relying upon traditional cryptographic mechanisms. Compared
+to conventional upper-layer cryptographic schemes, PLS has
+the advantages of low computational complexity and low
+resource consumption [1]. Massive multiple-input multiple-
+output (MIMO) systems provide another disruptive technol-
+ogy for fifth generation (5G) cellular communications, and
+have shown great potential in improving spectral and energy
+efficiency. The use of large-scale antenna arrays in massive
+MIMO provides a large excess of redundant spatial degrees
+of freedom (DoF), which can be exploited to achieve secure
+physical layer transmission. This idea has been attracting
+increasing research interest in the past few years [2], [3].
+Massive MIMO transmission requires a very high power
+consumption if high-resolution digital-to-analog converters
+(DACs) are employed in the RF chains for each antenna.
+At the transmitter, power expenditure is dominated by power
+amplifiers (PAs), which are usually required to operate within
+a high linearity regime to avoid distortion. A practical solution
+to the above challenge is to use low-resolution DACs, which
+relaxes the requirement of linearity and allows the amplifiers
+to operate closer to saturation, thus increasing the efficiency of
+PAs [4], [5]. In [6], both finite-bit DACs at base station (BS)
+and finite-bit analog-to-digital converters (ADCs) at user side
+D. Yang, J. Xu, W. Xu, and B. Sheng are with the National Mobile
+Communications Research Laboratory, Southeast University, Nanjing 210096,
+China (email: dyang@seu.edu.cn; jdxu@seu.edu.cn; wxu@seu.edu.cn; sb-
+dtt@seu.edu.cn).
+N. Wang is with the School of Information Engineering, Zhengzhou
+University, Zhengzhou 450001, China.
+A. Lee Swindlehurst is with the Center for Pervasive Communications and
+Computing, University of California at Irvine, Irvine, CA 92697 USA (e-mail:
+swindle@uci.edu).
+were analyzed in the massive MIMO downlink. The work was
+then extended in [7] by considering spatially correlated chan-
+nels. Further in [8], a constant envelope precoding technique
+was devised for the multiuser MIMO with one-bit DACs.
+The effect of hardware impairments (HWIs) on spectral effi-
+ciency of massive MIMO systems has been studied in [9]. Re-
+garding the secrecy performance, the authors in [10] analyzed
+the effects of HWIs on secrecy rate, where ideal converters
+with infinite resolution were considered. Secure communica-
+tion in a massive MIMO system with low-resolution DACs was
+investigated in [11], which revealed that low-resolution DACs
+can achieve superior secrecy rate under certain conditions, e.g.,
+at low SNR or with a large power allocation factor.
+Most of the existing works on low-resolution DACs trans-
+missions have focused on the assumption of independent
+identically distributed (i.i.d.) channels for massive MIMO.
+However, in practice, the limited space between the BS anten-
+nas as well as the rich scattering propagation environment can
+result in spatial correlation. The impact of correlated Rayleigh
+fading channels on optimal multiuser loading was analyzed in
+[6] by applying asymptotic random matrix theory. How spatial
+correlation impacts secure massive MIMO communication
+with low-resolution DACs is still an open problem.
+In this paper, we focus on secure transmission in the massive
+MIMO downlink when low-resolution DACs are employed. A
+tight lower bound for the ergodic secrecy rate is derived that
+explicitly characterizes the impact of channel correlation on
+the secrecy rate for typical correlated channels. An optimal
+power allocation strategy is proposed, which suggests that
+more power should be allocated to AN when strong channel
+correlation is present. It is revealed that using low-resolution
+DACs can improve the secrecy performance for a fixed power
+allocation factor under strong spatially correlated channels.
+Notation: X∗, XT , XH and tr(X) represent the conju-
+gate, transpose, conjugate transpose and trace of matrix X,
+respectively. E{·} is the expectation operator. diag(·) denotes
+a diagonal matrix that retains only the diagonal elements of
+the input matrix, and �
+diag(·) represents a diagonal matrix with
+the input vector as its diagonal entries.
+II. SYSTEM MODEL
+The secure massive MIMO system under investigation
+comprises one N-antenna BS, K single-antenna legitimate
+users, and one M-antenna passive eavesdropper. The channel
+matrices are modeled based on the Kronecker channel model
+as shown in [12]. To make the problem more tractable, we con-
+sider the system with a common correlation matrix at the BS.
+Specifically, the channel between the BS and the users is mod-
+
+2
+eled as H = D
+1
+2 �HR
+1
+2 , where the elements of �H ∈ CK×N
+are i.i.d. Gaussian random variables with zero mean and unit
+variance, the diagonal matrix D ∈ CK×K characterizes the
+large-scale fading with its kth diagonal element given by βk,
+and R ∈ CN×N is the transmit covariance matrix satisfying
+tr(R) = N. Similarly, the channel matrix between the BS and
+the eavesdropper is He = D
+1
+2e �HeR
+1
+2 , where �He ∈ CM×N
+contains i.i.d. Rayleigh fading channel coefficients following
+CN(0, 1). The diagonal matrix De represents the large-scale
+fading at the eavesdropper with identical diagonal entries βe.
+The
+BS
+desires
+to
+transmit
+the
+symbols
+s
+=
+[s1, s2, ..., sK]
+∈
+CK×1
+to
+the
+legitimate
+users
+with
+E{ssH} = IK using a linear precoding matrix W ∈ CN×K.
+The eavesdropper’s channel state information (CSI) is assumed
+unknown to the BS, and AN is injected to ensure confidential
+communication. The AN vector t
+∼
+CN(0, IN−K) is
+precoded by an AN shaping matrix V ∈ CN×(N−K). Denote
+by P the total transmit power. The power allocation factor
+ξ ∈ (0, 1] aims to strike a balance between the transmit signal
+and the AN. The unquantized downlink transmit signal vector
+x is then expressed as
+x = √µWs + √νVt,
+(1)
+where µ ≜ ξP
+K and ν ≜ (1−ξ)P
+N−K .
+The precoded signal is transmitted after DAC quantization,
+which is denoted by Q(x). Establishing the non-linear quan-
+tization model of a finite-bit DAC is challenging. We follow a
+popular way of charactering the quantizer by a linear function
+applying the simple additive quantization noise model. The
+quantized signal vector can accordingly be decomposed as
+z = Q(x) =
+�
+1 − ρx + q,
+(2)
+where the quantization noise q is assumed to be uncorrelated
+with the input signal x, and
+Cq = E{qqH} = ρE
+�
+diag(xxH)
+�
+.
+(3)
+The value of the distortion factor ρ depends on the DAC
+resolution; for example, it can be chosen as in [5] for DAC
+resolutions of less than 5 bits, or as ρ =
+√
+3π
+2
+· 2−2b for
+scenarios with higher precision, where b represents the number
+of quantization bits. From (1) and (3), the covariance matrix
+of the quantization noise equals
+Cq = ρ
+�
+µdiag(WWH) + νdiag(VVH)
+�
+.
+(4)
+Given the CSI of the legitimate channels, the matrix V is
+designed to lie in the null space of the channel matrix H, i.e.,
+HV = 0, which (ideally) makes the AN “invisible” to the
+legitimate users [13]. Using (1) and (2), the signals received
+at the users and the eavesdropper are expressed as
+y =
+�
+1 − ρ(√µHWs + √νHVt) + Hq + n
+(5)
+ye =
+�
+1 − ρ(√µHeWs + √νHeVt) + Heq + ne,
+(6)
+where n ∼ CN(0, σ2
+nIK) and ne ∼ CN(0, σ2
+eIM) respec-
+tively represent the additive noise terms at the users and at
+the eavesdropper.
+III. ACHIEVABLE ERGODIC SECRECY RATE ANALYSIS
+In this section, we derive a tight lower bound for the ergodic
+secrecy rate of the secure multiuser massive MIMO downlink
+and analyze the impact of spatial correlation on the secrecy
+rate in the presence of low-resolution DACs.
+A. Lower Bound on the Achievable Ergodic Secrecy Rate
+We adopt linear matched filter (MF) precoding for data
+transmission, i.e., W = H/∥ H ∥. The received signal at the
+kth user according to (5) is expressed as
+yk =
+�
+1 − ρ
+�√µhT
+k Ws + √νhT
+k Vt
+�
++ hT
+k q + nk.
+(7)
+Then, under the assumption of Gaussian distributed interfer-
+ence, a lower bound on the ergodic rate for the kth user can
+be calculated as
+Rk = E
+�
+log2(1 + γk)
+�
+,
+(8)
+γk =
+(1 − ρ)µ
+��hT
+k wk
+��2
+̺ + hT
+k Cqh∗
+k + (1 − ρ)νhT
+k VVHh∗
+k + σ2n
+,
+(9)
+where ̺ = (1 − ρ)µ �
+j̸=k
+��hT
+k wj
+��2, hT
+k denotes the kth row of
+H, and wk is the kth column of W. Note that the numerator
+of γk is the power of the desired signal component for the kth
+user, and the denominator represents the power from inter-
+user interference, quantization noise from the low-resolution
+DACs, AN leakage, and thermal noise.
+Lemma 1: A lower bound on the achievable rate (8) of user
+k is given by
+Rk = log2
+�
+1 + (1 − ρ)β2
+kγ0ξN/ �K
+i=1 βi
+̺′ + ρβkγ0 + 1
+�
+,
+(10)
+where ̺′ = (1 − ρ)ξγ0βktr(R2) �
+j̸=k
+βj/(N �K
+i=1 βi), and γ0 =
+P
+σ2n is the average SNR.
+Proof: Please refer to Appendix A.
+■
+To guarantee secure communication in the worst case, we
+assume that the eavesdropper has perfect CSI of all legitimate
+users and can remove all the interference from the legitimate
+users [2], [3], [10], [11]. According to (6), the ergodic rate of
+the eavesdropper is expressed as
+C = E
+�
+log2
+�
+1 + (1 − ρ)µwH
+k HH
+e X−1Hewk
+��
+,
+(11)
+where X is defined as
+X = (1 − ρ)νHeVVHHH
+e + HeCqHH
+e .
+(12)
+Furthermore, we assume that σ2
+e is negligibly small corre-
+sponding to the worst case, and consequently, C is independent
+of the path-loss of the eavesdropper βe [2], [3], [10], [11]. A
+tight upper bound for C is derived in the following lemma.
+Lemma 2: For N → ∞, an upper bound on the eavesdrop-
+ping rate is given by
+C = log2
+�
+1 +
+φMξκβk/ �K
+i=1 βi
+φκ2�
+N
+tr(R2) − a
+�
+− ̟
+�
+,
+(13)
+where a = M
+N , b = K
+N , ρ′ =
+ρ
+1−ρ, φ = 1 − b, κ = 1 − ξ + ρ′, and
+̟ = ab(1 − ξ)2.
+Proof: Please refer to Appendix B.
+■
+Applying Lemma 1 and Lemma 2, a lower bound on the
+ergodic secrecy rate of the kth user is obtained in Theorem 1.
+Theorem 1: For N → ∞, the achievable ergodic secrecy
+rate for the kth user is lower bounded by
+Rsec ≜ [Rk − C]+,
+(14)
+where [x]+ = max{0, x}, and Rk and C are given in (10)
+and (13), respectively.
+
+3
+If no spatial correlation is present, i.e., R = I, then (14)
+reduces to
+Rsec =
+�
+log2
+�
+1 +
+(1 − ρ)β2
+kγ0ξN/ �K
+i=1 βi
+(1 − ρ)γ0βkξ �
+j̸=k
+βj/ �K
+i=1 βi + ρβkγ0 + 1
+�
+− log2
+�
+1 + φMξκβk/ �K
+i=1 βi
+φκ2(1 − a) − ̟
+��+
+.
+(15)
+As expected, Rsec increases with N and γ0.
+B. Optimal Power Allocation Strategy for AN
+Here we investigate the impact of the power allocation factor
+on the ergodic secrecy rate in (14) under spatially correlated
+channels. Assume ab ≪ 1 in (13), which is reasonable in
+massive MIMO equipped with a large number of antennas.
+The derivative of Rsec w.r.t. ξ is calculated as
+∂Rsec
+∂ξ
+=
+L1L2
+ln2(L3ξ + L2)[L2 + ξ(L1 + L3)]
+−
+Mtr(R2)(1 + ρ′)βk
+ln2
+� �K
+i=1 βi
+�
+N − tr(R2)a
+�
+κ2 + Mξβktr(R2)κ
+�,
+(16)
+where L1 = (1 − ρ)β2
+kγ0N/ �K
+i=1 βi, L2 = ρβkγ0 + 1, and
+L3 = (1 − ρ)γ0βktr(R2) �
+j̸=k
+βj/(N �K
+i=1 βi). Since
+∂Rsec
+∂ξ
+> 0
+for small ξ and
+∂Rsec
+∂ξ
+< 0 for large ξ, the optimal power
+allocation factor ξ∗ that achieves the highest secrecy rate is
+obtained by setting
+∂Rsec
+∂ξ
+= 0. A closed-form expression for
+ξ∗ can be founded as follows:
+ξ∗ = −B −
+√
+B2 − 4AC
+2A
+,
+(17)
+where the parameters A, B, and C are given by
+A = L1L2G2 − L1L2G3 − G1L3(L1 + L3),
+(18)
+B = (1 + ρ′)L1L2(G3 − 2G2) − G1L2(L1 + 2L3),
+(19)
+C = G2L1L2(1 + ρ′)2 − G1L2
+2,
+(20)
+and G1 = Mtr(R2)(1 + ρ′)βk, G2 = �K
+i=1 βi
+�
+N − tr(R2)a
+�,
+and G3 = Mβktr(R2).
+Assuming βk = 1, 1 ≤ k ≤ K, we can simplify the above
+expressions to evaluate the impact of spatial correlation on
+ξ∗ for different DAC resolutions. Comparing the value of ξ∗
+for the special case of an i.i.d. channel, i.e.,tr(R2) = N
+with a fully correlated channel, i.e., tr(R2) = N 2 for a
+Hermitian Toeplitz correlation matrix, we can easily observe
+that ξ∗ decreases when tr(R2) increases from N to N 2. The
+relationship between ξ∗ and the design parameters, including
+the DAC resolution and channel correlation coefficient, is
+verified in Section IV through numerical results.
+C. Impact of Spatial Correlation
+We first analyze the impact of the antenna ratio a under
+the correlated channel condition when AN is injected. In (14),
+Rsec decreases with respect to a. Considering the special case
+of βk = β, 1 ≤ k ≤ K, and ξ → 0, by setting Rsec = 0, the
+maximum number of eavesdropper antennas that still allows
+for a positive secrecy rate can be obtained from the following
+proposition.
+Proposition 1: If a positive secrecy rate can be achieved,
+then the maximum antenna ratio a is obtained as
+asec =
+(1 − b)Nγ0
+tr(R2)
+�
+γ0ρb(ρ − β − 2) + γ0(1 + βρ) + 1 − b
+�.
+(21)
+Remark 1: By direct inspection of (21), the maximum
+number of eavesdropper antennas that can be tolerated for
+secure transmission decreases with ρ and the spatial correlation
+level because Eve can wiretap more information under strongly
+correlated channels. For the special case of ρ → 0 and
+tr(R2) = N 2, we have asec =
+(1−b)γ0
+N(1−b+γ0), which indicates
+that asec is independent of the large-scale fading factor with
+infinite-resolution DACs.
+To extract clear insights, we further consider a representative
+exponential correlation model [14]
+Rij = ζ|i−j|,
+(22)
+where ζ denotes the correlation coefficient. The exponential
+model is widely adopted in literature and is applicable to
+analysis for a massive MIMO system with uniform planar
+array (UPA) scenarios [15].
+Proposition 2: The secrecy rate gap for different DAC
+resolutions decreases with the correlation coefficient ζ.
+Proof: lim
+N→∞
+tr(R2)
+N
+= 1+ζ2
+1−ζ2 exists under the exponential
+correlation model in (22). From (14), we have ∂Rsec
+∂ρ
+= ∂Rk
+∂ρ −
+∂C
+∂ρ . The first term ∂Rk
+∂ρ is given by
+∂Rk
+∂ρ = −
+β2
+kγ0ξN(1 + βkγ0) �K
+i=1 βi
+ln2(Υβkγ0 + �K
+i=1 βi)(Ψβkγ0 + �K
+i=1 βi)
+,
+(23)
+where Υ = (1 − ρ)(Nβk + �ζ �
+j̸=k βj)ξ + ρ �K
+i=1 βi, Ψ =
+ρ �K
+i=1 βi + (1 − ρ)ξ�ζ �
+j̸=k βj, and �ζ = 1+ζ2
+1−ζ2 . The expression
+of ∂C
+∂ρ is shown in (24), on the top of the next page. Assuming
+ab ≪ 1 for typical massive MIMO systems, (24) can be
+simplified as
+∂C
+∂ρ = −
+Mξφβk�ζ/ �K
+i=1 βi
+ln2(1 − ρ)2��
+κ − (Mξβk/ �K
+i=1 βi − aκ)�ζ
+�
+κφ
+�. (25)
+Focusing on the impact of ζ, we observe that
+∂C
+∂ρ
+< 0
+and decreases with ζ, while
+∂Rk
+∂ρ
+< 0 and increases with
+ζ. Therefore,
+∂Rsec
+∂ρ
+is an increasing function of ζ, which
+completes the proof.
+■
+Remark 2: From (23) and (25), it shows that
+∂Rsec
+∂ρ
+< 0 and
+∂Rsec
+∂ρ
+is a monotonically increasing function in terms of the
+level of spatial correlation ζ. It implies that the eavesdropper’s
+capacity C degrades faster than Rk does at large ζ. Thus, we
+conclude that there exists a threshold of correlation coefficient,
+i.e., ζ, where lower-resolution DACs achieve a higher secrecy
+rate for ζ ∈ (ζ, 1). The value of ζ is obtained from the solution
+of
+∂Rsec
+∂ρ
+= 0 by focusing on the impact of spatial correlation.
+Note that the higher the correlation the lower the effective
+dimension (d.o.f.), in the extreme case of ζ = 1, the users and
+Eve are separated only in the angle of arrival domain, which
+only has dimension 1 instead of N. Therefore, quantization
+noise from lower-resolution DACs could compensate for AN
+to improve secrecy rate under spatially correlated channel.
+IV. NUMERICAL RESULTS
+In this section, the analytical results are validated through
+Monte-Carlo simulation. We consider a system with N = 256,
+K = 16, and M = 4 in all simulations. The large-scale fading
+is modeled as βk = (dref/dk)η, where η = 3.8 denotes the
+path loss exponent, dref = 300 (m) and dk ≤ 500 (m) are,
+respectively, the reference distance and the distance between
+
+4
+∂C
+∂ρ = −
+Mξφβk�ζ[(1 − a�ζ)φκ2 + ̟�ζ]/ �K
+i=1 βi
+ln2(1 − ρ)2�
+(a�ζ − )φκ2 + ̟�ζ
+���
+(aκ2 − Mξκβk/ �K
+i=1 βi)�ζ − κ2�
+φ + ̟�ζ
+�
+(24)
+the BS and the kth user. The expected values in (14) were
+evaluated by averaging over 1000 random channel realizations.
+-6
+-4
+-2
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+20
+SNR (dB)
+0
+0.5
+1
+1.5
+2
+2.5
+3
+3.5
+4
+Ergodic secrecy rate (bit/s/Hz)
+=0
+=0.7
+Simulation results (b=1)
+Analytical results in (14) (b=1)
+Simulation results (b=2)
+Analytical results in (14) (b=2)
+Simulation results (b=
+)
+Analytical results in (14) (b=
+)
+Fig. 1.
+Ergodic secrecy rate and analytical lower bound versus SNR for
+different spatial correlation coefficient ζ (ξ = 0.7)
+Fig. 1 shows the ergodic secrecy rate versus the average
+SNR γ0 under different DAC resolutions and spatial correla-
+tions. The derived lower bound on the secrecy rate is fairly
+accurate and tight for the entire range of SNR. In addition, it
+is observed that the secrecy rate is decreasing as ζ increases.
+Fig. 2 plots the ergodic secrecy rate as a function of the
+power allocation factor ξ. The optimal power allocation factor
+ξ∗ largely depends on ζ. Specifically, It is observed that ξ∗
+decreases with ζ. The information signal leakage grows when
+the spatial correlation is strong. Thus, more power should be
+allocated for AN to ensure secure communication.
+In Fig. 3 (a) we show the ergodic secrecy rate versus ζ with
+different DAC resolutions for γ0 = 10 dB. We choose a fixed
+power allocation factor ξ due to the difficulties in optimizing
+ξ theoretically. The secrecy rate loss due to low-resolution
+DACs decreases with ζ as predicted in Remark 2. Interestingly,
+although the channel correlation has a detrimental effect on the
+secrecy rate, the use of 1-bit DACs can improve the secrecy
+rate when the spatial correlation coefficient is large. This is
+because the additional quantization noise serves to increase the
+level of AN, which is beneficial for spatially colored channels
+if the AN level has not already been optimized. Finally, Fig.
+3 (b) presents the secrecy rate versus ζ assuming the optimal
+power allocation ξ∗ in (17) is chosen. The secrecy rate gaps
+are ∆Rsec = 0.697 bit/s/Hz at ζ = 0 and ∆Rsec = 0.434
+bit/s/Hz at ζ = 0.8, respectively. If optimal power allocation
+is adopted, then using infinite-resolution DACs can always
+achieve a higher secrecy rate. In this case, quantization noise
+from lower-resolution DACs does not compensate for the AN
+anymore. However, we observe that the secrecy rate loss due
+to low-resolution DACs decreases with channel correlation
+coefficient, regardless of the value of ξ.
+For comparison, Fig. 4 plots the Monte-Carlo simulation by
+using the spatial correlation model in [9], denoted by [R]s,m =
+β
+L
+�L
+l=1 ejπ(s−m) sin(ϕl)e− ∆2
+2
+�
+π(s−m) cos(ϕl)
+�2
+, where β is the
+large scale fading coefficient, ϕ is the actual angle-of-arrival
+and ∆ is the azimuth angular spread. We consider L = 10
+scattering clusters and ϕ ∼ [ −∆
+2 ,
+∆
+2 ]. It is observed that
+transitioning from larger to smaller angular spread (∆ = 50o
+to ∆ = 12o) significantly reduces the secrecy rate of the
+kth user for different DAC resolutions. However, the lower
+resolution DAC is always beneficial for secrecy rate with a
+fixed ξ under highly correlated channels as expected.
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+0
+0.5
+1
+1.5
+2
+2.5
+3
+3.5
+4
+Ergodic secrecy rate (bit/s/Hz)
+=0
+=0.6
+Simulation results (b=1)
+Analytical results in (14) (b=1)
+Simulation results (b=2)
+Analytical results in (14) (b=2)
+Simulation results (b=3)
+Analytical results in (14) (b=3)
+The optimal  in (17)
+Fig. 2. Achievable ergodic secrecy rate versus the power allocation factor ξ
+for different DAC resolutions (γ0 = 10 dB)
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0
+0.5
+1
+1.5
+2
+2.5
+3
+3.5
+Ergodic secrecy rate (bit/s/Hz)
+b=1, fixed =0.7
+b=2, fixed =0.7
+b=3, fixed =0.7
+b=
+, fixed =0.7
+(a) with fixed ξ=0.7
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+1
+1.5
+2
+2.5
+3
+3.5
+4
+Ergodic secrecy rate (bit/s/Hz)
+b=1
+b=2
+b=3
+b=
+Rsec=0.434 bit/s/Hz
+Rsec=0.697 bit/s/Hz
+(b) with optimal ξ∗ in (17)
+Fig. 3. Achievable ergodic secrecy rate versus ζ for different DAC resolutions
+-6
+-4
+-2
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+20
+SNR (dB)
+0
+0.5
+1
+1.5
+2
+2.5
+3
+3.5
+4
+Ergodic secrecy rate (bit/s/Hz)
+=50 deg
+=12 deg
+b=1
+b=2
+b=
+Fig. 4. Ergodic secrecy rate versus SNR (ξ = 0.7)
+V. CONCLUSION
+This paper has characterized the performance of AN-based
+secure transmission in a massive MIMO downlink system with
+low-resolution DACs under spatially correlated channels. In
+particular, it is shown that optimal secrecy performance can
+be obtained by increasing the amount of power dedicated
+to artificial noise when the channel correlation increases.
+Furthermore, the use of low-resolution DACs has been shown
+to be beneficial to the secrecy performance for a fixed power
+allocation factor when the channels possess strong spatial
+correlation. Interesting future extension of this paper includes
+
+5
+studying the impact of different spatial correlation matrices at
+both transmitter and the eavesdropper.
+APPENDIX A
+Consider MF precoding satisfying tr(WWH) = K, which
+leads to W =
+�
+K
+N �K
+i=1 βi H. First, we directly obtain
+��hT
+k wk
+��2 =
+K
+N �K
+i=1 βi
+��hT
+k hk
+��2
+=
+Kβ2
+k
+N �K
+i=1 βi
+�
+tr(R)
+�2
+a.s.
+−−→ KNβ2
+k
+�K
+i=1 βi
+,
+(26)
+where we have used
+1
+√
+N �hT
+k R
+1
+√
+N �h∗
+k −
+1
+N tr(R)
+a.s.
+−−→ 0 in [16,
+Lemma 4]. Then, the inter-user interference is calculated as
+̺ = (1 − ρ)µ
+�
+j̸=k
+K
+N �K
+i=1 βi
+��hT
+k hj
+��2
+a.s.
+−−→ (1 − ρ)µKβktr(R2)
+�
+j̸=k
+βj
+��
+N
+K
+�
+i=1
+βi
+�
+.
+(27)
+For large N and K, Cq converges to
+Cq
+a.s.
+−−→ ρ P
+N IN,
+(28)
+where we use the definition of µ and ν, and the fact that
+diag(WWH)
+a.s.
+−−→
+K
+N IN and diag(VVH)
+a.s.
+−−→
+N−K
+N
+IN due
+to the strong law of large numbers. Further, we obtain the
+component of the quantization noise as
+hT
+k Cqh∗
+k
+a.s.
+−−→ ρ P
+N βktr(R) = ρPβk.
+(29)
+Regarding the AN power, it follows that
+hT
+k VVHh∗
+k = 0,
+(30)
+since HV = 0. Finally, by substituting (26), (27), (29), (30)
+and the definition of µ and ν into (8), and according to the
+Continuous Mapping Theorem, we complete the proof.
+APPENDIX B
+By applying Jensen’s inequality, the capacity of the eaves-
+dropper can be upper bounded as
+C ≤ log2
+�
+1 + (1 − ρ)µE
+�
+wH
+k HH
+e X−1Hewk
+��
+.
+(31)
+Let us first focus on the term X and by substituting (28) into
+(12) yields
+X
+a.s.
+−−→
+�
+(1 − ρ)ν + ρ P
+N
+�
+X1 + ρ P
+N X2,
+(32)
+where X1 = HeVVHHH
+e
+and X2 = HeV0VH
+0 HH
+e . It is
+obvious that [V V0][V V0]H = IM, because [V V0] forms
+a complete orthogonal basis. Eigendecompose R such that
+R = UΛUH to decorrelate matrix He as Z = HeΛ− 1
+2 UH,
+where Λ =
+�
+diag(λ1, ..., λN) is the diagonal matrix of the
+eigenvalues of R and the columns of U consist of the
+corresponding eigenvectors. Since U is unitary, the statistics
+of ZU are identical to those of Z. Thereby, the distributions
+of X1 and X2 are the same as
+N
+�
+i=1
+N
+�
+j=1
+λ
+1
+2
+i λ
+1
+2
+j zivivH
+j zH
+j
+(33)
+and
+N
+�
+i=1
+N
+�
+j=1
+λ
+1
+2
+i λ
+1
+2
+j ziv0,ivH
+0,jzH
+j ,
+(34)
+where zi is the ith row of Z, vi and v0,i are ith column of
+V and V0, respectively. Following the same approach in [17],
+Y =
+�
+(1 − ρ)ν + ρ P
+N
+�
+Y1 + ρ P
+N Y2 may be accurately approx-
+imated as a single scaled Wishart matrix Y ∼ WM(η, ϕIM),
+where we define Y1 = �N
+m=1 λmzmvmvH
+mzH
+m and Y2 =
+�N
+n=1 λnznv0,nvH
+0,nzH
+n . Equating the first two moments of
+those matrices with Y1 ∼ �N
+m=1 λmWM(N − K, 1
+N IM) and
+Y2 ∼ �N
+n=1 λnWM(K, 1
+N IM) leads to
+ηϕ =
+�
+(1 − ρ)ν + ρ P
+N
+�
+(N − K) + ρ P
+N K
+(35)
+and
+ηϕ2 = tr(R2)
+N
+��
+(1−ρ)ν +ρ P
+N
+�2
+(N −K)+
+�
+ρ P
+N
+�2
+K
+�
+, (36)
+where we use �N
+i=1 λi = tr(R) and �N
+i=1 λ2
+i = tr(R2). By
+exploiting the independence of the elements in �He, we can
+further obtain X−1
+a.s.
+−−→ 1/(ϕ(η − M))IM with η > M, where
+we use the property A−1
+a.s.
+−−→ 1/(n − m)Im for a Wishart
+matrix A ∼ Wm(n, Im) with n > m [4]. Substituting this result
+and E
+�
+wH
+k HH
+e Hewk
+�
+=
+MKβk
+N �K
+i=1 βi tr(R2) into (31) completes
+the proof.
+REFERENCES
+[1] F. Oggier and B. Hassibi, “The secrecy capacity of the MIMO wiretap
+channel,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 4961–4972, Jul.
+2011.
+[2] J. Zhu, R. Schober, and V. K. Bhargava, “Secure transmission in
+multicell massive MIMO systems,” IEEE Trans. Wireless Commun., vol.
+13, no. 9, pp. 4766–4781, Sep. 2014.
+[3] J. Zhu, R. Schober, and V. K. Bhargava, “Linear precoding of data and
+artificial noise in secure massive MIMO systems,” IEEE Trans. Wireless
+Commun., vol. 15, no. 3, pp. 2245–2261, Mar. 2016.
+[4] A. K. Saxena, I. Fijalkow, and A. L. Swindlehurst, “Analysis of one-bit
+quantized precoding for the multiuser massive MIMO downlink,” IEEE
+Trans. Signal Process., vol. 65, no. 17, pp. 4624–4634, Sep. 2017.
+[5] Y. Li, C. Tao, A. Lee Swindlehurst, A. Mezghani, and L. Liu, “Downlink
+achievable rate analysis in massive MIMO systems with one-bit DACs,”
+IEEE Commun. Lett., vol. 21, no. 7, pp. 1669–1672, Jul. 2017.
+[6] J. Xu, W. Xu, and F. Gong, “On performance of quantized transceiver
+in multiuser massive MIMO downlinks,” IEEE Wireless Commun. Lett.,
+vol. 6, no. 5, pp. 562–565, Jun. 2017.
+[7] J. Xu, W. Xu, F. Gong, H. Zhang, and X. You, “Optimal multiuser
+loading in quantized massive MIMO under spatially correlated chan-
+nels,” IEEE Trans. Veh. Technol., vol. 68, no. 2, pp. 1459–1471, Feb.
+2019.
+[8] H. Jedda, A. Mezghani, A. L. Swindlehurst, and J. A. Nossek, “Quan-
+tized constant envelope precoding with PSK and QAM signaling,” IEEE
+Trans. Wireless Commun., vol. 17, no. 12, pp. 8022–8034, Dec. 2018.
+[9] E. Bj¨ornson, J. Hoydis, and L. Sanguinetti, “Massive MIMO networks:
+Spectral, energy, and hardware efficiency,” Found. Trends Signal Pro-
+cess., vol. 11, nos. 3–4, pp. 154–655, 2017.
+[10] J. Zhu, D. W. K. Ng, N. Wang, R. Schober, and V. K. Bhargava,
+“Analysis and design of secure massive MIMO systems in the presence
+of hardware impairments,” IEEE Trans. Wireless Commun., vol. 16, no.
+3, pp. 2001–2016, Mar. 2017.
+[11] J. Xu, W. Xu, J. Zhu, D. W. K. Ng, and A. Lee Swindlehurst, “Secure
+massive MIMO communication with low-resolution DACs,”
+IEEE
+Trans. Commun., vol. 67, no. 5, pp. 3265–3278, May 2019.
+[12] D.-S. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fading
+correlation and its effect on the capacity of multielement antenna
+systems,” IEEE Trans. Commun., vol. 48, no. 3, pp. 502–513, Mar. 2000.
+[13] S. Goel and R. Negi, “Guaranteeing secrecy using artificial noise,” IEEE
+Trans. Wireless Commun., vol. 7, no. 6, pp. 2180–2189, Jun. 2008.
+[14] S. L. Loyka, “Channel capacity of MIMO architecture using the ex-
+ponential correlation matrix,”
+IEEE Commun. Lett., vol. 5, no. 9, pp.
+369–371, Sep. 2001.
+[15] H. Lim, Y. Jang, and D. Yoon, “Bounds for eigenvalues of spatial
+correlation matrices with the exponential model in MIMO systems,”
+IEEE Trans. Wireless Commun., vol. 16, no. 2, pp. 1196–1204, Feb.
+2017.
+[16] J. Hoydis, S. ten Brink, and M. Debbah, “Massive MIMO in the UL/DL
+of cellular networks: How many antennas do we need?” IEEE J. Sel.
+Areas Commun., vol. 31, no. 2, pp. 160–171, Feb. 2013.
+[17] Q. T. Zhang and D. P. Liu, “A simple capacity formula for correlated
+diversity Rician channels,” IEEE Commun. Lett., vol. 6, no. 11, pp.
+481–483, Nov. 2002.
+
diff --git a/_tE2T4oBgHgl3EQfQwb6/content/tmp_files/load_file.txt b/_tE2T4oBgHgl3EQfQwb6/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf,len=498
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='03775v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='IT]  10 Jan 2023  1  Secure Communication for Spatially Correlated Massive  MIMO with Low-Resolution DACs  Dan Yang, Student Member, IEEE, Jindan Xu, Member, IEEE, Wei Xu, Senior Member, IEEE,  Ning Wang, Member, IEEE, Bin Sheng, Member, IEEE, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lee Swindlehurst, Fellow, IEEE  Abstract—In this paper, the performance of a secure massive  multiple-input multiple-output (MIMO) system adopting low-  resolution digital-to-analog converters (DACs) is analyzed over  spatially correlated wireless channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' A tight lower bound for  the achievable secrecy rate is derived with artificial noise (AN)  transmitted in the null space of the user channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Using the  analytical results, the impact of spatial correlation on the secrecy  rate is explicitly evaluated in the presence of low-resolution DACs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  The analytical observations reveal that using low-resolution DACs  can be beneficial to the secrecy performance compared with ideal  DACs, when the channels are strongly correlated and optimal  power allocation is not employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Index Terms—Physical layer security, massive MIMO, spatial  correlation, digital-to-analog converters (DACs)  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' INTRODUCTION  P  HYSICAL layer security (PLS) has become an emerging  technology for securing wireless communication without  relying upon traditional cryptographic mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Compared  to conventional upper-layer cryptographic schemes, PLS has  the advantages of low computational complexity and low  resource consumption [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Massive multiple-input multiple-  output (MIMO) systems provide another disruptive technol-  ogy for fifth generation (5G) cellular communications, and  have shown great potential in improving spectral and energy  efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The use of large-scale antenna arrays in massive  MIMO provides a large excess of redundant spatial degrees  of freedom (DoF), which can be exploited to achieve secure  physical layer transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' This idea has been attracting  increasing research interest in the past few years [2], [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Massive MIMO transmission requires a very high power  consumption if high-resolution digital-to-analog converters  (DACs) are employed in the RF chains for each antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  At the transmitter, power expenditure is dominated by power  amplifiers (PAs), which are usually required to operate within  a high linearity regime to avoid distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' A practical solution  to the above challenge is to use low-resolution DACs, which  relaxes the requirement of linearity and allows the amplifiers  to operate closer to saturation, thus increasing the efficiency of  PAs [4], [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' In [6], both finite-bit DACs at base station (BS)  and finite-bit analog-to-digital converters (ADCs) at user side  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Xu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Xu, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Sheng are with the National Mobile  Communications Research Laboratory, Southeast University, Nanjing 210096,  China (email: dyang@seu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' jdxu@seu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' wxu@seu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' sb-  dtt@seu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='cn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Wang is with the School of Information Engineering, Zhengzhou  University, Zhengzhou 450001, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lee Swindlehurst is with the Center for Pervasive Communications and  Computing, University of California at Irvine, Irvine, CA 92697 USA (e-mail:  swindle@uci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='edu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  were analyzed in the massive MIMO downlink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The work was  then extended in [7] by considering spatially correlated chan-  nels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Further in [8], a constant envelope precoding technique  was devised for the multiuser MIMO with one-bit DACs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  The effect of hardware impairments (HWIs) on spectral effi-  ciency of massive MIMO systems has been studied in [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Re-  garding the secrecy performance, the authors in [10] analyzed  the effects of HWIs on secrecy rate, where ideal converters  with infinite resolution were considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Secure communica-  tion in a massive MIMO system with low-resolution DACs was  investigated in [11], which revealed that low-resolution DACs  can achieve superior secrecy rate under certain conditions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=',  at low SNR or with a large power allocation factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Most of the existing works on low-resolution DACs trans-  missions have focused on the assumption of independent  identically distributed (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=') channels for massive MIMO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  However, in practice, the limited space between the BS anten-  nas as well as the rich scattering propagation environment can  result in spatial correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The impact of correlated Rayleigh  fading channels on optimal multiuser loading was analyzed in  [6] by applying asymptotic random matrix theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' How spatial  correlation impacts secure massive MIMO communication  with low-resolution DACs is still an open problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  In this paper, we focus on secure transmission in the massive  MIMO downlink when low-resolution DACs are employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' A  tight lower bound for the ergodic secrecy rate is derived that  explicitly characterizes the impact of channel correlation on  the secrecy rate for typical correlated channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' An optimal  power allocation strategy is proposed, which suggests that  more power should be allocated to AN when strong channel  correlation is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' It is revealed that using low-resolution  DACs can improve the secrecy performance for a fixed power  allocation factor under strong spatially correlated channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Notation: X∗, XT , XH and tr(X) represent the conju-  gate, transpose, conjugate transpose and trace of matrix X,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' E{·} is the expectation operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' diag(·) denotes  a diagonal matrix that retains only the diagonal elements of  the input matrix, and �  diag(·) represents a diagonal matrix with  the input vector as its diagonal entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' SYSTEM MODEL  The secure massive MIMO system under investigation  comprises one N-antenna BS, K single-antenna legitimate  users, and one M-antenna passive eavesdropper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The channel  matrices are modeled based on the Kronecker channel model  as shown in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' To make the problem more tractable, we con-  sider the system with a common correlation matrix at the BS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Specifically, the channel between the BS and the users is mod-  2  eled as H = D  1  2 �HR  1  2 , where the elements of �H ∈ CK×N  are i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Gaussian random variables with zero mean and unit  variance, the diagonal matrix D ∈ CK×K characterizes the  large-scale fading with its kth diagonal element given by βk,  and R ∈ CN×N is the transmit covariance matrix satisfying  tr(R) = N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Similarly, the channel matrix between the BS and  the eavesdropper is He = D  1  2e �HeR  1  2 , where �He ∈ CM×N  contains i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Rayleigh fading channel coefficients following  CN(0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The diagonal matrix De represents the large-scale  fading at the eavesdropper with identical diagonal entries βe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  The  BS  desires  to  transmit  the  symbols  s  =  [s1, s2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', sK]  ∈  CK×1  to  the  legitimate  users  with  E{ssH} = IK using a linear precoding matrix W ∈ CN×K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  The eavesdropper’s channel state information (CSI) is assumed  unknown to the BS, and AN is injected to ensure confidential  communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The AN vector t  ∼  CN(0, IN−K) is  precoded by an AN shaping matrix V ∈ CN×(N−K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Denote  by P the total transmit power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The power allocation factor  ξ ∈ (0, 1] aims to strike a balance between the transmit signal  and the AN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The unquantized downlink transmit signal vector  x is then expressed as  x = √µWs + √νVt,  (1)  where µ ≜ ξP  K and ν ≜ (1−ξ)P  N−K .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  The precoded signal is transmitted after DAC quantization,  which is denoted by Q(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Establishing the non-linear quan-  tization model of a finite-bit DAC is challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' We follow a  popular way of charactering the quantizer by a linear function  applying the simple additive quantization noise model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The  quantized signal vector can accordingly be decomposed as  z = Q(x) =  �  1 − ρx + q,  (2)  where the quantization noise q is assumed to be uncorrelated  with the input signal x, and  Cq = E{qqH} = ρE  �  diag(xxH)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (3)  The value of the distortion factor ρ depends on the DAC  resolution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' for example, it can be chosen as in [5] for DAC  resolutions of less than 5 bits, or as ρ =  √  3π  2  2−2b for  scenarios with higher precision, where b represents the number  of quantization bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' From (1) and (3), the covariance matrix  of the quantization noise equals  Cq = ρ  �  µdiag(WWH) + νdiag(VVH)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (4)  Given the CSI of the legitimate channels, the matrix V is  designed to lie in the null space of the channel matrix H, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=',  HV = 0, which (ideally) makes the AN “invisible” to the  legitimate users [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Using (1) and (2), the signals received  at the users and the eavesdropper are expressed as  y =  �  1 − ρ(√µHWs + √νHVt) + Hq + n  (5)  ye =  �  1 − ρ(√µHeWs + √νHeVt) + Heq + ne,  (6)  where n ∼ CN(0, σ2  nIK) and ne ∼ CN(0, σ2  eIM) respec-  tively represent the additive noise terms at the users and at  the eavesdropper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' ACHIEVABLE ERGODIC SECRECY RATE ANALYSIS  In this section, we derive a tight lower bound for the ergodic  secrecy rate of the secure multiuser massive MIMO downlink  and analyze the impact of spatial correlation on the secrecy  rate in the presence of low-resolution DACs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lower Bound on the Achievable Ergodic Secrecy Rate  We adopt linear matched filter (MF) precoding for data  transmission, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', W = H/∥ H ∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The received signal at the  kth user according to (5) is expressed as  yk =  �  1 − ρ  �√µhT  k Ws + √νhT  k Vt  �  + hT  k q + nk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (7)  Then, under the assumption of Gaussian distributed interfer-  ence, a lower bound on the ergodic rate for the kth user can  be calculated as  Rk = E  �  log2(1 + γk)  �  ,  (8)  γk =  (1 − ρ)µ  ��hT  k wk  ��2  ̺ + hT  k Cqh∗  k + (1 − ρ)νhT  k VVHh∗  k + σ2n  ,  (9)  where ̺ = (1 − ρ)µ �  j̸=k  ��hT  k wj  ��2, hT  k denotes the kth row of  H, and wk is the kth column of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Note that the numerator  of γk is the power of the desired signal component for the kth  user, and the denominator represents the power from inter-  user interference, quantization noise from the low-resolution  DACs, AN leakage, and thermal noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Lemma 1: A lower bound on the achievable rate (8) of user  k is given by  Rk = log2  �  1 + (1 − ρ)β2  kγ0ξN/ �K  i=1 βi  ̺′ + ρβkγ0 + 1  �  ,  (10)  where ̺′ = (1 − ρ)ξγ0βktr(R2) �  j̸=k  βj/(N �K  i=1 βi), and γ0 =  P  σ2n is the average SNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Proof: Please refer to Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  ■  To guarantee secure communication in the worst case, we  assume that the eavesdropper has perfect CSI of all legitimate  users and can remove all the interference from the legitimate  users [2], [3], [10], [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' According to (6), the ergodic rate of  the eavesdropper is expressed as  C = E  �  log2  �  1 + (1 − ρ)µwH  k HH  e X−1Hewk  ��  ,  (11)  where X is defined as  X = (1 − ρ)νHeVVHHH  e + HeCqHH  e .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (12)  Furthermore, we assume that σ2  e is negligibly small corre-  sponding to the worst case, and consequently, C is independent  of the path-loss of the eavesdropper βe [2], [3], [10], [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' A  tight upper bound for C is derived in the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Lemma 2: For N → ∞, an upper bound on the eavesdrop-  ping rate is given by  C = log2  �  1 +  φMξκβk/ �K  i=1 βi  φκ2�  N  tr(R2) − a  �  − ̟  �  ,  (13)  where a = M  N , b = K  N , ρ′ =  ρ  1−ρ, φ = 1 − b, κ = 1 − ξ + ρ′, and  ̟ = ab(1 − ξ)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Proof: Please refer to Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  ■  Applying Lemma 1 and Lemma 2, a lower bound on the  ergodic secrecy rate of the kth user is obtained in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Theorem 1: For N → ∞, the achievable ergodic secrecy  rate for the kth user is lower bounded by  Rsec ≜ [Rk − C]+,  (14)  where [x]+ = max{0, x}, and Rk and C are given in (10)  and (13), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  3  If no spatial correlation is present, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', R = I, then (14)  reduces to  Rsec =  �  log2  �  1 +  (1 − ρ)β2  kγ0ξN/ �K  i=1 βi  (1 − ρ)γ0βkξ �  j̸=k  βj/ �K  i=1 βi + ρβkγ0 + 1  �  − log2  �  1 + φMξκβk/ �K  i=1 βi  φκ2(1 − a) − ̟  ��+  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (15)  As expected, Rsec increases with N and γ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Optimal Power Allocation Strategy for AN  Here we investigate the impact of the power allocation factor  on the ergodic secrecy rate in (14) under spatially correlated  channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Assume ab ≪ 1 in (13), which is reasonable in  massive MIMO equipped with a large number of antennas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  The derivative of Rsec w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' ξ is calculated as  ∂Rsec  ∂ξ  =  L1L2  ln2(L3ξ + L2)[L2 + ξ(L1 + L3)]  −  Mtr(R2)(1 + ρ′)βk  ln2  � �K  i=1 βi  �  N − tr(R2)a  �  κ2 + Mξβktr(R2)κ  �,  (16)  where L1 = (1 − ρ)β2  kγ0N/ �K  i=1 βi, L2 = ρβkγ0 + 1, and  L3 = (1 − ρ)γ0βktr(R2) �  j̸=k  βj/(N �K  i=1 βi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Since  ∂Rsec  ∂ξ  > 0  for small ξ and  ∂Rsec  ∂ξ  < 0 for large ξ, the optimal power  allocation factor ξ∗ that achieves the highest secrecy rate is  obtained by setting  ∂Rsec  ∂ξ  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' A closed-form expression for  ξ∗ can be founded as follows:  ξ∗ = −B −  √  B2 − 4AC  2A  ,  (17)  where the parameters A, B, and C are given by  A = L1L2G2 − L1L2G3 − G1L3(L1 + L3),  (18)  B = (1 + ρ′)L1L2(G3 − 2G2) − G1L2(L1 + 2L3),  (19)  C = G2L1L2(1 + ρ′)2 − G1L2  2,  (20)  and G1 = Mtr(R2)(1 + ρ′)βk, G2 = �K  i=1 βi  �  N − tr(R2)a  �,  and G3 = Mβktr(R2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Assuming βk = 1, 1 ≤ k ≤ K, we can simplify the above  expressions to evaluate the impact of spatial correlation on  ξ∗ for different DAC resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Comparing the value of ξ∗  for the special case of an i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' channel, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=',tr(R2) = N  with a fully correlated channel, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', tr(R2) = N 2 for a  Hermitian Toeplitz correlation matrix, we can easily observe  that ξ∗ decreases when tr(R2) increases from N to N 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The  relationship between ξ∗ and the design parameters, including  the DAC resolution and channel correlation coefficient, is  verified in Section IV through numerical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Impact of Spatial Correlation  We first analyze the impact of the antenna ratio a under  the correlated channel condition when AN is injected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' In (14),  Rsec decreases with respect to a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Considering the special case  of βk = β, 1 ≤ k ≤ K, and ξ → 0, by setting Rsec = 0, the  maximum number of eavesdropper antennas that still allows  for a positive secrecy rate can be obtained from the following  proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Proposition 1: If a positive secrecy rate can be achieved,  then the maximum antenna ratio a is obtained as  asec =  (1 − b)Nγ0  tr(R2)  �  γ0ρb(ρ − β − 2) + γ0(1 + βρ) + 1 − b  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (21)  Remark 1: By direct inspection of (21), the maximum  number of eavesdropper antennas that can be tolerated for  secure transmission decreases with ρ and the spatial correlation  level because Eve can wiretap more information under strongly  correlated channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' For the special case of ρ → 0 and  tr(R2) = N 2, we have asec =  (1−b)γ0  N(1−b+γ0), which indicates  that asec is independent of the large-scale fading factor with  infinite-resolution DACs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  To extract clear insights, we further consider a representative  exponential correlation model [14]  Rij = ζ|i−j|,  (22)  where ζ denotes the correlation coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The exponential  model is widely adopted in literature and is applicable to  analysis for a massive MIMO system with uniform planar  array (UPA) scenarios [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Proposition 2: The secrecy rate gap for different DAC  resolutions decreases with the correlation coefficient ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Proof: lim  N→∞  tr(R2)  N  = 1+ζ2  1−ζ2 exists under the exponential  correlation model in (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' From (14), we have ∂Rsec  ∂ρ  = ∂Rk  ∂ρ −  ∂C  ∂ρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The first term ∂Rk  ∂ρ is given by  ∂Rk  ∂ρ = −  β2  kγ0ξN(1 + βkγ0) �K  i=1 βi  ln2(Υβkγ0 + �K  i=1 βi)(Ψβkγ0 + �K  i=1 βi)  ,  (23)  where Υ = (1 − ρ)(Nβk + �ζ �  j̸=k βj)ξ + ρ �K  i=1 βi, Ψ =  ρ �K  i=1 βi + (1 − ρ)ξ�ζ �  j̸=k βj, and �ζ = 1+ζ2  1−ζ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The expression  of ∂C  ∂ρ is shown in (24), on the top of the next page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Assuming  ab ≪ 1 for typical massive MIMO systems, (24) can be  simplified as  ∂C  ∂ρ = −  Mξφβk�ζ/ �K  i=1 βi  ln2(1 − ρ)2��  κ − (Mξβk/ �K  i=1 βi − aκ)�ζ  �  κφ  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' (25)  Focusing on the impact of ζ, we observe that  ∂C  ∂ρ  < 0  and decreases with ζ, while  ∂Rk  ∂ρ  < 0 and increases with  ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Therefore,  ∂Rsec  ∂ρ  is an increasing function of ζ, which  completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  ■  Remark 2: From (23) and (25), it shows that  ∂Rsec  ∂ρ  < 0 and  ∂Rsec  ∂ρ  is a monotonically increasing function in terms of the  level of spatial correlation ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' It implies that the eavesdropper’s  capacity C degrades faster than Rk does at large ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Thus, we  conclude that there exists a threshold of correlation coefficient,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', ζ, where lower-resolution DACs achieve a higher secrecy  rate for ζ ∈ (ζ, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The value of ζ is obtained from the solution  of  ∂Rsec  ∂ρ  = 0 by focusing on the impact of spatial correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Note that the higher the correlation the lower the effective  dimension (d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' ), in the extreme case of ζ = 1, the users and  Eve are separated only in the angle of arrival domain, which  only has dimension 1 instead of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Therefore, quantization  noise from lower-resolution DACs could compensate for AN  to improve secrecy rate under spatially correlated channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' NUMERICAL RESULTS  In this section, the analytical results are validated through  Monte-Carlo simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' We consider a system with N = 256,  K = 16, and M = 4 in all simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The large-scale fading  is modeled as βk = (dref/dk)η, where η = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='8 denotes the  path loss exponent, dref = 300 (m) and dk ≤ 500 (m) are,  respectively, the reference distance and the distance between  4  ∂C  ∂ρ = −  Mξφβk�ζ[(1 − a�ζ)φκ2 + ̟�ζ]/ �K  i=1 βi  ln2(1 − ρ)2�  (a�ζ − \uf731)φκ2 + ̟�ζ  ���  (aκ2 − Mξκβk/ �K  i=1 βi)�ζ − κ2�  φ + ̟�ζ  �  (24)  the BS and the kth user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The expected values in (14) were  evaluated by averaging over 1000 random channel realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  6  4  2  0  2  4  6  8  10  12  14  16  18  20  SNR (dB)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  4  Ergodic secrecy rate (bit/s/Hz)  =0  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  Simulation results (b=1)  Analytical results in (14) (b=1)  Simulation results (b=2)  Analytical results in (14) (b=2)  Simulation results (b=  )  Analytical results in (14) (b=  )  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Ergodic secrecy rate and analytical lower bound versus SNR for  different spatial correlation coefficient ζ (ξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 1 shows the ergodic secrecy rate versus the average  SNR γ0 under different DAC resolutions and spatial correla-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The derived lower bound on the secrecy rate is fairly  accurate and tight for the entire range of SNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' In addition, it  is observed that the secrecy rate is decreasing as ζ increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2 plots the ergodic secrecy rate as a function of the  power allocation factor ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The optimal power allocation factor  ξ∗ largely depends on ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Specifically, It is observed that ξ∗  decreases with ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The information signal leakage grows when  the spatial correlation is strong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Thus, more power should be  allocated for AN to ensure secure communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 3 (a) we show the ergodic secrecy rate versus ζ with  different DAC resolutions for γ0 = 10 dB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' We choose a fixed  power allocation factor ξ due to the difficulties in optimizing  ξ theoretically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The secrecy rate loss due to low-resolution  DACs decreases with ζ as predicted in Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Interestingly,  although the channel correlation has a detrimental effect on the  secrecy rate, the use of 1-bit DACs can improve the secrecy  rate when the spatial correlation coefficient is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' This is  because the additional quantization noise serves to increase the  level of AN, which is beneficial for spatially colored channels  if the AN level has not already been optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Finally, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  3 (b) presents the secrecy rate versus ζ assuming the optimal  power allocation ξ∗ in (17) is chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' The secrecy rate gaps  are ∆Rsec = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='697 bit/s/Hz at ζ = 0 and ∆Rsec = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='434  bit/s/Hz at ζ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='8, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' If optimal power allocation  is adopted, then using infinite-resolution DACs can always  achieve a higher secrecy rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' In this case, quantization noise  from lower-resolution DACs does not compensate for the AN  anymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' However, we observe that the secrecy rate loss due  to low-resolution DACs decreases with channel correlation  coefficient, regardless of the value of ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  For comparison, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 4 plots the Monte-Carlo simulation by  using the spatial correlation model in [9], denoted by [R]s,m =  β  L  �L  l=1 ejπ(s−m) sin(ϕl)e− ∆2  2  �  π(s−m) cos(ϕl)  �2  , where β is the  large scale fading coefficient, ϕ is the actual angle-of-arrival  and ∆ is the azimuth angular spread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' We consider L = 10  scattering clusters and ϕ ∼ [ −∆  2 ,  ∆  2 ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' It is observed that  transitioning from larger to smaller angular spread (∆ = 50o  to ∆ = 12o) significantly reduces the secrecy rate of the  kth user for different DAC resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' However, the lower  resolution DAC is always beneficial for secrecy rate with a  fixed ξ under highly correlated channels as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='9  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  4  Ergodic secrecy rate (bit/s/Hz)  =0  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='6  Simulation results (b=1)  Analytical results in (14) (b=1)  Simulation results (b=2)  Analytical results in (14) (b=2)  Simulation results (b=3)  Analytical results in (14) (b=3)  The optimal  in (17)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Achievable ergodic secrecy rate versus the power allocation factor ξ  for different DAC resolutions (γ0 = 10 dB)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  Ergodic secrecy rate (bit/s/Hz)  b=1, fixed =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  b=2, fixed =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  b=3, fixed =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  b=  , fixed =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  (a) with fixed ξ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='8  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  4  Ergodic secrecy rate (bit/s/Hz)  b=1  b=2  b=3  b=  Rsec=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='434 bit/s/Hz  Rsec=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='697 bit/s/Hz  (b) with optimal ξ∗ in (17)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Achievable ergodic secrecy rate versus ζ for different DAC resolutions  6  4  2  0  2  4  6  8  10  12  14  16  18  20  SNR (dB)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='5  4  Ergodic secrecy rate (bit/s/Hz)  =50 deg  =12 deg  b=1  b=2  b=  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Ergodic secrecy rate versus SNR (ξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='7)  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' CONCLUSION  This paper has characterized the performance of AN-based  secure transmission in a massive MIMO downlink system with  low-resolution DACs under spatially correlated channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' In  particular, it is shown that optimal secrecy performance can  be obtained by increasing the amount of power dedicated  to artificial noise when the channel correlation increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Furthermore, the use of low-resolution DACs has been shown  to be beneficial to the secrecy performance for a fixed power  allocation factor when the channels possess strong spatial  correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Interesting future extension of this paper includes  5  studying the impact of different spatial correlation matrices at  both transmitter and the eavesdropper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  APPENDIX A  Consider MF precoding satisfying tr(WWH) = K, which  leads to W =  �  K  N �K  i=1 βi H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' First, we directly obtain  ��hT  k wk  ��2 =  K  N �K  i=1 βi  ��hT  k hk  ��2  =  Kβ2  k  N �K  i=1 βi  �  tr(R)  �2  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→ KNβ2  k  �K  i=1 βi  ,  (26)  where we have used  1  √  N �hT  k R  1  √  N �h∗  k −  1  N tr(R)  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→ 0 in [16,  Lemma 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Then, the inter-user interference is calculated as  ̺ = (1 − ρ)µ  �  j̸=k  K  N �K  i=1 βi  ��hT  k hj  ��2  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→ (1 − ρ)µKβktr(R2)  �  j̸=k  βj  ��  N  K  �  i=1  βi  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (27)  For large N and K, Cq converges to  Cq  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→ ρ P  N IN,  (28)  where we use the definition of µ and ν, and the fact that  diag(WWH)  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→  K  N IN and diag(VVH)  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→  N−K  N  IN due  to the strong law of large numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Further, we obtain the  component of the quantization noise as  hT  k Cqh∗  k  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→ ρ P  N βktr(R) = ρPβk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (29)  Regarding the AN power, it follows that  hT  k VVHh∗  k = 0,  (30)  since HV = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Finally, by substituting (26), (27), (29), (30)  and the definition of µ and ν into (8), and according to the  Continuous Mapping Theorem, we complete the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  APPENDIX B  By applying Jensen’s inequality, the capacity of the eaves-  dropper can be upper bounded as  C ≤ log2  �  1 + (1 − ρ)µE  �  wH  k HH  e X−1Hewk  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  (31)  Let us first focus on the term X and by substituting (28) into  (12) yields  X  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→  �  (1 − ρ)ν + ρ P  N  �  X1 + ρ P  N X2,  (32)  where X1 = HeVVHHH  e  and X2 = HeV0VH  0 HH  e .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' It is  obvious that [V V0][V V0]H = IM, because [V V0] forms  a complete orthogonal basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Eigendecompose R such that  R = UΛUH to decorrelate matrix He as Z = HeΛ− 1  2 UH,  where Λ =  �  diag(λ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', λN) is the diagonal matrix of the  eigenvalues of R and the columns of U consist of the  corresponding eigenvectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Since U is unitary, the statistics  of ZU are identical to those of Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Thereby, the distributions  of X1 and X2 are the same as  N  �  i=1  N  �  j=1  λ  1  2  i λ  1  2  j zivivH  j zH  j  (33)  and  N  �  i=1  N  �  j=1  λ  1  2  i λ  1  2  j ziv0,ivH  0,jzH  j ,  (34)  where zi is the ith row of Z, vi and v0,i are ith column of  V and V0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Following the same approach in [17],  Y =  �  (1 − ρ)ν + ρ P  N  �  Y1 + ρ P  N Y2 may be accurately approx-  imated as a single scaled Wishart matrix Y ∼ WM(η, ϕIM),  where we define Y1 = �N  m=1 λmzmvmvH  mzH  m and Y2 =  �N  n=1 λnznv0,nvH  0,nzH  n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Equating the first two moments of  those matrices with Y1 ∼ �N  m=1 λmWM(N − K, 1  N IM) and  Y2 ∼ �N  n=1 λnWM(K, 1  N IM) leads to  ηϕ =  �  (1 − ρ)ν + ρ P  N  �  (N − K) + ρ P  N K  (35)  and  ηϕ2 = tr(R2)  N  ��  (1−ρ)ν +ρ P  N  �2  (N −K)+  �  ρ P  N  �2  K  �  , (36)  where we use �N  i=1 λi = tr(R) and �N  i=1 λ2  i = tr(R2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' By  exploiting the independence of the elements in �He, we can  further obtain X−1  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→ 1/(ϕ(η − M))IM with η > M, where  we use the property A−1  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  −−→ 1/(n − m)Im for a Wishart  matrix A ∼ Wm(n, Im) with n > m [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Substituting this result  and E  �  wH  k HH  e Hewk  �  =  MKβk  N �K  i=1 βi tr(R2) into (31) completes  the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  REFERENCES  [1] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Oggier and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Hassibi, “The secrecy capacity of the MIMO wiretap  channel,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Theory, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 57, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 4961–4972, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Zhu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Schober, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Bhargava, “Secure transmission in  multicell massive MIMO systems,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 4766–4781, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Zhu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Schober, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Bhargava, “Linear precoding of data and  artificial noise in secure massive MIMO systems,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Wireless  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2245–2261, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Saxena, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Fijalkow, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Swindlehurst, “Analysis of one-bit  quantized precoding for the multiuser massive MIMO downlink,” IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Signal Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 65, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 17, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 4624–4634, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [5] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Tao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lee Swindlehurst, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Mezghani, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Liu, “Downlink  achievable rate analysis in massive MIMO systems with one-bit DACs,”  IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 1669–1672, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Xu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Xu, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Gong, “On performance of quantized transceiver  in multiuser massive MIMO downlinks,” IEEE Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 562–565, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Xu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Xu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Gong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Zhang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' You, “Optimal multiuser  loading in quantized massive MIMO under spatially correlated chan-  nels,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Veh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 68, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 1459–1471, Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Jedda, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Mezghani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Swindlehurst, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Nossek, “Quan-  tized constant envelope precoding with PSK and QAM signaling,” IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 8022–8034, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [9] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Bj¨ornson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Hoydis, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Sanguinetti, “Massive MIMO networks:  Spectral, energy, and hardware efficiency,” Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Trends Signal Pro-  cess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 11, nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 3–4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 154–655, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Zhu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Ng, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Schober, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Bhargava,  “Analysis and design of secure massive MIMO systems in the presence  of hardware impairments,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2001–2016, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Xu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Zhu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Ng, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lee Swindlehurst, “Secure  massive MIMO communication with low-resolution DACs,”  IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 67, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 3265–3278, May 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Shiu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Foschini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Gans, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Kahn, “Fading  correlation and its effect on the capacity of multielement antenna  systems,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 48, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 502–513, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Goel and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Negi, “Guaranteeing secrecy using artificial noise,” IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2180–2189, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Loyka, “Channel capacity of MIMO architecture using the ex-  ponential correlation matrix,”  IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  369–371, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Jang, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Yoon, “Bounds for eigenvalues of spatial  correlation matrices with the exponential model in MIMO systems,”  IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 1196–1204, Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Hoydis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' ten Brink, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Debbah, “Massive MIMO in the UL/DL  of cellular networks: How many antennas do we need?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' IEEE J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Sel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  Areas Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 31, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 160–171, Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  [17] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Zhang and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Liu, “A simple capacity formula for correlated  diversity Rician channels,” IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content='  481–483, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
+page_content=' 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_tE2T4oBgHgl3EQfQwb6/content/2301.03775v1.pdf'}
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+1
+Learning Good Features to Transfer
+Across Tasks and Domains
+Pierluigi Zama Ramirez*1, Adriano Cardace*1, Luca De Luigi*1,
+Alessio Tonioni2, Samuele Salti1, Luigi Di Stefano1
+1University of Bologna, Italy
+2Google Inc.
+{pierluigi.zama,adriano.cardace2,luca.deluigi4,samuele.salti,luigi.distefano}@unibo.it
+alessiot@google.com
+Abstract—Availability of labelled data is the major obstacle to the deployment of deep learning algorithms for computer vision tasks in
+new domains. The fact that many frameworks adopted to solve different tasks share the same architecture suggests that there should
+be a way of reusing the knowledge learned in a specific setting to solve novel tasks with limited or no additional supervision. In this
+work, we first show that such knowledge can be shared across tasks by learning a mapping between task-specific deep features in a
+given domain. Then, we show that this mapping function, implemented by a neural network, is able to generalize to novel unseen
+domains. Besides, we propose a set of strategies to constrain the learned feature spaces, to ease learning and increase the
+generalization capability of the mapping network, thereby considerably improving the final performance of our framework. Our proposal
+obtains compelling results in challenging synthetic-to-real adaptation scenarios by transferring knowledge between monocular depth
+estimation and semantic segmentation tasks.
+Index Terms—Domain Adaptation, Task Transfer, Semantic Segmentation, Depth estimation
+!
+1
+INTRODUCTION
+D
+EEP learning has revolutionized computer vision by
+providing an effective solution to address a wide range
+of tasks (e.g., classification, depth estimation, semantic seg-
+mentation, etc.). The rise of a common framework has
+allowed incredible leaps forward for the whole research
+community thanks to the ability to reuse architectural and
+algorithmic improvements discovered to solve one task
+across many others. However, the real knowledge of a neu-
+ral network is stored inside its trained parameters and we
+still have no simple way of sharing this knowledge across
+different tasks and domains (i.e., datasets). As such, the first
+step for every practitioner faced with a new problem or do-
+main deals with acquisition and labeling of a new training
+set, an extremely tedious, expensive and time consuming
+operation. We argue that sharing the knowledge acquired
+by a neural network to solve a specific task in a specific
+domain across other tasks and domains could be a more
+straightforward and cost-effective way to tackle them.
+Indeed, this is demonstrated by the widespread use
+and success of transfer learning. Transfer learning concerns
+solving new tasks by initializing a network with pre-trained
+weights, thereby providing a basic approach to knowledge
+reuse. However, it still requires a new annotated dataset to
+fine tune the pretrained network on the the task at hand. A
+few works focused on the related task transfer (TT) problem
+[1], [2], i.e., on exploiting supervised data to tackle multiple
+tasks in a single domain more effectively by leveraging on
+the relationships between the learned representations. As
+unlabeled domains are not considered in TT problem for-
+mulations, the proposed methodologies still rely on transfer
+* Equal contribution.
+Fig. 1. Our framework transfers knowledge across tasks and domains.
+Given two tasks (1 and 2) and two domains (A and B), with supervision
+for both tasks in A but only for one task in B, we learn the dependency
+between the tasks in A and exploit this in B in order to solve task 2
+without the need of supervision.
+learning and availability of a small annotated training set
+in order to address new datasets. On the other hand, the
+unsupervised domain adaptation literature (DA) [3] studies
+how the need for annotated data can be removed when
+leveraging on knowledge reuse to solve the same task across
+different domains, but it does not consider different tasks.
+Differently, we propose to merge DA and TT by ex-
+plicitly addressing a cross domain and cross task problem
+where on one source domain (e.g., synthetic data) we have
+supervision for many tasks, while in another target one (e.g.,
+real data) annotations are available only for a specific task
+while we wish to solve many. A schematic representation
+of our problem formulation with two domains and two
+tasks is shown in the right part of Figure 1. Following this
+schematic representation we will consider a scenario with
+arXiv:2301.11310v1  [cs.CV]  26 Jan 2023
+
+Task 1
+Task 2
+Domain A
+AIDT
+Domain
+Task
+Transfer
+Transfer
+DomainB
+?
+Transfer Learning2
+two domains (a source one and a target one, namely A
+and B) and two tasks (again a source one and a target one,
+namely task 1 and 2), but nothing prevents our method to
+be extended to more. In domain A we use the available
+supervision to learn two models for the source and target
+tasks, while in the target domain B we can do the same
+for the source task only. In domain A we use the trained
+task-specific models to learn a mapping function (G1→2
+in Figure 1) between deep features extracted to solve the
+source task and those extracted to solve the target task. This
+mapping function is then applied in domain B to solve the
+target task by transforming the features extracted to solve
+the source task.
+The key component of our framework is the mapping
+function between the two task-specific deep features. In [4]
+we proposed a preliminary formulation of our framework
+by modeling the mapping function as a deep convolutional
+neural network and optimizing its parameters by standard
+supervised learning in the source domain A. In this work,
+we expand and improve upon our preliminary formula-
+tion by proposing two features alignment strategies aimed
+at learning the feature mapping function more effectively.
+Firstly, we align feature representations across domains
+using a novel norm discrepancy alignment (NDA) loss that
+constraints the feature space by penalizing features with
+very different norms in a spatially-aware manner. Secondly,
+we align feature representations across tasks by using them
+as inputs to solve a common auxiliary task. This pretext
+problem acts as a bridge between the source and the target
+tasks: in fact, if the deep features extracted to solve them in-
+dependently can be used to address effectively an additional
+common task, we are pushed to believe that those features
+present the same semantic content and encode it in a similar
+manner.
+We test the effectiveness of our proposal in a challenging
+autonomous driving scenario where we try to solve the two
+related dense prediction tasks of monocular depth estima-
+tion and semantic segmentation [5]. We select edge detection
+as the auxiliary task since color edges provide oftentimes
+detailed key information related to both the semantic as well
+as the depth structure of the scene. Many edge detectors
+have been proposed during the years, with recent deep
+learning based approaches outperforming classical hand-
+crafted methods even in the most challenging scenarios [6],
+[7], [8]. Interestingly, such deep models present good gener-
+alization capabilities, allowing us to use the state-of-the-art
+approach [6] to generate proxy supervision for the auxiliary
+task without extra labels. Thanks to our formulation, we
+can use a fully supervised and completely synthetic domain
+(i.e., the Carla simulator [9]) to improve the performance on
+a partially labeled real domain (i.e., Cityscapes [10]).
+The contributions of this paper can be summarized as
+follow:
+•
+We propose for the first time to study a cross domain
+and cross task problem where supervision for all
+tasks is available in one domain whilst only for a
+subset of them in the other. This is done by learning
+a mapping between deep representations.
+•
+We demonstrate how constraining explicitly deep
+features across domains with a novel norm discrep-
+ancy alignment loss improves the learning of the
+mapping function.
+•
+We further show how the learning of the mapping
+function can be improved by deploying an auxiliary
+task.
+•
+Considering the dense prediction tasks of monocular
+depth estimation and semantic segmentation, we
+achieve results close to the practical upper bound
+when transferring knowledge between a synthetic
+and a real domain.
+2
+RELATED WORKS
+2.1
+Transfer Learning and Task Transfer
+Collecting training data is often expensive, time-consuming,
+or even unrealistic in many scenarios. Many works have
+tackled this problem by exploiting the existence of a rela-
+tionship between the weights of CNNs trained for different
+tasks [11]. In particular, [12] showed that this strategy, re-
+ferred to as transfer learning, can lead to better results than
+using random initialization even if applied on quite diverse
+tasks. Transfer learning has become a common practice, for
+instance, in object detection, where networks are usually
+initialized with Imagenet [13] classification weights [14],
+[15], [16], [17]. Additional insights on the transferability of
+learned representations between different visual tasks were
+provided in [1], where the authors present Taskonomy, a
+computational approach to represent a taxonomy of rela-
+tionships among visual tasks. Along similar lines, [18] pro-
+posed to exploit the correlation between known supervised
+tasks and novel target tasks, in order to predict the param-
+eters of models deployed to solve the target tasks starting
+from the parameters of networks trained on the known
+tasks. While [1] and [18] study the correlation between tasks
+in a given domain and assume either full or no supervision,
+we explicitly address a multi-domain scenario assuming full
+supervision in one domain and partial supervision in the
+target one.
+2.2
+Domain Adaptation
+Domain adaptation techniques aim at reducing the perfor-
+mance drop of a model deployed on a domain different from
+the one the model was trained on [3]. Throughout the years,
+adaptation has been performed at different levels. Early
+approaches tried to model a shared feature space relying on
+statistical metrics such as MMD [19], [20]. Later, some works
+proposed to align domains by adversarial training [21],
+[22], [23]. Recently [24] noticed that, for classification tasks,
+aligning feature norms to an arbitrarily large value results in
+better transferability across domains. Generative adversarial
+networks [25] have also been employed to perform image-
+to-image translation between different domains [26], [27],
+[28], and, in particular, to render cheaply labelled syn-
+thetic images similar to real images from a target domain.
+However, when dealing with dense tasks such as semantic
+segmentation, feature-based domain adaptation approaches
+tend to fail as deeply discussed in [29] . Thus, several ap-
+proaches to address domain adaptation for dense tasks, such
+as semantic segmentation [5], [29], [30], [31], [32], [33], [34],
+[35], [36], [37], [38], [39], [40] or depth estimation [41], [42],
+
+3
+[43] have been proposed recently. Among them, SPIGAN
+[44] uses extra supervision coming from synthetic depth
+of the source domain to improve the quality of an image-
+to-image translation network and consequently achieving
+better adaptation performances. Akin to DA methods, we
+learn from a labeled source domain to perform well on a
+different target domain. However, unlike the classical DA
+setting, we assume the existence of an additional task where
+supervision is available for both domains.
+2.3
+Multi-task Learning
+The goal of multi-task learning is to solve many tasks si-
+multaneously. By pursuing this rather than solving the tasks
+independently, a neural network may use more information
+to obtain more robust and reliable predictions. Many works
+try to tackle several tasks jointly [45], [46], [47], [48]. For
+example, [47] showed that by learning to correctly weigh
+each task loss, multi-task learning methods can outperform
+separate models trained individually. [5], [48] show how
+learning multiple perception tasks jointly while enforcing
+geometrical consistency across them can lead to better per-
+formances for almost all tasks. Recently, [2] proposes a
+method to improve the performances of multiple single-
+task networks by imposing consistency across them during
+training. Finally, Taskonomy [1] investigates the relationship
+between the deployed tasks to accomplish multi-task learn-
+ing effectively. However, multi-task learning approaches
+usually try to achieve the best balance between tasks in
+a single-domain scenario. We instead tackle a multi-task
+and multi-domain problem. Nevertheless, taking inspiration
+from multi-task learning, we show how jointly learning an
+auxiliary task while learning the two task networks helps
+the alignment of features across tasks.
+2.4
+Task Transfer and Domain Adaptation
+Most existing approaches address independently either task
+transfer or domain adaptation. Yet, a few works have pro-
+posed to tackle these two problems jointly. [49] was the first
+paper to propose a cross-tasks and cross-domains adapta-
+tion approach, considering as tasks different image classifi-
+cations problems. UM-Adapt [50], instead, learns a cross-
+task distillation framework with full supervision on the
+source domain and deploys such framework on the target
+domain in a fully unsupervised manner, while minimizing
+adversarially the discrepancy between the two domains.
+Differently, in a preliminary version of this work [4], we in-
+troduced AT/DT (Across Tasks and Domains Transfer) and
+set forth a novel learning framework, where the relationship
+between a set of tasks is learned on the source domain and it
+is later deployed to solve a specific task on the target domain
+without supervision thanks to the availability of ground-
+truth for all the tasks except the target one. In this work we
+will expand and improve this methodology.
+3
+METHOD
+We introduce the problem we are trying to solve with a
+practical example. Imagine we aim to solve semantic seg-
+mentation in a real domain but we only have labels for a
+closely related task (e.g., depth estimation). Moreover, let
+Fig. 2. AT/DT framework: here N1 and N2 are trained separately to solve
+tasks T1 and T2. While N2 is trained only on images from domain A,
+N1 is trained jointly on both domain A and domain B, to enable the
+extraction of domain invariant features. Then, encoders from the two
+networks are frozen and used to learn the transfer function G1→2, which
+aims at transforming features extracted for T1 in features that are good
+for T2. This step is performed only on domain A, since we have no
+supervision for T2 on domain B. Finally, at inference time, features are
+extracted from E1 starting from images of domain B, transformed with
+the G1→2 and fed to D2 to produce the final predictions.
+us suppose to have access to a synthetic domain, where
+labels can be easily obtained for both tasks. Unsupervised
+domain adaptation may be used in this synthetic to real
+scenario. However, we wish to go one step further, trying to
+answer this question: can we exploit the depth estimation
+task to boost the performance of semantic segmentation in
+the real domain? The answer is yes, thanks to our novel
+framework AT/DT. In AT/DT we first learn a mapping
+function in the synthetic domain between deep features of
+two networks trained for depth estimation and semantic
+segmentation. This mapping function captures the relation-
+ship between the two tasks. Once learned, we use the map-
+ping on depth features extracted from real samples to solve
+semantic segmentation in the real domain without the need
+of labels for it, thereby transferring knowledge across tasks
+and domains. To further improve performance, we propose
+two strategies aimed at increasing the transferability of the
+learned features, namely leveraging on a norm discrepancy
+alignment loss and an auxiliary task.
+
+A
+A
+L (A,YA)
+E1
+D
+B
+L (V,P)
+N1
+Training N1
+E2
+L, (V2, J2)
+N2
+Training N2
+E1
+LTr
+E2
+Training G1-2
+B
+Ei
+D
+Inference4
+Fig. 3. Features alignment strategies across tasks and domains. We train jointly the networks N1, N2 and a shared auxiliary decoder Daux. We
+train N1 to solve T1 on images from domains A and B using a supervised loss LT1 for T1 alongside a novel feature Norm Discrepancy Alignment
+loss LNDA which helps better aligning the features computed by N1 across the two domains. We train N2 using a supervised loss LT2 for T2 on
+images from B. Daux is trained to solve an auxiliary task Taux using the loss Laux and based on the features computed by E1 on images from A
+and B as well as by E2 on images from B.
+In the following sub-sections, we first describe the base
+AT/DT framework and then delineate its improved formu-
+lation which includes the norm discrepancy alignment loss
+and auxiliary task.
+3.1
+Notation
+We consider two tasks, T1 and T2, as well as two domains,
+A and B. We denote the images belonging to A and B as
+xA and xB, respectively. We have labels for T1 in A and B,
+denoted as yA
+1 and yB
+1 , respectively. On the other hand, we
+have labels for T2 only in A, denoted as yA
+2 . Our aim is to
+solve T2 in B, where we do not have supervision. We assume
+T1 and T2 to be both dense tasks, which can therefore be
+addressed by an encoder-decoder architecture. We denote as
+N1 and N2 two networks that solve T1 and T2, respectively.
+Each network Nk, k ∈ {1, 2} consists of an encoder Ek and
+a decoder Dk, such that Nk(x) = Dk(Ek(x)), x being the
+input image.
+3.2
+Across Tasks and Domains Transfer
+In
+our
+AT/DT
+framework
+we
+aim
+at
+learning
+the
+relationships between T1 and T2 through a neural network.
+This is achieved by 3 steps, each represented as a block in
+Figure 2:
+Training N1 and N2. We train N1 and N2 to solve
+T1 and T2. Since we assume supervision for T1 on both
+domains, N1 is trained with images from A and B. This
+enables N1 to learn a feature space shared across the two
+domains. N2, instead, is trained only on A. Both networks
+are trained with a specific supervised task loss LTk for Tk.
+Training G1→2. Considering only domain A, where we
+have supervision for both tasks, we then train a trans-
+fer network G1→2 to map the features computed by N1,
+f A
+1 = E1(xA), into those computed by N2, f A
+2 = E2(xA).
+Denoting the transferred features as f A
+1→2 = G1→2(f A
+1 ), we
+train the transfer network by minimizing the L2 loss:
+LT r = ||f A
+1→2 − f A
+2 ||2
+(1)
+Inference. Once G1→2 has been trained, we can ad-
+dress T2 in B by computing the features to solve T1,
+f B
+1 = E1(xB), transform them into features amenable to T2,
+f B
+1→2 = G1→2(f B
+1 ), and finally decode these features into
+the required dense output by D2:
+ˆyB
+2 = D2(f B
+1→2)
+(2)
+After presenting the base AT/DT framework, in the
+next sub-sections we will describe two strategies deployed
+to boost the feature alignment across domains and tasks.
+Figure 3 provides a detailed view of these two strategies
+which in our final proposed framework replace the initial
+steps of the training protocol (i.e., Training N1 and N2).
+3.3
+Feature Alignment Across Domains
+For the effectiveness of the approach delineated in subsec-
+tion 3.2, it is crucial that G1→2 can generalize well to the
+target unseen domain B even if trained only with data from
+the source domain A.
+The DA literature presents us with several ways to
+accomplish this. One may operate on the input space [27], on
+the feature space [23] or on the output space of the network
+[29]. In our setting, though, both input and output space of
+G1→2 are high dimensional latent spaces and, as reported
+in [29], unsupervised domain adaptation techniques tend to
+fail when applied to such spaces while addressing dense
+tasks. Yet, we can address the domain shift issue with a
+
+L (VA,JA)
+E1
+D1
+-NDA
+L (VB,JP)
+xn
+N1
+DB
+aux
+laux
+aux
+laux
+X
+y2
+xnp7
+aux
+Zaux
+L (V, J)
+N2
+Training N1 e N25
+Fig. 4. Two task transfer scenarios: depth-to-semantic on the left, the opposite on the right. First row: ground-truth depth and semantic segmentation
+maps; second row: corresponding edge maps. Red circles highlight information needed in the target task but missing in the source one.
+direct approach in the input space of G1→2, i.e., the feature
+space of N1, which is already shared between A and B
+due to the network being trained supervisedly with images
+from both domains. We leverage on the intuition that scene
+spatial priors are typically domain invariant in many adap-
+tation scenarios. We consider it as a reasonable assumption
+for several domain adaptation settings, where we select the
+source domain by considering visual similarities with the
+target domain. For instance, in autonomous driving scenar-
+ios we typically have cameras placed from a car viewpoint,
+and scenes are urban scenarios in both synthetic [9], [51]
+and real [10], [52], [53] datasets. Thus, if we consider the
+task of semantic segmentation in all datasets (synthetic and
+real) we typically find road pixels in the bottom part of the
+images and instead sky pixels in the top part of the images.
+To visualize this property we select a synthetic domain A
+CARLA [9] and a real domain B Cityscapes [10]. Then, we
+count for each pixel location the number of occurrences of
+each class. We show the result of this experiment in Figure 5,
+using a viridis colormap to display these occurrency maps
+for each class and for both domains A and B. We can clearly
+see that the maps have a structure similar across domains,
+e.g., building are concentrated in the top image regions.
+Leveraging this property, we propose to align more
+closely the features computed by E1 on the images from
+both domains, i.e., f A
+1
+and f B
+1 , by enforcing similarity of
+the L2 norms across channels at the same spatial loca-
+tion. Starting from features f A
+1
+and f B
+1
+of dimensionality
+H × W × C, where H, W and C are the height, width
+and number of channels of the feature maps, we calculate
+the L2 norm along the C axis and minimize the absolute
+difference at each spatial location i, j. Hence, our NDA
+(Norm Discrepancy Alignment) Loss is defined as follows:
+LNDA =
+1
+W × H
+H
+�
+i=1
+W
+�
+j=1
+���∥f A
+1i,j∥2 − ∥f B
+1i,j∥2
+���
+(3)
+3.4
+Feature Alignment Across Tasks
+While the NDA loss presented above aims at improving
+the generalization across domains of the feature mapping
+network G1→2, its effectiveness can be further improved by
+aligning features also across tasks. Accordingly, we conjec-
+ture that f1 features should capture as much information as
+possible on the details of the scene, even though some of
+this information may not be necessary to solve T1, because,
+when transferred by G1→2, such a richer representation
+could help to solve T2 more effectively. For this reason, while
+training N1 for T1, we train jointly an additional decoder,
+Daux, to solve an auxiliary task, Taux, aimed at enriching
+the learnt representation f1 . However, though multi-task
+learning of T1 and Taux could help to encode more detailed
+information into f1 features, it does not guarantee that
+the decoder D2, used at inference time on the features
+f1→2 transferred from T1 to T2, may effectively deploy this
+additional information if it has been trained only to solve
+T2 in isolation. This leads us to reckon that Daux should
+be trained jointly with N2 too, such that the additional
+information required to solve Taux may be incorporated also
+within the features f2 learnt by E2.
+Therefore, given auxiliary task labels yA
+aux and yB
+aux for
+A and B, we train N1 and N2 jointly with a single auxiliary
+decoder Daux using an auxiliary loss Laux. Purposely, we
+obtain auxiliary predictions from both encoders with the
+shared decoder Daux as ˆykaux = Daux(Ek(x)), k ∈ {1, 2}.
+Similarly to the simpler formulation of our framework pre-
+sented in subsection 3.2, to compute the auxiliary loss we
+feed images of both domains through E1, while we pass
+only images from A through E2. We do not pass images
+belonging to B through E2 while training Daux since this
+would be the only kind of supervision for E2 in B and it
+may skew E2 output to be more effective on Taux than on
+T2.
+3.5
+Overall N1 and N2 loss
+When training simultaneously N1 and N2, the overall loss
+is:
+
+6
+A
+B
+A
+B
+A
+B
+A
+B
+Road
+Sidewalk
+Wall
+Fence
+A
+B
+A
+B
+A
+B
+A
+B
+Person
+Pole
+Vegetation
+Vehicle
+A
+B
+A
+B
+A
+B
+Traffic Signs
+Building
+Sky
+Fig. 5. Spatial Priors Similarities Across Domains. Considered the semantic segmentation task, we compute the number of occurrences of each
+class at each pixel location for both domains. Domain A is CARLA, B is Cityscapes. We visualize the occurrence maps with a viridis colormap.
+L = λT1LT1(yA
+1 , ˆyA
+1 ) + λT1LT1(yB
+1 , ˆyB
+1 )
++λT2LT2(yA
+2 , ˆyA
+2 ) + λauxLaux(yA
+1aux, ˆyA
+1aux)+
+λauxLaux(yB
+1aux, ˆyB
+1aux) + λauxLaux(yA
+2aux, ˆyA
+2aux)+
+λNDALNDA(f A
+1 , f B
+1 )
+(4)
+4
+EXPERIMENTAL SETTINGS
+Tasks. We fix T1 and T2 to be monocular depth estimation
+and semantic segmentation, or vice versa. These two visual
+tasks can be addressed using the same encoder-decoder
+architecture, with changes needed only in the final layer.
+Semantic segmentation is solved by minimizing a pixel-
+wise cross entropy loss, monocular depth estimation by
+minimizing an L1 loss. We select edge detection as our
+Taux since it seems particularly amenable to improve
+the effectiveness of our framework in capturing and
+transferring important structural information that might
+otherwise be lost. Let us consider the case of T1 being depth
+estimation and T2 semantic segmentation. The features
+f1 needed to compute depth may ignore the boundaries
+between semantically distinct regions showing up at the
+same distance from the camera: in Figure 4 (left) this is
+the case, e.g., of the boundaries between legs or tyres
+and ground, as well as between street signs and poles.
+Therefore, even if fed to a perfect G1→2, f1 may not
+contain all the information needed to restore the semantic
+structure of the image. By solving jointly edge detection
+on the input image, instead, we force our N1 network to
+extract additional information that would not need to be
+captured should the learning objective be concerned with
+depth estimation only. Similarly, Figure 4 (right) highlights
+how depth discontinuities do not necessarily correspond
+to semantic boundaries, such that a network N1 trained
+in isolation to assign semantic labels to pixels may not
+need to learn information relevant to estimate the depth
+structure of the image. Besides, it is worth pointing out that
+edge detection can be solved using again the same decoder
+architecture as T1 and T2. Since the edge proxy-labels that
+we adopt are gray-scale images [6], in our experiments we
+implement the Laux loss introduced in subsection 3.4 as a
+standard L2 loss. In all our experiments we set λaux to 0.5,
+λNDA to 0.001, λT1 and λT2 to 1 to balance loss values.
+Datasets. We test the effectiveness of our method in
+an autonomous driving scenario. We set A and B to be
+a synthetic and a real dataset, respectively. The former
+consists of a collection of images generated with the Carla
+simulator [9], while the latter is the popular Cityscapes
+dataset [10]. We generated the Carla dataset mimicking
+the camera settings of the real scenes. We render 3500,
+500, and 1000 images for training, validation, and testing,
+respectively. For each image, we store the associated
+depth and semantic labels provided by the simulator. The
+Cityscapes dataset is a collection of 2975 and 500 images to
+be used for training and validation, respectively. As for our
+evaluation, we use the 500 Cityscapes validation images
+since test images are not equipped with labels. Moreover,
+as in Cityscapes only the semantic labels are provided,
+we use depth proxy-labels obtained with the SGM stereo
+algorithm [54], by filtering the erroneous predictions in the
+generated disparities with a left-right consistency check.
+This can be considered as an added value because it shows
+the ability to transfer knowledge when learning from noisy
+labels. Finally, we use a pre-trained1 state-of-the-art neural
+network [6] as an off-the-shelf edge detector to extract
+from the images belonging to A and B the edges used as
+proxy-labels to train Taux.
+Architecture. To solve each task, we use two dilated
+ResNet50 [55] as encoder and a stack of bilinear upsample
+plus convolutional layers as decoder. The encoder shrinks
+both input dimensions with a factor of 1/16, while the
+decoder upsamples the feature map until a prediction with
+the same spatial resolution as the input image is obtained.
+The two networks for T1 and T2 are identical, but for the
+final prediction layer, which is task dependent. The two
+previously defined encoders are also used to capture good
+features for edge detection, which is solved using Daux,
+that shares the same architecture as the decoders used in
+1. Neither A nor B belong to the training set of this network.
+
+7
+N1 and N2. G1→2 is a simple CNN made out of 6 pairs of
+convolutional and batch normalization layers with kernel
+size 3 × 3 which do not perform any downsampling or
+upsampling operation.
+Training and Evaluation Protocol. During the training
+phase of the transfer network G1→2, the model is evaluated
+on the validation set of Carla. Of course, it is possible that
+optimality on Carla does not translate into optimal per-
+formance on Cityscapes. Yet, we cannot use data from the
+target domain neither for hyper-parameters tuning nor for
+early stopping, because in our setting these data would not
+be available in any real scenario. Therefore, the Cityscapes
+validation set is only used at test time to measure the final
+performances of our framework method.
+Fig. 6. From left to right: RGB input image of domain A , depth prediction
+from N1, edges from f1, semantic segmentation from N2 and edges
+from f2. Task features f1 and f2 encode richer details than strictly
+needed to solve either tasks as we can recover all edges from both of
+them by Daux.
+Metrics. To evaluate the performance on the semantic
+segmentation task two metrics are used: pixel accuracy,
+shortened Acc. (i.e the percentage of pixels with a cor-
+rect predicted label) and Mean Intersection Over Union,
+shortened mIoU, as defined in [10]. To render these metrics
+comparable among the used datasets, we solve semantic
+segmentation on the 10 shared classes (Road, Sidewalk,
+Walls, Fence, Person, Poles, Vegetation, Vehicles, Traffic
+Signs, Building) plus the Sky category, which is defined as
+the set of points with infinite depth. Some of the Cityscapes
+classes are collapsed into one class: car and bicycle into
+vehicle, traffic signs and traffic light into traffic sign. The
+remaining categories of Cityscapes are instead ignored.
+When testing the depth estimation task, we report the
+standard metrics described in [57]: Absolute Relative Error
+(Abs Rel), Square Relative Error (Sq Rel), Root Mean Square
+Error (RMSE), logarithmic RMSE and δ1, δ2 and δ3 accuracy
+scores. Each δα is obtained by computing, for each pixel
+of the input image, the maximum among ratio and inverse
+ratio between the predicted value and the ground-truth. δα
+represents the percentage of pixels whose such ratio is lower
+than 1.25α.
+5
+EXPERIMENTAL RESULTS
+We provide results for two different settings: transferring
+features from depth estimation to semantic segmentation
+(subsection 5.1) as well as from semantic segmentation to
+depth estimation (subsection 5.2).
+In both scenarios, as already mentioned, we used edge
+detection as auxiliary task, motivated by the idea that either
+semantic segmentation and depth estimation can benefit
+from edge information. Figure 6 shows that with our multi-
+task learning protocol we are able to restore all the details
+of the scene from both f1 and f2, proving that N1 and
+N2 have indeed learned to encode into their features richer
+information than that strictly needed to solve T1 and T2.
+5.1
+Depth to Semantics
+In this setup, denoted as Dep → Sem, the goal of our
+framework is to transform depth features into semantic
+segmentation features. This mapping is learned using Carla
+as domain A and Cityscapes as domain B. We report results
+in Table 1: the first row shows results obtained with no
+adaptation (i.e., training N2 on Carla and testing it directly
+on Cityscapes), while from the second row we can see that
+our final framework yields 51.28% mIoU and 87.57% Acc
+with an improvement of +12.48% and +8.99% wrt to the
+baseline.
+Even though AT/DT is the first work to address the
+across tasks and domains scenario, we compare it against
+a related work, ZDDA [56], which also leverage auxiliary
+data from a different tasks to perform domain adaptation.
+We apply it in our setup using as the ”Source” and ”Target”
+domains Carla and Cityscapes respectively. We address
+the Dep → Sem scenario using depth maps as ”task-
+irrelevant” data. We skip the last sensor fusion step (Step
+3) because it was not applicable in our scenario since we
+do not have task-irrelevant data at test time, and thus we
+stop training after the adaptation step (Step 2). We report
+results of this alternative approach in the second row of
+Table 1. As we can notice, ZDDA is effective in our scenario
+and achieves better performance compared to the baseline.
+However, AT/DT obtains much better results, surpassing
+ZDDA in all metrics. This is not surprising since ZDDA
+focus on extracting features only from task-irrelevant data,
+which can be sub-optimal for the relevant task as these
+data do not provide the same amount of information as the
+task-relevant data, e.g., features extracted only from depth
+images would not contain several useful information for
+semantic segmentation such as colors or textures.
+Furthermore, as we are transferring features from an-
+other task, it is worth trying to investigate on the upper
+bound in performance due to the inherent transferability
+of the features between the two tasks. Purposely, we train
+G1→2 using only Cityscapes to learn a mapping function in
+a supervised fashion as explained in subsection 3.4 on B and
+test on the validation set of B. These results are shown in the
+third row of the table (denoted as Transfer Oracle): given a
+transfer architecture, there seems to be an upper bound in
+performance due to the nature of the two tasks, which in
+the considered setting amounts to a 58.5% mIoU. Thus, our
+proposal exhibit a gap wrt the Transfer Oracle that is only
+about -7.2% mIoU. We also report the performance of N2
+trained on B and tested on B, i.e., the absolute upper bound
+in performance (last row of the table, denoted as Oracle).
+Some qualitative results dealing with the Dep → Sem
+scenario are depicted in Figure 7. It is possible to appreciate
+the overall improvement of our method wrt the baseline,
+either in flat areas (e.g., roads, sidelwalks and walls), objects
+shapes (e.g., cars and persons) and fine-grained details (e.g.,
+poles and traffic signs).
+
+.8
+TABLE 1
+Experimental results of Dep → Sem scenario. Baseline stands for N2 trained on A and tested on B, Transfer Oracle represents G1→2 trained
+only on B, Oracle refers to N2 trained and tested on B. Best results highlighted in bold.
+A
+B
+Method
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+Carla CS
+Baseline
+78.99 38.81
+1.34
+5.80
+24.02 24.47 71.98 52.23
+5.57
+65.17 59.10
+38.86
+78.58
+Carla CS
+ZDDA [56]
+85.93 41.28
+4.62
+8.63
+38.80 25.94 72.78 58.37 18.44 73.74 78.16
+46.06
+82.82
+Carla CS
+AT/DT
+90.57 48.46
+7.37
+12.27 41.16 31.90 81.96 72.77 23.44 77.85 76.33
+51.28
+87.57
+CS
+CS Transfer Oracle 89.69 48.05 11.46 29.58 59.68 35.84 85.83 85.57 34.03 78.17 85.54
+58.50
+88.84
+-
+CS
+Oracle
+96.74 78.28 29.26 40.78 72.39 51.28 90.69 91.94 58.92 86.33 89.23
+71.44
+93.90
+Fig. 7. Qualitative results of the Dep → Sem scenario. From left to right: RGB image, ground-truth, baseline trained only on domain A, ours.
+5.2
+Semantics to Depth
+In this setup, which we define as Sem → Dep, the goal
+of our framework is to transform semantic features into
+depth features. This mapping is learned using Carla as
+domain A and Cityscapes as domain B, as done for the
+Dep → Sem scenario. Results are reported in Table 2.
+Similarly to the Dep → Sem scenario, in the first row
+we show results with no adaptation (i.e., our baseline),
+while the third row presents the ones obtained with our
+framework. Also for this setup we report performances of
+ZDDA [56] (second row), in which we use semantic maps as
+task-irrelevant data. We can see that ZDDA achieves slight
+better performance of the baseline in 5 metrics out of 7, but
+still inferior to our approach. Moreover, we report results
+from the Transfer Oracle and the Oracle, implemented as
+described for the Dep → Sem scenario. It is possible to
+appreciate that our framework outperforms the baseline on
+6 out of 7 metrics, closing remarkably the gap with the
+practical upper bound of the Transfer Oracle. In Figure 8, we
+show some qualitative results of the Sem → Dep scenario.
+While predictions look quite noisy in the background, we
+can see a good improvement in the foreground area thanks
+to our method. Shapes are recovered almost perfectly, both
+for big and small objects, even with difficult subjects like
+the crowd in the bottom row. It is also worth pointing out
+that the depth predictions yielded by our method turn out
+much smoother than the ones produced by the baseline and
+generally less noisy than the ground-truth that, as explained
+in section 4, consists of proxy-labels computed with SGM
+[54].
+6
+ABLATION STUDIES
+In the following sections, we study the effectiveness of the
+key design choices behind our proposal.
+6.1
+Contribution of Taux and NDA Loss
+We start by studying the effect of introducing in our
+framework the auxiliary task and the NDA loss, analyzing
+their contribution when used separately as well as when
+combined together. The second and third row of Table 3
+report the results obtained in the Dep → Sem setting by
+integrating in our method either the auxiliary task (i.e., edge
+detection) or the NDA loss, respectively. We can see that
+both design choices bring in an improvement of about +2%
+in terms of mIoU with respect to the base AT/DT framework
+(first row). Moreover, the last row of the table shows that
+the auxiliary edge detection task and the NDA loss turn out
+complementary because, when combined together, they can
+provide an overall improvement of +3.34% mIoU.
+Figure 9 presents some zoomed-in qualitative results: we
+can see that, even if the base version of AT/DT already
+produces satisfactory results at a coarse level, the complete
+version of our framework can produce much more accurate
+predictions, especially regarding small details, such as poles,
+traffic signs and car outlines.
+
+9
+TABLE 2
+Experimental results of Sem → Dep scenario. Baseline stands for N2 trained on A and tested on B, Transfer Oracle represents G1→2 trained
+only on B, Oracle refers to N2 trained and tested on B. Best results highlighted in bold.
+Lower is better
+Higher is better
+A
+B
+Method
+Abs Rel Sq Rel RMSE RMSE log
+δ1
+δ2
+δ3
+Carla CS
+Baseline
+0.7398
+15.169 14.774
+0.641
+0.406 0.650 0.781
+Carla CS
+ZDDA [56]
+0.5206
+7.5491 13.347
+0.633
+0.345 0.638 0.858
+Carla CS
+AT/DT
+0.3928
+4.9094 12.363
+0.444
+0.372 0.757 0.923
+CS
+CS Transfer Oracle
+0.2210
+2.2962
+9.032
+0.275
+0.669 0.914 0.972
+-
+CS
+Oracle
+0.1372
+1.6214
+8.566
+0.244
+0.816 0.938 0.976
+Fig. 8. Qualitative result of the Sem → Dep scenario. From left to right: RGB image, ground-truth, baseline network trained only on domain A, ours.
+TABLE 3
+Ablation study in the Dep → Sem scenario. Best results highlighted in bold. Aux refers to the framework trained with the auxiliary task. NDA refers
+to the framework trained with our NDA loss.
+A
+B
+Aux
+NDA
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+Carla CS
+89.95 46.77 5.16 10.21 28.93 28.92 77.50 71.37 19.24 75.29 75.12 48.04 85.90
+Carla CS ✓
+90.12 48.90 4.18 11.63 37.40 31.98 82.34 71.50 15.11 78.04 80.61 50.16 87.21
+Carla CS
+✓ 91.21 50.16 5.14 13.78 36.99 32.10 77.72 73.38 23.47 76.67 72.67 50.30 86.77
+Carla CS ✓ ✓ 90.57 48.46 7.37 12.27 41.16 31.90 81.96 72.77 23.44 77.85 76.33 51.28 87.57
+Fig. 9. Zoomed results in a Dep → Sem scenario. From left to right: base AT/DT without edge and NDA, our proposed method, ground-truth. We
+notice how, unlike base AT/DT, our method is able to recover the fine-grained details of the scene.
+
+10
+6.2
+Effectiveness of edge detection as auxiliary task
+In this section, we show empirically that in our framework
+the choice of the proper auxiliary task is key to performance.
+In both the Dep → Sem and the Sem → Dep scenarios,
+we propose to use edge detection as auxiliary task because
+it captures information about the shapes of the objects in the
+input images and allows for straightforward computation of
+proxy-labels. To validate this design choice, we tested our
+framework in the Dep → Sem setting, using Daux to recon-
+struct the input images both from f1 and f2, i.e., the classical
+autoencoder setting (results in Table 4). Interestingly, using
+image reconstruction as auxiliary task results in an mIoU
+score almost identical to the base AT/DT. We consider that
+the autoencoder task is guided by a reconstruction loss
+which makes no distinction between the pixels of the input
+image: such supervision cannot guide effectively f1 and f2
+to encapsulate the high-frequency components of the image
+that are needed to predict the fine-grained details of the
+scene, which is instead obtained by adopting edge detection
+as auxiliary task.
+6.3
+Auxiliary tasks as source tasks
+The main difference between a source and an auxiliary
+task is that the auxiliary task alone cannot provide enough
+information to solve T2, but it is useful to enrich T1 features
+and align feature content across tasks. To better support
+our claims, we investigated AT/DT behaviour when using
+auxiliary tasks Taux as source tasks T1 and semantic seg-
+mentation as target task T2. The results of these experiments
+are reported in Table 5. All rows of the table show results of
+the base AT/DT i.e., trained without Laux and LNDA losses.
+As we can notice, using as source task T1 a standard image-
+reconstruction (row 1, autoencoder) or an edge detection
+(row 2) lead to much worse results than using depth esti-
+mation (row 3). We argue that features extracted by N1 for
+these tasks do not contain enough information to perform
+semantic segmentation, which are yet contained in features
+for depth estimation. Similar finding were also made by
+Taskonomy [1], in which they show that edge detection and
+image reconstruction (aka autoencoder) are less correlated
+to semantic segmentation than depth estimation. On the
+contrary, we have shown that Edge Detection can be a
+good auxiliary task in the Dep → Sem scenario since it
+can enrich depth features with missing edges useful for
+semantic segmentation and it can increase transferability
+aligning depth and semantic features.
+6.4
+Importance of simultaneous training of N1, N2 and
+Daux
+In our experiments we use edge detection as auxiliary task
+and train a shared decoder Daux to reconstruct the edges of
+the input image from the features extracted by both E1 and
+E2. In fact, we argue that this procedure should force E1 to
+encode into the extracted features also edge information that
+may be not necessary to solve T1 but that may be relevant for
+T2. Besides, we believe that simultaneous training of N1, N2
+and Daux is crucial to encourage features coming from E1
+and E2 to represent edge information in a similar manner,
+making it easier to learn G1→2.
+In Table 6 we report the results concerning the ablation
+study conducted to validate these intuitions. We consider
+the Dep → Sem scenario using the Carla dataset as domain
+A and Cityscapes as domain B. The four rows of the table
+deal with the following training schemes:
+1)
+The base AT/DT (i.e., without Taux and NDA loss)
+as baseline.
+2)
+We first train N1 and Daux on both A and B. Then,
+we train N2 on A. Finally, we train G1→2 on features
+extracted by E1 and E2 on domain A.
+3)
+We train N1 and a first D1
+aux on both A and B. Then,
+we train N2 and a second D2
+aux on A. Finally, we
+train G1→2 on features extracted by E1 and E2 on
+domain A
+4)
+Our proposed method, which trains N1, N2 and a
+shared Daux simultaneously.
+The introduction of edge detection as auxiliary task helps
+in every scenario. In fact, if we use Daux only while training
+N1 (second row), we already see an increase of 0.6% in
+the overall mIoU. We believe that this is explained by the
+presence of edge details (not strictly necessary to solve
+T1 but relevant for T2) in the features extracted by E1.
+However, G1→2 may experience difficulties in adapting f1
+into f2 if edge information is not explicitly present in f2.
+This is confirmed by the results in the third row of the table,
+where an additional increase of 1.3% in the overall mIoU is
+attained by using two different Daux (one during training of
+N1 and one during training of N2). Finally, the best results
+in terms of mIoU and Acc are achieved by our method, i.e.,
+when training N1, N2 and a shared Daux simultaneously.
+This vouches for the benefit of encoding in a similar manner
+the edge information in f1 and f2 in order to enforce feature
+alignment across tasks.
+6.5
+Alignment strategies for N1
+An alternative approach to align N1 features between do-
+mains to ease the transfer process and favor the generaliza-
+tion of G1→2 consists in leveraging on the widely adopted
+adversarial training in feature space. In our setting, this
+can be obtained by adding a critic that must discriminate
+whether the features produced by E1 come from A or B.
+Thus, the encoder E1 not only has to learn a good feature
+space for its task, but it is also asked to fool the critic. After-
+wards, we can proceed to learn a mapping function G1→2
+among tasks as usual. In Table 7 we compare this standard
+DA methodology to our NDA loss. Adversarial training
+(second row) does not introduce significant improvements
+with respect to not performing DA for T1 (i.e., base AT/DT,
+first row), while constraining the features extracted by E1
+in a norm aligned space (third row) significantly increases
+both performance metrics with respect to the baseline. Our
+intuition is that, although adversarial training can be useful
+for domain alignment, it alters the learned feature space
+with the goal of fooling the critic and this training objective
+can lead to worse performances on the current task. Our
+NDA loss, on the other hand, acts as a regularizer that
+favors the learning of an homogeneous latent space across
+the domains involved in our experiments, improving the
+generalization capability of the transfer network without
+
+11
+TABLE 4
+Comparison between autoencoder and edge detection as auxiliary tasks in the Dep → Sem scenario. Best results highlighted in bold.
+Taux
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+None
+89.95 46.77 5.16 10.21 28.93 28.92 77.50 71.37 19.24 75.29 75.12
+48.04
+85.90
+Autoencoder
+90.68 50.12 7.45
+9.08
+31.40 29.43 78.72 68.51 12.95 74.67 75.68
+48.07
+86.31
+Edge detection 90.12 48.90 4.18 11.63 37.40 31.98 82.34 71.50 15.11 78.04 80.61
+50.16
+87.21
+TABLE 5
+Auxiliary tasks as source tasks in the Dep → Sem scenario. Best results highlighted in bold.
+Taux as T1
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+Autoencoder
+60.24 19.33 1.67
+1.67
+4.12
+8.00
+33.15 10.49
+0.69
+17.89 62.66
+19.99
+52.91
+Edge Detection 63.82 16.60 0.67
+1.37
+6.55
+10.26 47.62
+4.42
+0.11
+33.90 38.87
+20.38
+58.33
+Depth
+89.95 46.77 5.16 10.21 28.93 28.92 77.50 71.37 19.24 75.29 75.12
+48.04
+85.90
+TABLE 6
+Ablation study on the importance of simultaneous training of the T1, T2, and the auxiliary task. Best results highlighted in bold. See text for a
+detailed explanation of the training protocol used in each row.
+method
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+base AT/DT
+89.95 46.77 5.16 10.21 28.93 28.92 77.50 71.37 19.24 75.29 75.12
+48.04
+85.90
+Separate (N1 + edge), N2
+87.24 43.30 3.08 10.17 41.77 29.04 81.81 72.35 16.58 77.10 73.10
+48.69
+85.89
+Separate (N1 + edge), (N2 + edge) 88.83 47.31 7.10
+8.59
+44.53 30.99 83.24 73.54 18.05 78.10 69.66
+49.99
+86.72
+Simultaneous (N1 + N2 + edge)
+90.12 48.90 4.18 11.63 37.40 31.98 82.34 71.50 15.11 78.04 80.61
+50.16
+87.21
+degrading the performances in the single tasks. Then, from
+the third to the fifth row, we compare our NDA loss with
+another strategy, LargerNorm [24], that also align features
+across domains operating on the feature norms. They show
+that features are more transferable across domains if we
+constrain feature norms to be equal to an arbitrary large
+number. We notice that the method is very sensible to the
+norm value, and it could be hard to select without using
+target labels. When using an appropriate norm value (25,
+fourth row), the method achieves a slight improvement over
+the baseline without alignment. However, since it just force
+all features globally to be a large number, it is not well-
+suited for tasks in which we have a spatial dimensions
+such as semantic segmentation. Moreover, in the sixth row,
+we experiment also with a more recent adversarial loss
+formulation, Asymmetric Adv. [58], which preserve discrim-
+inability while performing domain alignment by chang-
+ing only target features instead of both source and target
+ones. However, we notice that this method is achieving
+the worst results among feature alignment strategies, even
+worse than the baseline. Our motivation is that aligning
+feature distribution in such a high dimensional feature space
+with a spatial structure might be too difficult to achieve by
+only changing target features. Finally, we notice that NDA
+achieves the best performance probably because it only align
+features norm rather than the whole marginal distribution,
+which is an easier goal that can be achieved also in high-
+dimensional space. Moreover, NDA operates at each spatial
+location independently rather than globally, exploiting the
+spatial priors similarity across domains, reaching better
+performances.
+6.6
+Aligning N2 features
+We tried to perform feature alignment across domains also
+on the features f2 extracted by E2, either by deploying
+adversarial training or imposing our NDA loss. The idea
+is to favor the generalization of G1→2 by making more
+homogeneous not only its input space (i.e., the features
+produced by E1, aligned with our NDA loss), but also its
+output space, i.e., the features produced by E2. However,
+the setting is not completely symmetric: when learning E2,
+we do not have supervision available for B, and the only
+loss shaping the feature space for its images would be the
+alignment loss. We report results of this ablation study in
+Table 8 and discuss them below.
+In the first row, we report the results provided by the
+base AT/DT (without LNDA and Laux). In the following
+two rows, we show results obtained by an adversarial (row
+2) and an asymmetric adversarial [58] (row 3) training
+
+12
+TABLE 7
+Comparison between NDA loss and other strategies to align E1 features. Best results highlighted in bold.
+E1 Align.
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+None
+89.95 46.77 5.16 10.21 28.93 28.92 77.50 71.37 19.24 75.29 75.12
+48.04
+85.90
+Adv.
+89.89 46.01 4.22 11.89 38.20 30.65 77.00 63.68 12.99 74.35 81.16
+48.19
+85.42
+LargerNorm [24] (1)
+38.37 24.17 0.56
+3.66
+10.50 23.04 52.61
+9.41
+3.42
+52.64 10.54
+20.81
+51.49
+LargerNorm [24] (25)
+86.82 42.23 1.94
+9.00
+34.92 29.02 76.39 70.97 23.38 74.97 80.00
+48.15
+84.62
+LargerNorm [24] (500) 78.94 31.25 2.53
+6.00
+22.08 20.55 68.18 26.21
+4.35
+62.28 63.53
+35.08
+76.53
+Asymmetric Adv. [58]
+86.69 38.57 5.92
+5.72
+27.43 22.91 70.81 70.71
+7.86
+72.15 75.18
+44.00
+83.38
+NDA
+91.21 50.16 5.14 13.78 36.99 32.10 77.72 73.38 23.47 76.67 72.67
+50.30
+86.77
+TABLE 8
+Results of aligning output space of E2 in a Dep → Sem scenario. Best results highlighted in bold.
+E2 Align.
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+None
+89.95 46.77 5.16 10.21 28.93 28.92 77.50 71.37 19.24 75.29 75.12
+48.04
+85.90
+Adv.
+89.36 46.03 5.59
+8.22
+36.45 25.44 75.15 72.29 12.69 74.12 75.79
+47.38
+85.31
+Asymmetric Adversarial [58] 87.90 42.81 7.64
+8.44
+26.02 29.11 72.54 69.01 24.01 71.71 70.42
+46.33
+83.61
+NDA
+44.94 23.82 3.81
+2.09
+30.74 24.21 42.08 68.84 11.69 35.67 11.10
+27.18
+56.17
+TABLE 9
+Results of aligning output space of D2 in a Dep → Sem scenario. Best results highlighted in bold.
+D2 Align.
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+None
+89.95 46.77 5.16 10.21 28.93 28.92 77.50 71.37 19.24 75.29 75.12
+48.04
+85.90
+Adv.
+87.48 45.73 0.63
+2.12
+26.22 26.39 61.40 66.92 12.97 66.39 74.77
+42.82
+81.87
+TABLE 10
+Results of aligning input and/or output space of G1→2 in a Dep → Sem scenario. Best results highlighted in bold.
+Input Align. Output Align.
+Road
+Sidewalk
+Walls
+Fence
+Person
+Poles
+Vegetation
+Vehicles
+Tr. Signs
+Building
+Sky
+mIoU
+Acc
+-
+NDA
+42.97 19.60 2.31
+1.36
+4.21
+15.74 18.42 11.77
+7.19
+36.72 38.99
+18.12
+43.63
+-
+Adv
+90.80 48.91 6.16 11.84 35.32 30.29 78.78 71.17 18.51 75.66 75.03
+49.32
+86.43
+Asymmetric Adv. [58] 85.49 40.70 4.94 10.49 34.02 30.26 76.31 70.30 17.07 74.30 72.94
+46.99
+83.86
+-
+NDA + Adv
+91.03 48.93 6.14 12.24 35.91 31.05 77.93 70.28 16.65 75.50 74.47
+49.10
+86.28
+-
+Adv D2
+90.20 47.54 5.92 11.76 37.03 29.52 77.98 72.42 19.28 75.82 77.03
+49.50
+86.28
+NDA
+Adv
+90.67 49.49 5.54 12.29 36.73 28.49 78.28 70.19 22.05 76.47 76.35
+49.69
+86.73
+NDA
+-
+91.21 50.16 5.14 13.78 36.99 32.10 77.72 73.38 23.47 76.67 72.67
+50.30
+86.77
+on the features f2, using the same procedures described
+in the previous sub-section for f1. We can observe that,
+not only both adversarial trainings does not improve (like
+adversarial training applied to E1), but they even decrease
+the overall mIoU compared to the baseline. Finally, in the
+fourth row, we report the results obtained by our NDA loss
+on f2: the NDA loss destroys the feature space of T2 when
+applied in this context, as vouched by the drop of 20% in
+the overall mIoU wrt to base AT/DT.
+During AT/DT inference, we use also D2 to yield the
+final task predictions. Nevertheless, D2 has been trained
+only on A, thus its performance may be harmed when
+using B images. Thus, we ran an additional test reported in
+Table 9. Following [29] we train N2 (i.e., E2 and D2) using
+an adversarial loss on the D2 output space, thus making
+D2 aware of B. Then, we train G1→2 to map features of
+E1 into features of E2, and during inference we employ the
+previously trained decoder D2 to produce the final outputs
+reporting the results in row Adv.. We notice a clear drop
+in performance w.r.t. base AT/DT (row None), i.e. AT/DT
+trained without LNDA and Laux.
+We formulate the following hypothesis to explain the
+
+13
+above results: all adversarial trainings and NDA loss try
+to align f A
+2
+and f B
+2 . While f A
+2
+are shaped also by the su-
+pervision of T2, f B
+2 evolve only according to the additional
+loss we impose, as we do not have supervision for T2 on
+B. However, E2 is shared across domains, and therefore
+may be pushed to produce worse representations for both
+domains while it tries to accomplish the adversarial objec-
+tives or the NDA loss minimization for B. If this happens,
+mappings learned by G1→2 from f A
+1 to f A
+2 will hallucinate
+worse features for T2 on B. To understand why adversarial
+trainings leads to small decreases in performances com-
+pared to the use of NDA loss, we ought to consider that
+adversarial training implies a discriminator that cannot be
+easily fooled by totally degenerated features, while, without
+any additional constrain from task supervision, the NDA
+loss may yield totally collapsed representation.
+6.7
+Aligning G1→2 features
+Although feature alignment does not turn out beneficial
+when training N2, one may still expect to obtain better
+hallucinated features if the representations obtained when
+transferring f A
+1 and f B
+1 are aligned. We empirically found
+out that even though output space aligning strategies de-
+ployed when training G1→2 can lead to improvements in
+performance, input space alignment using our NDA loss
+deployed when training N1 is more effective. Moreover,
+combining input and output space alignment techniques
+does not lead to further improvements. We performed this
+ablation study in the Dep → Sem scenario using Carla as
+A and Cityscapes as B. The results of these experiments are
+reported in Table 10.
+First, we applied our NDA loss to the output-space of
+G1→2. Similarly to what discussed in the previous section,
+we notice that, without supervision on B, the representa-
+tions transformed from G1→2 while minimizing the NDA
+loss yield a drastic drop in the framework performance
+(row 1). We also tried to align the output space features by
+training G1→2 alongside a discriminator in an adversarial
+fashion. We wanted to fool the discriminator in order to
+generate indistinguishable features from A or B. We notice
+that this strategy allows us to reach good overall perfor-
+mances with a 49.32 mIoU on Cityscapes (second row).
+Moreover, we thought that, as adversarial training provides
+a supervision on B, using the NDA loss in combination with
+the adversarial loss could avoid producing degenerated
+features for B while reaching a better overall alignment
+between A and B. However, we notice that the combination
+of the two losses leads us to slightly worse results than
+adversarial training alone (rows 2 vs 3). Furthermore, since
+using an adversarial loss on the output space of G1→2 lead
+us to good overall performances, we tested it in combination
+with the best input space alignment from Table 7, i.e. NDA
+loss applied when training N1. However, the combination
+of these two methods achieves worse performance than
+using only the NDA loss on input space (rows 6 vs 7).
+Finally, we also experimented a different alignment strategy
+for the G1→2 output space. Instead of directly applying
+adversarial loss in E2 feature space, we apply adversarial
+loss in D2 output space while training G1→2. As discussed
+in [29], output space is easier to align than feature space for
+several reasons: i) the scene semantic structure is typically
+similar across domains ii) the feature space encode many
+information such as color, light, textures iii) the feature
+space has higher dimensions. By aligning D2 output space
+we indirectly influence also E2 features making them more
+domain aligned. During training, we keep D2 frozen and
+we update only G1→2 weights. Also in this case, if compare
+this methodology with simply using LNDA alone (row 6 vs
+row 7), it achieves worse results.
+7
+CONCLUDING REMARKS
+We have introduced a framework to transfer knowledge
+between different tasks by learning an explicit mapping
+function between deep features. This mapping function can
+be parametrized by a neural network and show interesting
+generalization capabilities across domains. To further ame-
+liorate performance we have proposed two novel feature
+alignment strategies. At a domain level, we showed that
+the transfer function presented in our framework can be
+boosted by making its input space more homogeneous
+across domains with our simple yet effective NDA loss.
+At a task level, instead, we reported how deep features
+extracted for different tasks can be enriched and aligned
+with the introduction of a shared auxiliary task, which
+we implemented as edge detection in our experiments. We
+reported good results in the challenging synthetic to real
+scenario while transferring knowledge between the seman-
+tic segmentation and monocular depth estimation tasks.
+Our proposal is complementary to the whole domain
+adaptation literature and might be integrated with it. While
+DA directly applied to the learned feature space does not
+seems effective (see Table 8) more modern techniques either
+try to align the prediction in the final label space [29] or
+rely on self-ensembling for pseudo labeling [59]. We plan to
+incorporate these promising direction into our framework
+as part of future developments.
+REFERENCES
+[1]
+A. R. Zamir, A. Sax, W. Shen, L. J. Guibas, J. Malik, and S. Savarese,
+“Taskonomy: Disentangling task transfer learning,” in Proceedings
+of the IEEE Conference on Computer Vision and Pattern Recognition,
+2018, pp. 3712–3722.
+[2]
+A. R. Zamir, A. Sax, N. Cheerla, R. Suri, Z. Cao, J. Malik, and
+L. J. Guibas, “Robust learning through cross-task consistency,”
+in Proceedings of the IEEE/CVF Conference on Computer Vision and
+Pattern Recognition, 2020, pp. 11 197–11 206.
+[3]
+M. Wang and W. Deng, “Deep visual domain adaptation: A
+survey,” Neurocomputing, vol. 312, p. 135–153, Oct 2018. [Online].
+Available: http://dx.doi.org/10.1016/j.neucom.2018.05.083
+[4]
+P. Z. Ramirez, A. Tonioni, S. Salti, and L. D. Stefano, “Learning
+across tasks and domains,” in Proceedings of the IEEE International
+Conference on Computer Vision, 2019, pp. 8110–8119.
+[5]
+P. Z. Ramirez, A. Tonioni, and L. Di Stefano, “Exploiting semantics
+in adversarial training for image-level domain adaptation,” in
+2018 IEEE International Conference on Image Processing, Applications
+and Systems (IPAS).
+IEEE, 2018, pp. 49–54.
+[6]
+X. Soria, E. Riba, and A. Sappa, “Dense extreme inception network:
+Towards a robust cnn model for edge detection,” in The IEEE
+Winter Conference on Applications of Computer Vision (WACV ’20),
+2020.
+[7]
+S.
+Xie
+and
+Z.
+Tu,
+“Holistically-nested
+edge
+detection,”
+CoRR,
+vol.
+abs/1504.06375,
+2015.
+[Online].
+Available:
+http:
+//arxiv.org/abs/1504.06375
+
+14
+[8]
+Y. Wang, X. Zhao, Y. Li, and K. Huang, “Deep crisp boundaries:
+From boundaries to higher-level tasks,” IEEE Transactions on
+Image Processing, vol. 28, no. 3, p. 1285–1298, Mar 2019. [Online].
+Available: http://dx.doi.org/10.1109/TIP.2018.2874279
+[9]
+A. Dosovitskiy, G. Ros, F. Codevilla, A. Lopez, and V. Koltun,
+“CARLA: An open urban driving simulator,” in Proceedings of the
+1st Annual Conference on Robot Learning, 2017, pp. 1–16.
+[10] M. Cordts, M. Omran, S. Ramos, T. Rehfeld, M. Enzweiler, R. Be-
+nenson, U. Franke, S. Roth, and B. Schiele, “The cityscapes dataset
+for semantic urban scene understanding,” in The IEEE Conference
+on Computer Vision and Pattern Recognition (CVPR), June 2016.
+[11] F. Zhuang, Z. Qi, K. Duan, D. Xi, Y. Zhu, H. Zhu, H. Xiong,
+and Q. He, “A comprehensive survey on transfer learning,” arXiv
+preprint arXiv:1911.02685, 2019.
+[12] J. Yosinski, J. Clune, Y. Bengio, and H. Lipson, “How transferable
+are features in deep neural networks?” in Advances in neural
+information processing systems, 2014, pp. 3320–3328.
+[13] J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei, “Im-
+agenet: A large-scale hierarchical image database,” in 2009 IEEE
+conference on computer vision and pattern recognition.
+Ieee, 2009, pp.
+248–255.
+[14] J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, “You only look
+once: Unified, real-time object detection,” in Proceedings of the IEEE
+conference on computer vision and pattern recognition, 2016, pp. 779–
+788.
+[15] S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards
+real-time
+object
+detection
+with
+region
+proposal
+networks,”
+IEEE Transactions on Pattern Analysis and Machine Intelligence,
+vol. 39, no. 6, p. 1137–1149, Jun 2017. [Online]. Available:
+http://dx.doi.org/10.1109/TPAMI.2016.2577031
+[16] K. He, G. Gkioxari, P. Dollar, and R. Girshick, “Mask r-cnn,” 2017
+IEEE International Conference on Computer Vision (ICCV), Oct 2017.
+[Online]. Available: http://dx.doi.org/10.1109/ICCV.2017.322
+[17] W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y. Fu,
+and A. C. Berg, “Ssd: Single shot multibox detector,” in European
+conference on computer vision.
+Springer, 2016, pp. 21–37.
+[18] A. Pal and V. N. Balasubramanian, “Zero-shot task transfer,” in The
+IEEE Conference on Computer Vision and Pattern Recognition (CVPR),
+June 2019.
+[19] B. Gong, Y. Shi, F. Sha, and K. Grauman, “Geodesic flow kernel for
+unsupervised domain adaptation,” in Computer Vision and Pattern
+Recognition (CVPR), 2012 IEEE Conference on. IEEE, 2012, pp. 2066–
+2073.
+[20] M. Long, Y. Cao, J. Wang, and M. Jordan, “Learning transferable
+features with deep adaptation networks,” in Proceedings of the 32nd
+International Conference on Machine Learning, ser. Proceedings of
+Machine Learning Research, vol. 37.
+PMLR, 2015, pp. 97–105.
+[21] Y. Ganin and V. Lempitsky, “Unsupervised domain adaptation by
+backpropagation,” in International Conference on Machine Learning,
+2015, pp. 1180–1189.
+[22] Y. Ganin, E. Ustinova, H. Ajakan, P. Germain, H. Larochelle,
+F.
+Laviolette,
+M.
+Marchand,
+and
+V.
+Lempitsky,
+“Domain-
+adversarial training of neural networks,” The Journal of Machine
+Learning Research, vol. 17, no. 1, pp. 2096–2030, 2016.
+[23] E. Tzeng, J. Hoffman, K. Saenko, and T. Darrell, “Adversarial
+discriminative domain adaptation,” in Computer Vision and Pattern
+Recognition (CVPR), 2017.
+[24] R. Xu, G. Li, J. Yang, and L. Lin, “Larger norm more transferable:
+An adaptive feature norm approach for unsupervised domain
+adaptation,” in Proceedings of the IEEE International Conference on
+Computer Vision, 2019, pp. 1426–1435.
+[25] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley,
+S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial
+nets,” in Advances in neural information processing systems, 2014, pp.
+2672–2680.
+[26] J.-Y. Zhu, T. Park, P. Isola, and A. A. Efros, “Unpaired image-to-
+image translation using cycle-consistent adversarial networks,” in
+The IEEE International Conference on Computer Vision (ICCV), Oct
+2017.
+[27] K. Bousmalis, N. Silberman, D. Dohan, D. Erhan, and D. Krishnan,
+“Unsupervised pixel-level domain adaptation with generative
+adversarial networks,” 2017 IEEE Conference on Computer Vision
+and Pattern Recognition (CVPR), Jul 2017. [Online]. Available:
+http://dx.doi.org/10.1109/CVPR.2017.18
+[28] P. Isola, J.-Y. Zhu, T. Zhou, and A. A. Efros, “Image-to-image
+translation with conditional adversarial networks,” in The IEEE
+Conference on Computer Vision and Pattern Recognition (CVPR), July
+2017.
+[29] Y.-H. Tsai, W.-C. Hung, S. Schulter, K. Sohn, M.-H. Yang, and
+M. Chandraker, “Learning to adapt structured output space for
+semantic segmentation,” 2018 IEEE/CVF Conference on Computer
+Vision and Pattern Recognition, Jun 2018. [Online]. Available:
+http://dx.doi.org/10.1109/CVPR.2018.00780
+[30] W. Hong, Z. Wang, M. Yang, and J. Yuan, “Conditional gener-
+ative adversarial network for structured domain adaptation,” in
+Proceedings of the IEEE Conference on Computer Vision and Pattern
+Recognition, 2018, pp. 1335–1344.
+[31] F. Pizzati, R. d. Charette, M. Zaccaria, and P. Cerri, “Domain
+bridge for unpaired image-to-image translation and unsupervised
+domain adaptation,” in The IEEE Winter Conference on Applications
+of Computer Vision, 2020, pp. 2990–2998.
+[32] J. Hoffman, D. Wang, F. Yu, and T. Darrell, “Fcns in the wild: Pixel-
+level adversarial and constraint-based adaptation,” arXiv preprint
+arXiv:1612.02649, 2016.
+[33] Y. Zhang, P. David, and B. Gong, “Curriculum domain adaptation
+for semantic segmentation of urban scenes,” in The IEEE Interna-
+tional Conference on Computer Vision (ICCV), 2017.
+[34] W.-L. Chang, H.-P. Wang, W.-H. Peng, and W.-C. Chiu, “All
+about structure: Adapting structural information across domains
+for boosting semantic segmentation,” in Proceedings of the IEEE
+Conference on Computer Vision and Pattern Recognition, 2019, pp.
+1900–1909.
+[35] J. Hoffman, E. Tzeng, T. Park, J.-Y. Zhu, P. Isola, K. Saenko,
+A. Efros, and T. Darrell, “CyCADA: Cycle-consistent adversarial
+domain adaptation,” in Proceedings of the 35th International Con-
+ference on Machine Learning, ser. Proceedings of Machine Learning
+Research, J. Dy and A. Krause, Eds., vol. 80.
+Stockholmsm¨assan,
+Stockholm Sweden: PMLR, 10–15 Jul 2018, pp. 1989–1998.
+[36] A. Shrivastava, T. Pfister, O. Tuzel, J. Susskind, W. Wang, and
+R. Webb, “Learning from simulated and unsupervised images
+through adversarial training,” in The IEEE Conference on Computer
+Vision and Pattern Recognition (CVPR), 2017.
+[37] Y. Zhang, Z. Qiu, T. Yao, D. Liu, and T. Mei, “Fully convolutional
+adaptation networks for semantic segmentation,” 2018 IEEE/CVF
+Conference on Computer Vision and Pattern Recognition, Jun 2018.
+[Online]. Available: http://dx.doi.org/10.1109/CVPR.2018.00712
+[38] S.
+Sankaranarayanan,
+Y.
+Balaji,
+A.
+Jain,
+S.
+N.
+Lim,
+and
+R. Chellappa, “Learning from synthetic data: Addressing domain
+shift for semantic segmentation,” 2018 IEEE/CVF Conference on
+Computer Vision and Pattern Recognition, Jun 2018. [Online].
+Available: http://dx.doi.org/10.1109/CVPR.2018.00395
+[39] F. Pan, I. Shin, F. Rameau, S. Lee, and I. S. Kweon, “Unsupervised
+intra-domain adaptation for semantic segmentation through self-
+supervision,” in Proceedings of the IEEE/CVF Conference on Computer
+Vision and Pattern Recognition, 2020, pp. 3764–3773.
+[40] M. Kim and H. Byun, “Learning texture invariant representation
+for domain adaptation of semantic segmentation,” in Proceedings of
+the IEEE/CVF Conference on Computer Vision and Pattern Recognition,
+2020, pp. 12 975–12 984.
+[41] A. Tonioni, M. Poggi, S. Mattoccia, and L. Di Stefano, “Unsu-
+pervised adaptation for deep stereo,” in The IEEE International
+Conference on Computer Vision (ICCV), Oct 2017.
+[42] C. Zheng, T.-J. Cham, and J. Cai, “T2net: Synthetic-to-realistic
+translation for solving single-image depth estimation tasks,” in The
+European Conference on Computer Vision (ECCV), September 2018.
+[43] A. Tonioni, F. Tosi, M. Poggi, S. Mattoccia, and L. D. Stefano, “Real-
+time self-adaptive deep stereo,” in The IEEE Conference on Computer
+Vision and Pattern Recognition (CVPR), June 2019.
+[44] K.-H. Lee, G. Ros, J. Li, and A. Gaidon, “SPIGAN: Privileged
+adversarial learning from simulation,” in International Conference
+on
+Learning Representations,
+2019. [Online].
+Available:
+https:
+//openreview.net/forum?id=rkxoNnC5FQ
+[45] I. Kokkinos, “Ubernet: Training a universal convolutional neural
+network for low-, mid-, and high-level vision using diverse
+datasets and limited memory,” 2017 IEEE Conference on Computer
+Vision and Pattern Recognition (CVPR), Jul 2017. [Online]. Available:
+http://dx.doi.org/10.1109/CVPR.2017.579
+[46] P. Z. Ramirez, M. Poggi, F. Tosi, S. Mattoccia, and L. Di Stefano,
+“Geometry meets semantics for semi-supervised monocular depth
+estimation,” in Asian Conference on Computer Vision.
+Springer,
+2018, pp. 298–313.
+[47] R. Cipolla, Y. Gal, and A. Kendall, “Multi-task learning using
+uncertainty to weigh losses for scene geometry and semantics,”
+
+15
+2018
+IEEE/CVF
+Conference
+on
+Computer
+Vision
+and
+Pattern
+Recognition, 2018. [Online]. Available: http://dx.doi.org/10.1109/
+CVPR.2018.00781
+[48] F. Tosi, F. Aleotti, P. Z. Ramirez, M. Poggi, S. Salti, L. Di Stefano,
+and S. Mattoccia, “Distilled semantics for comprehensive scene
+understanding from videos,” in Proceedings of the IEEE Conference
+on Computer Vision and Pattern Recognition, 2020.
+[49] E. Tzeng, J. Hoffman, T. Darrell, and K. Saenko, “Simultaneous
+deep transfer across domains and tasks,” in Proceedings of the IEEE
+International Conference on Computer Vision, 2015, pp. 4068–4076.
+[50] J. N. Kundu, N. Lakkakula, and R. V. Babu, “Um-adapt: Unsuper-
+vised multi-task adaptation using adversarial cross-task distilla-
+tion,” in Proceedings of the IEEE International Conference on Computer
+Vision, 2019, pp. 1436–1445.
+[51] S. R. Richter, Z. Hayder, and V. Koltun, “Playing for benchmarks,”
+in IEEE International Conference on Computer Vision, ICCV 2017,
+Venice, Italy, October 22-29, 2017, 2017, pp. 2232–2241. [Online].
+Available: https://doi.org/10.1109/ICCV.2017.243
+[52] F. Yu, H. Chen, X. Wang, W. Xian, Y. Chen, F. Liu, V. Madhavan,
+and T. Darrell, “Bdd100k: A diverse driving dataset for heteroge-
+neous multitask learning,” in Proceedings of the IEEE/CVF conference
+on computer vision and pattern recognition, 2020, pp. 2636–2645.
+[53] A. Geiger, P. Lenz, C. Stiller, and R. Urtasun, “Vision meets
+robotics: The kitti dataset,” International Journal of Robotics Research
+(IJRR), 2013.
+[54] H. Hirschmuller, “Accurate and efficient stereo processing by
+semi-global matching and mutual information,” in Computer Vision
+and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society
+Conference on, vol. 2.
+IEEE, 2005, pp. 807–814.
+[55] F. Yu, V. Koltun, and T. Funkhouser, “Dilated residual networks,”
+in Computer Vision and Pattern Recognition (CVPR), 2017.
+[56] K.-C. Peng, Z. Wu, and J. Ernst, “Zero-shot deep domain adapta-
+tion,” in Proceedings of the European Conference on Computer Vision
+(ECCV), 2018, pp. 764–781.
+[57] D. Eigen, C. Puhrsch, and R. Fergus, “Depth map prediction from
+a single image using a multi-scale deep network,” in Advances in
+neural information processing systems, 2014, pp. 2366–2374.
+[58] J. Yang, H. Zou, Y. Zhou, Z. Zeng, and L. Xie, “Mind the
+discriminability: Asymmetric adversarial domain adaptation,” in
+European Conference on Computer Vision.
+Springer, 2020, pp. 589–
+606.
+[59] J. Choi, T. Kim, and C. Kim, “Self-ensembling with gan-based data
+augmentation for domain adaptation in semantic segmentation,”
+in Proceedings of the IEEE international conference on computer vision,
+2019, pp. 6830–6840.
+Pierluigi Zama Ramirez is a Post Doc at the
+Computer Vision Laboratory (CVLab), University
+of Bologna. His research interests include deep
+learning, semantic segmentation, depth estima-
+tion, optical flow and domain adaptation. He has
+authored more than 10 papers on these sub-
+jects.
+Adriano Cardace is a PhD student at the Com-
+puter Vision Laboratory (CVLab), University of
+Bologna. His research interests include deep
+learning for Computer Vision problems, espe-
+cially semantic segmentation, domain adapta-
+tion and self-supervised learning.
+Luca De Luigi is a PhD student at the Computer
+Vision Laboratory (CVLab) at the University of
+Bologna. His research focuses on deep learning
+for computer vision problems, especially dealing
+with 3D geometry and implicit neural represen-
+tations.
+Alessio Tonioni received his PhD degree in
+Computer Science and Engineering from Uni-
+versity of Bologna in 2019. Currently, he is a
+research scientist at Google Zurich. His research
+interest concerns machine learning for depth es-
+timation, domain adaptation and generalization.
+He has authored more than 15 papers on these
+subjects.
+Samuele Salti is currently assistant professor
+at the Department of Computer Science and
+Engineering (DISI) of the University of Bologna,
+Italy. Before joining the University of Bologna,
+he was leading the Data Science team at Veri-
+zon Connect, the world leading company in fleet
+management products and connected vehicles
+services. His main research interest is computer
+vision, in particular 3D computer vision, and ma-
+chine/deep learning applied to computer vision
+problems. Dr. Salti has co-authored 42 publi-
+cations in international conferences and journals and 8 international
+patents. In 2020, he co-founded the start-up eyecan.ai. He was awarded
+the best paper award runner-up at 3DIMPVT 2011, the top international
+conference on 3D computer vision, and was nominated outstanding
+reviewer at CVPR 2020 and NeurIPS 2020.
+Luigi Di Stefano received the PhD degree in
+electronic engineering and computer science
+from the University of Bologna, in 1994. He is
+currently a full professor with the Department of
+Computer Science and Engineering, University
+of Bologna, where he founded and leads the
+Computer Vision Laboratory (CVLab). His re-
+search interests include image processing, com-
+puter vision and machine/deep learning. He is
+the author of more than 150 papers and several
+patents. He has been scientific consultant for
+major companies in the fields of computer vision and machine learning.
+He is a member of the IEEE Computer Society, IEEE, and the IAPR-IC.
+
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+page_content='salti,luigi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='distefano}@unibo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='it  alessiot@google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='com  Abstract—Availability of labelled data is the major obstacle to the deployment of deep learning algorithms for computer vision tasks in  new domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The fact that many frameworks adopted to solve different tasks share the same architecture suggests that there should  be a way of reusing the knowledge learned in a specific setting to solve novel tasks with limited or no additional supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In this  work, we first show that such knowledge can be shared across tasks by learning a mapping between task-specific deep features in a  given domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Then, we show that this mapping function, implemented by a neural network, is able to generalize to novel unseen  domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Besides, we propose a set of strategies to constrain the learned feature spaces, to ease learning and increase the  generalization capability of the mapping network, thereby considerably improving the final performance of our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Our proposal  obtains compelling results in challenging synthetic-to-real adaptation scenarios by transferring knowledge between monocular depth  estimation and semantic segmentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Index Terms—Domain Adaptation, Task Transfer, Semantic Segmentation, Depth estimation  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  1  INTRODUCTION  D  EEP learning has revolutionized computer vision by  providing an effective solution to address a wide range  of tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', classification, depth estimation, semantic seg-  mentation, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The rise of a common framework has  allowed incredible leaps forward for the whole research  community thanks to the ability to reuse architectural and  algorithmic improvements discovered to solve one task  across many others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, the real knowledge of a neu-  ral network is stored inside its trained parameters and we  still have no simple way of sharing this knowledge across  different tasks and domains (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', datasets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' As such, the first  step for every practitioner faced with a new problem or do-  main deals with acquisition and labeling of a new training  set, an extremely tedious, expensive and time consuming  operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We argue that sharing the knowledge acquired  by a neural network to solve a specific task in a specific  domain across other tasks and domains could be a more  straightforward and cost-effective way to tackle them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Indeed, this is demonstrated by the widespread use  and success of transfer learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Transfer learning concerns  solving new tasks by initializing a network with pre-trained  weights, thereby providing a basic approach to knowledge  reuse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, it still requires a new annotated dataset to  fine tune the pretrained network on the the task at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' A  few works focused on the related task transfer (TT) problem  [1], [2], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', on exploiting supervised data to tackle multiple  tasks in a single domain more effectively by leveraging on  the relationships between the learned representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' As  unlabeled domains are not considered in TT problem for-  mulations, the proposed methodologies still rely on transfer  Equal contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Our framework transfers knowledge across tasks and domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Given two tasks (1 and 2) and two domains (A and B), with supervision  for both tasks in A but only for one task in B, we learn the dependency  between the tasks in A and exploit this in B in order to solve task 2  without the need of supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  learning and availability of a small annotated training set  in order to address new datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' On the other hand, the  unsupervised domain adaptation literature (DA) [3] studies  how the need for annotated data can be removed when  leveraging on knowledge reuse to solve the same task across  different domains, but it does not consider different tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Differently, we propose to merge DA and TT by ex-  plicitly addressing a cross domain and cross task problem  where on one source domain (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', synthetic data) we have  supervision for many tasks, while in another target one (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=',  real data) annotations are available only for a specific task  while we wish to solve many.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' A schematic representation  of our problem formulation with two domains and two  tasks is shown in the right part of Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Following this  schematic representation we will consider a scenario with  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='11310v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='CV]  26 Jan 2023  Task 1  Task 2  Domain A  AIDT  Domain  Task  Transfer  Transfer  DomainB  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Transfer Learning2  two domains (a source one and a target one, namely A  and B) and two tasks (again a source one and a target one,  namely task 1 and 2), but nothing prevents our method to  be extended to more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In domain A we use the available  supervision to learn two models for the source and target  tasks, while in the target domain B we can do the same  for the source task only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In domain A we use the trained  task-specific models to learn a mapping function (G1→2  in Figure 1) between deep features extracted to solve the  source task and those extracted to solve the target task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This  mapping function is then applied in domain B to solve the  target task by transforming the features extracted to solve  the source task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  The key component of our framework is the mapping  function between the two task-specific deep features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In [4]  we proposed a preliminary formulation of our framework  by modeling the mapping function as a deep convolutional  neural network and optimizing its parameters by standard  supervised learning in the source domain A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In this work,  we expand and improve upon our preliminary formula-  tion by proposing two features alignment strategies aimed  at learning the feature mapping function more effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Firstly, we align feature representations across domains  using a novel norm discrepancy alignment (NDA) loss that  constraints the feature space by penalizing features with  very different norms in a spatially-aware manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Secondly,  we align feature representations across tasks by using them  as inputs to solve a common auxiliary task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This pretext  problem acts as a bridge between the source and the target  tasks: in fact, if the deep features extracted to solve them in-  dependently can be used to address effectively an additional  common task, we are pushed to believe that those features  present the same semantic content and encode it in a similar  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  We test the effectiveness of our proposal in a challenging  autonomous driving scenario where we try to solve the two  related dense prediction tasks of monocular depth estima-  tion and semantic segmentation [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We select edge detection  as the auxiliary task since color edges provide oftentimes  detailed key information related to both the semantic as well  as the depth structure of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Many edge detectors  have been proposed during the years, with recent deep  learning based approaches outperforming classical hand-  crafted methods even in the most challenging scenarios [6],  [7], [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Interestingly, such deep models present good gener-  alization capabilities, allowing us to use the state-of-the-art  approach [6] to generate proxy supervision for the auxiliary  task without extra labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Thanks to our formulation, we  can use a fully supervised and completely synthetic domain  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', the Carla simulator [9]) to improve the performance on  a partially labeled real domain (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', Cityscapes [10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  The contributions of this paper can be summarized as  follow: We propose for the first time to study a cross domain  and cross task problem where supervision for all  tasks is available in one domain whilst only for a  subset of them in the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This is done by learning  a mapping between deep representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We demonstrate how constraining explicitly deep  features across domains with a novel norm discrep-  ancy alignment loss improves the learning of the  mapping function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We further show how the learning of the mapping  function can be improved by deploying an auxiliary  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Considering the dense prediction tasks of monocular  depth estimation and semantic segmentation, we  achieve results close to the practical upper bound  when transferring knowledge between a synthetic  and a real domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  2  RELATED WORKS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1  Transfer Learning and Task Transfer  Collecting training data is often expensive, time-consuming,  or even unrealistic in many scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Many works have  tackled this problem by exploiting the existence of a rela-  tionship between the weights of CNNs trained for different  tasks [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In particular, [12] showed that this strategy, re-  ferred to as transfer learning, can lead to better results than  using random initialization even if applied on quite diverse  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Transfer learning has become a common practice, for  instance, in object detection, where networks are usually  initialized with Imagenet [13] classification weights [14],  [15], [16], [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Additional insights on the transferability of  learned representations between different visual tasks were  provided in [1], where the authors present Taskonomy, a  computational approach to represent a taxonomy of rela-  tionships among visual tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Along similar lines, [18] pro-  posed to exploit the correlation between known supervised  tasks and novel target tasks, in order to predict the param-  eters of models deployed to solve the target tasks starting  from the parameters of networks trained on the known  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' While [1] and [18] study the correlation between tasks  in a given domain and assume either full or no supervision,  we explicitly address a multi-domain scenario assuming full  supervision in one domain and partial supervision in the  target one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2  Domain Adaptation  Domain adaptation techniques aim at reducing the perfor-  mance drop of a model deployed on a domain different from  the one the model was trained on [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Throughout the years,  adaptation has been performed at different levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Early  approaches tried to model a shared feature space relying on  statistical metrics such as MMD [19], [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Later, some works  proposed to align domains by adversarial training [21],  [22], [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Recently [24] noticed that, for classification tasks,  aligning feature norms to an arbitrarily large value results in  better transferability across domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Generative adversarial  networks [25] have also been employed to perform image-  to-image translation between different domains [26], [27],  [28], and, in particular, to render cheaply labelled syn-  thetic images similar to real images from a target domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  However, when dealing with dense tasks such as semantic  segmentation, feature-based domain adaptation approaches  tend to fail as deeply discussed in [29] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Thus, several ap-  proaches to address domain adaptation for dense tasks, such  as semantic segmentation [5], [29], [30], [31], [32], [33], [34],  [35], [36], [37], [38], [39], [40] or depth estimation [41], [42],  3  [43] have been proposed recently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Among them, SPIGAN  [44] uses extra supervision coming from synthetic depth  of the source domain to improve the quality of an image-  to-image translation network and consequently achieving  better adaptation performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Akin to DA methods, we  learn from a labeled source domain to perform well on a  different target domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, unlike the classical DA  setting, we assume the existence of an additional task where  supervision is available for both domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='3  Multi-task Learning  The goal of multi-task learning is to solve many tasks si-  multaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' By pursuing this rather than solving the tasks  independently, a neural network may use more information  to obtain more robust and reliable predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Many works  try to tackle several tasks jointly [45], [46], [47], [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' For  example, [47] showed that by learning to correctly weigh  each task loss, multi-task learning methods can outperform  separate models trained individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [5], [48] show how  learning multiple perception tasks jointly while enforcing  geometrical consistency across them can lead to better per-  formances for almost all tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Recently, [2] proposes a  method to improve the performances of multiple single-  task networks by imposing consistency across them during  training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Finally, Taskonomy [1] investigates the relationship  between the deployed tasks to accomplish multi-task learn-  ing effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, multi-task learning approaches  usually try to achieve the best balance between tasks in  a single-domain scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We instead tackle a multi-task  and multi-domain problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Nevertheless, taking inspiration  from multi-task learning, we show how jointly learning an  auxiliary task while learning the two task networks helps  the alignment of features across tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='4  Task Transfer and Domain Adaptation  Most existing approaches address independently either task  transfer or domain adaptation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yet, a few works have pro-  posed to tackle these two problems jointly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [49] was the first  paper to propose a cross-tasks and cross-domains adapta-  tion approach, considering as tasks different image classifi-  cations problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' UM-Adapt [50], instead, learns a cross-  task distillation framework with full supervision on the  source domain and deploys such framework on the target  domain in a fully unsupervised manner, while minimizing  adversarially the discrepancy between the two domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Differently, in a preliminary version of this work [4], we in-  troduced AT/DT (Across Tasks and Domains Transfer) and  set forth a novel learning framework, where the relationship  between a set of tasks is learned on the source domain and it  is later deployed to solve a specific task on the target domain  without supervision thanks to the availability of ground-  truth for all the tasks except the target one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In this work we  will expand and improve this methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  3  METHOD  We introduce the problem we are trying to solve with a  practical example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Imagine we aim to solve semantic seg-  mentation in a real domain but we only have labels for a  closely related task (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', depth estimation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Moreover, let  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' AT/DT framework: here N1 and N2 are trained separately to solve  tasks T1 and T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' While N2 is trained only on images from domain A,  N1 is trained jointly on both domain A and domain B, to enable the  extraction of domain invariant features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Then, encoders from the two  networks are frozen and used to learn the transfer function G1→2, which  aims at transforming features extracted for T1 in features that are good  for T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This step is performed only on domain A, since we have no  supervision for T2 on domain B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Finally, at inference time, features are  extracted from E1 starting from images of domain B, transformed with  the G1→2 and fed to D2 to produce the final predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  us suppose to have access to a synthetic domain, where  labels can be easily obtained for both tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Unsupervised  domain adaptation may be used in this synthetic to real  scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, we wish to go one step further, trying to  answer this question: can we exploit the depth estimation  task to boost the performance of semantic segmentation in  the real domain?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The answer is yes, thanks to our novel  framework AT/DT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In AT/DT we first learn a mapping  function in the synthetic domain between deep features of  two networks trained for depth estimation and semantic  segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This mapping function captures the relation-  ship between the two tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Once learned, we use the map-  ping on depth features extracted from real samples to solve  semantic segmentation in the real domain without the need  of labels for it, thereby transferring knowledge across tasks  and domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' To further improve performance, we propose  two strategies aimed at increasing the transferability of the  learned features, namely leveraging on a norm discrepancy  alignment loss and an auxiliary task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  A  A  L (A,YA)  E1  D  B  L (V,P)  N1  Training N1  E2  L, (V2, J2)  N2  Training N2  E1  LTr  E2  Training G1-2  B  Ei  D  Inference4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Features alignment strategies across tasks and domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We train jointly the networks N1, N2 and a shared auxiliary decoder Daux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We  train N1 to solve T1 on images from domains A and B using a supervised loss LT1 for T1 alongside a novel feature Norm Discrepancy Alignment  loss LNDA which helps better aligning the features computed by N1 across the two domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We train N2 using a supervised loss LT2 for T2 on  images from B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Daux is trained to solve an auxiliary task Taux using the loss Laux and based on the features computed by E1 on images from A  and B as well as by E2 on images from B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  In the following sub-sections, we first describe the base  AT/DT framework and then delineate its improved formu-  lation which includes the norm discrepancy alignment loss  and auxiliary task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1  Notation  We consider two tasks, T1 and T2, as well as two domains,  A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We denote the images belonging to A and B as  xA and xB, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We have labels for T1 in A and B,  denoted as yA  1 and yB  1 , respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' On the other hand, we  have labels for T2 only in A, denoted as yA  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Our aim is to  solve T2 in B, where we do not have supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We assume  T1 and T2 to be both dense tasks, which can therefore be  addressed by an encoder-decoder architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We denote as  N1 and N2 two networks that solve T1 and T2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Each network Nk, k ∈ {1, 2} consists of an encoder Ek and  a decoder Dk, such that Nk(x) = Dk(Ek(x)), x being the  input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2  Across Tasks and Domains Transfer  In  our  AT/DT  framework  we  aim  at  learning  the  relationships between T1 and T2 through a neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  This is achieved by 3 steps, each represented as a block in  Figure 2:  Training N1 and N2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We train N1 and N2 to solve  T1 and T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Since we assume supervision for T1 on both  domains, N1 is trained with images from A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This  enables N1 to learn a feature space shared across the two  domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' N2, instead, is trained only on A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Both networks  are trained with a specific supervised task loss LTk for Tk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Training G1→2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Considering only domain A, where we  have supervision for both tasks, we then train a trans-  fer network G1→2 to map the features computed by N1,  f A  1 = E1(xA), into those computed by N2, f A  2 = E2(xA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Denoting the transferred features as f A  1→2 = G1→2(f A  1 ), we  train the transfer network by minimizing the L2 loss:  LT r = ||f A  1→2 − f A  2 ||2  (1)  Inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Once G1→2 has been trained, we can ad-  dress T2 in B by computing the features to solve T1,  f B  1 = E1(xB), transform them into features amenable to T2,  f B  1→2 = G1→2(f B  1 ), and finally decode these features into  the required dense output by D2:  ˆyB  2 = D2(f B  1→2)  (2)  After presenting the base AT/DT framework, in the  next sub-sections we will describe two strategies deployed  to boost the feature alignment across domains and tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Figure 3 provides a detailed view of these two strategies  which in our final proposed framework replace the initial  steps of the training protocol (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', Training N1 and N2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='3  Feature Alignment Across Domains  For the effectiveness of the approach delineated in subsec-  tion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2, it is crucial that G1→2 can generalize well to the  target unseen domain B even if trained only with data from  the source domain A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  The DA literature presents us with several ways to  accomplish this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' One may operate on the input space [27], on  the feature space [23] or on the output space of the network  [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In our setting, though, both input and output space of  G1→2 are high dimensional latent spaces and, as reported  in [29], unsupervised domain adaptation techniques tend to  fail when applied to such spaces while addressing dense  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yet, we can address the domain shift issue with a  L (VA,JA)  E1  D1  NDA  L (VB,JP)  xn  N1  DB  aux  laux  aux  laux  X  y2  xnp7  aux  Zaux  L (V, J)  N2  Training N1 e N25  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Two task transfer scenarios: depth-to-semantic on the left, the opposite on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' First row: ground-truth depth and semantic segmentation  maps;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' second row: corresponding edge maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Red circles highlight information needed in the target task but missing in the source one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  direct approach in the input space of G1→2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', the feature  space of N1, which is already shared between A and B  due to the network being trained supervisedly with images  from both domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We leverage on the intuition that scene  spatial priors are typically domain invariant in many adap-  tation scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We consider it as a reasonable assumption  for several domain adaptation settings, where we select the  source domain by considering visual similarities with the  target domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' For instance, in autonomous driving scenar-  ios we typically have cameras placed from a car viewpoint,  and scenes are urban scenarios in both synthetic [9], [51]  and real [10], [52], [53] datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Thus, if we consider the  task of semantic segmentation in all datasets (synthetic and  real) we typically find road pixels in the bottom part of the  images and instead sky pixels in the top part of the images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  To visualize this property we select a synthetic domain A  CARLA [9] and a real domain B Cityscapes [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Then, we  count for each pixel location the number of occurrences of  each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We show the result of this experiment in Figure 5,  using a viridis colormap to display these occurrency maps  for each class and for both domains A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We can clearly  see that the maps have a structure similar across domains,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', building are concentrated in the top image regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Leveraging this property, we propose to align more  closely the features computed by E1 on the images from  both domains, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', f A  1  and f B  1 , by enforcing similarity of  the L2 norms across channels at the same spatial loca-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Starting from features f A  1  and f B  1  of dimensionality  H × W × C, where H, W and C are the height, width  and number of channels of the feature maps, we calculate  the L2 norm along the C axis and minimize the absolute  difference at each spatial location i, j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hence, our NDA  (Norm Discrepancy Alignment) Loss is defined as follows:  LNDA =  1  W × H  H  �  i=1  W  �  j=1  ���∥f A  1i,j∥2 − ∥f B  1i,j∥2  ���  (3)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='4  Feature Alignment Across Tasks  While the NDA loss presented above aims at improving  the generalization across domains of the feature mapping  network G1→2, its effectiveness can be further improved by  aligning features also across tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Accordingly, we conjec-  ture that f1 features should capture as much information as  possible on the details of the scene, even though some of  this information may not be necessary to solve T1, because,  when transferred by G1→2, such a richer representation  could help to solve T2 more effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' For this reason, while  training N1 for T1, we train jointly an additional decoder,  Daux, to solve an auxiliary task, Taux, aimed at enriching  the learnt representation f1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, though multi-task  learning of T1 and Taux could help to encode more detailed  information into f1 features, it does not guarantee that  the decoder D2, used at inference time on the features  f1→2 transferred from T1 to T2, may effectively deploy this  additional information if it has been trained only to solve  T2 in isolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This leads us to reckon that Daux should  be trained jointly with N2 too, such that the additional  information required to solve Taux may be incorporated also  within the features f2 learnt by E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Therefore, given auxiliary task labels yA  aux and yB  aux for  A and B, we train N1 and N2 jointly with a single auxiliary  decoder Daux using an auxiliary loss Laux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Purposely, we  obtain auxiliary predictions from both encoders with the  shared decoder Daux as ˆykaux = Daux(Ek(x)), k ∈ {1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Similarly to the simpler formulation of our framework pre-  sented in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2, to compute the auxiliary loss we  feed images of both domains through E1, while we pass  only images from A through E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We do not pass images  belonging to B through E2 while training Daux since this  would be the only kind of supervision for E2 in B and it  may skew E2 output to be more effective on Taux than on  T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='5  Overall N1 and N2 loss  When training simultaneously N1 and N2, the overall loss  is:  6  A  B  A  B  A  B  A  B  Road  Sidewalk  Wall  Fence  A  B  A  B  A  B  A  B  Person  Pole  Vegetation  Vehicle  A  B  A  B  A  B  Traffic Signs  Building  Sky  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Spatial Priors Similarities Across Domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Considered the semantic segmentation task, we compute the number of occurrences of each  class at each pixel location for both domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Domain A is CARLA, B is Cityscapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We visualize the occurrence maps with a viridis colormap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  L = λT1LT1(yA  1 , ˆyA  1 ) + λT1LT1(yB  1 , ˆyB  1 )  +λT2LT2(yA  2 , ˆyA  2 ) + λauxLaux(yA  1aux, ˆyA  1aux)+  λauxLaux(yB  1aux, ˆyB  1aux) + λauxLaux(yA  2aux, ˆyA  2aux)+  λNDALNDA(f A  1 , f B  1 )  (4)  4  EXPERIMENTAL SETTINGS  Tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We fix T1 and T2 to be monocular depth estimation  and semantic segmentation, or vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' These two visual  tasks can be addressed using the same encoder-decoder  architecture, with changes needed only in the final layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Semantic segmentation is solved by minimizing a pixel-  wise cross entropy loss, monocular depth estimation by  minimizing an L1 loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We select edge detection as our  Taux since it seems particularly amenable to improve  the effectiveness of our framework in capturing and  transferring important structural information that might  otherwise be lost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Let us consider the case of T1 being depth  estimation and T2 semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The features  f1 needed to compute depth may ignore the boundaries  between semantically distinct regions showing up at the  same distance from the camera: in Figure 4 (left) this is  the case, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', of the boundaries between legs or tyres  and ground, as well as between street signs and poles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Therefore, even if fed to a perfect G1→2, f1 may not  contain all the information needed to restore the semantic  structure of the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' By solving jointly edge detection  on the input image, instead, we force our N1 network to  extract additional information that would not need to be  captured should the learning objective be concerned with  depth estimation only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Similarly, Figure 4 (right) highlights  how depth discontinuities do not necessarily correspond  to semantic boundaries, such that a network N1 trained  in isolation to assign semantic labels to pixels may not  need to learn information relevant to estimate the depth  structure of the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Besides, it is worth pointing out that  edge detection can be solved using again the same decoder  architecture as T1 and T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Since the edge proxy-labels that  we adopt are gray-scale images [6], in our experiments we  implement the Laux loss introduced in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='4 as a  standard L2 loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In all our experiments we set λaux to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='5,  λNDA to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='001, λT1 and λT2 to 1 to balance loss values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We test the effectiveness of our method in  an autonomous driving scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We set A and B to be  a synthetic and a real dataset, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The former  consists of a collection of images generated with the Carla  simulator [9], while the latter is the popular Cityscapes  dataset [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We generated the Carla dataset mimicking  the camera settings of the real scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We render 3500,  500, and 1000 images for training, validation, and testing,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' For each image, we store the associated  depth and semantic labels provided by the simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The  Cityscapes dataset is a collection of 2975 and 500 images to  be used for training and validation, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' As for our  evaluation, we use the 500 Cityscapes validation images  since test images are not equipped with labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Moreover,  as in Cityscapes only the semantic labels are provided,  we use depth proxy-labels obtained with the SGM stereo  algorithm [54], by filtering the erroneous predictions in the  generated disparities with a left-right consistency check.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  This can be considered as an added value because it shows  the ability to transfer knowledge when learning from noisy  labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Finally, we use a pre-trained1 state-of-the-art neural  network [6] as an off-the-shelf edge detector to extract  from the images belonging to A and B the edges used as  proxy-labels to train Taux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' To solve each task, we use two dilated  ResNet50 [55] as encoder and a stack of bilinear upsample  plus convolutional layers as decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The encoder shrinks  both input dimensions with a factor of 1/16, while the  decoder upsamples the feature map until a prediction with  the same spatial resolution as the input image is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  The two networks for T1 and T2 are identical, but for the  final prediction layer, which is task dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The two  previously defined encoders are also used to capture good  features for edge detection, which is solved using Daux,  that shares the same architecture as the decoders used in  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Neither A nor B belong to the training set of this network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  7  N1 and N2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' G1→2 is a simple CNN made out of 6 pairs of  convolutional and batch normalization layers with kernel  size 3 × 3 which do not perform any downsampling or  upsampling operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Training and Evaluation Protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' During the training  phase of the transfer network G1→2, the model is evaluated  on the validation set of Carla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Of course, it is possible that  optimality on Carla does not translate into optimal per-  formance on Cityscapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yet, we cannot use data from the  target domain neither for hyper-parameters tuning nor for  early stopping, because in our setting these data would not  be available in any real scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Therefore, the Cityscapes  validation set is only used at test time to measure the final  performances of our framework method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' From left to right: RGB input image of domain A , depth prediction  from N1, edges from f1, semantic segmentation from N2 and edges  from f2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Task features f1 and f2 encode richer details than strictly  needed to solve either tasks as we can recover all edges from both of  them by Daux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' To evaluate the performance on the semantic  segmentation task two metrics are used: pixel accuracy,  shortened Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e the percentage of pixels with a cor-  rect predicted label) and Mean Intersection Over Union,  shortened mIoU, as defined in [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' To render these metrics  comparable among the used datasets, we solve semantic  segmentation on the 10 shared classes (Road, Sidewalk,  Walls, Fence, Person, Poles, Vegetation, Vehicles, Traffic  Signs, Building) plus the Sky category, which is defined as  the set of points with infinite depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Some of the Cityscapes  classes are collapsed into one class: car and bicycle into  vehicle, traffic signs and traffic light into traffic sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The  remaining categories of Cityscapes are instead ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  When testing the depth estimation task, we report the  standard metrics described in [57]: Absolute Relative Error  (Abs Rel), Square Relative Error (Sq Rel), Root Mean Square  Error (RMSE), logarithmic RMSE and δ1, δ2 and δ3 accuracy  scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Each δα is obtained by computing, for each pixel  of the input image, the maximum among ratio and inverse  ratio between the predicted value and the ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' δα  represents the percentage of pixels whose such ratio is lower  than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='25α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  5  EXPERIMENTAL RESULTS  We provide results for two different settings: transferring  features from depth estimation to semantic segmentation  (subsection 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1) as well as from semantic segmentation to  depth estimation (subsection 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  In both scenarios, as already mentioned, we used edge  detection as auxiliary task, motivated by the idea that either  semantic segmentation and depth estimation can benefit  from edge information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Figure 6 shows that with our multi-  task learning protocol we are able to restore all the details  of the scene from both f1 and f2, proving that N1 and  N2 have indeed learned to encode into their features richer  information than that strictly needed to solve T1 and T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1  Depth to Semantics  In this setup, denoted as Dep → Sem, the goal of our  framework is to transform depth features into semantic  segmentation features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This mapping is learned using Carla  as domain A and Cityscapes as domain B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We report results  in Table 1: the first row shows results obtained with no  adaptation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', training N2 on Carla and testing it directly  on Cityscapes), while from the second row we can see that  our final framework yields 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='28% mIoU and 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='57% Acc  with an improvement of +12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='48% and +8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='99% wrt to the  baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Even though AT/DT is the first work to address the  across tasks and domains scenario, we compare it against  a related work, ZDDA [56], which also leverage auxiliary  data from a different tasks to perform domain adaptation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  We apply it in our setup using as the ”Source” and ”Target”  domains Carla and Cityscapes respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We address  the Dep → Sem scenario using depth maps as ”task-  irrelevant” data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We skip the last sensor fusion step (Step  3) because it was not applicable in our scenario since we  do not have task-irrelevant data at test time, and thus we  stop training after the adaptation step (Step 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We report  results of this alternative approach in the second row of  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' As we can notice, ZDDA is effective in our scenario  and achieves better performance compared to the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  However, AT/DT obtains much better results, surpassing  ZDDA in all metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This is not surprising since ZDDA  focus on extracting features only from task-irrelevant data,  which can be sub-optimal for the relevant task as these  data do not provide the same amount of information as the  task-relevant data, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', features extracted only from depth  images would not contain several useful information for  semantic segmentation such as colors or textures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Furthermore, as we are transferring features from an-  other task, it is worth trying to investigate on the upper  bound in performance due to the inherent transferability  of the features between the two tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Purposely, we train  G1→2 using only Cityscapes to learn a mapping function in  a supervised fashion as explained in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='4 on B and  test on the validation set of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' These results are shown in the  third row of the table (denoted as Transfer Oracle): given a  transfer architecture, there seems to be an upper bound in  performance due to the nature of the two tasks, which in  the considered setting amounts to a 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='5% mIoU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Thus, our  proposal exhibit a gap wrt the Transfer Oracle that is only  about -7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2% mIoU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We also report the performance of N2  trained on B and tested on B, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', the absolute upper bound  in performance (last row of the table, denoted as Oracle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Some qualitative results dealing with the Dep → Sem  scenario are depicted in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' It is possible to appreciate  the overall improvement of our method wrt the baseline,  either in flat areas (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', roads, sidelwalks and walls), objects  shapes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', cars and persons) and fine-grained details (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=',  poles and traffic signs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='8  TABLE 1  Experimental results of Dep → Sem scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Baseline stands for N2 trained on A and tested on B, Transfer Oracle represents G1→2 trained  only on B, Oracle refers to N2 trained and tested on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Best results highlighted in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  A  B  Method  Road  Sidewalk  Walls  Fence  Person  Poles  Vegetation  Vehicles  Tr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Signs  Building  Sky  mIoU  Acc  Carla CS  Baseline  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='99 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='81  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='34  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='80  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='02 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='47 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='98 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='23  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='57  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='17 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='10  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='86  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='58  Carla CS  ZDDA [56]  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='93 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='28  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='62  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='63  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='80 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='94 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='78 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='37 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='44 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='74 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='16  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='06  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='82  Carla CS  AT/DT  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='57 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='46  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='37  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='27 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='16 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='90 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='96 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='77 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='44 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='85 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='33  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='28  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='57  CS  CS Transfer Oracle 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='69 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='05 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='46 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='58 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='68 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='84 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='83 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='57 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='03 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='17 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='54  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='50  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='84 CS  Oracle  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='74 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='28 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='26 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='78 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='39 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='28 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='69 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='94 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='92 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='33 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='23  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='44  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='90  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Qualitative results of the Dep → Sem scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' From left to right: RGB image, ground-truth, baseline trained only on domain A, ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2  Semantics to Depth  In this setup, which we define as Sem → Dep, the goal  of our framework is to transform semantic features into  depth features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This mapping is learned using Carla as  domain A and Cityscapes as domain B, as done for the  Dep → Sem scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Results are reported in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Similarly to the Dep → Sem scenario, in the first row  we show results with no adaptation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', our baseline),  while the third row presents the ones obtained with our  framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Also for this setup we report performances of  ZDDA [56] (second row), in which we use semantic maps as  task-irrelevant data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We can see that ZDDA achieves slight  better performance of the baseline in 5 metrics out of 7, but  still inferior to our approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Moreover, we report results  from the Transfer Oracle and the Oracle, implemented as  described for the Dep → Sem scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' It is possible to  appreciate that our framework outperforms the baseline on  6 out of 7 metrics, closing remarkably the gap with the  practical upper bound of the Transfer Oracle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In Figure 8, we  show some qualitative results of the Sem → Dep scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  While predictions look quite noisy in the background, we  can see a good improvement in the foreground area thanks  to our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Shapes are recovered almost perfectly, both  for big and small objects, even with difficult subjects like  the crowd in the bottom row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' It is also worth pointing out  that the depth predictions yielded by our method turn out  much smoother than the ones produced by the baseline and  generally less noisy than the ground-truth that, as explained  in section 4, consists of proxy-labels computed with SGM  [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  6  ABLATION STUDIES  In the following sections, we study the effectiveness of the  key design choices behind our proposal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1  Contribution of Taux and NDA Loss  We start by studying the effect of introducing in our  framework the auxiliary task and the NDA loss, analyzing  their contribution when used separately as well as when  combined together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The second and third row of Table 3  report the results obtained in the Dep → Sem setting by  integrating in our method either the auxiliary task (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', edge  detection) or the NDA loss, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We can see that  both design choices bring in an improvement of about +2%  in terms of mIoU with respect to the base AT/DT framework  (first row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Moreover, the last row of the table shows that  the auxiliary edge detection task and the NDA loss turn out  complementary because, when combined together, they can  provide an overall improvement of +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='34% mIoU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Figure 9 presents some zoomed-in qualitative results: we  can see that, even if the base version of AT/DT already  produces satisfactory results at a coarse level, the complete  version of our framework can produce much more accurate  predictions, especially regarding small details, such as poles,  traffic signs and car outlines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  9  TABLE 2  Experimental results of Sem → Dep scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Baseline stands for N2 trained on A and tested on B, Transfer Oracle represents G1→2 trained  only on B, Oracle refers to N2 trained and tested on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Best results highlighted in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Lower is better  Higher is better  A  B  Method  Abs Rel Sq Rel RMSE RMSE log  δ1  δ2  δ3  Carla CS  Baseline  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='858  Carla CS  AT/DT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='923  CS  CS Transfer Oracle  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2210  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='1372  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Qualitative result of the Sem → Dep scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' From left to right: RGB image, ground-truth, baseline network trained only on domain A, ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  TABLE 3  Ablation study in the Dep → Sem scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Best results highlighted in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Aux refers to the framework trained with the auxiliary task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' NDA refers  to the framework trained with our NDA loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  A  B  Aux  NDA  Road  Sidewalk  Walls  Fence  Person  Poles  Vegetation  Vehicles  Tr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Signs  Building  Sky  mIoU  Acc  Carla CS  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zoomed results in a Dep → Sem scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' From left to right: base AT/DT without edge and NDA, our proposed method, ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We  notice how, unlike base AT/DT, our method is able to recover the fine-grained details of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  10  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2  Effectiveness of edge detection as auxiliary task  In this section, we show empirically that in our framework  the choice of the proper auxiliary task is key to performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  In both the Dep → Sem and the Sem → Dep scenarios,  we propose to use edge detection as auxiliary task because  it captures information about the shapes of the objects in the  input images and allows for straightforward computation of  proxy-labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' To validate this design choice, we tested our  framework in the Dep → Sem setting, using Daux to recon-  struct the input images both from f1 and f2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', the classical  autoencoder setting (results in Table 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Interestingly, using  image reconstruction as auxiliary task results in an mIoU  score almost identical to the base AT/DT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We consider that  the autoencoder task is guided by a reconstruction loss  which makes no distinction between the pixels of the input  image: such supervision cannot guide effectively f1 and f2  to encapsulate the high-frequency components of the image  that are needed to predict the fine-grained details of the  scene, which is instead obtained by adopting edge detection  as auxiliary task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='3  Auxiliary tasks as source tasks  The main difference between a source and an auxiliary  task is that the auxiliary task alone cannot provide enough  information to solve T2, but it is useful to enrich T1 features  and align feature content across tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' To better support  our claims, we investigated AT/DT behaviour when using  auxiliary tasks Taux as source tasks T1 and semantic seg-  mentation as target task T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The results of these experiments  are reported in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' All rows of the table show results of  the base AT/DT i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', trained without Laux and LNDA losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  As we can notice, using as source task T1 a standard image-  reconstruction (row 1, autoencoder) or an edge detection  (row 2) lead to much worse results than using depth esti-  mation (row 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We argue that features extracted by N1 for  these tasks do not contain enough information to perform  semantic segmentation, which are yet contained in features  for depth estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Similar finding were also made by  Taskonomy [1], in which they show that edge detection and  image reconstruction (aka autoencoder) are less correlated  to semantic segmentation than depth estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' On the  contrary, we have shown that Edge Detection can be a  good auxiliary task in the Dep → Sem scenario since it  can enrich depth features with missing edges useful for  semantic segmentation and it can increase transferability  aligning depth and semantic features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='4  Importance of simultaneous training of N1, N2 and  Daux  In our experiments we use edge detection as auxiliary task  and train a shared decoder Daux to reconstruct the edges of  the input image from the features extracted by both E1 and  E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In fact, we argue that this procedure should force E1 to  encode into the extracted features also edge information that  may be not necessary to solve T1 but that may be relevant for  T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Besides, we believe that simultaneous training of N1, N2  and Daux is crucial to encourage features coming from E1  and E2 to represent edge information in a similar manner,  making it easier to learn G1→2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  In Table 6 we report the results concerning the ablation  study conducted to validate these intuitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We consider  the Dep → Sem scenario using the Carla dataset as domain  A and Cityscapes as domain B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The four rows of the table  deal with the following training schemes:  1)  The base AT/DT (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', without Taux and NDA loss)  as baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  2)  We first train N1 and Daux on both A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Then,  we train N2 on A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Finally, we train G1→2 on features  extracted by E1 and E2 on domain A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  3)  We train N1 and a first D1  aux on both A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Then,  we train N2 and a second D2  aux on A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Finally, we  train G1→2 on features extracted by E1 and E2 on  domain A  4)  Our proposed method, which trains N1, N2 and a  shared Daux simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  The introduction of edge detection as auxiliary task helps  in every scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In fact, if we use Daux only while training  N1 (second row), we already see an increase of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='6% in  the overall mIoU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We believe that this is explained by the  presence of edge details (not strictly necessary to solve  T1 but relevant for T2) in the features extracted by E1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  However, G1→2 may experience difficulties in adapting f1  into f2 if edge information is not explicitly present in f2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  This is confirmed by the results in the third row of the table,  where an additional increase of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='3% in the overall mIoU is  attained by using two different Daux (one during training of  N1 and one during training of N2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Finally, the best results  in terms of mIoU and Acc are achieved by our method, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=',  when training N1, N2 and a shared Daux simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  This vouches for the benefit of encoding in a similar manner  the edge information in f1 and f2 in order to enforce feature  alignment across tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='5  Alignment strategies for N1  An alternative approach to align N1 features between do-  mains to ease the transfer process and favor the generaliza-  tion of G1→2 consists in leveraging on the widely adopted  adversarial training in feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In our setting, this  can be obtained by adding a critic that must discriminate  whether the features produced by E1 come from A or B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Thus, the encoder E1 not only has to learn a good feature  space for its task, but it is also asked to fool the critic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' After-  wards, we can proceed to learn a mapping function G1→2  among tasks as usual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In Table 7 we compare this standard  DA methodology to our NDA loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Adversarial training  (second row) does not introduce significant improvements  with respect to not performing DA for T1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', base AT/DT,  first row), while constraining the features extracted by E1  in a norm aligned space (third row) significantly increases  both performance metrics with respect to the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Our  intuition is that, although adversarial training can be useful  for domain alignment, it alters the learned feature space  with the goal of fooling the critic and this training objective  can lead to worse performances on the current task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Our  NDA loss, on the other hand, acts as a regularizer that  favors the learning of an homogeneous latent space across  the domains involved in our experiments, improving the  generalization capability of the transfer network without  11  TABLE 4  Comparison between autoencoder and edge detection as auxiliary tasks in the Dep → Sem scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Best results highlighted in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Taux  Road  Sidewalk  Walls  Fence  Person  Poles  Vegetation  Vehicles  Tr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Signs  Building  Sky  mIoU  Acc  None  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='95 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='77 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='16 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='21 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='93 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='92 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='50 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='37 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='24 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='29 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='12  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='04  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='90  Autoencoder  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='68 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='12 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='45  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='08  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='40 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='43 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='72 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='51 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='95 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='68  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='07  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='31  Edge detection 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='12 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='90 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='63 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='40 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='98 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='34 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='50 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='11 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='04 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='61  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='16  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='21  TABLE 5  Auxiliary tasks as source tasks in the Dep → Sem scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Best results highlighted in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Taux as T1  Road  Sidewalk  Walls  Fence  Person  Poles  Vegetation  Vehicles  Tr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Signs  Building  Sky  mIoU  Acc  Autoencoder  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='24 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='33 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='67  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='00  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='91  Edge Detection 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='90  TABLE 6  Ablation study on the importance of simultaneous training of the T1, T2, and the auxiliary task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Best results highlighted in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' See text for a  detailed explanation of the training protocol used in each row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  method  Road  Sidewalk  Walls  Fence  Person  Poles  Vegetation  Vehicles  Tr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Signs  Building  Sky  mIoU  Acc  base AT/DT  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='72  Simultaneous (N1 + N2 + edge)  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='50 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='11 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='04 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='61  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='16  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='21  degrading the performances in the single tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Then, from  the third to the fifth row, we compare our NDA loss with  another strategy, LargerNorm [24], that also align features  across domains operating on the feature norms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' They show  that features are more transferable across domains if we  constrain feature norms to be equal to an arbitrary large  number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We notice that the method is very sensible to the  norm value, and it could be hard to select without using  target labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' When using an appropriate norm value (25,  fourth row), the method achieves a slight improvement over  the baseline without alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, since it just force  all features globally to be a large number, it is not well-  suited for tasks in which we have a spatial dimensions  such as semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Moreover, in the sixth row,  we experiment also with a more recent adversarial loss  formulation, Asymmetric Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [58], which preserve discrim-  inability while performing domain alignment by chang-  ing only target features instead of both source and target  ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, we notice that this method is achieving  the worst results among feature alignment strategies, even  worse than the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Our motivation is that aligning  feature distribution in such a high dimensional feature space  with a spatial structure might be too difficult to achieve by  only changing target features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Finally, we notice that NDA  achieves the best performance probably because it only align  features norm rather than the whole marginal distribution,  which is an easier goal that can be achieved also in high-  dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Moreover, NDA operates at each spatial  location independently rather than globally, exploiting the  spatial priors similarity across domains, reaching better  performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='6  Aligning N2 features  We tried to perform feature alignment across domains also  on the features f2 extracted by E2, either by deploying  adversarial training or imposing our NDA loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The idea  is to favor the generalization of G1→2 by making more  homogeneous not only its input space (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', the features  produced by E1, aligned with our NDA loss), but also its  output space, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', the features produced by E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However,  the setting is not completely symmetric: when learning E2,  we do not have supervision available for B, and the only  loss shaping the feature space for its images would be the  alignment loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We report results of this ablation study in  Table 8 and discuss them below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  In the first row, we report the results provided by the  base AT/DT (without LNDA and Laux).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In the following  two rows, we show results obtained by an adversarial (row  2) and an asymmetric adversarial [58] (row 3) training  12  TABLE 7  Comparison between NDA loss and other strategies to align E1 features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Best results highlighted in bold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  E1 Align.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Road  Sidewalk  Walls  Fence  Person  Poles  Vegetation  Vehicles  Tr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Signs  Building  Sky  mIoU  Acc  None  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='95 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='77 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='92 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='50 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='37 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='24 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='29 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='12  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='04  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+page_content='10 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='72 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='38 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='47 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='67 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='67  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='30  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='77  on the features f2, using the same procedures described  in the previous sub-section for f1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We can observe that,  not only both adversarial trainings does not improve (like  adversarial training applied to E1), but they even decrease  the overall mIoU compared to the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Finally, in the  fourth row, we report the results obtained by our NDA loss  on f2: the NDA loss destroys the feature space of T2 when  applied in this context, as vouched by the drop of 20% in  the overall mIoU wrt to base AT/DT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  During AT/DT inference, we use also D2 to yield the  final task predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Nevertheless, D2 has been trained  only on A, thus its performance may be harmed when  using B images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Thus, we ran an additional test reported in  Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Following [29] we train N2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', E2 and D2) using  an adversarial loss on the D2 output space, thus making  D2 aware of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Then, we train G1→2 to map features of  E1 into features of E2, and during inference we employ the  previously trained decoder D2 to produce the final outputs  reporting the results in row Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='. We notice a clear drop  in performance w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' base AT/DT (row None), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' AT/DT  trained without LNDA and Laux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  We formulate the following hypothesis to explain the  13  above results: all adversarial trainings and NDA loss try  to align f A  2  and f B  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' While f A  2  are shaped also by the su-  pervision of T2, f B  2 evolve only according to the additional  loss we impose, as we do not have supervision for T2 on  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, E2 is shared across domains, and therefore  may be pushed to produce worse representations for both  domains while it tries to accomplish the adversarial objec-  tives or the NDA loss minimization for B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' If this happens,  mappings learned by G1→2 from f A  1 to f A  2 will hallucinate  worse features for T2 on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' To understand why adversarial  trainings leads to small decreases in performances com-  pared to the use of NDA loss, we ought to consider that  adversarial training implies a discriminator that cannot be  easily fooled by totally degenerated features, while, without  any additional constrain from task supervision, the NDA  loss may yield totally collapsed representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='7  Aligning G1→2 features  Although feature alignment does not turn out beneficial  when training N2, one may still expect to obtain better  hallucinated features if the representations obtained when  transferring f A  1 and f B  1 are aligned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We empirically found  out that even though output space aligning strategies de-  ployed when training G1→2 can lead to improvements in  performance, input space alignment using our NDA loss  deployed when training N1 is more effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Moreover,  combining input and output space alignment techniques  does not lead to further improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We performed this  ablation study in the Dep → Sem scenario using Carla as  A and Cityscapes as B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' The results of these experiments are  reported in Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  First, we applied our NDA loss to the output-space of  G1→2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Similarly to what discussed in the previous section,  we notice that, without supervision on B, the representa-  tions transformed from G1→2 while minimizing the NDA  loss yield a drastic drop in the framework performance  (row 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We also tried to align the output space features by  training G1→2 alongside a discriminator in an adversarial  fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We wanted to fool the discriminator in order to  generate indistinguishable features from A or B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We notice  that this strategy allows us to reach good overall perfor-  mances with a 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='32 mIoU on Cityscapes (second row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Moreover, we thought that, as adversarial training provides  a supervision on B, using the NDA loss in combination with  the adversarial loss could avoid producing degenerated  features for B while reaching a better overall alignment  between A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, we notice that the combination  of the two losses leads us to slightly worse results than  adversarial training alone (rows 2 vs 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Furthermore, since  using an adversarial loss on the output space of G1→2 lead  us to good overall performances, we tested it in combination  with the best input space alignment from Table 7, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' NDA  loss applied when training N1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' However, the combination  of these two methods achieves worse performance than  using only the NDA loss on input space (rows 6 vs 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Finally, we also experimented a different alignment strategy  for the G1→2 output space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Instead of directly applying  adversarial loss in E2 feature space, we apply adversarial  loss in D2 output space while training G1→2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' As discussed  in [29], output space is easier to align than feature space for  several reasons: i) the scene semantic structure is typically  similar across domains ii) the feature space encode many  information such as color, light, textures iii) the feature  space has higher dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' By aligning D2 output space  we indirectly influence also E2 features making them more  domain aligned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' During training, we keep D2 frozen and  we update only G1→2 weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Also in this case, if compare  this methodology with simply using LNDA alone (row 6 vs  row 7), it achieves worse results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  7  CONCLUDING REMARKS  We have introduced a framework to transfer knowledge  between different tasks by learning an explicit mapping  function between deep features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' This mapping function can  be parametrized by a neural network and show interesting  generalization capabilities across domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' To further ame-  liorate performance we have proposed two novel feature  alignment strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' At a domain level, we showed that  the transfer function presented in our framework can be  boosted by making its input space more homogeneous  across domains with our simple yet effective NDA loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  At a task level, instead, we reported how deep features  extracted for different tasks can be enriched and aligned  with the introduction of a shared auxiliary task, which  we implemented as edge detection in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We  reported good results in the challenging synthetic to real  scenario while transferring knowledge between the seman-  tic segmentation and monocular depth estimation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Our proposal is complementary to the whole domain  adaptation literature and might be integrated with it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' While  DA directly applied to the learned feature space does not  seems effective (see Table 8) more modern techniques either  try to align the prediction in the final label space [29] or  rely on self-ensembling for pseudo labeling [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' We plan to  incorporate these promising direction into our framework  as part of future developments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  REFERENCES  [1]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zamir, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Sax, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Shen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Guibas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Malik, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Savarese,  “Taskonomy: Disentangling task transfer learning,” in Proceedings  of the IEEE Conference on Computer Vision and Pattern Recognition,  2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 3712–3722.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [2]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zamir, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Sax, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Cheerla, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Suri, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Cao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Malik, and  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Guibas, “Robust learning through cross-task consistency,”  in Proceedings of the IEEE/CVF Conference on Computer Vision and  Pattern Recognition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 11 197–11 206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [3]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wang and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Deng, “Deep visual domain adaptation: A  survey,” Neurocomputing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 312, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 135–153, Oct 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Available: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='neucom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='083  [4]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ramirez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tonioni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Salti, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Stefano, “Learning  across tasks and domains,” in Proceedings of the IEEE International  Conference on Computer Vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 8110–8119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [5]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ramirez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tonioni, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Di Stefano, “Exploiting semantics  in adversarial training for image-level domain adaptation,” in  2018 IEEE International Conference on Image Processing, Applications  and Systems (IPAS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 49–54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [6]  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Soria, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Riba, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Sappa, “Dense extreme inception network:  Towards a robust cnn model for edge detection,” in The IEEE  Winter Conference on Applications of Computer Vision (WACV ’20),  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [7]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Xie  and  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Tu,  “Holistically-nested  edge  detection,”  CoRR,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  abs/1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='06375,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Available:  http:  //arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/abs/1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='06375  14  [8]  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Li, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Huang, “Deep crisp boundaries:  From boundaries to higher-level tasks,” IEEE Transactions on  Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 28, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1285–1298, Mar 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Available: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/TIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2874279  [9]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Dosovitskiy, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ros, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Codevilla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Lopez, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Koltun,  “CARLA: An open urban driving simulator,” in Proceedings of the  1st Annual Conference on Robot Learning, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Cordts, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Omran, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ramos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Rehfeld, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Enzweiler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Be-  nenson, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Franke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Roth, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Schiele, “The cityscapes dataset  for semantic urban scene understanding,” in The IEEE Conference  on Computer Vision and Pattern Recognition (CVPR), June 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [11] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhuang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Qi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Duan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Xi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Xiong,  and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' He, “A comprehensive survey on transfer learning,” arXiv  preprint arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='02685, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yosinski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Clune, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Bengio, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Lipson, “How transferable  are features in deep neural networks?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' in Advances in neural  information processing systems, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 3320–3328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Deng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Dong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Socher, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Li, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Fei-Fei, “Im-  agenet: A large-scale hierarchical image database,” in 2009 IEEE  conference on computer vision and pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Ieee, 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  248–255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Redmon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Divvala, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Girshick, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Farhadi, “You only look  once: Unified, real-time object detection,” in Proceedings of the IEEE  conference on computer vision and pattern recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 779–  788.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ren, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' He, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Girshick, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Sun, “Faster r-cnn: Towards  real-time  object  detection  with  region  proposal  networks,”  IEEE Transactions on Pattern Analysis and Machine Intelligence,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 39, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 6, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1137–1149, Jun 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Available:  http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/TPAMI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2577031  [16] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' He, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Gkioxari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Dollar, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Girshick, “Mask r-cnn,” 2017  IEEE International Conference on Computer Vision (ICCV), Oct 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Available: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/ICCV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='322  [17] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Anguelov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Erhan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Szegedy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Reed, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Fu,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Berg, “Ssd: Single shot multibox detector,” in European  conference on computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Springer, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 21–37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [18] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Pal and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Balasubramanian, “Zero-shot task transfer,” in The  IEEE Conference on Computer Vision and Pattern Recognition (CVPR),  June 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Gong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Shi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Sha, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Grauman, “Geodesic flow kernel for  unsupervised domain adaptation,” in Computer Vision and Pattern  Recognition (CVPR), 2012 IEEE Conference on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' IEEE, 2012, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 2066–  2073.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Long, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Cao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Jordan, “Learning transferable  features with deep adaptation networks,” in Proceedings of the 32nd  International Conference on Machine Learning, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Proceedings of  Machine Learning Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  PMLR, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 97–105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [21] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ganin and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Lempitsky, “Unsupervised domain adaptation by  backpropagation,” in International Conference on Machine Learning,  2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1180–1189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [22] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ganin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ustinova, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ajakan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Germain, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Larochelle,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Laviolette,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Marchand,  and  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Lempitsky,  “Domain-  adversarial training of neural networks,” The Journal of Machine  Learning Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 2096–2030, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [23] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tzeng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hoffman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Saenko, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Darrell, “Adversarial  discriminative domain adaptation,” in Computer Vision and Pattern  Recognition (CVPR), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [24] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Xu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Lin, “Larger norm more transferable:  An adaptive feature norm approach for unsupervised domain  adaptation,” in Proceedings of the IEEE International Conference on  Computer Vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1426–1435.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [25] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Goodfellow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Pouget-Abadie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Mirza, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Warde-Farley,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ozair, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Courville, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Bengio, “Generative adversarial  nets,” in Advances in neural information processing systems, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  2672–2680.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Park, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Isola, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Efros, “Unpaired image-to-  image translation using cycle-consistent adversarial networks,” in  The IEEE International Conference on Computer Vision (ICCV), Oct  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [27] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Bousmalis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Silberman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Dohan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Erhan, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Krishnan,  “Unsupervised pixel-level domain adaptation with generative  adversarial networks,” 2017 IEEE Conference on Computer Vision  and Pattern Recognition (CVPR), Jul 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Available:  http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='18  [28] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Isola, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhou, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Efros, “Image-to-image  translation with conditional adversarial networks,” in The IEEE  Conference on Computer Vision and Pattern Recognition (CVPR), July  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [29] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tsai, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Schulter, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Sohn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yang, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Chandraker, “Learning to adapt structured output space for  semantic segmentation,” 2018 IEEE/CVF Conference on Computer  Vision and Pattern Recognition, Jun 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Available:  http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='00780  [30] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yuan, “Conditional gener-  ative adversarial network for structured domain adaptation,” in  Proceedings of the IEEE Conference on Computer Vision and Pattern  Recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1335–1344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [31] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Pizzati, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Charette, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zaccaria, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Cerri, “Domain  bridge for unpaired image-to-image translation and unsupervised  domain adaptation,” in The IEEE Winter Conference on Applications  of Computer Vision, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 2990–2998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hoffman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yu, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Darrell, “Fcns in the wild: Pixel-  level adversarial and constraint-based adaptation,” arXiv preprint  arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='02649, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [33] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' David, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Gong, “Curriculum domain adaptation  for semantic segmentation of urban scenes,” in The IEEE Interna-  tional Conference on Computer Vision (ICCV), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [34] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Chang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Peng, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Chiu, “All  about structure: Adapting structural information across domains  for boosting semantic segmentation,” in Proceedings of the IEEE  Conference on Computer Vision and Pattern Recognition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  1900–1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hoffman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tzeng, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Isola, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Saenko,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Efros, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Darrell, “CyCADA: Cycle-consistent adversarial  domain adaptation,” in Proceedings of the 35th International Con-  ference on Machine Learning, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Proceedings of Machine Learning  Research, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Dy and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Krause, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Stockholmsm¨assan,  Stockholm Sweden: PMLR, 10–15 Jul 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1989–1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Shrivastava, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Pfister, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tuzel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Susskind, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wang, and  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Webb, “Learning from simulated and unsupervised images  through adversarial training,” in The IEEE Conference on Computer  Vision and Pattern Recognition (CVPR), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [37] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Qiu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Liu, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Mei, “Fully convolutional  adaptation networks for semantic segmentation,” 2018 IEEE/CVF  Conference on Computer Vision and Pattern Recognition, Jun 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Available: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='00712  [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Sankaranarayanan,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Balaji,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Jain,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Lim,  and  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Chellappa, “Learning from synthetic data: Addressing domain  shift for semantic segmentation,” 2018 IEEE/CVF Conference on  Computer Vision and Pattern Recognition, Jun 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Available: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='00395  [39] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Pan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Shin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Rameau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Lee, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Kweon, “Unsupervised  intra-domain adaptation for semantic segmentation through self-  supervision,” in Proceedings of the IEEE/CVF Conference on Computer  Vision and Pattern Recognition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 3764–3773.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Kim and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Byun, “Learning texture invariant representation  for domain adaptation of semantic segmentation,” in Proceedings of  the IEEE/CVF Conference on Computer Vision and Pattern Recognition,  2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 12 975–12 984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [41] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tonioni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Poggi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Mattoccia, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Di Stefano, “Unsu-  pervised adaptation for deep stereo,” in The IEEE International  Conference on Computer Vision (ICCV), Oct 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [42] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zheng, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Cham, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Cai, “T2net: Synthetic-to-realistic  translation for solving single-image depth estimation tasks,” in The  European Conference on Computer Vision (ECCV), September 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tonioni, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tosi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Poggi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Mattoccia, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Stefano, “Real-  time self-adaptive deep stereo,” in The IEEE Conference on Computer  Vision and Pattern Recognition (CVPR), June 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [44] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Lee, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ros, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Li, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Gaidon, “SPIGAN: Privileged  adversarial learning from simulation,” in International Conference  on  Learning Representations,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Available:  https:  //openreview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='net/forum?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='id=rkxoNnC5FQ  [45] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Kokkinos, “Ubernet: Training a universal convolutional neural  network for low-, mid-, and high-level vision using diverse  datasets and limited memory,” 2017 IEEE Conference on Computer  Vision and Pattern Recognition (CVPR), Jul 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Available:  http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='579  [46] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ramirez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Poggi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tosi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Mattoccia, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Di Stefano,  “Geometry meets semantics for semi-supervised monocular depth  estimation,” in Asian Conference on Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Springer,  2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 298–313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [47] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Cipolla, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Gal, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Kendall, “Multi-task learning using  uncertainty to weigh losses for scene geometry and semantics,”  15  2018  IEEE/CVF  Conference  on  Computer  Vision  and  Pattern  Recognition, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Available: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/  CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='00781  [48] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tosi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Aleotti, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ramirez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Poggi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Salti, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Di Stefano,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Mattoccia, “Distilled semantics for comprehensive scene  understanding from videos,” in Proceedings of the IEEE Conference  on Computer Vision and Pattern Recognition, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [49] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Tzeng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hoffman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Darrell, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Saenko, “Simultaneous  deep transfer across domains and tasks,” in Proceedings of the IEEE  International Conference on Computer Vision, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 4068–4076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [50] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Kundu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Lakkakula, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Babu, “Um-adapt: Unsuper-  vised multi-task adaptation using adversarial cross-task distilla-  tion,” in Proceedings of the IEEE International Conference on Computer  Vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 1436–1445.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Richter, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hayder, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Koltun, “Playing for benchmarks,”  in IEEE International Conference on Computer Vision, ICCV 2017,  Venice, Italy, October 22-29, 2017, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 2232–2241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Available: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='1109/ICCV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='243  [52] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Xian, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Chen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Liu, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Madhavan,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Darrell, “Bdd100k: A diverse driving dataset for heteroge-  neous multitask learning,” in Proceedings of the IEEE/CVF conference  on computer vision and pattern recognition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 2636–2645.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [53] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Geiger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Lenz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Stiller, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Urtasun, “Vision meets  robotics: The kitti dataset,” International Journal of Robotics Research  (IJRR), 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [54] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Hirschmuller, “Accurate and efficient stereo processing by  semi-global matching and mutual information,” in Computer Vision  and Pattern Recognition, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' CVPR 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' IEEE Computer Society  Conference on, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  IEEE, 2005, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 807–814.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [55] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yu, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Koltun, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Funkhouser, “Dilated residual networks,”  in Computer Vision and Pattern Recognition (CVPR), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [56] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Peng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Wu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Ernst, “Zero-shot deep domain adapta-  tion,” in Proceedings of the European Conference on Computer Vision  (ECCV), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 764–781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [57] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Eigen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Puhrsch, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Fergus, “Depth map prediction from  a single image using a multi-scale deep network,” in Advances in  neural information processing systems, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 2366–2374.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [58] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zhou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Zeng, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Xie, “Mind the  discriminability: Asymmetric adversarial domain adaptation,” in  European Conference on Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Springer, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 589–  606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  [59] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Choi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Kim, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Kim, “Self-ensembling with gan-based data  augmentation for domain adaptation in semantic segmentation,”  in Proceedings of the IEEE international conference on computer vision,  2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' 6830–6840.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Pierluigi Zama Ramirez is a Post Doc at the  Computer Vision Laboratory (CVLab), University  of Bologna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' His research interests include deep  learning, semantic segmentation, depth estima-  tion, optical flow and domain adaptation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' He has  authored more than 10 papers on these sub-  jects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Adriano Cardace is a PhD student at the Com-  puter Vision Laboratory (CVLab), University of  Bologna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' His research interests include deep  learning for Computer Vision problems, espe-  cially semantic segmentation, domain adapta-  tion and self-supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Luca De Luigi is a PhD student at the Computer  Vision Laboratory (CVLab) at the University of  Bologna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' His research focuses on deep learning  for computer vision problems, especially dealing  with 3D geometry and implicit neural represen-  tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Alessio Tonioni received his PhD degree in  Computer Science and Engineering from Uni-  versity of Bologna in 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Currently, he is a  research scientist at Google Zurich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' His research  interest concerns machine learning for depth es-  timation, domain adaptation and generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  He has authored more than 15 papers on these  subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Samuele Salti is currently assistant professor  at the Department of Computer Science and  Engineering (DISI) of the University of Bologna,  Italy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Before joining the University of Bologna,  he was leading the Data Science team at Veri-  zon Connect, the world leading company in fleet  management products and connected vehicles  services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' His main research interest is computer  vision, in particular 3D computer vision, and ma-  chine/deep learning applied to computer vision  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' Salti has co-authored 42 publi-  cations in international conferences and journals and 8 international  patents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' In 2020, he co-founded the start-up eyecan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' He was awarded  the best paper award runner-up at 3DIMPVT 2011, the top international  conference on 3D computer vision, and was nominated outstanding  reviewer at CVPR 2020 and NeurIPS 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  Luigi Di Stefano received the PhD degree in  electronic engineering and computer science  from the University of Bologna, in 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' He is  currently a full professor with the Department of  Computer Science and Engineering, University  of Bologna, where he founded and leads the  Computer Vision Laboratory (CVLab).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' His re-  search interests include image processing, com-  puter vision and machine/deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' He is  the author of more than 150 papers and several  patents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content=' He has been scientific consultant for  major companies in the fields of computer vision and machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
+page_content='  He is a member of the IEEE Computer Society, IEEE, and the IAPR-IC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFIT4oBgHgl3EQfmivq/content/2301.11310v1.pdf'}
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+MNRAS 000, 1–18 (2023)
+Preprint 10th January 2023
+Compiled using MNRAS LATEX style file v3.0
+An emulator-based halo model in modified gravity – I. The halo
+concentration-mass relation and density profile
+Cheng-Zong Ruan1,2, Carolina Cuesta-Lazaro1,3, Alexander Eggemeier4⋆, Baojiu Li1†,
+Carlton M. Baugh1,3, Christian Arnold1, Sownak Bose1, César Hernández-Aguayo5,6,
+Pauline Zarrouk7 and Christopher T. Davies8
+1Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
+2Institute of Theoretical Astrophysics, University of Oslo, 0315 Oslo, Norway
+3Institute for Data Science, Durham University, South Road, Durham DH1 3LE, UK
+4Argelander-Institut für Astronomie, Auf dem Hügel 71, D-53121 Bonn, Germany
+5Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild-Str 1, D-85748 Garching, Germany
+6Excellence Cluster ORIGINS, Boltzmannstrasse 2, D-85748 Garching, Germany
+7Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE),
+4 place Jussieu, F-75252, Paris Cedex 5, France
+8Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany
+Accepted XXX. Received YYY; in original form 10th January 2023
+ABSTRACT
+In this series of papers we present an emulator-based halo model for the non-linear clustering
+of galaxies in modified gravity cosmologies. In the first paper, we present emulators for the
+following halo properties: the halo mass function, concentration-mass relation and halo-matter
+cross-correlation function. The emulators are trained on data extracted from the FORGE
+and BRIDGE suites of N-body simulations, respectively for two modified gravity (MG)
+theories: f(R) gravity and the DGP model, varying three standard cosmological parameters
+Ωm0, H0, σ8, and one MG parameter, either ¯fR0 or rc. Our halo property emulators achieve
+an accuracy of ≲ 1% on independent test data sets. We demonstrate that the emulators can be
+combined with a galaxy-halo connection prescription to accurately predict the galaxy-galaxy
+and galaxy-matter correlation functions using the halo model framework.
+Key words: dark energy – large-scale structure of Universe – cosmology: miscellaneous –
+cosmology: theory.
+1
+INTRODUCTION
+Ongoing and upcoming galaxy surveys, such as those that will be
+made with the Dark Energy Spectroscopic Instrument (DESI; DESI
+Collaboration et al. 2016), the Vera Rubin Observatory (LSST Sci-
+ence Collaboration et al. 2009) and Euclid (Laureijs et al. 2011;
+Amendola et al. 2013; Troja et al. 2022) will map the large scale
+structure (LSS) of the Universe with unprecedented statistical pre-
+cision. Measurements of the large-scale structure can potentially be
+used to unveil the nature of the dark matter and dark energy, and
+to look for any deviation from the predictions of general relativ-
+ity (GR). Theories of gravity beyond GR – modified gravity (MG)
+models – can explain the observed accelerated expansion of the Uni-
+verse without invoking a cosmological constant (e.g. Koyama 2018;
+Ferreira 2019). Studies of such models will not only shed light on
+⋆ Argelander Fellow
+† E-mail: baojiu.li@durham.ac.uk
+the nature of the cosmic acceleration, but also serve as useful tests
+of GR on cosmic scales.
+The impact of modifications to GR has been well studied in
+terms of the cosmic expansion history and the large scale structure,
+i.e., at the background and linear perturbation levels. In the late
+universe, the growth of LSS eventually enters the non-linear regime
+over a wide range of length scales, and linear theory predictions
+cease to be valid. This point becomes even more acute in the context
+of MG, given that such models have intrinsically non-linear features,
+such as screening mechanisms and non-linear field equations for
+new degrees of freedom, which cannot be captured by linear theories
+(e.g. Li et al. 2013). Often a choice is made to exclude small scale
+data, thereby losing a wealth of information from high signal-to-
+noise ratio measurements. Such nonlinearities must be properly
+incorporated into theoretical modelling if one wishes to make the
+best use of the current and next generation cosmological surveys to
+constrain cosmological parameters and test gravity theories.
+A fully non-linear treatment – N-body simulations – is essen-
+tial to accurately solve the non-linear dynamics of cosmic struc-
+© 2023 The Authors
+arXiv:2301.02970v1  [astro-ph.CO]  8 Jan 2023
+
+2
+C. Ruan et al.
+ture formation (see e.g. Kuhlen et al. 2012; Angulo & Hahn 2022,
+for recent reivews). The main hurdle of N-body simulations is
+their expensive computational cost. A Monte Carlo Markov chain
+(MCMC) analysis, usually used to confront theoretical predictions
+with data, requires sampling at least 104-105 models in the cosmo-
+logical parameter space. Probing such a large number of models
+using simulations is computationally prohibitive. The situation is
+even worse for MG models, which usually involve partial differen-
+tial equations governing the new physics. Current MG simulations
+can take between 2 to O(10) times longer than standard ΛCDM
+simulations with the same specifications (e.g. Li et al. 2012; Arnold
+et al. 2019a).
+There are several approaches to dealing with the non-linear
+regime in addition to simulations. N-body simulation results can
+be used to develop phenomenological or semi-analytical fitting for-
+mulae to describe the statistical properties of matter and dark matter
+haloes, such as the halo mass function calibrated by Tinker et al.
+(2008), and the halofit prescription for the matter power spectrum
+(Smith et al. 2003; Takahashi et al. 2012; Smith & Angulo 2019;
+Mead et al. 2021) and bispectrum (Takahashi et al. 2020). The most
+up-to-date version of halofit implemented by Mead et al. (2021)
+achieves an accuracy of 5% down to deeply non-linear scales. How-
+ever, such parametric fits may no longer be fit for purpose with the
+advent of next-generation surveys that promise to reach measure-
+ments with per cent level precision.
+The halo model (Neyman & Scott 1952; Ma & Fry 2000;
+Peacock & Smith 2000; Seljak 2000; Cooray & Sheth 2002; Schmidt
+2016; Philcox et al. 2020) is a successful analytical description of
+the LSS in the non-linear regime. In this framework, all matter,
+including galaxies and any other tracers, is assumed to reside within
+haloes. Then, the problem of predicting the clustering can be split
+into the following steps:
+• the abundance of haloes as a function of halo mass, i.e. the
+halo mass function (HMF);
+• the distribution of tracers around the halo centre, i.e. the
+halo density profile, usually assumed to be a Navarro-Frenk-White
+(NFW) profile (Navarro et al. 1996, 1997) specified by a halo mass-
+concentration relation; and
+• the clustering of the haloes themselves, e.g., the halo two-point
+correlation function (TPCF) in configuration space and the halo auto
+power spectrum in Fourier space.
+These basic properties of dark matter haloes constitute the halo
+model ingredients. The halo model provides a physically motivated
+description of the clustering statistics and is flexible enough to
+be extended to incorporate new physics such as massive neutrinos
+and baryonic feedback (e.g. Massara et al. 2014; Bose et al. 2021;
+Carrilho et al. 2022), as well as models beyond ΛCDM and GR (e.g.
+Barreira et al. 2014; Lombriser et al. 2014; Hu et al. 2018; Cataneo
+et al. 2019).
+The halo model ingredients can be derived from analytic meth-
+ods. For example, the HMF can be predicted using the spherical
+collapse model of the linear matter density field (Press & Schechter
+1974) and the excursion set formalism (Bond et al. 1991; Sheth et al.
+2001), whereby the dependence of the HMF on redshift and cos-
+mology is expressed in terms of the root-mean-square fluctuations
+in the linear matter power spectrum. Jenkins et al. (2001) found
+that this universality of the HMF holds at an approximate level. As
+simulation predictions improved further, it was discovered that the
+redshift evolution of the mass function, even for ΛCDM, deviates
+from the universal prediction at the 5-10 per cent level, and several
+new fitting formulae were proposed (e.g. Tinker et al. 2008; Courtin
+et al. 2011). Moreover, the universality of the HMF is broken further
+in extensions of ΛCDM (e.g. Bhattacharya et al. 2011, for wCDM)
+and modified gravity models (e.g. Schmidt et al. 2010; Lam & Li
+2012; Li & Efstathiou 2012; Lombriser et al. 2013; Cataneo et al.
+2016; Gupta et al. 2022). In order to obtain even tighter constraints
+on cosmological parameters and to test gravity theories, one there-
+fore needs to proceed beyond the traditional approaches, given their
+limitations in accuracy and coverage of parameter space.
+In this series of papers, we develop simulation-based theoret-
+ical templates called emulators, to obtain accurate predictions for
+basic halo properties as a function of halo mass and (modified grav-
+ity) cosmology, and to construct accurate predictions for clustering
+observables in preparation for ongoing and future galaxy surveys.
+There have been several previous works on the emulation of cos-
+mological quantities in the ΛCDM model and its extensions, such
+as Heitmann et al. (2006); Habib et al. (2007), the Coyote Universe
+(Heitmann et al. 2010, 2009; Lawrence et al. 2010), PkANN (Agar-
+wal et al. 2012, 2014), the Mira-Titan Universe (Heitmann et al.
+2016; Lawrence et al. 2017; Bocquet et al. 2020), Kwan et al. (2013,
+2015), Aemulus (DeRose et al. 2019; McClintock et al. 2019; Zhai
+et al. 2019), Dark Quest (Nishimichi et al. 2019; Kobayashi et al.
+2020; Miyatake et al. 2020; Cuesta-Lazaro et al. 2022), matry-
+oshka (Donald-McCann et al. 2022) and AbacusSummit (Mak-
+simova et al. 2021; Yuan et al. 2022), as well as in non-standard
+cosmologies, such as Winther et al. (2019); Ramachandra et al.
+(2021); Arnold et al. (2022); Brando et al. (2022); Harnois-Déraps
+et al. (2022).
+To build emulators we use the machine-learning interpolation
+technique of neural networks, which allows us to predict halo proper-
+ties for any given cosmology within the range of parameters covered
+by the training data set. We use the FORGE (F-Of-R Gravity Emu-
+lator) and BRIDGE (BRaneworld-Inspired Dgp Gravity Emulator)
+modified gravity N-body simulations described in Arnold et al.
+(2022), which together cover a very broad range of parameters in
+two MG theories: f(R) gravity and the DGP model. The emulated
+halo properties incorporate all the complicated effects on non-linear
+scales, such as the non-linear halo bias, the halo exclusion effect and
+the screening mechanism.
+Following the spirit of the Dark Quest project (Nishimichi
+et al. 2019; Cuesta-Lazaro et al. 2022), we do not perform an end-
+to-end emulation of galaxy clustering statistics in the joint para-
+meter space of cosmological and galaxy-halo connection models.
+Instead, we develop emulators for each halo property separately,
+and assemble these ingredients within the halo model framework
+to construct analytical predictions of galaxy clustering statistics.
+This emulator-based halo model gives us the flexibility to insert dif-
+ferent prescriptions of galaxy-halo connection for different galaxy
+samples. Moreover, emulators for basic halo properties themselves
+are very useful. For example, calibrating the cosmology depend-
+ence of the HMF is crucial to control the systematic uncertainty
+in galaxy cluster abundance studies (e.g. McClintock et al. 2019;
+Bocquet et al. 2020).
+The layout of this paper is as follows. In Section 2, we present
+a short description of the modified gravity theories studied here and
+a brief overview of the FORGE and BRIDGE N-body simulation
+suites. In Section 3, we outline the measurement and post-processing
+of the halo properties from the simulations. Section 4 describes the
+construction of the halo property emulators using neural networks,
+and Section 5 shows their performance in reproducing the simula-
+tion results. In Section 6, we demonstrate how these emulators can
+be combined with a galaxy-halo connection prescription to predict
+galaxy statistics.
+MNRAS 000, 1–18 (2023)
+
+MG Emulator Halo Model I
+3
+Throughout this paper, we use log to denote the base-10 logar-
+ithm, log ≡ log10, and ln to indicate the natural logarithm. Unless
+otherwise stated, we use a subscript 0 to denote the present-day
+value of a physical quantity and an overbar for the background
+value of a quantity.
+2
+MODIFIED GRAVITY THEORIES AND SIMULATIONS
+We briefly describe the two modified gravity models analysed in this
+work, f(R) gravity (Hu & Sawicki 2007) and the Dvali-Gabadadze-
+Porrati (DGP) brane-world models (Dvali et al. 2000a). These are
+two of the most widely studied MG models and, as we discuss be-
+low, are representative examples of the two main classes of screen-
+ing mechanisms, which make them good test-beds for generic MG
+models. For more detailed descriptions of these models, we refer
+the reader to Sotiriou & Faraoni (2010) and De Felice & Tsujikawa
+(2010) for f(R) gravity, and Sahni & Shtanov (2003) and Maartens
+& Koyama (2010) for DGP models.
+2.1
+f(R) gravity
+The f(R) gravity is a generalisation of Einstein’s general relativity.
+In f(R) gravity, the Einstein-Hilbert action in GR has an additional
+term, which is a function of the Ricci scalar R,
+S =
+�
+d4x√−g
+�M 2
+Pl
+2 [R + f(R)] + Lm
+�
+,
+(1)
+where MPl = (8πG)−1/2 is the reduced Planck mass, G is New-
+ton’s constant, g is the determinant of the metric gµν and Lm is
+the Lagrangian density for matter fields. Varying the action with
+respect to the metric gµν gives the modified Einstein equation,
+Gµν + fRRµν −
+�1
+2f − □fR
+�
+gµν − ∇µ∇νfR = 8πGT m
+µν,
+(2)
+where
+Gµν ≡ Rµν − 1
+2gµνR,
+(3)
+is the Einstein tensor, fR ≡ df(R)/dR, ∇µ is the covariant deriv-
+ative corresponding to the metric gµν, □ ≡ ∇α∇α and T m
+µν is the
+energy momentum tensor for matter.
+Equation (2) is a fourth-order partial differential equation in
+gµν. This equation can also be considered as the standard Einstein
+equation in GR with a new dynamical degree of freedom, fR, which
+is dubbed the scalaron (e.g., Zhao et al. 2011). The equation of
+motion of fR can be obtained by taking the trace of Equation (2):
+□fR = 1
+3(R − fRR + 2f + 8πGρm) ,
+(4)
+where ρm is the matter density.
+For cosmological simulations in standard gravity, the Newto-
+nian limit is commonly adopted. This includes the approximations
+that the gravitational and scalar fields are weak (such that their
+higher-order terms can be neglected) and quasi-static (so that the
+time derivatives of the fields can be neglected compared to their
+spatial derivatives). Most modified gravity simulations (including
+the ones used in this work) adopt this assumption. In the context
+of f(R) gravity and the Newtonian limit, the modified Einstein
+equation (2) becomes
+∇2Φ ≈ 16πG
+3
+a2(ρm − ¯ρm) + 1
+6a2�
+R(fR) − ¯R
+�
+,
+(5)
+and the equation of motion of the scalaron reduces to
+∇2fR ≈ −1
+3a2�
+R(fR) − ¯R + 8πG(ρm − ¯ρm)
+�
+,
+(6)
+where Φ is the Newtonian potential, ∇ is the 3-dimensional gradient
+operator, and an overbar denotes the cosmic mean of a quantity.
+An f(R) gravity model is fully specified by the functional
+form of f(R). Here, we adopt the well-studied Hu-Sawicki model
+(Hu & Sawicki 2007), which is given by
+f(R) = −m2
+c1(−R/m2)n
+c2(−R/m2)n + 1 ,
+(7)
+where m2 ≡ Ωm0H2
+0, and c1, c2 and n are free parameters. The
+parameter n is a positive number, which is set to n = 1 in this
+work as in most previous studies of this model (however see e.g., Li
+& Hu 2011; Ramachandra et al. 2021; Ruan et al. 2022, for some
+examples of n ̸= 1). With this functional form, we have
+fR = −
+�� ¯fR0
+��
+� ¯R0
+R
+�n+1
+,
+(8)
+where ¯R0 and ¯fR0 are, respectively, the present-day values of
+the background Ricci scalar and ¯fR. For brevity, we will ad-
+opt the following nomenclature to label models: the model with
+− log10
+�
+| ¯fR0|
+�
+= 5.5 will be called F5.5, and so on.
+The remaining free parameter of the theory is the background
+value of the scalar field fR at redshift z = 0, ¯fR0. With a suitable
+choice of this parameter, f(R) gravity reverts to GR in high-density
+regions – this is necessary to be consistent with solar system tests
+through the associated chameleon mechanism (Khoury & Weltman
+2004b,a). A larger value of | ¯fR0| means a stronger deviation from
+standard gravity. The F5 model is in slight tension with small-scale
+tests, see, e.g., Lombriser (2014) for a recent review of current
+cosmological constraints on ¯fR0. But since we aim to test gravity
+on cosmic scales, models with such strength of MG are neverthe-
+less still valuable to study: given their stronger deviations from GR
+compared to models with smaller | ¯fR0|, they can lead to import-
+ant insights into how the deviations from GR can affect large-scale
+cosmological observables such as weak lensing and galaxy cluster-
+ing statistics. In order to fully explore the gravity testing capacities
+of upcoming cosmological observations, it is important to gain a
+detailed understanding of how these measures are influenced by
+possible modifications to gravity.
+2.2
+The Dvali-Gabadadze-Porrati (DGP) model
+In the Dvali-Gabadadze-Porrati braneworld model (Dvali et al.
+2000b), the universe is a four-dimensional brane embedded in a
+five-dimensional space-time (called the bulk). The gravitational ac-
+tion in this model is given by
+S =
+�
+brane
+d4x √−g
+�
+R
+16πG
+�
++
+�
+bulk
+d5x
+�
+−g(5)
+�
+R(5)
+16πG(5)
+�
+,
+(9)
+where a superscript (5) denotes the quantity in the five-dimensional
+bulk. This model has a self-accelerating branch of solution (sDGP),
+which gives a natural explanation for the cosmic acceleration. How-
+ever, the sDGP branch suffers from the ghost problems (Koyama
+2007) and cannot be considered as a physical model. Moreover, its
+predictions have been found to be inconsistent with observations
+such as cosmic microwave background (CMB) and local measure-
+ments of the Hubble parameter H0 (e.g., Song et al. 2007; Fang
+et al. 2008).
+MNRAS 000, 1–18 (2023)
+
+4
+C. Ruan et al.
+The so-called normal branch DGP (nDGP) gravity (Koyama
+2007) cannot accelerate cosmic expansion by itself, so in order to
+explain the cosmological observations it has to introduce additional
+dark energy components. This model is nevertheless still of interest
+as a useful toy model that features the Vainshtein screening mechan-
+ism (Vainshtein 1972). Here, we assume that there is an additional
+non-clustering dark energy component in this model, which results
+in its expansion history being identical to that of ΛCDM. The nDGP
+model provides an explanation of why gravity is much weaker than
+the other fundamental forces (Maartens & Koyama 2010): all matter
+species are assumed to be confined to the brane, while gravity could
+propagate through (leak into) the extra spatial dimensions. There is
+one new free parameter in the nDGP model, which can be defined
+as the ratio of G(5) and G, and is known as the crossover scale,
+rc ≡ 1
+2
+G(5)
+G
+.
+(10)
+The modified Friedmann equation in the normal branch DGP
+model is given by
+H(a)
+H0
+=
+�
+Ωm0a−3 + ΩDE0(a) + Ωrc −
+√
+Ωrc ,
+(11)
+where Ωrc ≡ 1/(4H2
+0r2
+c), and ΩDE0 is the density parameter of
+the additional dark energy component. The dimensionless quantity
+H0rc is used to quantify departures from the standard gravity. If
+H0rc → ∞ then Eqn. (11) returns to the ΛCDM case. A larger
+value of H0rc means a weaker deviation from GR. Hereafter, an
+nDGP model with H0rc = X will be referred to as NX. For
+example, a model with H0rc = 1 is called N1.
+The modified Poisson equation and the scalar field equation
+are given by (Koyama 2007),
+∇2Φ = 4πGa2δρm + 1
+2∇2ϕ ,
+(12)
+and
+∇2ϕ +
+r2
+c
+3β a2c2
+�
+(∇2ϕ)2 − (∇i∇jϕ)2�
+= 8π G a2
+3β
+δρm ,
+(13)
+where ϕ is a new scalar degree of freedom, δρm = ρm − ¯ρm and
+β(a) ≡ 1 + 2H rc
+�
+1 +
+˙H
+3H2
+�
+= 1 +
+Ωm0a−3 + 2ΩΛ0
+2
+�
+Ωrc(Ωm0a−3 + ΩΛ0)
+.
+(14)
+2.3
+Modified gravity N-body simulations
+To construct emulators for dark matter halo properties, we use the
+FORGE and BRIDGE suites of N-body simulations (Arnold et al.
+2022), covering 49 f(R) gravity and 49 DGP models, along with
+49 ΛCDM counterparts. The simulations were performed using
+10243 dark matter particles in a cube of side 500 h−1 Mpc (here-
+after the high-resolution runs, denoted HR) or 1500 h−1 Mpc (low-
+resolution runs, labelled LR), using the modified gravity version of
+the Arepo cosmological simulation code (Springel 2010; Arnold
+et al. 2019b; Weinberger et al. 2020). The mass resolutions of the
+HR and LR runs are 9.1 × 109 and 1.5 × 1012(Ωm0/0.3) h−1 M⊙,
+respectively. The gravitational softening lengths of simulations are
+15 (HR) and 75 h−1kpc (LR). The initial conditions were generated
+using second-order Lagrangian perturbation theory (2LPT, Crocce
+et al. (2006)) at zinit = 127. Each cosmology (also called “node”)
+has two independent realisations with the pairs of initial conditions
+selected to minimise the sample variance on large scales over the
+Figure 1. Visualisation of the cosmological parameters C (Equations (16)-
+(18)) covered in the FORGE and BRIDGE simulations. The 44 training
+cosmologies, 5 validation and 2 test cosmologies are shown as black dots,
+purple triangles and red stars, respectively. ΛCDM models corresponding
+to log | ¯fR0| = −∞ and log (H0rc) = ∞ are not shown in the last two
+rows. (source code)
+realisations. All nodes were initialised with the same (two) ran-
+dom seeds. See Section 3.2 of Arnold et al. (2022) for a detailed
+description.
+The cosmological parameters were drawn from a Latin hy-
+percube designed to efficiently sample a 4-dimensional parameter
+space (or a 3-dimensional space in the case of ΛCDM), as shown
+in Fig. 1, following a similar approach to that used in the cosmo-
+SLICS project (Harnois-Déraps et al. 2019). Since FORGE and
+BRIDGE were partly designed to emulate weak lensing statistics,
+they sampled directly in the composite structure growth parameter
+S8 ≡ σ8
+�
+Ωm0
+0.3 ,
+(15)
+instead of the physical matter fluctuation amplitude parameter σ8.
+The use of S8 accounts better for the degeneracy between Ωm0 and
+σ8 in the cosmic shear analysis. The 49 nodes form the training
+data set for each gravity model. It is common practice to use a
+small portion (called validation set) of the training set to determine
+whether the process has finished. We choose the nodes 11, 13, 22,
+34, 36 as the validation set.
+The following three standard cosmological parameters and one
+MG parameter are varied,
+C = {Ωm0, h, S8},
+for ΛCDM,
+(16)
+C =
+�
+Ωm0, h, S8, log10 | ¯fR0|
+�
+,
+for f(R),
+(17)
+C = {Ωm0, h, S8, log10(H0rc)},
+for DGP,
+(18)
+MNRAS 000, 1–18 (2023)
+
+training
+ validation
+test
+0.6
+0.9
+0.8
+0.7
+0.6
+R0
+-5.0
+5.5
+-6.0
+1.0
+0.5
+0.0
+-0.5
+0.7
+0.2
+0.4
+0.6
+0.8 0.6
+0.8
+h
+moMG Emulator Halo Model I
+5
+where h ≡ H0/(100 km s−1 Mpc−1) and H0 is the present day
+Hubble constant. The range of the parameters explored is
+0.11 < Ωm0 < 0.54
+0.61 < h < 0.81
+0.6 < S8 < 0.9
+−6.2 < log10 | ¯fR0| < −4.6
+−0.45 < log10(H0rc) < 1.0.
+(19)
+The density parameter of baryons was fixed to Ωb0 = 0.049199
+and massive neutrinos are ignored. The dark energy density is given
+by
+ΩΛ0 = 1 − Ωm0.
+(20)
+The remaining cosmological parameter is the slope of the primordial
+curvature power spectrum normalised at 0.05 Mpc−1, which is
+ns = 0.9652 (Arnold et al. 2022).
+We also need test data set to assess the performance of the
+emulators independently. In both cases, the test set consists of two
+models. The MG test cases are F5 and F6 for f(R) gravity, and
+for DGP they are N1 and N5, and they share the same cosmolo-
+gical parameters, given by the fiducial Planck cosmology (Planck
+Collaboration et al. 2020),
+Ωm0 = 0.31315,
+ΩΛ0 = 0.68685,
+Ωb0 = 0.049199,
+h = 0.6737,
+σ8 = 0.82172,
+ns = 0.9652.
+(21)
+Each test model has 8 realisations.
+The dark matter halo catalogues were obtained using the
+Subfind halo finder (Springel et al. 2001). The haloes were first
+identified using a fast parallel friends-of-friends (FOF) algorithm
+with link length set to b = 0.168 times the mean interparticle separ-
+ation. Spherical overdensity halo catalogues are then built out from
+the potential minimum of each FOF halo. The halo mass definition
+adopted is
+M200c ≡ 4π
+3 (R200c)3 × 200ρcrit,
+where ρcrit(z) ≡ 3H2(z)/(8πG) is the critical density of the
+Universe, and R200c is the spherical halo radius within which the
+spherically averaged mass density equals 200ρcrit. Only main ha-
+loes with masses above 1012 h−1M⊙ from the HR simulations are
+considered in this work. The halo catalogues at
+z = 0.00, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75 and 2.00
+are available for all nodes. Besides these common redshifts, Arnold
+et al. saved particle snapshots and halo catalogues at pre-selected
+redshifts to construct past light-cones for weak-lensing analysis,
+therefore enabling the emulation of halo properties as a function
+of redshift. In the main text, we present the performance of the
+emulators at redshift zero, since the measurement and emulation at
+other redshifts are performed in the same way.
+3
+DATA SET
+In this section we describe the measurement and post-processing
+of the halo properties from the simulations, including the halo
+mass function, concentration-mass relation and halo-matter cross-
+correlation function.
+3.1
+Halo Mass Functions
+The differential halo mass function (dHMF) quantifies the number
+density of haloes as a function of halo mass for a given cosmology
+C and redshift. It is denoted as
+dn(M; z, C)
+dM
+or
+dn(log M; z, C)
+d log M
+.
+(22)
+In the cumulative form, the cumulative HMF (cHMF) gives the
+number density of haloes above a given mass threshold M,
+n(> M; z, C) =
+� ∞
+M
+dm dn(m; z, C)
+dm
+.
+(23)
+The HMF is measured by creating a histogram of the halo mass,
+which is affected by shot noise and sample variance, especially for
+massive haloes. Also, HMFs span many orders of magnitude in
+abundance, typically from 10−3 to 10−8 (h−1Mpc)−3. Taking the
+logarithm of the HMF to reduce the dynamic range does not help
+much, since the interpolation errors in the logarithmic quantity
+would be exponentially amplified. To overcome these problems,
+a commonly used approach (e.g. followed by McClintock et al.
+2019; Nishimichi et al. 2019; Cuesta-Lazaro et al. 2022) is to fit
+the measured HMF using fitting formulae like those proposed by
+Jenkins et al. (2001); Tinker et al. (2008), and then to emulate the
+mass and cosmology dependence of the fitting parameters. However,
+the performance of such fitting functions in MG simulations is not
+guaranteed (e.g. Schmidt et al. 2009; Gupta et al. 2022) and therefore
+may cause systematic errors.
+We adopt an alternative method to emulate the HMF. The
+main ideas include: (1) Emulating the ratio between the simulation
+result for the HMF and a realistic fitting formula to reduce the
+dynamic range. (2) Considering the cumulative HMF instead of
+the differential one to allow for smaller steps in halo mass, thereby
+providing more training data.
+Tinker et al. (2008) (hereafter T08) derived fitting functions
+for the HMF applicable over a wide range of halo masses and halo
+definitions, with a precision of ≲ 5%. We work with the ratio of the
+cumulative HMFs between the simulation measurements and the
+T08 fitting formulae1,
+r(M; C, z) ≡ nsim
+h
+(> M; C, z)
+nT08
+h
+(> M; C, z).
+(24)
+The HMF ratios are then interpolated across parameter space using
+neural networks to construct the emulator. To obtain the differential
+HMF for any given cosmology Cany, one can calculate the ratio for
+this cosmology using the trained emulator, multiply it with the T08
+HMF and take the derivative. The emulation process is sketched in
+Fig. 2.
+In each snapshot, we measure the number densities of haloes
+more massive than a series of masses, beginning at 1012 h−1M⊙
+and increasing in steps with a bin width of ∆ log [M/(h−1M⊙)] =
+0.02. The maximum mass varies across redshifts. Fig. 3 presents the
+ratios of HMFs for 49 f(R) gravity simulations at z = 0. The ratios
+are gently varying functions over a lower dynamic range than HMFs
+themselves, therefore resulting in a higher emulation accuracy.
+1 Numerically implemented in the Python module hmf (Murray et al. 2013,
+2021).
+MNRAS 000, 1–18 (2023)
+
+6
+C. Ruan et al.
+Halo Catalogues
+M200c
+cumulative HMF
+nh,sim(>M|Ctrain)
+binning
+Fitting Function
+Tinker et al. (2008)
+cumulative HMF
+nh,T08(>M|Ctrain)
+integrate
+Emulated cHMF Ratio
+remu(M|Cany)
+cHMF Ratio
+r(M|Ctrain)=
+nh,sim(>M|Ctrain)/nh,T08(>M|Ctrain)
+emulation
+Emulated dHMF
+dnemu/dM(>M|Cany)
+differentiation
+Emulated cHMF
+nemu(>M|Cany)=
+remu(M|Cany) × nh,T08(>M|Cany)
+Figure 2. Flow chart illustrating the process of emulating halo mass func-
+tions. We start from measuring the cumulative HMF from the simulations in
+the training data set. For each simulation, we calculate the cHMF predicted
+by the fitting formula of Tinker et al. (2008) for the same cosmology C. We
+then interpolate the ratios between the two cHMFs across parameter space
+using neural networks. To obtain the commonly used differential HMF for
+any given cosmology Cany, we can calculate the ratio, multiply the ratio by
+the Tinker et al. (2008) function and take the derivative.
+Figure 3. Cumulative halo mass function (cHMF) ratios between simulation
+measurements for 49 f(R) gravity models and the fitting formula calibrated
+by Tinker et al. (2008) for the same cosmology (except for the MG parameter
+¯fR0, which is set to zero), at redshift 0. The dynamic range of the ratios
+are significantly decreased compared with cHMFs themselves, therefore
+increasing the emulation accuracy. (source code)
+3.2
+The individual halo density profile and the
+concentration-mass relation
+One of the most remarkable discoveries from cosmological N-body
+simulations was that dark matter haloes display a universal density
+profile (Navarro et al. 1996, 1997; Wang et al. 2020), from the host
+haloes of dwarf galaxies to those of massive galaxy clusters. Spe-
+cifically, it was shown that the spherically averaged density profile of
+individual relaxed haloes can be described by the well-known Nav-
+arro, Frenk & White (NFW) profile. The NFW profile is described
+by two parameters, the characteristic density and scale radius of a
+halo, or equivalently the halo mass and concentration,
+ρNFW(r|r−2, ρ−2) =
+4ρ−2
+� r
+r−2
+��
+1 +
+r
+r−2
+�2 ,
+(25)
+where r−2 is the characteristic radius (also denoted as rs) of a halo
+at which the logarithmic slope of the density profile equal to −2,
+d log [ρNFW(r)]
+d log r
+����
+r=r−2
+= −2,
+(26)
+and ρ−2 ≡ ρNFW(r = r−2). The halo concentration c is defined
+as the ratio between the halo radius (which is adopted as R200c in
+this work) and r−2,
+c ≡ R200c
+r−2 .
+(27)
+The other NFW parameter ρ−2 is related to the concentration as
+ρ−2 = ρcrit(a)
+4
+200
+3Ωm(a)
+c3
+f(c),
+(28)
+where Ωm(a) ≡ ¯ρm(a)/ρcrit(a) is the matter density parameter at
+a given scale factor a; f(c) ≡ ln(1 + c) − c/(1 + c).
+Previously, attention was focused on measuring halo concen-
+trations for the best-fitting WMAP or Planck cosmologies, or similar
+models close by in parameter space (e.g. Gao et al. 2008; Prada
+et al. 2012; Diemer & Kravtsov 2015; Klypin et al. 2016; Child
+et al. 2018). Such calibrated fitting functions cannot be simply ex-
+tended beyond the cosmological and gravity models for which they
+have been tested. In order to overcome potential problems associ-
+ated with the extrapolation of fitting functions to a wider range of
+cosmologies, we build emulators for the halo concentration-mass
+relation and halo density profiles.
+We study the concentration-mass relation for haloes in the cos-
+mologies covered by the FORGE and BRIDGE simulation suites.
+We consider only the haloes containing more than 1 000 particles,
+corresponding to a mass of 1013 h−1M⊙ for the fiducial Planck
+cosmology. For several reasons set out below we do not exclude
+unrelaxed haloes that contain a large amount of substructure as was
+done in some previous work (e.g. Neto et al. 2007; Prada et al. 2012;
+Klypin et al. 2016). First, our aim is to predict the halo profile as
+an ingredient of the halo model, instead of studying the formation
+and evolution of relaxed haloes. Galaxies are expected to reside
+in all haloes, regardless of their dynamic state. Second, excluding
+unrelaxed haloes would bias the concentration high because haloes
+in the rapid mass accretion stage tend to have low concentrations
+(Child et al. 2018). Third, such a cut removes typically 30-50%
+haloes, which would make the measurement of halo properties less
+reliable, by introducing larger statistical errors.
+To measure halo concentrations, we follow the approach taken
+by Mitchell et al. (2019) and briefly review the main aspects below.
+As mentioned in Section 2.3, we use M200c and R200c as the defin-
+itions of the halo mass and radius, respectively. The halo centre is
+MNRAS 000, 1–18 (2023)
+
+4
+3
+2
+sim
+u
+0
+1012
+1013
+1014
+M200c/ (h-1 MoMG Emulator Halo Model I
+7
+adopted as the gravitational potential minimum. The halo particles
+are split into 20 logarithmically spaced radial bins from the halo
+centre, covering the range [0.05, 1.00]R200c. We then fit the NFW
+profile (Eqn. (25)) to the density in the radial bins of each halo, treat-
+ing the characteristic density and concentration as free variables, by
+minimising an unweighted χ2,
+χ2 =
+�
+i
+[log ρsim(ri) − log ρNFW(ri|c, ρ−2)]2.
+(29)
+We have checked that weighting the χ2 function by the number of
+particles in each radial bin has a negligible impact on the best-fitting
+concentration values recovered.
+The mean value of the best-fitting concentration depends on
+technical details such as the halo finder used, and the number and
+range of the radial bins, which would have a non-negligible impact
+if the NFW profile is not a good fit to the halo profile (Meneghetti
+& Rasia 2013; Dooley et al. 2014). It has been argued that using the
+median instead of the mean concentration would avoid such non-
+convergence (Diemer & Kravtsov 2015). Neto et al. (2007) found
+that the median of the concentration depends only weakly on the
+radial range used in the fit, provided that the unrelaxed haloes are
+removed and rmin ≥ 0.05Rvir in the fitting.
+To test the robustness of the halo concentration measurement,
+we use three N-body simulations from Mitchell et al. (2021) with
+the same cosmology and particle number, Np = 10243, and dif-
+ferent box sizes, L = 200, 500 and 1000 h−1Mpc. We then bin
+the halo particles, fit the NFW profile and calculate the mean and
+median values of the concentrations in each mass bin, keeping the
+maximum radius fixed at R200c and checking the results for four
+different rmin values: (0.05, 0.07, 0.10 and 0.13)R200c. The results
+are shown in Fig. 4. All concentration-mass relations are well fitted
+by a power law,
+c(M) = c0M α,
+(30)
+with c0 the amplitude and α the index, as represented by the coloured
+bands in the figure. The median concentrations (as well as the mean)
+and the best-fitting amplitude are still sensitive to the minimum
+radius, with a relative difference of up to 10 per cent. However, the
+power indices are practically the same for different fitting ranges.
+The convergence test also confirms our choice of the min-
+imum particle-number cut applied to define the halo sample used.
+The concentrations from the lower resolution simulations start de-
+viating from those of the higher resolution runs around the halo
+mass corresponding to ∼ 800 times the particle mass. This pivot
+mass also depends weakly on the radial range used to fit the density
+profile, with smaller minimum scales having larger pivot masses.
+3.3
+The averaged halo profile estimated from the halo-mass
+correlation function
+The normalised halo density profile, u(r|M), that appears in the
+halo model can be estimated by measuring the halo-mass cross-
+correlation functions from an N-body simulation. As mentioned
+in Section 1, the halo model assumes that the matter density field
+consists of a superposition of haloes at locations xi with masses
+11.5
+12.0
+12.5
+13.0
+13.5
+14.0
+14.5
+log10
+�
+M200c/(h−1M⊙)�
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.85
+0.90
+log10 cmedian
+200c
+800 × mL200
+particle
+800 × mL500
+particle 800 × mL1000
+particle
+rmin = 0.05R200c
+rmin = 0.07R200c
+rmin = 0.10R200c
+rmin = 0.13R200c
+fit : c = 2.02M −0.097
+fit : c = 2.03M −0.099
+fit : c = 1.98M −0.097
+fit : c = 1.94M −0.095
+Figure 4. Convergence test of halo concentration measurements. We fit
+the NFW profile and measure the halo concentration from three N-body
+simulations with the same particle number and different box sizes, L200
+(the highest resolution run, thick solid lines), L500 (the medium run, thin
+dashed lines) and L1000 (the low resolution run, thin solid lines). Colours
+represent results obtained for different minimum radial ranges in the fitting,
+as shown by the key, with the maximum radial range fixed at R200c in
+each case. The vertical lines present the critical mass scales lower than
+which the concentration measurements are unreliable due to insufficient
+resolution, which are ∼ 800 times the mass resolutions mparticle, as long
+as rmin > 0.05R200c. The colour-shaded bands show the power fitting
+(c(M) = c0Mα) to the measured c(M) relations. (source code)
+Mi, so that the matter field can be written as
+ρm(x) =
+�
+i
+Mi u
+�
+|x − xi|
+���Mi
+�
+(31)
+=
+�
+d3x′
+�
+dM
+� �
+i
+δ(D)(M − Mi) δ(D)(x′ − xi)
+M u
+�
+|x − x′|
+���M
+��
+,
+(32)
+where
+• The summation is for all haloes; the same results can be derived
+by taking the summation over all microcells which are made to be
+so small that each cell contains no more than one halo centre (e.g.
+Peebles 1980);
+• δ(D)(· · · ) is the Dirac delta function;
+•
+�
+i
+δ(D)(M − Mi) δ(D)(x′ − xi) ≡ dn(x′; M)
+dM
+is the local
+HMF, whose integral over the halo mass gives the halo number
+density field at the field point x′:
+�
+dM dn(x′; M)
+dM
+= nh(x′),
+(33)
+MNRAS 000, 1–18 (2023)
+
+8
+C. Ruan et al.
+and its ensemble average gives the common dHMF,
+�dn(x′; M)
+dM
+�
+=
+��
+i
+δ(D)(M − Mi) δ(D)(x′ − xi)
+�
+= dn(M)
+dM
+;
+(34)
+• u
+�
+|x − xi|
+���Mi
+�
+≡
+ρh
+�
+|x − xi|
+���Mi
+�
+Mi
+denotes the density
+profile of a halo centred at xi, which is also assumed to be spheric-
+ally symmetric and depends only on its mass,
+u
+�
+|x − xi|
+��Mi
+�
+=
+�
+ρh
+�
+|x − xi|
+���Mi
+�
+/Mi,
+|x − xi| ≤ Rhalo;
+0,
+|x − xi| > Rhalo;
+(35)
+and u is normalised:
+�
+d3x u
+�
+|x − xi|
+��Mi
+�
+= 1.
+(36)
+For two different populations of objects with overdensity fields
+δa(x) and δb(x), the two-point cross-correlation function is defined
+as
+ξab(r) ≡ ⟨δa(x) δb(x + r)⟩ ,
+(37)
+where ⟨· · ·⟩ denotes ensemble averaging. Assuming statistical iso-
+tropy reduces ξab(r) to a function of separation only. In the case of
+the cross-correlation between halo centres and the matter field, the
+cross-correlation function is given by
+ξhm(r) ≡ ⟨δh(x) δm(x + r)⟩
+(38)
+=
+1
+¯nh¯ρm
+�
+nh(x) ρm(x′)
+�
+− 1,
+(39)
+where x′ ≡ x + r, and the halo number density fluctuation field is
+defined as
+δh(x) ≡ nh(x) − ¯nh
+¯nh
+.
+(40)
+Now we derive the expressions for the halo and matter fields
+in Eqn. (39) within the halo model framework. In realistic N-body
+simulations, halo catalogues always have a finite halo mass range,
+limited by the simulation force/mass resolution and the box size.
+We can define the halo selection function for a given mass range
+(MR) as
+φ(m|MR) ≡
+�
+1,
+if m ∈ MR,
+0,
+otherwise.
+(41)
+In practice, MR can be a narrow mass interval, [M, M + dM) ≈
+[M, M + ∆M), or a mass threshold interval, [M, ∞). For a given
+halo sample, the corresponding halo number density field can be
+expressed as
+nh(x) =
+�
+i
+δ(D)(x − xi) φ(mi|MR).
+(42)
+To obtain the expression for ⟨nh(x) ρm(x′)⟩ in the halo model, we
+can plug the expressions for the halo and mass fields, Eqns. (32) and
+(42), into Eqn. (39). The full expression can be found in Eqns. (7) and
+(8) of García et al. (2021). We focus only on the internal structure
+of the halo and, therefore, on the 1-halo term, which reads
+�
+nh(x) ρm(x′)
+�
+1h =
+�
+dm dn
+dmm φ(m|MR) u(r|m)
+(43)
+=
+�
+�
+�
+dn(M) M u(r|M),
+MR = [M, M + dM),
+� ∞
+M
+dm dn
+dm m u(r|m),
+MR = [M, ∞),
+(44)
+where dn(M) is the number density of halos in the mass range
+[M, M + dM). The 1-halo term of the halo-mass correlation func-
+tion is
+ξ1h
+hm(r|M) = M u(r|M)
+¯ρm
+− 1 = ρh(r|M)
+¯ρm
+− 1,
+(45)
+ξ1h
+hm(r|>M) =
+1
+¯ρm ¯nh(>M)
+� ∞
+M
+dm dn
+dm m u(r|m) − 1.
+(46)
+We are interested in the average density profile of haloes in a
+narrow mass interval [M, M +dM). However, the noise level of the
+simulation measurements for such halo properties and statistics is
+high because of the low number density. We bypass this problem by
+measuring ξ1h
+hm(r| > M) (which involves more haloes and therefore
+is a smoother function) and taking the partial derivative with respect
+to mass,
+u(r|M) = − ¯ρm
+M
+�dn(M)
+dM
+�−1
+×
+∂
+∂M
+�
+¯nh(> M)
+�
+1 + ξ1h
+hm(r| > M)
+��
+.
+(47)
+4
+USING NEURAL NETWORKS FOR REGRESSION
+PROBLEMS
+Given a data set comprised of independent variables (also called
+features) and dependent variables (labels), there exists an unknown
+underlying function mapping the inputs to the outputs. We can use
+supervised learning algorithms to approximate this function, which
+falls in the category of a regression problem. In the context of
+structure formation, the features consist of cosmologies C, redshifts
+z, halo masses M or number densities nh, etc. The labels of interest
+include basic properties of haloes such as halo mass functions,
+concentration-mass relations and correlation functions. In the case
+of structure formation, the “functions” between the features and
+labels are known but expensive: we can run N-body simulations
+given a set of cosmological parameters C, save the snapshot at
+a given redshift z, identify haloes and measure the properties of
+haloes. But it is computationally intractable to perform ≳ O(104)
+cosmological simulations to explore the parameter space in a typical
+MCMC analysis.
+As shown in previous works on cosmic emulation, such as
+Nishimichi et al. (2019); DeRose et al. (2019); Cuesta-Lazaro et al.
+(2022), and as we will report in the following sections, it is possible
+to construct emulators for halo properties by running affordable
+numbers (e.g., 50-100) of simulations and interpolating in a high-
+dimensional parameter space. Emulators can give accurate predic-
+tions for halo properties for new models without running additional
+simulations. Thanks to the development of algorithms and comput-
+ing power, statistics and machine learning provide us with a wealth
+of tools to solve such regression problems.
+In a regression analysis, the typical progress of approximating
+a function can be summarised as:
+• Define a functional form y = f(x|θ) with adjustable or train-
+able parameters θ. For example, in the simplest and most common
+form — linear regression — the labels are assumed to be linear
+combinations of the features and the coefficients are the trainable
+parameters.
+• Define a loss function on the training data set D to quantify
+the difference between the real and predicted values of the target,
+e.g., the sum of the absolute differences (which reduces the weight
+MNRAS 000, 1–18 (2023)
+
+MG Emulator Halo Model I
+9
+of outliers),
+L(θ|D) ≡
+�
+(xi,yi)∈D
+��yi − f(xi|θ)
+��.
+• Find the optimal parameters θ⋆ to minimise the loss function
+(train the model).
+Gaussian process (GP) regression (e.g. Williams & Rasmussen
+2006) has been widely adopted in cosmological emulation projects,
+such as Dark Quest (Nishimichi et al. 2019), Aemulus (DeRose
+et al. 2019), the Coyote Universe (Heitmann et al. 2010), the Mira-
+Titan Universe (Bocquet et al. 2020), Cosmic Emulators (Kwan
+et al. 2013) and FORGE (Arnold et al. 2022). GP regression is non-
+parametric, i.e., no specific functional form is assumed. However,
+GPs are not easy to apply to large data sets because of their O(N 3)
+scaling where N is the size of the training data. Therefore, the
+aforementioned projects usually emulate matter, halo and/or galaxy
+properties using a combination of principal component analysis,
+to reduce the dimensionality of the data vector, and GP, to fit the
+dependence of the principal component coefficients on cosmology.
+The machine learning algorithm we adopt is a fully connected
+neural network (e.g. Bishop et al. 1995; Alom et al. 2019; Zhang
+et al. 2021). This is a type of artificial neural network in which
+all neurons in one layer are connected to the neurons in the next
+layer. The neural network algorithm has been widely applied to
+cosmology (e.g., Agarwal et al. 2012, 2014; Jennings et al. 2019;
+Kobayashi et al. 2020; Cuesta-Lazaro et al. 2022), and its perform-
+ance has been shown to be competitive or sometimes better than
+other methods. Neural networks have a strong fitting ability, as re-
+flected by the universal approximation theorem (Cybenko 1989;
+Hornik et al. 1989; Goodfellow et al. 2016). However, this theorem
+does not provide a means to construct optimised neural networks,
+but merely guarantees their existence. Also, this strong fitting abil-
+ity also makes neural networks more susceptible to the overfitting
+problem compared to GPs. Therefore, we need to carefully check
+the emulator performance using independent test data sets and tune
+the network architecture so that the generalisation error is success-
+fully suppressed. Moreover, we show dimensionality reduction is
+not necessary when using neural networks, which also improves the
+accuracy of the emulator predictions.
+A neural network is an interconnection of neurons arranged in
+a series of layers, with each neuron in a layer connected to all other
+neurons in adjacent layers with different weightings. One can impart
+values on to the neurons of the first layer (called the input layer), have
+a number of hidden layers and finally obtain the output from the last
+layer. For example, in this work, the neural networks emulating the
+halo mass function at fixed redshift have five nodes in the input layer,
+corresponding to the halo mass and four cosmological parameters,
+and one node in the last layer outputting the HMF,
+n
+�
+> M|Ωm0, h, S8, log10 | ¯fR0| or log10 |H0rc|
+�
+.
+(48)
+Neural networks use activation functions to impart non-
+linearities into the fitting. Rectified Linear Unit (ReLU) (Agarap
+2018) is the most commonly used activation function in current
+neural networks used to add non-linearities in the mapping between
+inputs and outputs, which is defined as
+ReLU(x) = max(0, x),
+(49)
+where x is the output of the previous layer of the neural network.
+Note that the activations of ReLU are not differentiable at x = 0.
+Here, however, we are interested in functions that are differenti-
+able with respect to their inputs and, in particular, with respect to
+the cosmological parameters. Therefore, throughout, we use Gaus-
+sian error linear unit (GELU) (Hendrycks & Gimpel 2016) as the
+activation function instead,
+GELU(x) = 0.5x
+�
+1 + erf
+� x
+√
+2
+��
+.
+(50)
+To find the optimal parameters θ⋆ that reproduce the halo
+properties measured in the N-body simulations, we minimise the
+L1-norm loss function,
+L = 1
+N
+N
+�
+i=0
+|yi
+true − yi
+predicted|
+(51)
+using the Adam optimiser (Kingma & Ba 2014). Compared to the
+mean squared error, the loss of L1 reduces the importance given
+to outlier errors. To avoid fine-tuning the learning rate, we adopt a
+learning rate scheduler that reduces the learning rate by a factor of
+10 every time the validation loss does not improve after 30 epochs.
+We also stop the training process when the validation loss does not
+improve after 100 epochs. This iterative reduction of the learning
+rate allows the model to quickly learn the broad characteristics of
+the data and later reduce the errors with a smaller learning rate. The
+initial learning rate is always set to 0.01.
+4.1
+Ideal emulation tests
+To gain a preliminary impression of the emulation process, and to
+guide the design of emulators in the future, we perform emulation
+tests under ideal conditions. The halo properties are generated for a
+limited number of randomly selected cosmologies using analytical
+methods or fitting formulae, which are noise-free mappings from
+cosmologies to halo properties. Then we use these data to train
+neural networks and emulate the “true” model. To evaluate the
+performance of the emulator, we compare the true values with the
+emulator predictions using independent test data sets.
+The cosmologies of the training set cover 50 flat geometry
+(w0-wa) CDM models (Linder 2003), where the equation-of-state
+parameter for dark energy is parameterised in terms of the expansion
+factor, a, as
+w(a) = w0 + wa(1 − a).
+(52)
+A key aspect of building emulators is an efficient sampling scheme.
+As the training dataset, the 50 cosmologies were sampled using
+optimal minimax distance sliced Latin hypercube designs (Ba et al.
+2015) in a seven-dimensional cosmological parameter space,
+C =
+�
+Ωm0, Ωb0, h, σ8, ns, w0, wa
+�
+,
+(53)
+as shown by the grey dots in Fig. 5. The range of parameters is
+0.1 < Ωm0 < 0.7,
+0.02 < Ωb0 < 0.06,
+0.5 < h < 0.9,
+0.5 < σ8 < 1.2,
+0.92 < ns < 0.99,
+−1.3 < w0 < −0.7,
+−0.1 < wa < 0.1,
+(54)
+while the upper and lower parameter limits depart significantly from
+the current best-fitting ΛCDM background cosmology from the
+Planck satellite (Planck Collaboration et al. 2020). We also generate
+two test data sets that were not used in the training: both consist of
+500 random cosmologies; one set covers the same parameter range
+as that of the training set, and the other one covers the inner half-
+region (in terms of the length per dimension, instead of volume)
+of the parameter space. The cosmologies in the full- and half-range
+test data sets are shown in green and blue dots in Fig. 5, respectively.
+MNRAS 000, 1–18 (2023)
+
+10
+C. Ruan et al.
+Figure 5. Visualisation of the seven-parameter (w0-wa)CDM cosmologies
+studied in the ideal emulation tests. Grey dots show the training set including
+50 nodes. Green dots represent full-range test set consisting of 500 nodes
+covering the same range as that of the training set. Blue dots show the half-
+range test set including 500 nodes in the inner half region of the parameter
+space. (source code)
+We choose to emulate two basic properties of haloes in the
+tests: the concentration-mass relation c(M), and the cumulative
+HMF ¯nh(> M). For given cosmologies, we generate the c(M)
+relation calibrated in Prada et al. (2012), using the publicly available
+Python toolkit COLOSSUS (Diemer 2018), and compute the Tinker
+et al. (2008) HMF with the Python package hmf (Murray et al. 2013,
+2021). As described in Section 3.1 and Fig. 2, we train the emulators
+directly on the ratio of the cumulative HMF between the target HMF
+and a fitting formula to reduce the dynamic range and improve the
+interpolation accuracy. We choose the HMF calibrated in Jenkins
+et al. (2001) as the reference.
+The upper panels of Fig. 6 show the halo properties calculated
+using the fitting formulae and emulators. The fractional errors are
+shown in the lower sub-panels. The results show that the emulator
+reproduces the analytical halo c(M) relation with a sub-percent
+error in the 7D parameter space with only 50 training models. The
+performance of the HMF emulator is even better than that of the
+concentration emulator, although the HMF data span ∼ 20 orders of
+magnitude. The median absolute error of the emulator predictions
+is lower than 1 per cent for halo masses M ≲ 1016 h−1M⊙.
+We also note that the emulator precision is generally different
+at the edge and centre of the parameter space, as revealed by the
+green and blue lines in the bottom panels of Fig. 6. This suggests that
+we should design the parameter space to be wider than the existing
+cosmological constraints. The parameter space in our ideal tests is
+designed to be wide enough that covers some extreme cosmologies,
+such as Ωm0 = 0.7 and h = 0.5.
+In general, ideal emulation tests show that under noise-free
+conditions, neural network emulators can provide accurate inter-
+polations in high-dimensional parameter space, using 50 efficiently
+sampled models as the training set. In the next section, we will
+present the cosmic emulation in the real situation: the data are
+measured from simulations and, therefore, are influenced by sample
+variance and noise.
+5
+RESULTS
+In this section we demonstrate the ability of a fully connected neural
+network to reproduce the halo properties measured from FORGE
+and BRIDGE simulations. We train different emulators for each
+gravity theory: ΛCDM, f(R) gravity and DGP. The configurations
+of the neural networks for emulating three halo properties are sum-
+marised in Table 1.
+5.1
+The emulator for the halo mass function
+As discussed in Section 3.1, we train the neural network emulators
+directly on the ratio of the cumulative HMF between simulation
+measurements and the fitting formula calibrated in Tinker et al.
+(2008) to reduce the dynamic range and improve the emulation
+accuracy. Fig. 7 compares the cumulative and the differential HMFs
+from simulations and emulators at z = 0, for the ΛCDM, f(R)
+gravity and DGP models. The differential HMF of a given mass bin
+centred on log Mi is obtained by
+dn(M)
+d log M
+����
+log Mi
+≈ n(> log Mi − bw
+2 ) − n(> log Mi + bw
+2 )
+bw
+,
+(55)
+where bw ≡ log Mi+1 − log Mi is the bin width. The lower sub-
+panels show the fractional difference between the emulator predic-
+tion and the measured HMFs in a given mass bin,
+HMFemu − HMFsim
+HMFsim
+.
+(56)
+The performance of the emulator on the training data set is shown
+by the thin lines of Fig. 7. The emulator achieves sub-percent ac-
+curacy in reproducing most of the cumulative HMF for halo masses
+between 1012 and 1014 h−1M⊙. The residuals of the differential
+HMF obtained using Eqn. (55) are slightly larger but still show ≲ 2
+per cent scatter around zero, with a mean consistent with zero. The
+thick lines in Fig. 7 show the emulator predictions for three test mod-
+els which are not used in the training, as described in Section 2.3.
+We again find percent-level agreement between the emulator pre-
+dictions and simulation results. Furthermore, the fluctuations of the
+residuals in the test set are much smaller than those of the training
+models, since each test cosmology has 8 realisations and the sample
+variance of the measured dHMFs is suppressed. This confirms that
+the errors of the emulator predictions are mainly random instead of
+systematic.
+5.2
+The emulator for the concentration-mass relation
+As shown in Section 5.2 and Fig. 4, the halo concentrations meas-
+ured from simulations are sensitive to the radial range used in the
+fitting, which indicates that this is not the optimal way to describe
+the halo density profiles. However, the power law index is not sens-
+itive to the range adopted, which indicates that we can treat the
+amplitude of the concentration-mass relation as a free parameter
+to take into account this variation. We build an emulator for the
+c(M) relation taking rmin = 0.10R200c as a representative value.
+The performance of the emulator at z = 0 is shown in Fig. 8. The
+fractional errors are sub-percent for most of the cosmologies in the
+training and test data sets.
+MNRAS 000, 1–18 (2023)
+
+0.06
+0.0
+0.02
+1.25
+1.00
+-0.75
+Wo
+0.8
+0.6
+1.2
+1.0
+8
+0
+0.6
+0.98
+s 0.96
+n
+0.94
+0.92
+0.25
+0.50
+0.025
+0.050
+0.75
+0.5
+0.50
+1.0
+hMG Emulator Halo Model I
+11
+Figure 6. Ideal emulation tests. Top panels: The halo concentration-mass relation (left) and halo mass function (right) of the training (grey), full-range test
+(green) and half-range test (blue) sets, from the analytical methods (dots) and emulators (lines). Bottom panels: The absolute value of the relative difference
+between the models and emulators. The solid and dashed lines present the median and 90-th percentile of the emulation fractional errors among the training
+(black), test (green) and half-range test (blue) sets, which include 50, 500 and 500 cosmologies, respectively. (source code 1, 2)
+Table 1. Summary of the neural network configurations for emulating the halo properties. The architecture of a neural network is specified from the input to
+output layer as (Ninput, Nhidden1, Nhidden2, · · · , Noutput) with N the number of neurons in each layer.
+Halo
+Property
+Feature
+Label
+Neural Network
+Architecture
+Activation
+HMF
+C, M200c
+Equation (24)
+(5, 64, 32, 1)
+GELU
+Concentration
+C, M200c
+c200c
+(5, 32, 16, 1)
+GELU
+ξhm
+C, nh
+{r2
+i ξhm(ri)}N=30
+i=1
+(5, 128, 32, 30)
+GELU
+5.3
+The emulator for the halo-mass cross-correlation
+function
+As discussed in Section 3.3, the average halo profile can be es-
+timated from the halo-mass cross-correlation function. The halo
+profile u(r|M) is directly related to the matter density field
+cross-correlated with the halo sample in a narrow mass range
+[M, M+∆M]. However, such correlation functions measured from
+simulations would be rather noisy because of the low halo number
+density. To feed the neural networks with smoother data, we meas-
+ure the cross-correlation functions between the matter field and the
+halo samples with fixed number densities, ξhm(r|C, ¯nh). We then
+use the HMF emulator to translate ξhm(r|C, ¯nh) as a function of
+number density into ξhm(r|C, M) as a function of mass, according
+to Equation (47).
+We measure ξhm(r|C, ¯nh) using the high-performance code
+Corrfunc (Sinha & Garrison 2020) for the halo number densities
+in logarithmically spaced bins over the range
+log10
+�
+¯nh
+(h−1Mpc)−3
+�
+= [−5.1, −2.9],
+(57)
+using a bin width of ∆ log10 ¯nh = 0.05. The separation r is split
+into 30 logarithmically-spaced bins from 0.05 h−1Mpc (three times
+the force resolution) to 3 h−1Mpc. Furthermore, to reduce the
+dynamic range of the data vector, we opt to emulate r2ξhm(r)
+instead of ξhm(r) itself. The upper-left panel of Fig. 9 shows
+ξhm
+�
+r|¯nh = 10−3.5 (h−1 Mpc)−3�
+at z = 0 for the 49 ΛCDM
+gravity cosmologies along with the test models.
+The average halo profile is only related to the 1-halo term of
+ξhm. The halo-mass correlation enters the transition between 1- and
+2-halo terms as the scale increases. To estimate the range of the
+one-halo term, we only consider the scales below R200c, which is
+related to the adopted mass definition M200c as
+M200c(z) = 4π
+3 (R200c)3200ρcrit(z).
+(58)
+We then build emulators for ξhm(r|C, ¯nh) at each redshift,
+to reduce the number of features and minimise emulation errors.
+The lower left sub-panel of Fig. 9 shows the fractional difference
+between the simulation measurements and the emulator predictions,
+in the training set along with the test models. The emulator achieves
+sub-percent accuracy for the both the training and the test models.
+The average halo density profile can be estimated from ξhm
+using Eqn. (47). In the right panel of Fig. 9, we compare this type of
+profile with the NFW profiles combined with three concentration-
+mass relations from this work, Klypin et al. (2016) and Diemer
+& Joyce (2019), in five halo mass bins. We also fit the average
+profile with an NFW form, using the the data over the range of
+[0.1, 1.0]R200c.
+In the right sub-panel of Fig. 9, we check the relative difference
+between the average profiles measured from the simulations and the
+NFW fits. There is a ∼ 5% discrepancy between the two types of
+profiles, regardless of the concentration-mass relation, which shows
+that the differences between the NFW profiles with different c(M)
+relations are small. This level of difference is consistent with the
+results discovered in Section 5.1.2 of Nishimichi et al. (2019).
+MNRAS 000, 1–18 (2023)
+
+training,true
+20
+training, emulation
+test
+test, inner 50%
+15
+10
+5
+training, median
+test
+training, 90-th percentile
+test,inner 50%
+rue
+10
+10-3
+1012
+1013
+1014
+1015
+1016
+M /(h-Mo3
+10-4
+1
+(odWi-)/(W<)u
+10-8
+10-12
+training, simulation
+10-16
+training, emulation
+10-20
+test
+10-24
+test, inner 50%
+training, median
+test
+training, 90-th percentile
+test, inner 50%
+true
+△nhl /ni
+10-3
+1013
+1014
+1015
+1016
+1012
+M /(h-1M。)12
+C. Ruan et al.
+Figure 7. Cumulative (the first row) and differential (the second row) halo mass functions from simulation measurements and emulator predictions at z = 0,
+for ΛCDM (left), f(R) gravity (middle) and DGP (right). In each panel, the thin lines show the results of the 49 cosmologies in the training data set, and
+the thick lines represent those of the test models which were not used in the construction of the emulators. In the lower sub-panel, we compare the relative
+differences between simulations and emulators. The dark and light grey bands denote ±1%- and ±2%-level errors, respectively. The differential halo mass
+functions are obtained by finite difference of the cumulative HMFs according to Eqn. (55). (source code 1, 2)
+6
+EMULATOR APPLICATIONS
+With the emulators for the halo mass function and density profile as
+ingredients, we are able to predict galaxy clustering statistics using
+the halo model framework (Cooray & Sheth 2002), and therefore
+fit galaxy clustering measurements in the joint parameter space of
+cosmology and a galaxy-halo connection model. In this section,
+we demonstrate that the emulator-based halo model reproduces the
+signals measured from the mock HOD catalogues generated with
+the same specifications, such as the cosmology, HOD prescription,
+satellite profile and/or concentration-mass relation.
+MNRAS 000, 1–18 (2023)
+
+3
+ACDM
+f(R) gravity
+DGP
+10
+10
+training, simulation
+training, simulation
+training, simulation
+training, emulation
+training, emulation
+Nh(
+training, emulation
+test, F5
+test, Nl
+test, GR
+test, N5
+test, F6
+0.05
+rel.diff.
+0.00
+0.05
+1014 1012
+1013
+1013
+1014 1012
+1012
+1013
+1014
+/(h-1Mo)
+/(h-1Mo)
+/(h-1Mo)
+M200c/
+M200c/
+M200c/-2
+10~
+ACDM
+f(R) gravity
+DGP
+10
+dnh
+training, simulation
+training, simulation
+10
+training, simulation
+training, emulation
+training, emulation
+training, emulation
+test, F5
+test, N1
+test, GR
+test, N5
+test, F6
+rel.diff.
+0.00
+0.05
+1012
+10140
+101410
+10
+/(h-1M。)
+/(h-1 Mo)
+M200c/ (h-1 Mo)
+M200c/
+M200c/MG Emulator Halo Model I
+13
+Figure 8. Comparison between the halo concentration-mass relations from
+simulations (points) and emulators (lines), for the 49 f(R) gravity cosmo-
+logies in the training set (grey) and test models F5 (green), F6 (orange), N1
+(blue), N5 (purple) and the fiducial Planck cosmology (denoted as GR, in
+red). The results for the ΛCDM and DGP training sets are similar to those
+for f(R) gravity and are therefore not shown here. The lower sub-panel
+shows the relative difference of the halo concentration between simulations
+and emulators. The sub-percent differences between the emulator and sim-
+ulation results are much smaller than the differences between the results for
+different cosmologies. (source code)
+6.1
+Galaxy two-point correlation function
+We adopt the halo occupation distribution (HOD) (e.g. Zheng et al.
+2005) prescription to model the average number of galaxies in a halo
+as a function of halo mass. The occupation of central galaxies is
+parameterised as a Bernoulli distribution, whereas that of satellites
+is a Poisson distribution (Zheng et al. 2005). Both distributions are
+described by their mean occupation number,
+⟨Ng⟩ (M) = ⟨Nc⟩(M) + ⟨Ns⟩(M).
+(59)
+The galaxy number density ¯ng can then be obtained by integrating
+the HMF weighted by the mean occupation,
+¯ng =
+�
+dM dn(M)
+dM
+�
+⟨Nc⟩(M) + ⟨Ns⟩(M)
+�
+.
+(60)
+Following Cuesta-Lazaro et al. (2022), we adopt the HOD
+model in Zheng et al. (2007) by introducing the following HOD
+parameters,
+G =
+�
+Mmin, σlog M
+�
+��
+�
+Gcen
+, M1, κ, α
+�
+��
+�
+Gsat
+�
+.
+(61)
+The mean occupation number for central galaxies is given by
+⟨Nc⟩(M|G) = 1
+2
+�
+1 + erf
+�log M − log Mmin
+σlog M
+��
+.
+(62)
+The mean central HOD, ⟨Nc⟩(M) , can be interpreted as the prob-
+ability that a halo with mass M hosts a central galaxy. The mean
+central HOD considered here has the asymptotic behaviour that
+⟨Nc⟩ → 0 for haloes with M ≪ Mmin, while ⟨Nc⟩ → 1 for haloes
+with M ≫ Mmin.
+The mean satellite HOD is parameterised as
+⟨Ns⟩(M|G) = ⟨Nc⟩(M|G)λs(M),
+(63)
+where
+λs(M) =
+�M − κMmin
+M1
+�α
+.
+(64)
+Following the commonly-used prescription, we assume that satel-
+lite galaxies reside only in a halo that already hosts a central galaxy.
+Hence, in the above equation, satellite galaxies can only reside in
+haloes with ⟨Nc⟩ = 1. Then we assume that the number distribu-
+tion of satellite galaxies in a given host halo follows the Poisson
+distribution with mean λs(M):
+P(Ns|Nc = 1) = [λs(M)]Nse−λs(M)
+Ns!
+,
+(65)
+and
+P(Ns|Nc = 0) = δKr
+Ns,0,
+(66)
+where δKr
+ij stands for the Kronecker delta.
+Given the HOD model, we populate dark matter haloes in 8
+test simulations of the fiducial Planck cosmology with mock galax-
+ies and measure the galaxy clustering signals, using the following
+randomly selected HOD parameters:
+log [Mmin/(h−1M⊙)] = 12.5, σlog M = 0.6915,
+κ = 0.51, log [M1/(h−1M⊙)] = 12.9, and α = 0.9168.
+(67)
+We can also express the galaxy two-point correlation func-
+tion (TPCF) in terms of dark matter halo properties in the halo
+model framework. First, we split the one- and two-halo terms into
+correlations of central and satellite galaxies as
+ξgg(r) = ξ1h
+cs (r) + ξ1h
+ss (r)
++ ξ2h
+cc (r) + ξ2h
+cs (r) + ξ2h
+ss (r).
+(68)
+The terms involving both centrals and satellites lead to a con-
+volution of the halo profiles and/or the halo TPCF, following
+�
+d3x u(x|M) u
+�
+|x + r|
+���M
+�
+. It is therefore more convenient to
+compute these terms in Fourier space, where convolutions in co-
+ordinate space become simple products of the Fourier modes. Here,
+we focus on the one-halo term only. The two-halo term involving
+the emulation of halo clustering will be the topic of the subsequent
+papers in this series. The expressions for the 1-halo term of the
+galaxy TPCF after the central-satellite split are given by
+ξ(r) =
+� ∞
+0
+dk
+(2π)3 4πk2 sin(kr)
+kr
+P(k),
+(69)
+P 1h
+cs (k) = 1
+¯n2g
+�
+dM dn(M)
+dM
+⟨Nc⟩(M) λs(M) us(k|M),
+(70)
+P 1h
+ss (k) = 1
+¯n2g
+�
+dM dn(M)
+dM
+⟨Nc⟩(M)
+�
+λs(M)
+�2 �
+us(k|M)
+�2,
+(71)
+where us(k|M) is (the Fourier transformation of) the radial distri-
+bution of satellite galaxies within a halo, and we have highlighted
+the emulated quantities in blue. In this section, we assume that the
+MNRAS 000, 1–18 (2023)
+
+concentration
+6
+4
+training, simulation
+training,emulation
+3
+test, F5
+test, N1
+0.01
+test, F6
+test, N5
+test, GR
+0.00
+emu
+C
+-0.01
+13.0
+13.2
+13.4
+13.6
+13.8
+14.0
+log10[M200c/(h-1Mo)]14
+C. Ruan et al.
+2 × 10−1
+3 × 10−1
+4 × 10−1
+r2ρ(r|M)/M
+from ξhm(r|M)
+from ξhm(r|M), NFW fitting
+NFW, conc = this work
+NFW, conc = Diemer19
+NFW, conc = Klypin16
+M = 1013.00
+M = 1013.50
+M = 1014.00
+10−1
+100
+r/(h−1Mpc)
+−0.10
+−0.05
+0.00
+0.05
+0.10
+ρfrom ξhm/ρNFW − 1
+Figure 9. Left panel: Halo-mass cross-correlation functions from simulations and emulators at z = 0, for the 49 ΛCDM gravity cosmologies in the training
+set (grey), five test models F5 (cyan), F6 (orange), N1 (blue), N5 (purple) and the fiducial Planck ΛCDM model (red). In the lower sub-panel, we compare
+the relative difference between the simulations and emulators. Right panel: Comparison of the normalised halo density profiles, ρ(r|M)/M, truncated at
+r = R200c, for the fiducial Planck ΛCDM model (node 0) at z = 0. The average halo profiles estimated from ξhm(r) according to Equation (47) are
+represented by points. The solid lines show the fits to an NFW profile. The dashed, dotted and dash-dotted lines show the NFW profiles with three different
+concentration-mass relations: this work, Diemer & Joyce (2019) and Klypin et al. (2016). Colours denote different halo masses. The lower sub-panel shows the
+relative difference between the NFW profiles (lines) and the average profiles (points). (source code)
+distribution is given by an NFW profile with the concentration-mass
+relation from Diemer & Joyce (2019).
+The left panel of Fig. 10 compares the model predictions and
+the galaxy TPCF measured from mock HOD catalogues at z = 0.
+On the scales where the 1-halo term dominates (r ≲ 1 h−1Mpc),
+the fractional difference is within 1%. The colours in the plot rep-
+resent different contributions: the correlations of central-central,
+central-satellite and satellite-satellite galaxy pairs.
+As shown in Section 3.2 and Fig. 4, the halo concentrations
+measured from simulations are sensitive to the minimum radius in
+the fitting, with a relative difference of up to 10 per cent. To test
+the impact on galaxy clustering, we calculate the one-halo terms
+of ξgg (Eqns. (70) and (71)), adopting the NFW profile with the
+concentration-mass relations measured from this work and increas-
+ing or decreasing them by 10 per cent. Fig. 11 shows that a 10 per
+cent change in the concentration-mass relation will change the one-
+halo term by 5 per cent. The impact on the two-halo term and the
+degeneracy between the concentration amplitude and galaxy-halo
+connection model parameters will be left for future work.
+6.2
+Galaxy-matter cross-correlation function
+In the galaxy-galaxy weak lensing observations, the excess surface
+mass density profile around lensing galaxies, ∆Σgm(R) is meas-
+ured, which can be expressed in terms of the galaxy-matter cross-
+power spectrum as (e.g., Murata et al. 2018; Nishimichi et al. 2019)
+∆Σgm(R) = ¯ρm0
+� ∞
+0
+dk
+2π kPgm(k)J2(kR),
+(72)
+where J2(x) is the second-order Bessel function.
+In the halo model framework, we can accurately predict Pgm(k)
+with the emulators providing the model ingredients. Under the same
+configurations as in the last sub-section, Pgm(k) is related to the halo
+properties as
+Pgm(k) = 1
+¯ng
+�
+dM dn(M)
+dM
+⟨Nc⟩(M)×
+�
+1 + λs(M) us(k|M)
+�
+Phm(k|M).
+(73)
+Phm(k|M) is the cross-correlation between the matter overdensity
+field with the halo sample in a narrow mass bin [M, M + dM].
+The quantity that our halo-mass cross-correlation emulators output
+is Phm(k|nh(> M)), which can be converted as
+Phm(k|M) = −
+�dnh(M)
+dM
+�−1 ∂
+∂M
+�
+nh(> M)Phm
+�
+k
+��nh(> M)
+��
+.
+(74)
+We use the publicly available, open-source Python toolkit
+nbodykit (Hand et al. 2018) to measure the cross power spectra
+between the mock galaxy catalogues and the matter field, in linear k
+bins from 0.3 to 6 h Mpc−1 with a width of ∆k = 0.02 h Mpc−1.
+These measurements are compared with the halo model predictions
+MNRAS 000, 1–18 (2023)
+
+training, simulation
+training,emulation
+80
+test,GR
+60
+40
+20
+0.02
+test,F5
+test, N1
+test, F6
+test.N5
+0.00
+emu
+-0.02
+10-1
+100
+r/(h-1Mpc)MG Emulator Halo Model I
+15
+100
+101
+102
+r2ξgg(r)
+ξsimulation
+gg
+ξsimulation
+cc
+ξsimulation
+cs
+ξsimulation
+ss
+→ 2-halo term
+1-halo term ←
+10−1
+100
+101
+r/(h−1Mpc)
+−0.02
+0.00
+0.02
+∆ξ/ξsim
+theory, ξ1h
+gg
+theory, ξ1h
+ss
+theory, ξ1h
+cs
+0
+100
+200
+300
+400
+500
+600
+700
+800
+900
+kPgm(k)
+simulation, Pgm
+simulation, Pcm
+simulation, Psm
+1
+2
+3
+4
+5
+6
+k/(h Mpc−1)
+−0.01
+0.00
+0.01
+rel. diff.
+theory, Pcm
+theory, Psm
+theory, Pgm
+Figure 10. Emulator-based halo model predictions of galaxy clustering statistics. Left panel: Galaxy two-point correlation functions from simulations (marks)
+and emulator-based halo model predictions (solid lines), for the fiducial Planck cosmology of FORGE at z = 0. Colours represent different terms of galaxy
+correlations after the central/satellite split: galaxy-galaxy (black), central-central (red), central-satellite (orange) and satellite-satellite (green). Only the one-halo
+terms of theory predictions are shown. In the lower sub-panel, we show the relative difference between the 1-halo term and the full correlation function measured
+from simulations. Right panel: Similar to the left panel but for the galaxy-matter cross power spectrum for the same cosmology and HOD prescription. (source
+code)
+in the right panel of Fig. 10. The relative difference shown in the
+lower sub-panel is below 1 per cent except at low-k bins, where the
+cosmic variance dominates the error budget.
+7
+DISCUSSIONS AND CONCLUSIONS
+We present accurate emulators for the halo mass function,
+concentration-mass relation and halo-matter cross-correlation func-
+tion, for ΛCDM and two representative modified gravity theories,
+f(R) gravity and DGP, using the FORGE and BRIDGE suites of
+N-body simulations (Arnold et al. 2022). The cosmological para-
+meter space spans three non-MG parameters, Ωm0, h, S8, and one
+MG parameter, either ¯fR0 or H0rc, depending on which modified
+gravity model we are using.
+We construct emulators using fully connected neural net-
+works implemented using the open-source Python library PyTorch
+Lightning. We show the capabilities of neural networks under
+noise-free conditions by emulating the existing fitting formulae of
+halo properties, such as the fitting function for HMFs in Tinker et al.
+(2008). The emulators mimic analytical models in a 7-D parameter
+space with sub-percent accuracy, using only 50 training cosmolo-
+gies.
+For realistic cases where the data come from N-body simu-
+lations and therefore have noise, the accuracy of our halo property
+emulators is summarised in Figs. 7-9. The emulation error is less
+than 1% for most cosmologies in both the training and the test data
+sets, in the halo mass range of 1012 ≤ M200c/(h−1M⊙) ≤ 1014.
+The primary purpose of this series of papers is to extend the
+modelling of galaxy clustering to non-linear scales. We employ the
+halo model framework (Cooray & Sheth 2002) combined with an
+adopted galaxy-halo connection model to predict galaxy cluster-
+ing and other cosmological observables, following the spirit of the
+Dark Quest project (Nishimichi et al. 2019; Kobayashi et al. 2020;
+Cuesta-Lazaro et al. 2022). We demonstrate that the emulators can
+be applied to the halo model framework combined with the HOD
+prescription to predict the one-halo term of the galaxy clustering
+signal, achieving sub-percent accuracy. The main advantages of this
+emulator-based halo model approach can be summarised as follows.
+• Accuracy. The model ingredients provided by emulators in-
+corporate the major complicated effects in the non-linear regime
+of structure formation, such as non-linear halo bias and the halo
+exclusion effect.
+• Versatility. The halo model approach enables a joint modelling
+of cosmological observables, such as galaxy-galaxy and galaxy-
+matter correlation functions, for a single population of galaxies.
+The combination of different probes can mitigate the uncertainty of
+MNRAS 000, 1–18 (2023)
+
+16
+C. Ruan et al.
+10−1
+100
+0
+25
+50
+75
+100
+125
+r2ξ1h
+gg(r), halo model
+fiducial
+0.9 c(M)
+1.1 c(M)
+10−1
+100
+r/(h−1Mpc)
+−0.05
+0.00
+0.05
+ξ/ξfid − 1
+Figure 11. One-halo terms of the galaxy two-point correlation functions
+with the NFW profiles combined with different concentration-mass relations.
+The black line shows the fiducial case corresponding to the c(M) relation
+measured from this work. The other two coloured lines present the results
+for increasing and decreasing the concentration by 10 per cent. In the lower
+sub-panel, we show the relative difference with respect to the fiducial result.
+(source code)
+galaxy formation and evolution on cosmological parameter infer-
+ence.
+• Flexibility. Instead of making an end-to-end mapping between
+the cosmological and HOD parameters to the final clustering statist-
+ics with the emulation process, this “numerical” version of the halo
+model allows the flexibility of combining with any specific HOD
+prescription for different types of galaxies, without retraining the
+emulators.
+To perform cosmological parameter inference by confronting
+the emulator-based halo model prediction with galaxy survey ob-
+servations, we plan to implement the following improvements and
+extensions in the subsequent papers of this series.
+• The excellent performance of the emulators is partly due to the
+smaller number of parameters varied in the FORGE and BRIDGE
+simulations compared with other emulation projects, as well as the
+limited halo mass range due to the relatively small box size of the
+simulations. However, as indicated by the ideal emulation tests,
+neural networks are capable of emulating halo properties up to the
+halo masses of 1015.5 h−1M⊙ in a higher-dimensional parameter
+space with sub-percent accuracy. To extend the mass range of the
+emulators, we plan to run additional simulations with different spe-
+cifications, such as box size and number of particles, to obtain halo
+properties robustly and at low cost.
+• Galaxy clustering statistics are typically measured in redshift
+space from surveys, which involves not only the information about
+galaxy positions but also their peculiar velocities. We will build
+emulators for the halo peculiar velocity statistics, such as pairwise
+velocity moments, and combine them using a galaxy-halo connec-
+tion model (e.g. Kobayashi et al. 2020; Cuesta-Lazaro et al. 2022).
+• To resemble actual samples of galaxies, we need more realistic
+HOD prescriptions and check the accuracy of the emulator-based
+halo model.
+In the future, we plan to use the neural network emulators on the
+upcoming data from DESI and Euclid to constrain the cosmological
+and modified gravity parameters. This requires that the models be
+trained on simulations with higher resolution to meet the demand
+of the cutting-edge observational data with unprecedented volume
+and much better controlled systematic errors.
+ACKNOWLEDGEMENTS
+C-ZR thanks the Research Council of Norway for their support.
+C-ZR and BL are supported by the European Research Council
+(ERC) through a starting Grant (ERC-StG-716532 PUNCA). AE
+is supported at the AIfA by an Argelander Fellowship. CMB ac-
+knowledges support from the Science Technology Facilities Coun-
+cil through ST/T000244/1. BL and CMB are further supported by
+the UK Science and Technology Funding Council (STFC) Consol-
+idated Grant No. ST/I00162X/1 and ST/P000541/1. CTD is funded
+by the Deutsche Forschungsgemeinschaft (DFG, German Research
+Foundation) under Germany’s Excellence Strategy – EXC-2094 –
+390783311.
+This work used the DiRAC@Durham facility managed by
+the Institute for Computational Cosmology on behalf of the
+STFC DiRAC HPC Facility (www.dirac.ac.uk). The equipment
+was funded by BEIS capital funding via STFC capital grants
+ST/K00042X/1, ST/P002293/1, ST/R002371/1 and ST/S002502/1,
+Durham University and STFC operations grant ST/R000832/1.
+DiRAC is part of the National e-Infrastructure.
+DATA AVAILABILITY
+The data underlying this article will be shared on reasonable request
+to the corresponding author. The source code and data to generate
+the figures in this manuscript are available at this GitHub repository.
+References
+Agarap A. F., 2018, arXiv preprint arXiv:1803.08375
+Agarwal S., Abdalla F. B., Feldman H. A., Lahav O., Thomas S. A., 2012,
+MNRAS, 424, 1409
+Agarwal S., Abdalla F. B., Feldman H. A., Lahav O., Thomas S. A., 2014,
+MNRAS, 439, 2102
+Alom M. Z., et al., 2019, Electronics, 8
+Amendola L., et al., 2013, Living Reviews in Relativity, 16, 6
+Angulo R. E., Hahn O., 2022, Living Reviews in Computational Astrophys-
+ics, 8, 1
+Arnold C., Leo M., Li B., 2019a, Nature Astronomy, 3, 945
+Arnold C., Leo M., Li B., 2019b, Nature Astron., 3, 945
+Arnold C., Li B., Giblin B., Harnois-Déraps J., Cai Y.-C., 2022, MNRAS,
+515, 4161
+Ba S., Myers W. R., Brenneman W. A., 2015, Technometrics, 57, 479
+Barreira A., Li B., Hellwing W. A., Lombriser L., Baugh C. M., Pascoli S.,
+2014, J. Cosmology Astropart. Phys., 2014, 029
+Bhattacharya S., Heitmann K., White M., Lukić Z., Wagner C., Habib S.,
+2011, ApJ, 732, 122
+Bishop C. M., et al., 1995, Neural networks for pattern recognition. Oxford
+university press
+Bocquet S., Heitmann K., Habib S., Lawrence E., Uram T., Frontiere N.,
+Pope A., Finkel H., 2020, ApJ, 901, 5
+Bond J. R., Cole S., Efstathiou G., Kaiser N., 1991, ApJ, 379, 440
+MNRAS 000, 1–18 (2023)
+
+MG Emulator Halo Model I
+17
+Bose B., et al., 2021, MNRAS, 508, 2479
+Brando G., Fiorini B., Koyama K., Winther H. A., 2022, J. Cosmology
+Astropart. Phys., 2022, 051
+Carrilho P., Carrion K., Bose B., Pourtsidou A., Hidalgo J. C., Lombriser
+L., Baldi M., 2022, MNRAS, 512, 3691
+Cataneo M., Rapetti D., Lombriser L., Li B., 2016, J. Cosmology Astropart.
+Phys., 2016, 024
+Cataneo M., Lombriser L., Heymans C., Mead A. J., Barreira A., Bose S.,
+Li B., 2019, MNRAS, 488, 2121
+Child H. L., Habib S., Heitmann K., Frontiere N., Finkel H., Pope A.,
+Morozov V., 2018, ApJ, 859, 55
+Cooray A., Sheth R., 2002, Phys. Rep., 372, 1
+Courtin J., Rasera Y., Alimi J. M., Corasaniti P. S., Boucher V., Füzfa A.,
+2011, MNRAS, 410, 1911
+Crocce M., Pueblas S., Scoccimarro R., 2006, MNRAS, 373, 369
+Cuesta-Lazaro C., et al., 2022, arXiv e-prints, p. arXiv:2208.05218
+Cybenko G., 1989, Mathematics of control, signals and systems, 2, 303
+DESI Collaboration et al., 2016, arXiv e-prints, p. arXiv:1611.00036
+De Felice A., Tsujikawa S., 2010, Living Reviews in Relativity, 13, 3
+DeRose J., et al., 2019, ApJ, 875, 69
+Diemer B., 2018, ApJS, 239, 35
+Diemer B., Joyce M., 2019, ApJ, 871, 168
+Diemer B., Kravtsov A. V., 2015, ApJ, 799, 108
+Donald-McCann J., Beutler F., Koyama K., Karamanis M., 2022, MNRAS,
+511, 3768
+Dooley G. A., Griffen B. F., Zukin P., Ji A. P., Vogelsberger M., Hernquist
+L. E., Frebel A., 2014, ApJ, 786, 50
+Dvali G., Gabadadze G., Porrati M., 2000a, Physics Letters B, 485, 208
+Dvali G., Gabadadze G., Porrati M., 2000b, Physics Letters B, 485, 208
+Fang W., Wang S., Hu W., Haiman Z., Hui L., May M., 2008, Phys. Rev. D,
+78, 103509
+Ferreira P. G., 2019, ARA&A, 57, 335
+Gao L., Navarro J. F., Cole S., Frenk C. S., White S. D. M., Springel V.,
+Jenkins A., Neto A. F., 2008, MNRAS, 387, 536
+García R., Rozo E., Becker M. R., More S., 2021, MNRAS, 505, 1195
+Goodfellow I., Bengio Y., Courville A., 2016, Deep learning. MIT press
+Gupta S., Hellwing W. A., Bilicki M., García-Farieta J. E., 2022, Phys.
+Rev. D, 105, 043538
+Habib S., Heitmann K., Higdon D., Nakhleh C., Williams B., 2007, Phys.
+Rev. D, 76, 083503
+Hand N., Feng Y., Beutler F., Li Y., Modi C., Seljak U., Slepian Z., 2018,
+AJ, 156, 160
+Harnois-Déraps J., Giblin B., Joachimi B., 2019, A&A, 631, A160
+Harnois-Déraps J., Hernandez-Aguayo C., Cuesta-Lazaro C., Arnold C., Li
+B., Davies C. T., Cai Y.-C., 2022, arXiv e-prints, p. arXiv:2211.05779
+Heitmann K., Higdon D., Nakhleh C., Habib S., 2006, ApJ, 646, L1
+Heitmann K., Higdon D., White M., Habib S., Williams B. J., Lawrence E.,
+Wagner C., 2009, ApJ, 705, 156
+Heitmann K., White M., Wagner C., Habib S., Higdon D., 2010, ApJ, 715,
+104
+Heitmann K., et al., 2016, ApJ, 820, 108
+Hendrycks D., Gimpel K., 2016, arXiv e-prints, p. arXiv:1606.08415
+Hornik K., Stinchcombe M., White H., 1989, Neural networks, 2, 359
+Hu W., Sawicki I., 2007, Phys. Rev. D, 76, 064004
+Hu B., Liu X.-W., Cai R.-G., 2018, MNRAS, 476, L65
+Jenkins A., Frenk C. S., White S. D. M., Colberg J. M., Cole S., Evrard
+A. E., Couchman H. M. P., Yoshida N., 2001, MNRAS, 321, 372
+Jennings W. D., Watkinson C. A., Abdalla F. B., McEwen J. D., 2019,
+MNRAS, 483, 2907
+Khoury J., Weltman A., 2004a, Phys. Rev. D, 69, 044026
+Khoury J., Weltman A., 2004b, Phys. Rev. Lett., 93, 171104
+Kingma D. P., Ba J., 2014, arXiv e-prints, p. arXiv:1412.6980
+Klypin A., Yepes G., Gottlöber S., Prada F., Heß S., 2016, MNRAS, 457,
+4340
+Kobayashi Y., Nishimichi T., Takada M., Takahashi R., Osato K., 2020,
+Phys. Rev. D, 102, 063504
+Koyama K., 2007, Classical and Quantum Gravity, 24, R231
+Koyama K., 2018, International Journal of Modern Physics D, 27, 1848001
+Kuhlen M., Vogelsberger M., Angulo R., 2012, Physics of the Dark Universe,
+1, 50
+Kwan J., Bhattacharya S., Heitmann K., Habib S., 2013, ApJ, 768, 123
+Kwan J., Heitmann K., Habib S., Padmanabhan N., Lawrence E., Finkel H.,
+Frontiere N., Pope A., 2015, ApJ, 810, 35
+LSST Science Collaboration et al., 2009, arXiv e-prints, p. arXiv:0912.0201
+Lam T. Y., Li B., 2012, MNRAS, 426, 3260
+Laureijs R., et al., 2011, arXiv e-prints, p. arXiv:1110.3193
+Lawrence E., Heitmann K., White M., Higdon D., Wagner C., Habib S.,
+Williams B., 2010, ApJ, 713, 1322
+Lawrence E., et al., 2017, ApJ, 847, 50
+Li B., Efstathiou G., 2012, MNRAS, 421, 1431
+Li Y., Hu W., 2011, Phys. Rev. D, 84, 084033
+Li B., Zhao G.-B., Teyssier R., Koyama K., 2012, J. Cosmology Astropart.
+Phys., 2012, 051
+Li B., Hellwing W. A., Koyama K., Zhao G.-B., Jennings E., Baugh C. M.,
+2013, MNRAS, 428, 743
+Linder E. V., 2003, Phys. Rev. Lett., 90, 091301
+Lombriser L., 2014, Annalen der Physik, 264, 259
+Lombriser L., Li B., Koyama K., Zhao G.-B., 2013, Phys. Rev. D, 87, 123511
+Lombriser L., Koyama K., Li B., 2014, J. Cosmology Astropart. Phys., 2014,
+021
+Ma C.-P., Fry J. N., 2000, ApJ, 543, 503
+Maartens R., Koyama K., 2010, Living Reviews in Relativity, 13, 5
+Maksimova N. A., Garrison L. H., Eisenstein D. J., Hadzhiyska B., Bose S.,
+Satterthwaite T. P., 2021, MNRAS, 508, 4017
+Massara E., Villaescusa-Navarro F., Viel M., 2014, J. Cosmology Astropart.
+Phys., 2014, 053
+McClintock T., et al., 2019, ApJ, 872, 53
+Mead A. J., Brieden S., Tröster T., Heymans C., 2021, MNRAS, 502, 1401
+Meneghetti M., Rasia E., 2013, arXiv e-prints, p. arXiv:1303.6158
+Mitchell M. A., Arnold C., He J.-h., Li B., 2019, MNRAS, 487, 1410
+Mitchell M. A., Hernández-Aguayo C., Arnold C., Li B., 2021, MNRAS,
+508, 4140
+Miyatake H., et al., 2020, arXiv e-prints, p. arXiv:2101.00113
+Murata R., Nishimichi T., Takada M., Miyatake H., Shirasaki M., More S.,
+Takahashi R., Osato K., 2018, ApJ, 854, 120
+Murray S. G., Power C., Robotham A. S. G., 2013, Astronomy and Com-
+puting, 3, 23
+Murray S. G., Diemer B., Chen Z., Neuhold A. G., Schnapp M. A., Peruzzi
+T., Blevins D., Engelman T., 2021, Astronomy and Computing, 36,
+100487
+Navarro J. F., Frenk C. S., White S. D. M., 1996, ApJ, 462, 563
+Navarro J. F., Frenk C. S., White S. D. M., 1997, ApJ, 490, 493
+Neto A. F., et al., 2007, MNRAS, 381, 1450
+Neyman J., Scott E. L., 1952, ApJ, 116, 144
+Nishimichi T., et al., 2019, ApJ, 884, 29
+Peacock J. A., Smith R. E., 2000, MNRAS, 318, 1144
+Peebles P. J. E., 1980, The large-scale structure of the universe
+Philcox O. H. E., Spergel D. N., Villaescusa-Navarro F., 2020, Phys. Rev. D,
+101, 123520
+Planck Collaboration et al., 2020, A&A, 641, A6
+Prada F., Klypin A. A., Cuesta A. J., Betancort-Rijo J. E., Primack J., 2012,
+MNRAS, 423, 3018
+Press W. H., Schechter P., 1974, ApJ, 187, 425
+Ramachandra N., Valogiannis G., Ishak M., Heitmann K., LSST Dark En-
+ergy Science Collaboration 2021, Phys. Rev. D, 103, 123525
+Ruan C.-Z., Hernández-Aguayo C., Li B., Arnold C., Baugh C. M., Klypin
+A., Prada F., 2022, J. Cosmology Astropart. Phys., 2022, 018
+Sahni V., Shtanov Y., 2003, J. Cosmology Astropart. Phys., 2003, 014
+Schmidt F., 2016, Phys. Rev. D, 93, 063512
+Schmidt F., Lima M., Oyaizu H., Hu W., 2009, Phys. Rev. D, 79, 083518
+Schmidt F., Hu W., Lima M., 2010, Phys. Rev. D, 81, 063005
+Seljak U., 2000, MNRAS, 318, 203
+Sheth R. K., Mo H. J., Tormen G., 2001, MNRAS, 323, 1
+Sinha M., Garrison L. H., 2020, MNRAS, 491, 3022
+Smith R. E., Angulo R. E., 2019, MNRAS, 486, 1448
+Smith R. E., et al., 2003, MNRAS, 341, 1311
+MNRAS 000, 1–18 (2023)
+
+18
+C. Ruan et al.
+Song Y.-S., Sawicki I., Hu W., 2007, Phys. Rev. D, 75, 064003
+Sotiriou T. P., Faraoni V., 2010, Reviews of Modern Physics, 82, 451
+Springel V., 2010, MNRAS, 401, 791
+Springel V., White S. D. M., Tormen G., Kauffmann G., 2001, MNRAS,
+328, 726
+Takahashi R., Sato M., Nishimichi T., Taruya A., Oguri M., 2012, ApJ, 761,
+152
+Takahashi R., Nishimichi T., Namikawa T., Taruya A., Kayo I., Osato K.,
+Kobayashi Y., Shirasaki M., 2020, ApJ, 895, 113
+Tinker J., Kravtsov A. V., Klypin A., Abazajian K., Warren M., Yepes G.,
+Gottlöber S., Holz D. E., 2008, ApJ, 688, 709
+Troja A., Tutusaus I., Sorce J. G., 2022, arXiv e-prints, p. arXiv:2211.09668
+Vainshtein A. I., 1972, Physics Letters B, 39, 393
+Wang J., Bose S., Frenk C. S., Gao L., Jenkins A., Springel V., White
+S. D. M., 2020, Nature, 585, 39
+Weinberger R., Springel V., Pakmor R., 2020, ApJS, 248, 32
+Williams C. K., Rasmussen C. E., 2006, Gaussian processes for machine
+learning. MIT press Cambridge, MA
+Winther H. A., Casas S., Baldi M., Koyama K., Li B., Lombriser L., Zhao
+G.-B., 2019, Phys. Rev. D, 100, 123540
+Yuan S., Garrison L. H., Eisenstein D. J., Wechsler R. H., 2022, MNRAS,
+515, 871
+Zhai Z., et al., 2019, ApJ, 874, 95
+Zhang A., Lipton Z. C., Li M., Smola A. J., 2021, arXiv e-prints, p.
+arXiv:2106.11342
+Zhao G.-B., Li B., Koyama K., 2011, Phys. Rev. D, 83, 044007
+Zheng Z., et al., 2005, ApJ, 633, 791
+Zheng Z., Coil A. L., Zehavi I., 2007, ApJ, 667, 760
+This paper has been typeset from a TEX/LATEX file prepared by the author.
+MNRAS 000, 1–18 (2023)
+
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+page_content=' UK  4Argelander-Institut für Astronomie,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Auf dem Hügel 71,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D-53121 Bonn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Germany  5Max-Planck-Institut fur Astrophysik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Karl-Schwarzschild-Str 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D-85748 Garching,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Germany  6Excellence Cluster ORIGINS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Boltzmannstrasse 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D-85748 Garching,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Germany  7Sorbonne Université,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Université Paris Diderot,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Sorbonne Paris Cité,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' CNRS/IN2P3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  4 place Jussieu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' F-75252,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Paris Cedex 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' France  8Faculty of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ludwig-Maximilians-Universität,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Scheinerstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 1, 81679 Munich, Germany  Accepted XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Received YYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' in original form 10th January 2023  ABSTRACT  In this series of papers we present an emulator-based halo model for the non-linear clustering  of galaxies in modified gravity cosmologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the first paper, we present emulators for the  following halo properties: the halo mass function, concentration-mass relation and halo-matter  cross-correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The emulators are trained on data extracted from the FORGE  and BRIDGE suites of N-body simulations, respectively for two modified gravity (MG)  theories: f(R) gravity and the DGP model, varying three standard cosmological parameters  Ωm0, H0, σ8, and one MG parameter, either ¯fR0 or rc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Our halo property emulators achieve  an accuracy of ≲ 1% on independent test data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We demonstrate that the emulators can be  combined with a galaxy-halo connection prescription to accurately predict the galaxy-galaxy  and galaxy-matter correlation functions using the halo model framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Key words: dark energy – large-scale structure of Universe – cosmology: miscellaneous –  cosmology: theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  1  INTRODUCTION  Ongoing and upcoming galaxy surveys, such as those that will be  made with the Dark Energy Spectroscopic Instrument (DESI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' DESI  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2016), the Vera Rubin Observatory (LSST Sci-  ence Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2009) and Euclid (Laureijs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Amendola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Troja et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022) will map the large scale  structure (LSS) of the Universe with unprecedented statistical pre-  cision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Measurements of the large-scale structure can potentially be  used to unveil the nature of the dark matter and dark energy, and  to look for any deviation from the predictions of general relativ-  ity (GR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Theories of gravity beyond GR – modified gravity (MG)  models – can explain the observed accelerated expansion of the Uni-  verse without invoking a cosmological constant (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Koyama 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Ferreira 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Studies of such models will not only shed light on  ⋆ Argelander Fellow  † E-mail: baojiu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='li@durham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='uk  the nature of the cosmic acceleration, but also serve as useful tests  of GR on cosmic scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The impact of modifications to GR has been well studied in  terms of the cosmic expansion history and the large scale structure,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', at the background and linear perturbation levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the late  universe, the growth of LSS eventually enters the non-linear regime  over a wide range of length scales, and linear theory predictions  cease to be valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This point becomes even more acute in the context  of MG, given that such models have intrinsically non-linear features,  such as screening mechanisms and non-linear field equations for  new degrees of freedom, which cannot be captured by linear theories  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Often a choice is made to exclude small scale  data, thereby losing a wealth of information from high signal-to-  noise ratio measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Such nonlinearities must be properly  incorporated into theoretical modelling if one wishes to make the  best use of the current and next generation cosmological surveys to  constrain cosmological parameters and test gravity theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  A fully non-linear treatment – N-body simulations – is essen-  tial to accurately solve the non-linear dynamics of cosmic struc-  © 2023 The Authors  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02970v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='CO]  8 Jan 2023  2  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  ture formation (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Kuhlen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Angulo & Hahn 2022,  for recent reivews).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The main hurdle of N-body simulations is  their expensive computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A Monte Carlo Markov chain  (MCMC) analysis, usually used to confront theoretical predictions  with data, requires sampling at least 104-105 models in the cosmo-  logical parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Probing such a large number of models  using simulations is computationally prohibitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The situation is  even worse for MG models, which usually involve partial differen-  tial equations governing the new physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Current MG simulations  can take between 2 to O(10) times longer than standard ΛCDM  simulations with the same specifications (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Arnold  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  There are several approaches to dealing with the non-linear  regime in addition to simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' N-body simulation results can  be used to develop phenomenological or semi-analytical fitting for-  mulae to describe the statistical properties of matter and dark matter  haloes, such as the halo mass function calibrated by Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (2008), and the halofit prescription for the matter power spectrum  (Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Takahashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Smith & Angulo 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Mead et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2021) and bispectrum (Takahashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The most  up-to-date version of halofit implemented by Mead et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2021)  achieves an accuracy of 5% down to deeply non-linear scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' How-  ever, such parametric fits may no longer be fit for purpose with the  advent of next-generation surveys that promise to reach measure-  ments with per cent level precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The halo model (Neyman & Scott 1952;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ma & Fry 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Peacock & Smith 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Seljak 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cooray & Sheth 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Schmidt  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Philcox et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020) is a successful analytical description of  the LSS in the non-linear regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In this framework, all matter,  including galaxies and any other tracers, is assumed to reside within  haloes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Then, the problem of predicting the clustering can be split  into the following steps:  the abundance of haloes as a function of halo mass, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' the  halo mass function (HMF);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  the distribution of tracers around the halo centre, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' the  halo density profile, usually assumed to be a Navarro-Frenk-White  (NFW) profile (Navarro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 1996, 1997) specified by a halo mass-  concentration relation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' and  the clustering of the haloes themselves, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', the halo two-point  correlation function (TPCF) in configuration space and the halo auto  power spectrum in Fourier space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  These basic properties of dark matter haloes constitute the halo  model ingredients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo model provides a physically motivated  description of the clustering statistics and is flexible enough to  be extended to incorporate new physics such as massive neutrinos  and baryonic feedback (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Massara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Bose et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Carrilho et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022), as well as models beyond ΛCDM and GR (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Barreira et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Lombriser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Hu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cataneo  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The halo model ingredients can be derived from analytic meth-  ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For example, the HMF can be predicted using the spherical  collapse model of the linear matter density field (Press & Schechter  1974) and the excursion set formalism (Bond et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 1991;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Sheth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2001), whereby the dependence of the HMF on redshift and cos-  mology is expressed in terms of the root-mean-square fluctuations  in the linear matter power spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Jenkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2001) found  that this universality of the HMF holds at an approximate level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' As  simulation predictions improved further, it was discovered that the  redshift evolution of the mass function, even for ΛCDM, deviates  from the universal prediction at the 5-10 per cent level, and several  new fitting formulae were proposed (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Courtin  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Moreover, the universality of the HMF is broken further  in extensions of ΛCDM (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Bhattacharya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2011, for wCDM)  and modified gravity models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Schmidt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Lam & Li  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Li & Efstathiou 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Lombriser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cataneo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Gupta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In order to obtain even tighter constraints  on cosmological parameters and to test gravity theories, one there-  fore needs to proceed beyond the traditional approaches, given their  limitations in accuracy and coverage of parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  In this series of papers, we develop simulation-based theoret-  ical templates called emulators, to obtain accurate predictions for  basic halo properties as a function of halo mass and (modified grav-  ity) cosmology, and to construct accurate predictions for clustering  observables in preparation for ongoing and future galaxy surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  There have been several previous works on the emulation of cos-  mological quantities in the ΛCDM model and its extensions, such  as Heitmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2006);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Habib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2007), the Coyote Universe  (Heitmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2010, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Lawrence et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2010), PkANN (Agar-  wal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2012, 2014), the Mira-Titan Universe (Heitmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Lawrence et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Bocquet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020), Kwan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2013,  2015), Aemulus (DeRose et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' McClintock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Zhai  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019), Dark Quest (Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Kobayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Miyatake et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cuesta-Lazaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022), matry-  oshka (Donald-McCann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022) and AbacusSummit (Mak-  simova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022), as well as in non-standard  cosmologies, such as Winther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ramachandra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Brando et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Harnois-Déraps  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  To build emulators we use the machine-learning interpolation  technique of neural networks, which allows us to predict halo proper-  ties for any given cosmology within the range of parameters covered  by the training data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We use the FORGE (F-Of-R Gravity Emu-  lator) and BRIDGE (BRaneworld-Inspired Dgp Gravity Emulator)  modified gravity N-body simulations described in Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (2022), which together cover a very broad range of parameters in  two MG theories: f(R) gravity and the DGP model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The emulated  halo properties incorporate all the complicated effects on non-linear  scales, such as the non-linear halo bias, the halo exclusion effect and  the screening mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Following the spirit of the Dark Quest project (Nishimichi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cuesta-Lazaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022), we do not perform an end-  to-end emulation of galaxy clustering statistics in the joint para-  meter space of cosmological and galaxy-halo connection models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Instead, we develop emulators for each halo property separately,  and assemble these ingredients within the halo model framework  to construct analytical predictions of galaxy clustering statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  This emulator-based halo model gives us the flexibility to insert dif-  ferent prescriptions of galaxy-halo connection for different galaxy  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Moreover, emulators for basic halo properties themselves  are very useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For example, calibrating the cosmology depend-  ence of the HMF is crucial to control the systematic uncertainty  in galaxy cluster abundance studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' McClintock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Bocquet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The layout of this paper is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In Section 2, we present  a short description of the modified gravity theories studied here and  a brief overview of the FORGE and BRIDGE N-body simulation  suites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In Section 3, we outline the measurement and post-processing  of the halo properties from the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Section 4 describes the  construction of the halo property emulators using neural networks,  and Section 5 shows their performance in reproducing the simula-  tion results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In Section 6, we demonstrate how these emulators can  be combined with a galaxy-halo connection prescription to predict  galaxy statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  MNRAS 000, 1–18 (2023)  MG Emulator Halo Model I  3  Throughout this paper, we use log to denote the base-10 logar-  ithm, log ≡ log10, and ln to indicate the natural logarithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Unless  otherwise stated, we use a subscript 0 to denote the present-day  value of a physical quantity and an overbar for the background  value of a quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2  MODIFIED GRAVITY THEORIES AND SIMULATIONS  We briefly describe the two modified gravity models analysed in this  work, f(R) gravity (Hu & Sawicki 2007) and the Dvali-Gabadadze-  Porrati (DGP) brane-world models (Dvali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2000a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' These are  two of the most widely studied MG models and, as we discuss be-  low, are representative examples of the two main classes of screen-  ing mechanisms, which make them good test-beds for generic MG  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For more detailed descriptions of these models, we refer  the reader to Sotiriou & Faraoni (2010) and De Felice & Tsujikawa  (2010) for f(R) gravity, and Sahni & Shtanov (2003) and Maartens  & Koyama (2010) for DGP models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1  f(R) gravity  The f(R) gravity is a generalisation of Einstein’s general relativity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  In f(R) gravity, the Einstein-Hilbert action in GR has an additional  term, which is a function of the Ricci scalar R,  S =  �  d4x√−g  �M 2  Pl  2 [R + f(R)] + Lm  �  ,  (1)  where MPl = (8πG)−1/2 is the reduced Planck mass, G is New-  ton’s constant, g is the determinant of the metric gµν and Lm is  the Lagrangian density for matter fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Varying the action with  respect to the metric gµν gives the modified Einstein equation,  Gµν + fRRµν −  �1  2f − □fR  �  gµν − ∇µ∇νfR = 8πGT m  µν,  (2)  where  Gµν ≡ Rµν − 1  2gµνR,  (3)  is the Einstein tensor, fR ≡ df(R)/dR, ∇µ is the covariant deriv-  ative corresponding to the metric gµν, □ ≡ ∇α∇α and T m  µν is the  energy momentum tensor for matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Equation (2) is a fourth-order partial differential equation in  gµν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This equation can also be considered as the standard Einstein  equation in GR with a new dynamical degree of freedom, fR, which  is dubbed the scalaron (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The equation of  motion of fR can be obtained by taking the trace of Equation (2):  □fR = 1  3(R − fRR + 2f + 8πGρm) ,  (4)  where ρm is the matter density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  For cosmological simulations in standard gravity, the Newto-  nian limit is commonly adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This includes the approximations  that the gravitational and scalar fields are weak (such that their  higher-order terms can be neglected) and quasi-static (so that the  time derivatives of the fields can be neglected compared to their  spatial derivatives).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Most modified gravity simulations (including  the ones used in this work) adopt this assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the context  of f(R) gravity and the Newtonian limit, the modified Einstein  equation (2) becomes  ∇2Φ ≈ 16πG  3  a2(ρm − ¯ρm) + 1  6a2�  R(fR) − ¯R  �  ,  (5)  and the equation of motion of the scalaron reduces to  ∇2fR ≈ −1  3a2�  R(fR) − ¯R + 8πG(ρm − ¯ρm)  �  ,  (6)  where Φ is the Newtonian potential, ∇ is the 3-dimensional gradient  operator, and an overbar denotes the cosmic mean of a quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  An f(R) gravity model is fully specified by the functional  form of f(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Here, we adopt the well-studied Hu-Sawicki model  (Hu & Sawicki 2007), which is given by  f(R) = −m2  c1(−R/m2)n  c2(−R/m2)n + 1 ,  (7)  where m2 ≡ Ωm0H2  0, and c1, c2 and n are free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The  parameter n is a positive number, which is set to n = 1 in this  work as in most previous studies of this model (however see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li  & Hu 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ramachandra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022, for some  examples of n ̸= 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' With this functional form, we have  fR = −  �� ¯fR0  ��  � ¯R0  R  �n+1  ,  (8)  where ¯R0 and ¯fR0 are, respectively, the present-day values of  the background Ricci scalar and ¯fR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For brevity, we will ad-  opt the following nomenclature to label models: the model with  − log10  �  | ¯fR0|  �  = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5 will be called F5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5, and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The remaining free parameter of the theory is the background  value of the scalar field fR at redshift z = 0, ¯fR0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' With a suitable  choice of this parameter, f(R) gravity reverts to GR in high-density  regions – this is necessary to be consistent with solar system tests  through the associated chameleon mechanism (Khoury & Weltman  2004b,a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A larger value of | ¯fR0| means a stronger deviation from  standard gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The F5 model is in slight tension with small-scale  tests, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lombriser (2014) for a recent review of current  cosmological constraints on ¯fR0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' But since we aim to test gravity  on cosmic scales, models with such strength of MG are neverthe-  less still valuable to study: given their stronger deviations from GR  compared to models with smaller | ¯fR0|, they can lead to import-  ant insights into how the deviations from GR can affect large-scale  cosmological observables such as weak lensing and galaxy cluster-  ing statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In order to fully explore the gravity testing capacities  of upcoming cosmological observations, it is important to gain a  detailed understanding of how these measures are influenced by  possible modifications to gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2  The Dvali-Gabadadze-Porrati (DGP) model  In the Dvali-Gabadadze-Porrati braneworld model (Dvali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2000b), the universe is a four-dimensional brane embedded in a  five-dimensional space-time (called the bulk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The gravitational ac-  tion in this model is given by  S =  �  brane  d4x √−g  �  R  16πG  �  +  �  bulk  d5x  �  −g(5)  �  R(5)  16πG(5)  �  ,  (9)  where a superscript (5) denotes the quantity in the five-dimensional  bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This model has a self-accelerating branch of solution (sDGP),  which gives a natural explanation for the cosmic acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' How-  ever, the sDGP branch suffers from the ghost problems (Koyama  2007) and cannot be considered as a physical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Moreover, its  predictions have been found to be inconsistent with observations  such as cosmic microwave background (CMB) and local measure-  ments of the Hubble parameter H0 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Fang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  MNRAS 000, 1–18 (2023)  4  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The so-called normal branch DGP (nDGP) gravity (Koyama  2007) cannot accelerate cosmic expansion by itself, so in order to  explain the cosmological observations it has to introduce additional  dark energy components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This model is nevertheless still of interest  as a useful toy model that features the Vainshtein screening mechan-  ism (Vainshtein 1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Here, we assume that there is an additional  non-clustering dark energy component in this model, which results  in its expansion history being identical to that of ΛCDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The nDGP  model provides an explanation of why gravity is much weaker than  the other fundamental forces (Maartens & Koyama 2010): all matter  species are assumed to be confined to the brane, while gravity could  propagate through (leak into) the extra spatial dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' There is  one new free parameter in the nDGP model, which can be defined  as the ratio of G(5) and G, and is known as the crossover scale,  rc ≡ 1  2  G(5)  G  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (10)  The modified Friedmann equation in the normal branch DGP  model is given by  H(a)  H0  =  �  Ωm0a−3 + ΩDE0(a) + Ωrc −  √  Ωrc ,  (11)  where Ωrc ≡ 1/(4H2  0r2  c), and ΩDE0 is the density parameter of  the additional dark energy component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The dimensionless quantity  H0rc is used to quantify departures from the standard gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' If  H0rc → ∞ then Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (11) returns to the ΛCDM case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A larger  value of H0rc means a weaker deviation from GR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Hereafter, an  nDGP model with H0rc = X will be referred to as NX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For  example, a model with H0rc = 1 is called N1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The modified Poisson equation and the scalar field equation  are given by (Koyama 2007),  ∇2Φ = 4πGa2δρm + 1  2∇2ϕ ,  (12)  and  ∇2ϕ +  r2  c  3β a2c2  �  (∇2ϕ)2 − (∇i∇jϕ)2�  = 8π G a2  3β  δρm ,  (13)  where ϕ is a new scalar degree of freedom, δρm = ρm − ¯ρm and  β(a) ≡ 1 + 2H rc  �  1 +  ˙H  3H2  �  = 1 +  Ωm0a−3 + 2ΩΛ0  2  �  Ωrc(Ωm0a−3 + ΩΛ0)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (14)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3  Modified gravity N-body simulations  To construct emulators for dark matter halo properties, we use the  FORGE and BRIDGE suites of N-body simulations (Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2022), covering 49 f(R) gravity and 49 DGP models, along with  49 ΛCDM counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The simulations were performed using  10243 dark matter particles in a cube of side 500 h−1 Mpc (here-  after the high-resolution runs, denoted HR) or 1500 h−1 Mpc (low-  resolution runs, labelled LR), using the modified gravity version of  the Arepo cosmological simulation code (Springel 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Arnold  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Weinberger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The mass resolutions of the  HR and LR runs are 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1 × 109 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5 × 1012(Ωm0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3) h−1 M⊙,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The gravitational softening lengths of simulations are  15 (HR) and 75 h−1kpc (LR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The initial conditions were generated  using second-order Lagrangian perturbation theory (2LPT, Crocce  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2006)) at zinit = 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Each cosmology (also called “node”)  has two independent realisations with the pairs of initial conditions  selected to minimise the sample variance on large scales over the  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Visualisation of the cosmological parameters C (Equations (16)-  (18)) covered in the FORGE and BRIDGE simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The 44 training  cosmologies, 5 validation and 2 test cosmologies are shown as black dots,  purple triangles and red stars, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' ΛCDM models corresponding  to log | ¯fR0| = −∞ and log (H0rc) = ∞ are not shown in the last two  rows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source code)  realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' All nodes were initialised with the same (two) ran-  dom seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' See Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2 of Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2022) for a detailed  description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The cosmological parameters were drawn from a Latin hy-  percube designed to efficiently sample a 4-dimensional parameter  space (or a 3-dimensional space in the case of ΛCDM), as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 1, following a similar approach to that used in the cosmo-  SLICS project (Harnois-Déraps et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Since FORGE and  BRIDGE were partly designed to emulate weak lensing statistics,  they sampled directly in the composite structure growth parameter  S8 ≡ σ8  �  Ωm0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3 ,  (15)  instead of the physical matter fluctuation amplitude parameter σ8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The use of S8 accounts better for the degeneracy between Ωm0 and  σ8 in the cosmic shear analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The 49 nodes form the training  data set for each gravity model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' It is common practice to use a  small portion (called validation set) of the training set to determine  whether the process has finished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We choose the nodes 11, 13, 22,  34, 36 as the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The following three standard cosmological parameters and one  MG parameter are varied,  C = {Ωm0, h, S8},  for ΛCDM,  (16)  C =  �  Ωm0, h, S8, log10 | ¯fR0|  �  ,  for f(R),  (17)  C = {Ωm0, h, S8, log10(H0rc)},  for DGP,  (18)  MNRAS 000, 1–18 (2023)  training  validation  test  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6  R0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='8  h  moMG Emulator Halo Model I  5  where h ≡ H0/(100 km s−1 Mpc−1) and H0 is the present day  Hubble constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The range of the parameters explored is  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='11 < Ωm0 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='61 < h < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='81  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6 < S8 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9  −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2 < log10 | ¯fR0| < −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='45 < log10(H0rc) < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (19)  The density parameter of baryons was fixed to Ωb0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='049199  and massive neutrinos are ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The dark energy density is given  by  ΩΛ0 = 1 − Ωm0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (20)  The remaining cosmological parameter is the slope of the primordial  curvature power spectrum normalised at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05 Mpc−1, which is  ns = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9652 (Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We also need test data set to assess the performance of the  emulators independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In both cases, the test set consists of two  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The MG test cases are F5 and F6 for f(R) gravity, and  for DGP they are N1 and N5, and they share the same cosmolo-  gical parameters, given by the fiducial Planck cosmology (Planck  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020),  Ωm0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='31315,  ΩΛ0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='68685,  Ωb0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='049199,  h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6737,  σ8 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='82172,  ns = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9652.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (21)  Each test model has 8 realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The dark matter halo catalogues were obtained using the  Subfind halo finder (Springel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The haloes were first  identified using a fast parallel friends-of-friends (FOF) algorithm  with link length set to b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='168 times the mean interparticle separ-  ation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Spherical overdensity halo catalogues are then built out from  the potential minimum of each FOF halo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo mass definition  adopted is  M200c ≡ 4π  3 (R200c)3 × 200ρcrit,  where ρcrit(z) ≡ 3H2(z)/(8πG) is the critical density of the  Universe, and R200c is the spherical halo radius within which the  spherically averaged mass density equals 200ρcrit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Only main ha-  loes with masses above 1012 h−1M⊙ from the HR simulations are  considered in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo catalogues at  z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='25, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='50, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='75, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='25, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='50, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='75 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  are available for all nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Besides these common redshifts, Arnold  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' saved particle snapshots and halo catalogues at pre-selected  redshifts to construct past light-cones for weak-lensing analysis,  therefore enabling the emulation of halo properties as a function  of redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the main text, we present the performance of the  emulators at redshift zero, since the measurement and emulation at  other redshifts are performed in the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  3  DATA SET  In this section we describe the measurement and post-processing  of the halo properties from the simulations, including the halo  mass function, concentration-mass relation and halo-matter cross-  correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1  Halo Mass Functions  The differential halo mass function (dHMF) quantifies the number  density of haloes as a function of halo mass for a given cosmology  C and redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' It is denoted as  dn(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' z, C)  dM  or  dn(log M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' z, C)  d log M  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (22)  In the cumulative form, the cumulative HMF (cHMF) gives the  number density of haloes above a given mass threshold M,  n(> M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' z, C) =  � ∞  M  dm dn(m;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' z, C)  dm  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (23)  The HMF is measured by creating a histogram of the halo mass,  which is affected by shot noise and sample variance, especially for  massive haloes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Also, HMFs span many orders of magnitude in  abundance, typically from 10−3 to 10−8 (h−1Mpc)−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Taking the  logarithm of the HMF to reduce the dynamic range does not help  much, since the interpolation errors in the logarithmic quantity  would be exponentially amplified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To overcome these problems,  a commonly used approach (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' followed by McClintock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cuesta-Lazaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022) is to fit  the measured HMF using fitting formulae like those proposed by  Jenkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2001);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2008), and then to emulate the  mass and cosmology dependence of the fitting parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' However,  the performance of such fitting functions in MG simulations is not  guaranteed (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Schmidt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Gupta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022) and therefore  may cause systematic errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We adopt an alternative method to emulate the HMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The  main ideas include: (1) Emulating the ratio between the simulation  result for the HMF and a realistic fitting formula to reduce the  dynamic range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2) Considering the cumulative HMF instead of  the differential one to allow for smaller steps in halo mass, thereby  providing more training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2008) (hereafter T08) derived fitting functions  for the HMF applicable over a wide range of halo masses and halo  definitions, with a precision of ≲ 5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We work with the ratio of the  cumulative HMFs between the simulation measurements and the  T08 fitting formulae1,  r(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' C, z) ≡ nsim  h  (> M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' C, z)  nT08  h  (> M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' C, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (24)  The HMF ratios are then interpolated across parameter space using  neural networks to construct the emulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To obtain the differential  HMF for any given cosmology Cany, one can calculate the ratio for  this cosmology using the trained emulator, multiply it with the T08  HMF and take the derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The emulation process is sketched in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  In each snapshot, we measure the number densities of haloes  more massive than a series of masses, beginning at 1012 h−1M⊙  and increasing in steps with a bin width of ∆ log [M/(h−1M⊙)] =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The maximum mass varies across redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 3 presents the  ratios of HMFs for 49 f(R) gravity simulations at z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The ratios  are gently varying functions over a lower dynamic range than HMFs  themselves, therefore resulting in a higher emulation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  1 Numerically implemented in the Python module hmf (Murray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2013,  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  MNRAS 000, 1–18 (2023)  6  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Halo Catalogues  M200c  cumulative HMF  nh,sim(>M|Ctrain)  binning  Fitting Function  Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2008)  cumulative HMF  nh,T08(>M|Ctrain)  integrate  Emulated cHMF Ratio  remu(M|Cany)  cHMF Ratio  r(M|Ctrain)=  nh,sim(>M|Ctrain)/nh,T08(>M|Ctrain)  emulation  Emulated dHMF  dnemu/dM(>M|Cany)  differentiation  Emulated cHMF  nemu(>M|Cany)=  remu(M|Cany) × nh,T08(>M|Cany)  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Flow chart illustrating the process of emulating halo mass func-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We start from measuring the cumulative HMF from the simulations in  the training data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For each simulation, we calculate the cHMF predicted  by the fitting formula of Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2008) for the same cosmology C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We  then interpolate the ratios between the two cHMFs across parameter space  using neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To obtain the commonly used differential HMF for  any given cosmology Cany, we can calculate the ratio, multiply the ratio by  the Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2008) function and take the derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cumulative halo mass function (cHMF) ratios between simulation  measurements for 49 f(R) gravity models and the fitting formula calibrated  by Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2008) for the same cosmology (except for the MG parameter  ¯fR0, which is set to zero), at redshift 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The dynamic range of the ratios  are significantly decreased compared with cHMFs themselves, therefore  increasing the emulation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source code)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2  The individual halo density profile and the  concentration-mass relation  One of the most remarkable discoveries from cosmological N-body  simulations was that dark matter haloes display a universal density  profile (Navarro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 1996, 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020), from the host  haloes of dwarf galaxies to those of massive galaxy clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Spe-  cifically, it was shown that the spherically averaged density profile of  individual relaxed haloes can be described by the well-known Nav-  arro, Frenk & White (NFW) profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The NFW profile is described  by two parameters, the characteristic density and scale radius of a  halo, or equivalently the halo mass and concentration,  ρNFW(r|r−2, ρ−2) =  4ρ−2  � r  r−2  ��  1 +  r  r−2  �2 ,  (25)  where r−2 is the characteristic radius (also denoted as rs) of a halo  at which the logarithmic slope of the density profile equal to −2,  d log [ρNFW(r)]  d log r  ����  r=r−2  = −2,  (26)  and ρ−2 ≡ ρNFW(r = r−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo concentration c is defined  as the ratio between the halo radius (which is adopted as R200c in  this work) and r−2,  c ≡ R200c  r−2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (27)  The other NFW parameter ρ−2 is related to the concentration as  ρ−2 = ρcrit(a)  4  200  3Ωm(a)  c3  f(c),  (28)  where Ωm(a) ≡ ¯ρm(a)/ρcrit(a) is the matter density parameter at  a given scale factor a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' f(c) ≡ ln(1 + c) − c/(1 + c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Previously, attention was focused on measuring halo concen-  trations for the best-fitting WMAP or Planck cosmologies, or similar  models close by in parameter space (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Gao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Prada  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Diemer & Kravtsov 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Klypin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Child  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Such calibrated fitting functions cannot be simply ex-  tended beyond the cosmological and gravity models for which they  have been tested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In order to overcome potential problems associ-  ated with the extrapolation of fitting functions to a wider range of  cosmologies, we build emulators for the halo concentration-mass  relation and halo density profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We study the concentration-mass relation for haloes in the cos-  mologies covered by the FORGE and BRIDGE simulation suites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We consider only the haloes containing more than 1 000 particles,  corresponding to a mass of 1013 h−1M⊙ for the fiducial Planck  cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For several reasons set out below we do not exclude  unrelaxed haloes that contain a large amount of substructure as was  done in some previous work (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Neto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Prada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Klypin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' First, our aim is to predict the halo profile as  an ingredient of the halo model, instead of studying the formation  and evolution of relaxed haloes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Galaxies are expected to reside  in all haloes, regardless of their dynamic state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Second, excluding  unrelaxed haloes would bias the concentration high because haloes  in the rapid mass accretion stage tend to have low concentrations  (Child et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Third, such a cut removes typically 30-50%  haloes, which would make the measurement of halo properties less  reliable, by introducing larger statistical errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  To measure halo concentrations, we follow the approach taken  by Mitchell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2019) and briefly review the main aspects below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  As mentioned in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3, we use M200c and R200c as the defin-  itions of the halo mass and radius, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo centre is  MNRAS 000, 1–18 (2023)  4  3  2  sim  u  0  1012  1013  1014  M200c/ (h-1 MoMG Emulator Halo Model I  7  adopted as the gravitational potential minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo particles  are split into 20 logarithmically spaced radial bins from the halo  centre, covering the range [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00]R200c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We then fit the NFW  profile (Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (25)) to the density in the radial bins of each halo, treat-  ing the characteristic density and concentration as free variables, by  minimising an unweighted χ2,  χ2 =  �  i  [log ρsim(ri) − log ρNFW(ri|c, ρ−2)]2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (29)  We have checked that weighting the χ2 function by the number of  particles in each radial bin has a negligible impact on the best-fitting  concentration values recovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The mean value of the best-fitting concentration depends on  technical details such as the halo finder used, and the number and  range of the radial bins, which would have a non-negligible impact  if the NFW profile is not a good fit to the halo profile (Meneghetti  & Rasia 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Dooley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' It has been argued that using the  median instead of the mean concentration would avoid such non-  convergence (Diemer & Kravtsov 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Neto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2007) found  that the median of the concentration depends only weakly on the  radial range used in the fit, provided that the unrelaxed haloes are  removed and rmin ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05Rvir in the fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  To test the robustness of the halo concentration measurement,  we use three N-body simulations from Mitchell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2021) with  the same cosmology and particle number, Np = 10243, and dif-  ferent box sizes, L = 200, 500 and 1000 h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We then bin  the halo particles, fit the NFW profile and calculate the mean and  median values of the concentrations in each mass bin, keeping the  maximum radius fixed at R200c and checking the results for four  different rmin values: (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='07, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='10 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='13)R200c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The results  are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' All concentration-mass relations are well fitted  by a power law,  c(M) = c0M α,  (30)  with c0 the amplitude and α the index, as represented by the coloured  bands in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The median concentrations (as well as the mean)  and the best-fitting amplitude are still sensitive to the minimum  radius, with a relative difference of up to 10 per cent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' However, the  power indices are practically the same for different fitting ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The convergence test also confirms our choice of the min-  imum particle-number cut applied to define the halo sample used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The concentrations from the lower resolution simulations start de-  viating from those of the higher resolution runs around the halo  mass corresponding to ∼ 800 times the particle mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This pivot  mass also depends weakly on the radial range used to fit the density  profile, with smaller minimum scales having larger pivot masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3  The averaged halo profile estimated from the halo-mass  correlation function  The normalised halo density profile, u(r|M), that appears in the  halo model can be estimated by measuring the halo-mass cross-  correlation functions from an N-body simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' As mentioned  in Section 1, the halo model assumes that the matter density field  consists of a superposition of haloes at locations xi with masses  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5  log10  �  M200c/(h−1M⊙)�  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='90  log10 cmedian  200c  800 × mL200  particle  800 × mL500  particle 800 × mL1000  particle  rmin = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05R200c  rmin = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='07R200c  rmin = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='10R200c  rmin = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='13R200c  fit : c = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02M −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='097  fit : c = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='03M −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='099  fit : c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='98M −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='097  fit : c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='94M −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='095  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Convergence test of halo concentration measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We fit  the NFW profile and measure the halo concentration from three N-body  simulations with the same particle number and different box sizes, L200  (the highest resolution run, thick solid lines), L500 (the medium run, thin  dashed lines) and L1000 (the low resolution run, thin solid lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Colours  represent results obtained for different minimum radial ranges in the fitting,  as shown by the key, with the maximum radial range fixed at R200c in  each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The vertical lines present the critical mass scales lower than  which the concentration measurements are unreliable due to insufficient  resolution, which are ∼ 800 times the mass resolutions mparticle, as long  as rmin > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05R200c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The colour-shaded bands show the power fitting  (c(M) = c0Mα) to the measured c(M) relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source code)  Mi, so that the matter field can be written as  ρm(x) =  �  i  Mi u  �  |x − xi|  ���Mi  �  (31)  =  �  d3x′  �  dM  � �  i  δ(D)(M − Mi) δ(D)(x′ − xi)  M u  �  |x − x′|  ���M  ��  ,  (32)  where  The summation is for all haloes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' the same results can be derived  by taking the summation over all microcells which are made to be  so small that each cell contains no more than one halo centre (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Peebles 1980);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  δ(D)(· · · ) is the Dirac delta function;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' �  i  δ(D)(M − Mi) δ(D)(x′ − xi) ≡ dn(x′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M)  dM  is the local  HMF, whose integral over the halo mass gives the halo number  density field at the field point x′:  �  dM dn(x′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M)  dM  = nh(x′),  (33)  MNRAS 000, 1–18 (2023)  8  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  and its ensemble average gives the common dHMF,  �dn(x′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M)  dM  �  =  ��  i  δ(D)(M − Mi) δ(D)(x′ − xi)  �  = dn(M)  dM  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (34)  u  �  |x − xi|  ���Mi  �  ≡  ρh  �  |x − xi|  ���Mi  �  Mi  denotes the density  profile of a halo centred at xi, which is also assumed to be spheric-  ally symmetric and depends only on its mass,  u  �  |x − xi|  ��Mi  �  =  �  ρh  �  |x − xi|  ���Mi  �  /Mi,  |x − xi| ≤ Rhalo;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  0,  |x − xi| > Rhalo;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (35)  and u is normalised:  �  d3x u  �  |x − xi|  ��Mi  �  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (36)  For two different populations of objects with overdensity fields  δa(x) and δb(x), the two-point cross-correlation function is defined  as  ξab(r) ≡ ⟨δa(x) δb(x + r)⟩ ,  (37)  where ⟨· · ·⟩ denotes ensemble averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Assuming statistical iso-  tropy reduces ξab(r) to a function of separation only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the case of  the cross-correlation between halo centres and the matter field, the  cross-correlation function is given by  ξhm(r) ≡ ⟨δh(x) δm(x + r)⟩  (38)  =  1  ¯nh¯ρm  �  nh(x) ρm(x′)  �  − 1,  (39)  where x′ ≡ x + r, and the halo number density fluctuation field is  defined as  δh(x) ≡ nh(x) − ¯nh  ¯nh  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (40)  Now we derive the expressions for the halo and matter fields  in Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (39) within the halo model framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In realistic N-body  simulations, halo catalogues always have a finite halo mass range,  limited by the simulation force/mass resolution and the box size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We can define the halo selection function for a given mass range  (MR) as  φ(m|MR) ≡  �  1,  if m ∈ MR,  0,  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (41)  In practice, MR can be a narrow mass interval, [M, M + dM) ≈  [M, M + ∆M), or a mass threshold interval, [M, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For a given  halo sample, the corresponding halo number density field can be  expressed as  nh(x) =  �  i  δ(D)(x − xi) φ(mi|MR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (42)  To obtain the expression for ⟨nh(x) ρm(x′)⟩ in the halo model, we  can plug the expressions for the halo and mass fields, Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (32) and  (42), into Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The full expression can be found in Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (7) and  (8) of García et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We focus only on the internal structure  of the halo and, therefore, on the 1-halo term, which reads  �  nh(x) ρm(x′)  �  1h =  �  dm dn  dmm φ(m|MR) u(r|m)  (43)  =  �  �  �  dn(M) M u(r|M),  MR = [M, M + dM),  � ∞  M  dm dn  dm m u(r|m),  MR = [M, ∞),  (44)  where dn(M) is the number density of halos in the mass range  [M, M + dM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The 1-halo term of the halo-mass correlation func-  tion is  ξ1h  hm(r|M) = M u(r|M)  ¯ρm  − 1 = ρh(r|M)  ¯ρm  − 1,  (45)  ξ1h  hm(r|>M) =  1  ¯ρm ¯nh(>M)  � ∞  M  dm dn  dm m u(r|m) − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (46)  We are interested in the average density profile of haloes in a  narrow mass interval [M, M +dM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' However, the noise level of the  simulation measurements for such halo properties and statistics is  high because of the low number density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We bypass this problem by  measuring ξ1h  hm(r| > M) (which involves more haloes and therefore  is a smoother function) and taking the partial derivative with respect  to mass,  u(r|M) = − ¯ρm  M  �dn(M)  dM  �−1  ×  ∂  ∂M  �  ¯nh(> M)  �  1 + ξ1h  hm(r| > M)  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (47)  4  USING NEURAL NETWORKS FOR REGRESSION  PROBLEMS  Given a data set comprised of independent variables (also called  features) and dependent variables (labels), there exists an unknown  underlying function mapping the inputs to the outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We can use  supervised learning algorithms to approximate this function, which  falls in the category of a regression problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the context of  structure formation, the features consist of cosmologies C, redshifts  z, halo masses M or number densities nh, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The labels of interest  include basic properties of haloes such as halo mass functions,  concentration-mass relations and correlation functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the case  of structure formation, the “functions” between the features and  labels are known but expensive: we can run N-body simulations  given a set of cosmological parameters C, save the snapshot at  a given redshift z, identify haloes and measure the properties of  haloes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' But it is computationally intractable to perform ≳ O(104)  cosmological simulations to explore the parameter space in a typical  MCMC analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  As shown in previous works on cosmic emulation, such as  Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' DeRose et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cuesta-Lazaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (2022), and as we will report in the following sections, it is possible  to construct emulators for halo properties by running affordable  numbers (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 50-100) of simulations and interpolating in a high-  dimensional parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Emulators can give accurate predic-  tions for halo properties for new models without running additional  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Thanks to the development of algorithms and comput-  ing power, statistics and machine learning provide us with a wealth  of tools to solve such regression problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  In a regression analysis, the typical progress of approximating  a function can be summarised as:  Define a functional form y = f(x|θ) with adjustable or train-  able parameters θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For example, in the simplest and most common  form — linear regression — the labels are assumed to be linear  combinations of the features and the coefficients are the trainable  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Define a loss function on the training data set D to quantify  the difference between the real and predicted values of the target,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', the sum of the absolute differences (which reduces the weight  MNRAS 000, 1–18 (2023)  MG Emulator Halo Model I  9  of outliers),  L(θ|D) ≡  �  (xi,yi)∈D  ��yi − f(xi|θ)  ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Find the optimal parameters θ⋆ to minimise the loss function  (train the model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Gaussian process (GP) regression (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Williams & Rasmussen  2006) has been widely adopted in cosmological emulation projects,  such as Dark Quest (Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019), Aemulus (DeRose  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019), the Coyote Universe (Heitmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2010), the Mira-  Titan Universe (Bocquet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020), Cosmic Emulators (Kwan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2013) and FORGE (Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' GP regression is non-  parametric, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', no specific functional form is assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' However,  GPs are not easy to apply to large data sets because of their O(N 3)  scaling where N is the size of the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Therefore, the  aforementioned projects usually emulate matter, halo and/or galaxy  properties using a combination of principal component analysis,  to reduce the dimensionality of the data vector, and GP, to fit the  dependence of the principal component coefficients on cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The machine learning algorithm we adopt is a fully connected  neural network (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Bishop et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 1995;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Alom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Zhang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This is a type of artificial neural network in which  all neurons in one layer are connected to the neurons in the next  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The neural network algorithm has been widely applied to  cosmology (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2012, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Jennings et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Kobayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cuesta-Lazaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022), and its perform-  ance has been shown to be competitive or sometimes better than  other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Neural networks have a strong fitting ability, as re-  flected by the universal approximation theorem (Cybenko 1989;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Hornik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 1989;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' However, this theorem  does not provide a means to construct optimised neural networks,  but merely guarantees their existence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Also, this strong fitting abil-  ity also makes neural networks more susceptible to the overfitting  problem compared to GPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Therefore, we need to carefully check  the emulator performance using independent test data sets and tune  the network architecture so that the generalisation error is success-  fully suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Moreover, we show dimensionality reduction is  not necessary when using neural networks, which also improves the  accuracy of the emulator predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  A neural network is an interconnection of neurons arranged in  a series of layers, with each neuron in a layer connected to all other  neurons in adjacent layers with different weightings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' One can impart  values on to the neurons of the first layer (called the input layer), have  a number of hidden layers and finally obtain the output from the last  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For example, in this work, the neural networks emulating the  halo mass function at fixed redshift have five nodes in the input layer,  corresponding to the halo mass and four cosmological parameters,  and one node in the last layer outputting the HMF,  n  �  > M|Ωm0, h, S8, log10 | ¯fR0| or log10 |H0rc|  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (48)  Neural networks use activation functions to impart non-  linearities into the fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rectified Linear Unit (ReLU) (Agarap  2018) is the most commonly used activation function in current  neural networks used to add non-linearities in the mapping between  inputs and outputs, which is defined as  ReLU(x) = max(0, x),  (49)  where x is the output of the previous layer of the neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Note that the activations of ReLU are not differentiable at x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Here, however, we are interested in functions that are differenti-  able with respect to their inputs and, in particular, with respect to  the cosmological parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Therefore, throughout, we use Gaus-  sian error linear unit (GELU) (Hendrycks & Gimpel 2016) as the  activation function instead,  GELU(x) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5x  �  1 + erf  � x  √  2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (50)  To find the optimal parameters θ⋆ that reproduce the halo  properties measured in the N-body simulations, we minimise the  L1-norm loss function,  L = 1  N  N  �  i=0  |yi  true − yi  predicted|  (51)  using the Adam optimiser (Kingma & Ba 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Compared to the  mean squared error, the loss of L1 reduces the importance given  to outlier errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To avoid fine-tuning the learning rate, we adopt a  learning rate scheduler that reduces the learning rate by a factor of  10 every time the validation loss does not improve after 30 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We also stop the training process when the validation loss does not  improve after 100 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This iterative reduction of the learning  rate allows the model to quickly learn the broad characteristics of  the data and later reduce the errors with a smaller learning rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The  initial learning rate is always set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1  Ideal emulation tests  To gain a preliminary impression of the emulation process, and to  guide the design of emulators in the future, we perform emulation  tests under ideal conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo properties are generated for a  limited number of randomly selected cosmologies using analytical  methods or fitting formulae, which are noise-free mappings from  cosmologies to halo properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Then we use these data to train  neural networks and emulate the “true” model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To evaluate the  performance of the emulator, we compare the true values with the  emulator predictions using independent test data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The cosmologies of the training set cover 50 flat geometry  (w0-wa) CDM models (Linder 2003), where the equation-of-state  parameter for dark energy is parameterised in terms of the expansion  factor, a, as  w(a) = w0 + wa(1 − a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (52)  A key aspect of building emulators is an efficient sampling scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  As the training dataset, the 50 cosmologies were sampled using  optimal minimax distance sliced Latin hypercube designs (Ba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2015) in a seven-dimensional cosmological parameter space,  C =  �  Ωm0, Ωb0, h, σ8, ns, w0, wa  �  ,  (53)  as shown by the grey dots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The range of parameters is  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1 < Ωm0 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='7,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02 < Ωb0 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='06,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5 < h < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5 < σ8 < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='92 < ns < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='99,  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3 < w0 < −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='7,  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1 < wa < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1,  (54)  while the upper and lower parameter limits depart significantly from  the current best-fitting ΛCDM background cosmology from the  Planck satellite (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We also generate  two test data sets that were not used in the training: both consist of  500 random cosmologies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' one set covers the same parameter range  as that of the training set, and the other one covers the inner half-  region (in terms of the length per dimension, instead of volume)  of the parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The cosmologies in the full- and half-range  test data sets are shown in green and blue dots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 5, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  MNRAS 000, 1–18 (2023)  10  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Visualisation of the seven-parameter (w0-wa)CDM cosmologies  studied in the ideal emulation tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Grey dots show the training set including  50 nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Green dots represent full-range test set consisting of 500 nodes  covering the same range as that of the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Blue dots show the half-  range test set including 500 nodes in the inner half region of the parameter  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source code)  We choose to emulate two basic properties of haloes in the  tests: the concentration-mass relation c(M), and the cumulative  HMF ¯nh(> M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' For given cosmologies, we generate the c(M)  relation calibrated in Prada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2012), using the publicly available  Python toolkit COLOSSUS (Diemer 2018), and compute the Tinker  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2008) HMF with the Python package hmf (Murray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2013,  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' As described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2, we train the emulators  directly on the ratio of the cumulative HMF between the target HMF  and a fitting formula to reduce the dynamic range and improve the  interpolation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We choose the HMF calibrated in Jenkins  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2001) as the reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The upper panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 6 show the halo properties calculated  using the fitting formulae and emulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The fractional errors are  shown in the lower sub-panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The results show that the emulator  reproduces the analytical halo c(M) relation with a sub-percent  error in the 7D parameter space with only 50 training models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The  performance of the HMF emulator is even better than that of the  concentration emulator, although the HMF data span ∼ 20 orders of  magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The median absolute error of the emulator predictions  is lower than 1 per cent for halo masses M ≲ 1016 h−1M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We also note that the emulator precision is generally different  at the edge and centre of the parameter space, as revealed by the  green and blue lines in the bottom panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This suggests that  we should design the parameter space to be wider than the existing  cosmological constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The parameter space in our ideal tests is  designed to be wide enough that covers some extreme cosmologies,  such as Ωm0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='7 and h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  In general, ideal emulation tests show that under noise-free  conditions, neural network emulators can provide accurate inter-  polations in high-dimensional parameter space, using 50 efficiently  sampled models as the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the next section, we will  present the cosmic emulation in the real situation: the data are  measured from simulations and, therefore, are influenced by sample  variance and noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  5  RESULTS  In this section we demonstrate the ability of a fully connected neural  network to reproduce the halo properties measured from FORGE  and BRIDGE simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We train different emulators for each  gravity theory: ΛCDM, f(R) gravity and DGP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The configurations  of the neural networks for emulating three halo properties are sum-  marised in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1  The emulator for the halo mass function  As discussed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1, we train the neural network emulators  directly on the ratio of the cumulative HMF between simulation  measurements and the fitting formula calibrated in Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (2008) to reduce the dynamic range and improve the emulation  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 7 compares the cumulative and the differential HMFs  from simulations and emulators at z = 0, for the ΛCDM, f(R)  gravity and DGP models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The differential HMF of a given mass bin  centred on log Mi is obtained by  dn(M)  d log M  ����  log Mi  ≈ n(> log Mi − bw  2 ) − n(> log Mi + bw  2 )  bw  ,  (55)  where bw ≡ log Mi+1 − log Mi is the bin width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The lower sub-  panels show the fractional difference between the emulator predic-  tion and the measured HMFs in a given mass bin,  HMFemu − HMFsim  HMFsim  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (56)  The performance of the emulator on the training data set is shown  by the thin lines of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The emulator achieves sub-percent ac-  curacy in reproducing most of the cumulative HMF for halo masses  between 1012 and 1014 h−1M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The residuals of the differential  HMF obtained using Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (55) are slightly larger but still show ≲ 2  per cent scatter around zero, with a mean consistent with zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The  thick lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 7 show the emulator predictions for three test mod-  els which are not used in the training, as described in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We again find percent-level agreement between the emulator pre-  dictions and simulation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Furthermore, the fluctuations of the  residuals in the test set are much smaller than those of the training  models, since each test cosmology has 8 realisations and the sample  variance of the measured dHMFs is suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This confirms that  the errors of the emulator predictions are mainly random instead of  systematic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2  The emulator for the concentration-mass relation  As shown in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 4, the halo concentrations meas-  ured from simulations are sensitive to the radial range used in the  fitting, which indicates that this is not the optimal way to describe  the halo density profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' However, the power law index is not sens-  itive to the range adopted, which indicates that we can treat the  amplitude of the concentration-mass relation as a free parameter  to take into account this variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We build an emulator for the  c(M) relation taking rmin = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='10R200c as a representative value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The performance of the emulator at z = 0 is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The  fractional errors are sub-percent for most of the cosmologies in the  training and test data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  MNRAS 000, 1–18 (2023)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='75  Wo  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='98  s 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='96  n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='92  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  hMG Emulator Halo Model I  11  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ideal emulation tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Top panels: The halo concentration-mass relation (left) and halo mass function (right) of the training (grey), full-range test  (green) and half-range test (blue) sets, from the analytical methods (dots) and emulators (lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Bottom panels: The absolute value of the relative difference  between the models and emulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The solid and dashed lines present the median and 90-th percentile of the emulation fractional errors among the training  (black), test (green) and half-range test (blue) sets, which include 50, 500 and 500 cosmologies, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source code 1, 2)  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Summary of the neural network configurations for emulating the halo properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The architecture of a neural network is specified from the input to  output layer as (Ninput, Nhidden1, Nhidden2, · · · , Noutput) with N the number of neurons in each layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Halo  Property  Feature  Label  Neural Network  Architecture  Activation  HMF  C, M200c  Equation (24)  (5, 64, 32, 1)  GELU  Concentration  C, M200c  c200c  (5, 32, 16, 1)  GELU  ξhm  C, nh  {r2  i ξhm(ri)}N=30  i=1  (5, 128, 32, 30)  GELU  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3  The emulator for the halo-mass cross-correlation  function  As discussed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3, the average halo profile can be es-  timated from the halo-mass cross-correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo  profile u(r|M) is directly related to the matter density field  cross-correlated with the halo sample in a narrow mass range  [M, M+∆M].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' However, such correlation functions measured from  simulations would be rather noisy because of the low halo number  density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To feed the neural networks with smoother data, we meas-  ure the cross-correlation functions between the matter field and the  halo samples with fixed number densities, ξhm(r|C, ¯nh).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We then  use the HMF emulator to translate ξhm(r|C, ¯nh) as a function of  number density into ξhm(r|C, M) as a function of mass, according  to Equation (47).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We measure ξhm(r|C, ¯nh) using the high-performance code  Corrfunc (Sinha & Garrison 2020) for the halo number densities  in logarithmically spaced bins over the range  log10  �  ¯nh  (h−1Mpc)−3  �  = [−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1, −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9],  (57)  using a bin width of ∆ log10 ¯nh = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The separation r is split  into 30 logarithmically-spaced bins from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05 h−1Mpc (three times  the force resolution) to 3 h−1Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Furthermore, to reduce the  dynamic range of the data vector, we opt to emulate r2ξhm(r)  instead of ξhm(r) itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The upper-left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 9 shows  ξhm  �  r|¯nh = 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5 (h−1 Mpc)−3�  at z = 0 for the 49 ΛCDM  gravity cosmologies along with the test models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The average halo profile is only related to the 1-halo term of  ξhm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo-mass correlation enters the transition between 1- and  2-halo terms as the scale increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To estimate the range of the  one-halo term, we only consider the scales below R200c, which is  related to the adopted mass definition M200c as  M200c(z) = 4π  3 (R200c)3200ρcrit(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (58)  We then build emulators for ξhm(r|C, ¯nh) at each redshift,  to reduce the number of features and minimise emulation errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The lower left sub-panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 9 shows the fractional difference  between the simulation measurements and the emulator predictions,  in the training set along with the test models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The emulator achieves  sub-percent accuracy for the both the training and the test models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The average halo density profile can be estimated from ξhm  using Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (47).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 9, we compare this type of  profile with the NFW profiles combined with three concentration-  mass relations from this work, Klypin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2016) and Diemer  & Joyce (2019), in five halo mass bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We also fit the average  profile with an NFW form, using the the data over the range of  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0]R200c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  In the right sub-panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 9, we check the relative difference  between the average profiles measured from the simulations and the  NFW fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' There is a ∼ 5% discrepancy between the two types of  profiles, regardless of the concentration-mass relation, which shows  that the differences between the NFW profiles with different c(M)  relations are small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This level of difference is consistent with the  results discovered in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2 of Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  MNRAS 000, 1–18 (2023)  training,true  20  training, emulation  test  test, inner 50%  15  10  5  training, median  test  training, 90-th percentile  test,inner 50%  rue  10  10-3  1012  1013  1014  1015  1016  M /(h-Mo3  10-4  1  (odWi-)/(W<)u  10-8  10-12  training, simulation  10-16  training, emulation  10-20  test  10-24  test, inner 50%  training, median  test  training, 90-th percentile  test, inner 50%  true  △nhl /ni  10-3  1013  1014  1015  1016  1012  M /(h-1M。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=')12  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cumulative (the first row) and differential (the second row) halo mass functions from simulation measurements and emulator predictions at z = 0,  for ΛCDM (left), f(R) gravity (middle) and DGP (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In each panel, the thin lines show the results of the 49 cosmologies in the training data set, and  the thick lines represent those of the test models which were not used in the construction of the emulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the lower sub-panel, we compare the relative  differences between simulations and emulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The dark and light grey bands denote ±1%- and ±2%-level errors, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The differential halo mass  functions are obtained by finite difference of the cumulative HMFs according to Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (55).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source code 1, 2)  6  EMULATOR APPLICATIONS  With the emulators for the halo mass function and density profile as  ingredients, we are able to predict galaxy clustering statistics using  the halo model framework (Cooray & Sheth 2002), and therefore  fit galaxy clustering measurements in the joint parameter space of  cosmology and a galaxy-halo connection model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In this section,  we demonstrate that the emulator-based halo model reproduces the  signals measured from the mock HOD catalogues generated with  the same specifications, such as the cosmology, HOD prescription,  satellite profile and/or concentration-mass relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  MNRAS 000, 1–18 (2023)  3  ACDM  f(R) gravity  DGP  10  10  training, simulation  training, simulation  training, simulation  training, emulation  training, emulation  Nh(  training, emulation  test, F5  test, Nl  test, GR  test, N5  test, F6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05  rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05  1014 1012  1013  1013  1014 1012  1012  1013  1014  /(h-1Mo)  /(h-1Mo)  /(h-1Mo)  M200c/  M200c/  M200c/-2  10~  ACDM  f(R) gravity  DGP  10  dnh  training, simulation  training, simulation  10  training, simulation  training, emulation  training, emulation  training, emulation  test, F5  test, N1  test, GR  test, N5  test, F6  rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05  1012  10140  101410  10  /(h-1M。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=')  /(h-1 Mo)  M200c/ (h-1 Mo)  M200c/  M200c/MG Emulator Halo Model I  13  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Comparison between the halo concentration-mass relations from  simulations (points) and emulators (lines), for the 49 f(R) gravity cosmo-  logies in the training set (grey) and test models F5 (green), F6 (orange), N1  (blue), N5 (purple) and the fiducial Planck cosmology (denoted as GR, in  red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The results for the ΛCDM and DGP training sets are similar to those  for f(R) gravity and are therefore not shown here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The lower sub-panel  shows the relative difference of the halo concentration between simulations  and emulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The sub-percent differences between the emulator and sim-  ulation results are much smaller than the differences between the results for  different cosmologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source code)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1  Galaxy two-point correlation function  We adopt the halo occupation distribution (HOD) (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2005) prescription to model the average number of galaxies in a halo  as a function of halo mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The occupation of central galaxies is  parameterised as a Bernoulli distribution, whereas that of satellites  is a Poisson distribution (Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Both distributions are  described by their mean occupation number,  ⟨Ng⟩ (M) = ⟨Nc⟩(M) + ⟨Ns⟩(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (59)  The galaxy number density ¯ng can then be obtained by integrating  the HMF weighted by the mean occupation,  ¯ng =  �  dM dn(M)  dM  �  ⟨Nc⟩(M) + ⟨Ns⟩(M)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (60)  Following Cuesta-Lazaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2022), we adopt the HOD  model in Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2007) by introducing the following HOD  parameters,  G =  �  Mmin, σlog M  �  ��  �  Gcen  , M1, κ, α  �  ��  �  Gsat  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (61)  The mean occupation number for central galaxies is given by  ⟨Nc⟩(M|G) = 1  2  �  1 + erf  �log M − log Mmin  σlog M  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (62)  The mean central HOD, ⟨Nc⟩(M) , can be interpreted as the prob-  ability that a halo with mass M hosts a central galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The mean  central HOD considered here has the asymptotic behaviour that  ⟨Nc⟩ → 0 for haloes with M ≪ Mmin, while ⟨Nc⟩ → 1 for haloes  with M ≫ Mmin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The mean satellite HOD is parameterised as  ⟨Ns⟩(M|G) = ⟨Nc⟩(M|G)λs(M),  (63)  where  λs(M) =  �M − κMmin  M1  �α  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (64)  Following the commonly-used prescription, we assume that satel-  lite galaxies reside only in a halo that already hosts a central galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Hence, in the above equation, satellite galaxies can only reside in  haloes with ⟨Nc⟩ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Then we assume that the number distribu-  tion of satellite galaxies in a given host halo follows the Poisson  distribution with mean λs(M):  P(Ns|Nc = 1) = [λs(M)]Nse−λs(M)  Ns!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  ,  (65)  and  P(Ns|Nc = 0) = δKr  Ns,0,  (66)  where δKr  ij stands for the Kronecker delta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Given the HOD model, we populate dark matter haloes in 8  test simulations of the fiducial Planck cosmology with mock galax-  ies and measure the galaxy clustering signals, using the following  randomly selected HOD parameters:  log [Mmin/(h−1M⊙)] = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5, σlog M = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6915,  κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='51, log [M1/(h−1M⊙)] = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9, and α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (67)  We can also express the galaxy two-point correlation func-  tion (TPCF) in terms of dark matter halo properties in the halo  model framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' First, we split the one- and two-halo terms into  correlations of central and satellite galaxies as  ξgg(r) = ξ1h  cs (r) + ξ1h  ss (r)  + ξ2h  cc (r) + ξ2h  cs (r) + ξ2h  ss (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (68)  The terms involving both centrals and satellites lead to a con-  volution of the halo profiles and/or the halo TPCF, following  �  d3x u(x|M) u  �  |x + r|  ���M  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' It is therefore more convenient to  compute these terms in Fourier space, where convolutions in co-  ordinate space become simple products of the Fourier modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Here,  we focus on the one-halo term only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The two-halo term involving  the emulation of halo clustering will be the topic of the subsequent  papers in this series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The expressions for the 1-halo term of the  galaxy TPCF after the central-satellite split are given by  ξ(r) =  � ∞  0  dk  (2π)3 4πk2 sin(kr)  kr  P(k),  (69)  P 1h  cs (k) = 1  ¯n2g  �  dM dn(M)  dM  ⟨Nc⟩(M) λs(M) us(k|M),  (70)  P 1h  ss (k) = 1  ¯n2g  �  dM dn(M)  dM  ⟨Nc⟩(M)  �  λs(M)  �2 �  us(k|M)  �2,  (71)  where us(k|M) is (the Fourier transformation of) the radial distri-  bution of satellite galaxies within a halo, and we have highlighted  the emulated quantities in blue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In this section, we assume that the  MNRAS 000, 1–18 (2023)  concentration  6  4  training, simulation  training,emulation  3  test, F5  test, N1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='01  test, F6  test, N5  test, GR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  emu  C  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='01  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='4  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='8  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0  log10[M200c/(h-1Mo)]14  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  2 × 10−1  3 × 10−1  4 × 10−1  r2ρ(r|M)/M  from ξhm(r|M)  from ξhm(r|M), NFW fitting  NFW, conc = this work  NFW, conc = Diemer19  NFW, conc = Klypin16  M = 1013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  M = 1013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='50  M = 1014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  10−1  100  r/(h−1Mpc)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='10  ρfrom ξhm/ρNFW − 1  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Left panel: Halo-mass cross-correlation functions from simulations and emulators at z = 0, for the 49 ΛCDM gravity cosmologies in the training  set (grey), five test models F5 (cyan), F6 (orange), N1 (blue), N5 (purple) and the fiducial Planck ΛCDM model (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the lower sub-panel, we compare  the relative difference between the simulations and emulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Right panel: Comparison of the normalised halo density profiles, ρ(r|M)/M, truncated at  r = R200c, for the fiducial Planck ΛCDM model (node 0) at z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The average halo profiles estimated from ξhm(r) according to Equation (47) are  represented by points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The solid lines show the fits to an NFW profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The dashed, dotted and dash-dotted lines show the NFW profiles with three different  concentration-mass relations: this work, Diemer & Joyce (2019) and Klypin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Colours denote different halo masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The lower sub-panel shows the  relative difference between the NFW profiles (lines) and the average profiles (points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source code)  distribution is given by an NFW profile with the concentration-mass  relation from Diemer & Joyce (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 10 compares the model predictions and  the galaxy TPCF measured from mock HOD catalogues at z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  On the scales where the 1-halo term dominates (r ≲ 1 h−1Mpc),  the fractional difference is within 1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The colours in the plot rep-  resent different contributions: the correlations of central-central,  central-satellite and satellite-satellite galaxy pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  As shown in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 4, the halo concentrations  measured from simulations are sensitive to the minimum radius in  the fitting, with a relative difference of up to 10 per cent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To test  the impact on galaxy clustering, we calculate the one-halo terms  of ξgg (Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (70) and (71)), adopting the NFW profile with the  concentration-mass relations measured from this work and increas-  ing or decreasing them by 10 per cent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 11 shows that a 10 per  cent change in the concentration-mass relation will change the one-  halo term by 5 per cent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The impact on the two-halo term and the  degeneracy between the concentration amplitude and galaxy-halo  connection model parameters will be left for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='2  Galaxy-matter cross-correlation function  In the galaxy-galaxy weak lensing observations, the excess surface  mass density profile around lensing galaxies, ∆Σgm(R) is meas-  ured, which can be expressed in terms of the galaxy-matter cross-  power spectrum as (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Murata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019)  ∆Σgm(R) = ¯ρm0  � ∞  0  dk  2π kPgm(k)J2(kR),  (72)  where J2(x) is the second-order Bessel function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  In the halo model framework, we can accurately predict Pgm(k)  with the emulators providing the model ingredients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Under the same  configurations as in the last sub-section, Pgm(k) is related to the halo  properties as  Pgm(k) = 1  ¯ng  �  dM dn(M)  dM  ⟨Nc⟩(M)×  �  1 + λs(M) us(k|M)  �  Phm(k|M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (73)  Phm(k|M) is the cross-correlation between the matter overdensity  field with the halo sample in a narrow mass bin [M, M + dM].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The quantity that our halo-mass cross-correlation emulators output  is Phm(k|nh(> M)), which can be converted as  Phm(k|M) = −  �dnh(M)  dM  �−1 ∂  ∂M  �  nh(> M)Phm  �  k  ��nh(> M)  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (74)  We use the publicly available, open-source Python toolkit  nbodykit (Hand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2018) to measure the cross power spectra  between the mock galaxy catalogues and the matter field, in linear k  bins from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3 to 6 h Mpc−1 with a width of ∆k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02 h Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  These measurements are compared with the halo model predictions  MNRAS 000, 1–18 (2023)  training, simulation  training,emulation  80  test,GR  60  40  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02  test,F5  test, N1  test, F6  test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='N5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  emu  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02  10-1  100  r/(h-1Mpc)MG Emulator Halo Model I  15  100  101  102  r2ξgg(r)  ξsimulation  gg  ξsimulation  cc  ξsimulation  cs  ξsimulation  ss  → 2-halo term  1-halo term ←  10−1  100  101  r/(h−1Mpc)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='02  ∆ξ/ξsim  theory, ξ1h  gg  theory, ξ1h  ss  theory, ξ1h  cs  0  100  200  300  400  500  600  700  800  900  kPgm(k)  simulation, Pgm  simulation, Pcm  simulation, Psm  1  2  3  4  5  6  k/(h Mpc−1)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='01  rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  theory, Pcm  theory, Psm  theory, Pgm  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Emulator-based halo model predictions of galaxy clustering statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Left panel: Galaxy two-point correlation functions from simulations (marks)  and emulator-based halo model predictions (solid lines), for the fiducial Planck cosmology of FORGE at z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Colours represent different terms of galaxy  correlations after the central/satellite split: galaxy-galaxy (black), central-central (red), central-satellite (orange) and satellite-satellite (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Only the one-halo  terms of theory predictions are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the lower sub-panel, we show the relative difference between the 1-halo term and the full correlation function measured  from simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Right panel: Similar to the left panel but for the galaxy-matter cross power spectrum for the same cosmology and HOD prescription.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' (source  code)  in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The relative difference shown in the  lower sub-panel is below 1 per cent except at low-k bins, where the  cosmic variance dominates the error budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  7  DISCUSSIONS AND CONCLUSIONS  We present accurate emulators for the halo mass function,  concentration-mass relation and halo-matter cross-correlation func-  tion, for ΛCDM and two representative modified gravity theories,  f(R) gravity and DGP, using the FORGE and BRIDGE suites of  N-body simulations (Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The cosmological para-  meter space spans three non-MG parameters, Ωm0, h, S8, and one  MG parameter, either ¯fR0 or H0rc, depending on which modified  gravity model we are using.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  We construct emulators using fully connected neural net-  works implemented using the open-source Python library PyTorch  Lightning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We show the capabilities of neural networks under  noise-free conditions by emulating the existing fitting formulae of  halo properties, such as the fitting function for HMFs in Tinker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The emulators mimic analytical models in a 7-D parameter  space with sub-percent accuracy, using only 50 training cosmolo-  gies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  For realistic cases where the data come from N-body simu-  lations and therefore have noise, the accuracy of our halo property  emulators is summarised in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 7-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The emulation error is less  than 1% for most cosmologies in both the training and the test data  sets, in the halo mass range of 1012 ≤ M200c/(h−1M⊙) ≤ 1014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The primary purpose of this series of papers is to extend the  modelling of galaxy clustering to non-linear scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We employ the  halo model framework (Cooray & Sheth 2002) combined with an  adopted galaxy-halo connection model to predict galaxy cluster-  ing and other cosmological observables, following the spirit of the  Dark Quest project (Nishimichi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Kobayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Cuesta-Lazaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We demonstrate that the emulators can  be applied to the halo model framework combined with the HOD  prescription to predict the one-halo term of the galaxy clustering  signal, achieving sub-percent accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The main advantages of this  emulator-based halo model approach can be summarised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The model ingredients provided by emulators in-  corporate the major complicated effects in the non-linear regime  of structure formation, such as non-linear halo bias and the halo  exclusion effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Versatility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The halo model approach enables a joint modelling  of cosmological observables, such as galaxy-galaxy and galaxy-  matter correlation functions, for a single population of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The combination of different probes can mitigate the uncertainty of  MNRAS 000, 1–18 (2023)  16  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  10−1  100  0  25  50  75  100  125  r2ξ1h  gg(r), halo model  fiducial  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='9 c(M)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='1 c(M)  10−1  100  r/(h−1Mpc)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05  ξ/ξfid − 1  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' One-halo terms of the galaxy two-point correlation functions  with the NFW profiles combined with different concentration-mass relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The black line shows the fiducial case corresponding to the c(M) relation  measured from this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The other two coloured lines present the results  for increasing and decreasing the concentration by 10 per cent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' In the lower  sub-panel, we show the relative difference with respect to the fiducial result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  (source code)  galaxy formation and evolution on cosmological parameter infer-  ence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Instead of making an end-to-end mapping between  the cosmological and HOD parameters to the final clustering statist-  ics with the emulation process, this “numerical” version of the halo  model allows the flexibility of combining with any specific HOD  prescription for different types of galaxies, without retraining the  emulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  To perform cosmological parameter inference by confronting  the emulator-based halo model prediction with galaxy survey ob-  servations, we plan to implement the following improvements and  extensions in the subsequent papers of this series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  The excellent performance of the emulators is partly due to the  smaller number of parameters varied in the FORGE and BRIDGE  simulations compared with other emulation projects, as well as the  limited halo mass range due to the relatively small box size of the  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' However, as indicated by the ideal emulation tests,  neural networks are capable of emulating halo properties up to the  halo masses of 1015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='5 h−1M⊙ in a higher-dimensional parameter  space with sub-percent accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' To extend the mass range of the  emulators, we plan to run additional simulations with different spe-  cifications, such as box size and number of particles, to obtain halo  properties robustly and at low cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Galaxy clustering statistics are typically measured in redshift  space from surveys, which involves not only the information about  galaxy positions but also their peculiar velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' We will build  emulators for the halo peculiar velocity statistics, such as pairwise  velocity moments, and combine them using a galaxy-halo connec-  tion model (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Kobayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cuesta-Lazaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  To resemble actual samples of galaxies, we need more realistic  HOD prescriptions and check the accuracy of the emulator-based  halo model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  In the future, we plan to use the neural network emulators on the  upcoming data from DESI and Euclid to constrain the cosmological  and modified gravity parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' This requires that the models be  trained on simulations with higher resolution to meet the demand  of the cutting-edge observational data with unprecedented volume  and much better controlled systematic errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  C-ZR thanks the Research Council of Norway for their support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  C-ZR and BL are supported by the European Research Council  (ERC) through a starting Grant (ERC-StG-716532 PUNCA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' AE  is supported at the AIfA by an Argelander Fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' CMB ac-  knowledges support from the Science Technology Facilities Coun-  cil through ST/T000244/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' BL and CMB are further supported by  the UK Science and Technology Funding Council (STFC) Consol-  idated Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' ST/I00162X/1 and ST/P000541/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' CTD is funded  by the Deutsche Forschungsgemeinschaft (DFG, German Research  Foundation) under Germany’s Excellence Strategy – EXC-2094 –  390783311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  This work used the DiRAC@Durham facility managed by  the Institute for Computational Cosmology on behalf of the  STFC DiRAC HPC Facility (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='dirac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='uk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The equipment  was funded by BEIS capital funding via STFC capital grants  ST/K00042X/1, ST/P002293/1, ST/R002371/1 and ST/S002502/1,  Durham University and STFC operations grant ST/R000832/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  DiRAC is part of the National e-Infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  DATA AVAILABILITY  The data underlying this article will be shared on reasonable request  to the corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' The source code and data to generate  the figures in this manuscript are available at this GitHub repository.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  References  Agarap A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2018, arXiv preprint arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='08375  Agarwal S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Abdalla F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Feldman H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lahav O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Thomas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2012,  MNRAS, 424, 1409  Agarwal S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Abdalla F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Feldman H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lahav O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Thomas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014,  MNRAS, 439, 2102  Alom M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, Electronics, 8  Amendola L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2013, Living Reviews in Relativity, 16, 6  Angulo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hahn O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, Living Reviews in Computational Astrophys-  ics, 8, 1  Arnold C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Leo M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019a, Nature Astronomy, 3, 945  Arnold C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Leo M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019b, Nature Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 3, 945  Arnold C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Giblin B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Harnois-Déraps J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Cai Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, MNRAS,  515, 4161  Ba S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Myers W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Brenneman W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2015, Technometrics, 57, 479  Barreira A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hellwing W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lombriser L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Baugh C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Pascoli S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  2014, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014, 029  Bhattacharya S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lukić Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Wagner C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  2011, ApJ, 732, 122  Bishop C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1995, Neural networks for pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Oxford  university press  Bocquet S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lawrence E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Uram T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Frontiere N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Pope A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Finkel H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020, ApJ, 901, 5  Bond J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Cole S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Efstathiou G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Kaiser N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1991, ApJ, 379, 440  MNRAS 000, 1–18 (2023)  MG Emulator Halo Model I  17  Bose B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2021, MNRAS, 508, 2479  Brando G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Fiorini B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Winther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cosmology  Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, 051  Carrilho P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Carrion K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Bose B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Pourtsidou A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hidalgo J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lombriser  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Baldi M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, MNRAS, 512, 3691  Cataneo M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Rapetti D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lombriser L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2016, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2016, 024  Cataneo M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lombriser L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heymans C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Mead A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Barreira A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Bose S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, MNRAS, 488, 2121  Child H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Frontiere N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Finkel H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Pope A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Morozov V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2018, ApJ, 859, 55  Cooray A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Sheth R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2002, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 372, 1  Courtin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Rasera Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Alimi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Corasaniti P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Boucher V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Füzfa A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  2011, MNRAS, 410, 1911  Crocce M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Pueblas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Scoccimarro R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2006, MNRAS, 373, 369  Cuesta-Lazaro C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05218  Cybenko G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1989, Mathematics of control, signals and systems, 2, 303  DESI Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2016, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00036  De Felice A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Tsujikawa S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2010, Living Reviews in Relativity, 13, 3  DeRose J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, ApJ, 875, 69  Diemer B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2018, ApJS, 239, 35  Diemer B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Joyce M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, ApJ, 871, 168  Diemer B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Kravtsov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2015, ApJ, 799, 108  Donald-McCann J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Beutler F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Karamanis M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, MNRAS,  511, 3768  Dooley G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Griffen B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Zukin P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Ji A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Vogelsberger M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hernquist  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Frebel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014, ApJ, 786, 50  Dvali G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Gabadadze G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Porrati M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2000a, Physics Letters B, 485, 208  Dvali G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Gabadadze G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Porrati M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2000b, Physics Letters B, 485, 208  Fang W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Wang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hu W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Haiman Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hui L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', May M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2008, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D,  78, 103509  Ferreira P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, ARA&A, 57, 335  Gao L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Navarro J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Cole S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Frenk C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Springel V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Jenkins A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Neto A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2008, MNRAS, 387, 536  García R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Rozo E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Becker M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', More S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2021, MNRAS, 505, 1195  Goodfellow I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Bengio Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Courville A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2016, Deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' MIT press  Gupta S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hellwing W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Bilicki M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', García-Farieta J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 105, 043538  Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Higdon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Nakhleh C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Williams B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2007, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 76, 083503  Hand N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Feng Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Beutler F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Modi C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Seljak U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Slepian Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2018,  AJ, 156, 160  Harnois-Déraps J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Giblin B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Joachimi B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, A&A, 631, A160  Harnois-Déraps J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hernandez-Aguayo C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Cuesta-Lazaro C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Arnold C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Davies C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Cai Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='05779  Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Higdon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Nakhleh C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2006, ApJ, 646, L1  Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Higdon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Williams B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lawrence E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Wagner C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2009, ApJ, 705, 156  Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Wagner C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Higdon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2010, ApJ, 715,  104  Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2016, ApJ, 820, 108  Hendrycks D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Gimpel K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2016, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='08415  Hornik K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Stinchcombe M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1989, Neural networks, 2, 359  Hu W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Sawicki I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2007, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 76, 064004  Hu B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Liu X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Cai R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2018, MNRAS, 476, L65  Jenkins A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Frenk C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Colberg J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Cole S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Evrard  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Couchman H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Yoshida N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2001, MNRAS, 321, 372  Jennings W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Watkinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Abdalla F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', McEwen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019,  MNRAS, 483, 2907  Khoury J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Weltman A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2004a, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 69, 044026  Khoury J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Weltman A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2004b, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 93, 171104  Kingma D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Ba J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6980  Klypin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Yepes G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Gottlöber S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Prada F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heß S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2016, MNRAS, 457,  4340  Kobayashi Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Nishimichi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Takada M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Takahashi R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Osato K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 102, 063504  Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2007, Classical and Quantum Gravity, 24, R231  Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2018, International Journal of Modern Physics D, 27, 1848001  Kuhlen M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Vogelsberger M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Angulo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2012, Physics of the Dark Universe,  1, 50  Kwan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Bhattacharya S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2013, ApJ, 768, 123  Kwan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Padmanabhan N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lawrence E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Finkel H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Frontiere N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Pope A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2015, ApJ, 810, 35  LSST Science Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2009, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:0912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='0201  Lam T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2012, MNRAS, 426, 3260  Laureijs R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2011, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='3193  Lawrence E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Higdon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Wagner C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Habib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Williams B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2010, ApJ, 713, 1322  Lawrence E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2017, ApJ, 847, 50  Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Efstathiou G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2012, MNRAS, 421, 1431  Li Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hu W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2011, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 84, 084033  Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Zhao G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Teyssier R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2012, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2012, 051  Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hellwing W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Zhao G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Jennings E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Baugh C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  2013, MNRAS, 428, 743  Linder E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2003, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 90, 091301  Lombriser L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014, Annalen der Physik, 264, 259  Lombriser L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Zhao G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2013, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 87, 123511  Lombriser L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014,  021  Ma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Fry J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2000, ApJ, 543, 503  Maartens R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2010, Living Reviews in Relativity, 13, 5  Maksimova N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Garrison L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Eisenstein D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hadzhiyska B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Bose S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Satterthwaite T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2021, MNRAS, 508, 4017  Massara E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Villaescusa-Navarro F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Viel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2014, 053  McClintock T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, ApJ, 872, 53  Mead A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Brieden S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Tröster T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heymans C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2021, MNRAS, 502, 1401  Meneghetti M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Rasia E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2013, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:1303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='6158  Mitchell M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Arnold C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', He J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, MNRAS, 487, 1410  Mitchell M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hernández-Aguayo C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Arnold C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2021, MNRAS,  508, 4140  Miyatake H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='00113  Murata R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Nishimichi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Takada M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Miyatake H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Shirasaki M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', More S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Takahashi R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Osato K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2018, ApJ, 854, 120  Murray S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Power C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Robotham A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2013, Astronomy and Com-  puting, 3, 23  Murray S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Diemer B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Chen Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Neuhold A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Schnapp M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Peruzzi  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Blevins D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Engelman T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2021, Astronomy and Computing, 36,  100487  Navarro J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Frenk C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1996, ApJ, 462, 563  Navarro J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Frenk C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1997, ApJ, 490, 493  Neto A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2007, MNRAS, 381, 1450  Neyman J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Scott E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1952, ApJ, 116, 144  Nishimichi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, ApJ, 884, 29  Peacock J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Smith R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2000, MNRAS, 318, 1144  Peebles P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1980, The large-scale structure of the universe  Philcox O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Spergel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Villaescusa-Navarro F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D,  101, 123520  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020, A&A, 641, A6  Prada F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Klypin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Cuesta A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Betancort-Rijo J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Primack J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2012,  MNRAS, 423, 3018  Press W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Schechter P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1974, ApJ, 187, 425  Ramachandra N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Valogiannis G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Ishak M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Heitmann K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', LSST Dark En-  ergy Science Collaboration 2021, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 103, 123525  Ruan C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hernández-Aguayo C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Arnold C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Baugh C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Klypin  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Prada F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, 018  Sahni V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Shtanov Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2003, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2003, 014  Schmidt F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2016, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 93, 063512  Schmidt F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lima M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Oyaizu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hu W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2009, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 79, 083518  Schmidt F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hu W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lima M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2010, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 81, 063005  Seljak U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2000, MNRAS, 318, 203  Sheth R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Mo H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Tormen G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2001, MNRAS, 323, 1  Sinha M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Garrison L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020, MNRAS, 491, 3022  Smith R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Angulo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, MNRAS, 486, 1448  Smith R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2003, MNRAS, 341, 1311  MNRAS 000, 1–18 (2023)  18  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Ruan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  Song Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Sawicki I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Hu W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2007, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 75, 064003  Sotiriou T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Faraoni V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2010, Reviews of Modern Physics, 82, 451  Springel V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2010, MNRAS, 401, 791  Springel V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Tormen G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Kauffmann G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2001, MNRAS,  328, 726  Takahashi R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Sato M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Nishimichi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Taruya A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Oguri M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2012, ApJ, 761,  152  Takahashi R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Nishimichi T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Namikawa T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Taruya A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Kayo I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Osato K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Kobayashi Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Shirasaki M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020, ApJ, 895, 113  Tinker J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Kravtsov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Klypin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Abazajian K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Warren M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Yepes G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=',  Gottlöber S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Holz D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2008, ApJ, 688, 709  Troja A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Tutusaus I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Sorce J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='09668  Vainshtein A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 1972, Physics Letters B, 39, 393  Wang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Bose S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Frenk C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Gao L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Jenkins A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Springel V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', White  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020, Nature, 585, 39  Weinberger R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Springel V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Pakmor R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2020, ApJS, 248, 32  Williams C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Rasmussen C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2006, Gaussian processes for machine  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' MIT press Cambridge, MA  Winther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Casas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Baldi M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lombriser L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Zhao  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 100, 123540  Yuan S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Garrison L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Eisenstein D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Wechsler R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2022, MNRAS,  515, 871  Zhai Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2019, ApJ, 874, 95  Zhang A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Lipton Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Smola A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2021, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='11342  Zhao G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Koyama K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2011, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' D, 83, 044007  Zheng Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2005, ApJ, 633, 791  Zheng Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Coil A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', Zehavi I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content=', 2007, ApJ, 667, 760  This paper has been typeset from a TEX/LATEX file prepared by the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
+page_content='  MNRAS 000, 1–18 (2023)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cNE1T4oBgHgl3EQfLAMX/content/2301.02970v1.pdf'}
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+arXiv:2301.04334v1  [gr-qc]  11 Jan 2023
+Fixing cosmological constant on the event horizon
+Merab Gogberashvili1,2
+1Javakhishvili State University, 3 Chavchavadze Ave., Tbilisi 0179, Georgia
+2Andronikashvili Institute of Physics, 6 Tamarashvili St., Tbilisi 0177, Georgia
+January 12, 2023
+Abstract
+Standard cosmological equations are written for the Hubble volume, while the real boundary of
+space-time is the event horizon. Within the unimodular and thermodynamic approaches to gravity, the
+dark energy term in cosmological equations appears as an integration constant, which we fix at the event
+horizon and obtain the observed value for the cosmological constant.
+PACS numbers: 98.80.Es; 04.50.Kd; 98.80.Bp,
+Keywords: Dark Energy; Thermodynamic gravity; Cosmological horizons
+Numerous observations imply that the late universe is in accelerated expansion [1, 2].
+Within the
+framework of the standard cosmological model, an accelerated expansion can be accounted for by a positive
+cosmological constant Λ, which presents in the system of equations for a homogeneous, isotropic and flat
+universe (k = 0),
+H2
+=
+8πG
+3
+ρ + Λ
+3 ,
+(1)
+¨a
+a ≡ ˙H + H2
+=
+−4πG
+3 (ρ + 3p) + Λ
+3 .
+(2)
+Here overdots denote derivatives with respect to the cosmic time, H ≡ ˙a/a is the Hubble parameter, G is
+the gravitational constant, and ρ and p are the mass and pressure densities of cosmological fluids (we use
+the system of units where c = ℏ = kB = 1).
+In (1) and (2) the cosmological constant Λ is a free parameter and is fixed only from observations,
+which for the value of dark energy density gives [3],
+ΩΛ =
+Λ
+3H2
+0
+≈ 0.692 ,
+(3)
+where H0 denotes the present value of the Hubble parameter.
+One of the main problems of standard
+cosmology is that the measured value of Λ is much smaller than theoretical estimations obtained from the
+standard quantum field theory. In order to resolve this discrepancy, various models have been proposed
+(see the reviews [4,5]).
+It is known that, using the Friedmann equation (1), the acceleration equation (2) can be expressed
+without Λ,
+˙H = −4πG(ρ + p) .
+(4)
+Also, combining (1) and (2), one can obtain the matter energy-momentum conservation equation,
+˙ρ = −3H(ρ + p) ,
+(5)
+1
+
+where the cosmological constant Λ does not appear as well. If instead of (1) and (2), one will choose (4)
+and (5) as the independent system of cosmological equations, Λ obtains the role of integration constant.
+Indeed, excluding (ρ + p) from (4) and (5),
+4πG
+3
+˙ρ = H ˙H ,
+(6)
+and integrating this relation over the time, we obtain the Friedmann equation (1),
+H2 = 8πG
+3
+ρ + C ,
+(7)
+but with an integration constant C instead of Λ/3. So, in a cosmological models where the system (4) – (5)
+is primary, and the Friedmann equation (1) represents its first integral, the value of Λ can be obtained from
+boundary conditions of the model. The examples of scenarios where Λ arises as an integration constant
+are unimodular relativity [6–9] and thermodynamic approach to gravity [10–16].
+Key ingredient in thermodynamic model of gravity is entropy, which allows us to study different aspects
+of various physical systems using a similar mathematical framework (see the recent review [17]). Most
+thermodynamic cosmological scenarios are based on the holographic principle (see the review [18]) and for
+an associated entropy of a volume usually is used the Bekenstein–Hawking formula for black holes [19,20],
+SBH = A
+4G = πR2
+G
+,
+(8)
+where R denotes the radius and A = 4πR2 is the surface area. In thermodynamic cosmology, to the Hubble
+sphere of radius
+RH = 1
+H ,
+(9)
+having the surface and volume
+AH = 4π
+H2 ,
+VH = 4π
+3H3 ,
+(10)
+can be associated the temperature [21],
+TH = H
+2π ,
+(11)
+and the black hole type entropy (8),
+SH = AH
+4G =
+π
+GH2 > 0 .
+(12)
+In thermodynamic approach, the Friedmann equation (7) has the natural interpretation as the balance of
+gravitational and matter heat densities in the spirit of the first law of thermodynamics [15,16], while the
+acceleration equation (4) can be obtained by equating the entropy input in the Hubble volume to the sum
+of entropy flux (entropy received per unit surface) transferred through the horizon and the entropy supplied
+by internal sources (entropy generated per unit volume). Indeed, if we neglect the entropy supplied by
+internal sources, the time derivative of the entropy contained within the Hubble volume, SH, should be
+equal to the flux of the matter entropy density, Sm, through the boundary AH,
+˙SH = SmAH .
+(13)
+Using the classical Gibbs–Duhem relation,
+ρ + p = THSm ,
+(14)
+the equation (13) takes the form:
+˙AH = 4G(ρ + p) AH
+TH
+,
+(15)
+2
+
+which, using (10) and (11), reduces to the standard acceleration equation (4). Note that in thermodynamic
+picture the Universe cannot export the entropy to any external universes and it seems that its total entropy
+is conserved [22–25].
+Thus, in various scenarios, the Friedmann equation (7) contains the integration constant C (the dark
+energy term). This change of the role of Λ from a parameter of the matter action to a property of states
+does not solve the cosmological constant problem, but it does change it from a question of fine-tuning to
+a question of boundary conditions [26, 27]. To find proper boundary conditions, note that cosmological
+equations are written for the Hubble volume, since as a proper causal boundary of the classical space-time
+(for the flat universe, k = 0) usually the Hubble horizon is considered [28,29]. Then the metric fluctuations
+are bounded by RH and thermodynamic laws also are satisfied on this boundary [30,31].
+On the other hand, the quantum fluctuations of matter fields should be limited not by the Hubble
+horizon RH, but by the event horizon Re ≥ RH, which represents a real boundary of space-time [32, 33].
+Then, cosmological equations should also contain the energy density corresponding to entanglements of
+quantum particles across the Hubble horizon [34] and can be taken into account by introducing a surface
+term at RH. It was found that the perfect fluid of entanglement has a negative pressure [35] and can be
+interpreted as the origin of dark energy [13].
+The value of the event horizon at the current cosmic time can be estimated as (see, for example, [36]):
+Re = 1
+H0
+� 0
+−1
+dy
+�
+Ωm(1 + y)3 + ΩΛ
+≈ 0.96 RH
+√ΩΛ
+,
+(16)
+where Ωm denotes the matter density. While particle entanglements can be effective up to Re, in the
+context of cosmology (as well as in the context of black holes), (16) is always defined globally (see more
+discussions in [37]) and at the event horizon we can assume absence of matter,
+Ωm|R→Re → 0 .
+(17)
+Using this assumption, we can fix the integration constant in (7):
+C = H2|R→Re = 1
+R2e
+.
+(18)
+Therefore, for the dark energy density we obtain the value
+C
+H2
+0
+= R2
+H
+R2e
+≈ 1.08 ΩΛ ,
+(19)
+which almost coincides with the observed density of the dark energy (3), within the uncertainties in
+measurements of Ωm and ΩΛ in (16).
+To summarize, in this paper we have noted that within the unimodular or thermodynamic approaches
+to gravity, in the Friedmann equation (7) the cosmological term appears as an integration constant, i.e.
+is not associated with the large vacuum expectation values and can be fixed from boundary conditions.
+Since the real boundary of space-time is the event horizon and not the Hubble sphere, we assume that
+cosmological equations should contain the terms corresponding to the entanglements of quantum particles
+across the apparent horizon. Using the fact that in a region enclosed by an event horizon, like a black hole,
+interior matter density should tend to zero at the horizon (17), in the Friedmann equation (7) we fix the
+integration constant (18) and obtain the value for the dark energy density (19) that almost coincides with
+the observations (3).
+References
+[1] S. Perlmutter et al. [Supernova Cosmology Project], “Measurements of Ω and Λ from 42 high redshift
+supernovae,” Astrophys. J. 517 (1999) 565, doi: 10.1086/307221 [arXiv: astro-ph/9812133].
+3
+
+[2] A. G. Riess et al. [Supernova Search Team], “Observational evidence from supernovae for an acceler-
+ating universe and a cosmological constant,” Astron. J. 116 (1998) 1009, doi: 10.1086/300499 [arXiv:
+astro-ph/9805201].
+[3] P. A. R. Ade et al. [Planck], “Planck 2015 results. XIII. Cosmological parameters,” Astron. Astrophys.
+594 (2016) A13, doi: 10.1051/0004-6361/201525830 [arXiv: 1502.01589 [astro-ph.CO]].
+[4] T. Padmanabhan, “Cosmological constant: The weight of the vacuum,” Phys. Rept. 380 (2003) 235,
+doi: 10.1016/S0370-1573(03)00120-0 [arXiv: hep-th/0212290].
+[5] K. Bamba, S. Capozziello, S. Nojiri and S. D. Odintsov, “Dark energy cosmology: the equivalent
+description via different theoretical models and cosmography tests,” Astrophys. Space Sci. 342 (2012)
+155, doi: 10.1007/s10509-012-1181-8 [arXiv: 1205.3421 [gr-qc]].
+[6] Y. J. Ng and H. van Dam, “Unimodular theory of gravity and the cosmological constant,” J. Math.
+Phys. 32 (1991) 1337, doi: 10.1063/1.529283.
+[7] D. R. Finkelstein, A. A. Galiautdinov and J. E. Baugh, “Unimodular relativity and cosmological
+constant,” J. Math. Phys. 42 (2001) 340, doi: 10.1063/1.1328077 [arXiv: gr-qc/0009099 [gr-qc]].
+[8] A. Padilla and I. D. Saltas, “A note on classical and quantum unimodular gravity,” Eur. Phys. J. C
+75 (2015) 561, doi: 10.1140/epjc/s10052-015-3767-0 [arXiv: 1409.3573 [gr-qc]].
+[9] R. Carballo-Rubio, L. J. Garay and G. Garc´ıa-Moreno, “Unimodular Gravity vs General Relativity:
+A status report,” [arXiv: 2207.08499 [gr-qc]].
+[10] T. Padmanabhan, “Emergence and expansion of cosmic space as due to the quest for holographic
+equipartition,” [arXiv: 1206.4916 [hep-th]].
+[11] T. Padmanabhan, “Emergent perspective of gravity and dark energy,” Res. Astron. Astrophys. 12
+(2012) 891, doi: 10.1088/1674-4527/12/8/003 [arXiv: 1207.0505 [astro-ph.CO]].
+[12] N. Komatsu, “Generalized thermodynamic constraints on holographic-principle-based cosmological
+scenarios,” Phys. Rev. D 99 (2019) 043523, doi: 10.1103/PhysRevD.99.043523 [arXiv: 1810.11138
+[gr-qc]].
+[13] M. Gogberashvili, “Cosmological constant from the entropy balance condition,” Adv. High Energy
+Phys. 2018 (2018) 3702498, doi: 10.1155/2018/3702498 [arXiv: 1807.06943 [physics.gen-ph]].
+[14] M. Gogberashvili and I. Kanatchikov, “Cosmological parameters from the thermodynamic model of
+gravity,” Int. J. Theor. Phys. 53 (2014) 1779, doi: 10.1007/s10773-013-1976-6 [arXiv: 1210.4618
+[physics.gen-ph]].
+[15] T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys. Rev. Lett. 75
+(1995) 1260, doi: 10.1103/PhysRevLett.75.1260 [arXiv: gr-qc/9504004].
+[16] T. Padmanabhan, “Thermodynamical aspects of gravity: New insights,” Rept. Prog. Phys. 73 (2010)
+046901, doi: 10.1088/0034-4885/73/4/046901 [arXiv: 0911.5004 [gr-qc]].
+[17] M, Ribeiro, et al., “The entropy universe,” Entropy 23 (2021) 222, doi: 10.3390/e23020222.
+[18] R. Bousso, “The holographic principle,” Rev. Mod. Phys. 74 (2002) 825, doi: 10.1103/RevMod-
+Phys.74.825 [arXiv: hep-th/0203101].
+[19] J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7 (1973) 2333, doi:
+10.1103/Phys-
+RevD.7.2333.
+4
+
+[20] S. W. Hawking, “Black hole explosions?” Nature 248 (1974) 30, doi: 10.1038/248030a0.
+[21] S. W. Hawking, “Particle creation by black holes,” Commun. Math. Phys. 43 (1975) 199 [erratum:
+Commun. Math. Phys. 46 (1976) 206], doi: 10.1007/BF02345020.
+[22] R. Landauer, “Information is physical,” Phys. Today 44 (1991) 23, doi: 10.1063/1.881299.
+[23] M. Gogberashvili, “Information-probabilistic description of the universe,” Int. J. Theor. Phys. 55
+(2016) 4185, doi: 10.1007/s10773-016-3045-4 [arXiv: 1504.06183 [physics.gen-ph]].
+[24] M. Gogberashvili and B. Modrekiladze, “Probing the information-probabilistic description,” Int. J.
+Theor. Phys. 61 (2022) 149, doi: 10.1007/s10773-022-05129-3 [arXiv: 2105.05034 [gr-qc]].
+[25] M. Gogberashvili, “Towards an information description of space-time,” Found. Phys. 52 (2022) 74,
+doi: 10.1007/s10701-022-00594-6 [arXiv: 2208.13738 [physics.gen-ph]].
+[26] W. Buchmuller and N. Dragon, “The cosmological constant as a boundary term,” JHEP 08 (2022)
+167, doi: 10.1007/JHEP08(2022)167 [arXiv: 2203.15714 [hep-th]].
+[27] M. Gogberashvili and U. Chutkerashvili, “Cosmological constant in the thermodynamic models of
+gravity,” Theor. Phys. 2 (2017) 163, doi: 10.22606/tp.2017.24002 [arXiv: 1605.04197 [physics.gen-
+ph]].
+[28] S. A. Hayward, S. Mukohyama and M. C. Ashworth, “Dynamic black hole entropy,” Phys. Lett. A
+256 (1999) 347, doi: 10.1016/S0375-9601(99)00225-X [arXiv: gr-qc/9810006].
+[29] D. Bak and S. J. Rey, “Cosmic holography,” Class. Quant. Grav. 17 (2000) L83, doi: 10.1088/0264-
+9381/17/15/101 [arXiv: hep-th/9902173].
+[30] R. G. Cai and S. P. Kim, “First law of thermodynamics and Friedmann equations of Friedmann-
+Robertson-Walker universe,” JHEP 02 (2005) 050, doi: 10.1088/1126-6708/2005/02/050 [arXiv: hep-
+th/0501055].
+[31] M. Akbar and R. G. Cai, “Thermodynamic behavior of Friedmann equations at apparent horizon
+of FRW universe,” Phys. Rev. D 75 (2007) 084003, doi: 10.1103/PhysRevD.75.084003 [arXiv: hep-
+th/0609128].
+[32] E. Gaztanaga, “The cosmological constant as a zero action boundary,” Mon. Not. Roy. Astron. Soc.
+502 (2021) 436, doi: 10.1093/mnras/stab056 [arXiv: 2101.07368 [gr-qc]].
+[33] E. Gaztanaga, “The cosmological constant as event horizon,” Symmetry 14 (2022) 300, doi:
+10.3390/sym14020300 [arXiv: 2202.00641 [astro-ph.CO]].
+[34] S. Mukohyama, M. Seriu and H. Kodama, “Can the entanglement entropy be the origin of black hole
+entropy?” Phys. Rev. D 55 (1997) 7666, doi: 10.1103/PhysRevD.55.7666 [arXiv: gr-qc/9701059].
+[35] J. W. Lee, J. Lee and H. C. Kim, “Dark energy from vacuum entanglement,” JCAP 08 (2007) 005,
+doi: 10.1088/1475-7516/2007/08/005 [arXiv: hep-th/0701199].
+[36] B. Margalef-Bentabol, J. Margalef-Bentabol and J. Cepa, “Evolution of the cosmological horizons in a
+concordance universe,” JCAP 12 (2012) 035, doi: 10.1088/1475-7516/2012/12/035 [arXiv: 1302.1609
+[astro-ph.CO]].
+[37] M.
+Li,
+“A
+model
+of
+holographic
+dark
+energy,”
+Phys.
+Lett.
+B
+603
+(2004)
+1,
+doi:
+10.1016/j.physletb.2004.10.014 [arXiv: hep-th/0403127].
+5
+
diff --git a/htE3T4oBgHgl3EQfIgkt/content/tmp_files/load_file.txt b/htE3T4oBgHgl3EQfIgkt/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf,len=339
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='04334v1  [gr-qc]  11 Jan 2023  Fixing cosmological constant on the event horizon  Merab Gogberashvili1,2  1Javakhishvili State University, 3 Chavchavadze Ave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=', Tbilisi 0179, Georgia  2Andronikashvili Institute of Physics, 6 Tamarashvili St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=', Tbilisi 0177, Georgia  January 12, 2023  Abstract  Standard cosmological equations are written for the Hubble volume, while the real boundary of  space-time is the event horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Within the unimodular and thermodynamic approaches to gravity, the  dark energy term in cosmological equations appears as an integration constant, which we fix at the event  horizon and obtain the observed value for the cosmological constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  PACS numbers: 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='Es;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='Kd;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='Bp,  Keywords: Dark Energy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Thermodynamic gravity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Cosmological horizons  Numerous observations imply that the late universe is in accelerated expansion [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Within the  framework of the standard cosmological model, an accelerated expansion can be accounted for by a positive  cosmological constant Λ, which presents in the system of equations for a homogeneous, isotropic and flat  universe (k = 0),  H2  =  8πG  3  ρ + Λ  3 ,  (1)  ¨a  a ≡ ˙H + H2  =  −4πG  3 (ρ + 3p) + Λ  3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  (2)  Here overdots denote derivatives with respect to the cosmic time, H ≡ ˙a/a is the Hubble parameter, G is  the gravitational constant, and ρ and p are the mass and pressure densities of cosmological fluids (we use  the system of units where c = ℏ = kB = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  In (1) and (2) the cosmological constant Λ is a free parameter and is fixed only from observations,  which for the value of dark energy density gives [3],  ΩΛ =  Λ  3H2  0  ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='692 ,  (3)  where H0 denotes the present value of the Hubble parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  One of the main problems of standard  cosmology is that the measured value of Λ is much smaller than theoretical estimations obtained from the  standard quantum field theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' In order to resolve this discrepancy, various models have been proposed  (see the reviews [4,5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  It is known that, using the Friedmann equation (1), the acceleration equation (2) can be expressed  without Λ,  ˙H = −4πG(ρ + p) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  (4)  Also, combining (1) and (2), one can obtain the matter energy-momentum conservation equation,  ˙ρ = −3H(ρ + p) ,  (5)  1  where the cosmological constant Λ does not appear as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' If instead of (1) and (2), one will choose (4)  and (5) as the independent system of cosmological equations, Λ obtains the role of integration constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Indeed, excluding (ρ + p) from (4) and (5),  4πG  3  ˙ρ = H ˙H ,  (6)  and integrating this relation over the time, we obtain the Friedmann equation (1),  H2 = 8πG  3  ρ + C ,  (7)  but with an integration constant C instead of Λ/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' So, in a cosmological models where the system (4) – (5)  is primary, and the Friedmann equation (1) represents its first integral, the value of Λ can be obtained from  boundary conditions of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' The examples of scenarios where Λ arises as an integration constant  are unimodular relativity [6–9] and thermodynamic approach to gravity [10–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Key ingredient in thermodynamic model of gravity is entropy, which allows us to study different aspects  of various physical systems using a similar mathematical framework (see the recent review [17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Most  thermodynamic cosmological scenarios are based on the holographic principle (see the review [18]) and for  an associated entropy of a volume usually is used the Bekenstein–Hawking formula for black holes [19,20],  SBH = A  4G = πR2  G  ,  (8)  where R denotes the radius and A = 4πR2 is the surface area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' In thermodynamic cosmology, to the Hubble  sphere of radius  RH = 1  H ,  (9)  having the surface and volume  AH = 4π  H2 ,  VH = 4π  3H3 ,  (10)  can be associated the temperature [21],  TH = H  2π ,  (11)  and the black hole type entropy (8),  SH = AH  4G =  π  GH2 > 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  (12)  In thermodynamic approach, the Friedmann equation (7) has the natural interpretation as the balance of  gravitational and matter heat densities in the spirit of the first law of thermodynamics [15,16], while the  acceleration equation (4) can be obtained by equating the entropy input in the Hubble volume to the sum  of entropy flux (entropy received per unit surface) transferred through the horizon and the entropy supplied  by internal sources (entropy generated per unit volume).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Indeed, if we neglect the entropy supplied by  internal sources, the time derivative of the entropy contained within the Hubble volume, SH, should be  equal to the flux of the matter entropy density, Sm, through the boundary AH,  ˙SH = SmAH .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  (13)  Using the classical Gibbs–Duhem relation,  ρ + p = THSm ,  (14)  the equation (13) takes the form:  ˙AH = 4G(ρ + p) AH  TH  ,  (15)  2  which, using (10) and (11), reduces to the standard acceleration equation (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Note that in thermodynamic  picture the Universe cannot export the entropy to any external universes and it seems that its total entropy  is conserved [22–25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Thus, in various scenarios, the Friedmann equation (7) contains the integration constant C (the dark  energy term).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' This change of the role of Λ from a parameter of the matter action to a property of states  does not solve the cosmological constant problem, but it does change it from a question of fine-tuning to  a question of boundary conditions [26, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' To find proper boundary conditions, note that cosmological  equations are written for the Hubble volume, since as a proper causal boundary of the classical space-time  (for the flat universe, k = 0) usually the Hubble horizon is considered [28,29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Then the metric fluctuations  are bounded by RH and thermodynamic laws also are satisfied on this boundary [30,31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  On the other hand, the quantum fluctuations of matter fields should be limited not by the Hubble  horizon RH, but by the event horizon Re ≥ RH, which represents a real boundary of space-time [32, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Then, cosmological equations should also contain the energy density corresponding to entanglements of  quantum particles across the Hubble horizon [34] and can be taken into account by introducing a surface  term at RH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' It was found that the perfect fluid of entanglement has a negative pressure [35] and can be  interpreted as the origin of dark energy [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  The value of the event horizon at the current cosmic time can be estimated as (see, for example, [36]):  Re = 1  H0  � 0  −1  dy  �  Ωm(1 + y)3 + ΩΛ  ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='96 RH  √ΩΛ  ,  (16)  where Ωm denotes the matter density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' While particle entanglements can be effective up to Re, in the  context of cosmology (as well as in the context of black holes), (16) is always defined globally (see more  discussions in [37]) and at the event horizon we can assume absence of matter,  Ωm|R→Re → 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  (17)  Using this assumption, we can fix the integration constant in (7):  C = H2|R→Re = 1  R2e  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  (18)  Therefore, for the dark energy density we obtain the value  C  H2  0  = R2  H  R2e  ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='08 ΩΛ ,  (19)  which almost coincides with the observed density of the dark energy (3), within the uncertainties in  measurements of Ωm and ΩΛ in (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  To summarize, in this paper we have noted that within the unimodular or thermodynamic approaches  to gravity, in the Friedmann equation (7) the cosmological term appears as an integration constant, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  is not associated with the large vacuum expectation values and can be fixed from boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Since the real boundary of space-time is the event horizon and not the Hubble sphere, we assume that  cosmological equations should contain the terms corresponding to the entanglements of quantum particles  across the apparent horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Using the fact that in a region enclosed by an event horizon, like a black hole,  interior matter density should tend to zero at the horizon (17), in the Friedmann equation (7) we fix the  integration constant (18) and obtain the value for the dark energy density (19) that almost coincides with  the observations (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  References  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Perlmutter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' [Supernova Cosmology Project], “Measurements of Ω and Λ from 42 high redshift  supernovae,” Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 517 (1999) 565, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1086/307221 [arXiv: astro-ph/9812133].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  3  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' [Supernova Search Team], “Observational evidence from supernovae for an acceler-  ating universe and a cosmological constant,” Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 116 (1998) 1009, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1086/300499 [arXiv:  astro-ph/9805201].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Ade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' [Planck], “Planck 2015 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' XIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Cosmological parameters,” Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  594 (2016) A13, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1051/0004-6361/201525830 [arXiv: 1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='01589 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='CO]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Padmanabhan, “Cosmological constant: The weight of the vacuum,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 380 (2003) 235,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1016/S0370-1573(03)00120-0 [arXiv: hep-th/0212290].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [5] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Bamba, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Capozziello, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Nojiri and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Odintsov, “Dark energy cosmology: the equivalent  description via different theoretical models and cosmography tests,” Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 342 (2012)  155, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1007/s10509-012-1181-8 [arXiv: 1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='3421 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [6] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Ng and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' van Dam, “Unimodular theory of gravity and the cosmological constant,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 32 (1991) 1337, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='529283.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Finkelstein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Galiautdinov and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Baugh, “Unimodular relativity and cosmological  constant,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 42 (2001) 340, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1328077 [arXiv: gr-qc/0009099 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Padilla and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Saltas, “A note on classical and quantum unimodular gravity,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' C  75 (2015) 561, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1140/epjc/s10052-015-3767-0 [arXiv: 1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='3573 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [9] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Carballo-Rubio, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Garay and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Garc´ıa-Moreno, “Unimodular Gravity vs General Relativity:  A status report,” [arXiv: 2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='08499 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [10] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Padmanabhan, “Emergence and expansion of cosmic space as due to the quest for holographic  equipartition,” [arXiv: 1206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='4916 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Padmanabhan, “Emergent perspective of gravity and dark energy,” Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 12  (2012) 891, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1088/1674-4527/12/8/003 [arXiv: 1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='0505 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='CO]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [12] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Komatsu, “Generalized thermodynamic constraints on holographic-principle-based cosmological  scenarios,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' D 99 (2019) 043523, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='043523 [arXiv: 1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='11138  [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Gogberashvili, “Cosmological constant from the entropy balance condition,” Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' High Energy  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 2018 (2018) 3702498, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1155/2018/3702498 [arXiv: 1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='06943 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='gen-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Gogberashvili and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Kanatchikov, “Cosmological parameters from the thermodynamic model of  gravity,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 53 (2014) 1779, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1007/s10773-013-1976-6 [arXiv: 1210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='4618  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='gen-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [15] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 75  (1995) 1260, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1260 [arXiv: gr-qc/9504004].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [16] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Padmanabhan, “Thermodynamical aspects of gravity: New insights,” Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 73 (2010)  046901, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1088/0034-4885/73/4/046901 [arXiv: 0911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='5004 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [17] M, Ribeiro, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=', “The entropy universe,” Entropy 23 (2021) 222, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='3390/e23020222.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Bousso, “The holographic principle,” Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 74 (2002) 825, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1103/RevMod-  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='825 [arXiv: hep-th/0203101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Bekenstein, “Black holes and entropy,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' D 7 (1973) 2333, doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1103/Phys-  RevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='2333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  4  [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Hawking, “Black hole explosions?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Nature 248 (1974) 30, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1038/248030a0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Hawking, “Particle creation by black holes,” Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 43 (1975) 199 [erratum:  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 46 (1976) 206], doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1007/BF02345020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [22] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Landauer, “Information is physical,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Today 44 (1991) 23, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='881299.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Gogberashvili, “Information-probabilistic description of the universe,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 55  (2016) 4185, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1007/s10773-016-3045-4 [arXiv: 1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='06183 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='gen-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Gogberashvili and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Modrekiladze, “Probing the information-probabilistic description,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 61 (2022) 149, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1007/s10773-022-05129-3 [arXiv: 2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='05034 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Gogberashvili, “Towards an information description of space-time,” Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 52 (2022) 74,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1007/s10701-022-00594-6 [arXiv: 2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='13738 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='gen-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [26] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Buchmuller and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Dragon, “The cosmological constant as a boundary term,” JHEP 08 (2022)  167, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1007/JHEP08(2022)167 [arXiv: 2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='15714 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Gogberashvili and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Chutkerashvili, “Cosmological constant in the thermodynamic models of  gravity,” Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 2 (2017) 163, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='22606/tp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='24002 [arXiv: 1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='04197 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='gen-  ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Hayward, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Mukohyama and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Ashworth, “Dynamic black hole entropy,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' A  256 (1999) 347, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1016/S0375-9601(99)00225-X [arXiv: gr-qc/9810006].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Bak and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Rey, “Cosmic holography,” Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' 17 (2000) L83, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1088/0264-  9381/17/15/101 [arXiv: hep-th/9902173].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [30] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Cai and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Kim, “First law of thermodynamics and Friedmann equations of Friedmann-  Robertson-Walker universe,” JHEP 02 (2005) 050, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1088/1126-6708/2005/02/050 [arXiv: hep-  th/0501055].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Akbar and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Cai, “Thermodynamic behavior of Friedmann equations at apparent horizon  of FRW universe,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' D 75 (2007) 084003, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='084003 [arXiv: hep-  th/0609128].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [32] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Gaztanaga, “The cosmological constant as a zero action boundary,” Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  502 (2021) 436, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1093/mnras/stab056 [arXiv: 2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='07368 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [33] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Gaztanaga, “The cosmological constant as event horizon,” Symmetry 14 (2022) 300, doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='3390/sym14020300 [arXiv: 2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='00641 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='CO]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Mukohyama, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Seriu and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Kodama, “Can the entanglement entropy be the origin of black hole  entropy?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' D 55 (1997) 7666, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='7666 [arXiv: gr-qc/9701059].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Lee and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Kim, “Dark energy from vacuum entanglement,” JCAP 08 (2007) 005,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1088/1475-7516/2007/08/005 [arXiv: hep-th/0701199].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [36] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Margalef-Bentabol, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Margalef-Bentabol and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content=' Cepa, “Evolution of the cosmological horizons in a  concordance universe,” JCAP 12 (2012) 035, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1088/1475-7516/2012/12/035 [arXiv: 1302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1609  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='CO]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  [37] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Li,  “A  model  of  holographic  dark  energy,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  B  603  (2004)  1,  doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='physletb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='014 [arXiv: hep-th/0403127].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
+page_content='  5' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/htE3T4oBgHgl3EQfIgkt/content/2301.04334v1.pdf'}
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+MITP-23-002
+A Lighter QCD Axion from Anarchy
+Fatemeh Elahi,1, ∗ Gilly Elor,1, † Alexey Kivel,1, ‡ Julien Laux,1, § Saereh Najjari,1, ¶ and Felix Yu1, ∗∗
+1PRISMA+ Cluster of Excellence & Mainz Institute for Theoretical Physics
+Johannes Gutenberg University, 55099 Mainz, Germany
+We introduce the Anarchic Axion, a class of axion models which solves the Strong CP problem
+with a lighter than usual QCD axion, thus populating new parameter space that ongoing and future
+experiments target.
+The Anarchic Axion is driven light by a soft breaking of the Peccei-Quinn
+symmetry, which also predicts a residual neutron electric dipole moment. We introduce a novel
+measure to quantify the tuning required for large deviations from the usual QCD axion band. In
+addition to motivating searches for unusually light axions, this work establishes a new target for
+axion effective field theory.
+The Peccei-Quinn (PQ) solution [1, 2] to the Strong
+Charge-Parity (CP) problem of quantum chromodynam-
+ics (QCD) predicts relationships between the axion mass
+ma, decay constant fa and axion-photon coupling gaγγ.
+In this Letter, we introduce a new class of multi-scalar
+axion models — The Anarchic Axion —so dubbed as to
+emphasize that the PQ symmetry arises accidentally.
+The U(1)PQ symmetry is softly broken leading to a so-
+lution to the Strong CP problem that deviates from the
+traditional QCD axion band, importantly populating a
+region of parameter space targeted by many on-going ex-
+periments. Related work to solving the strong CP prob-
+lem departing from the canonical band include Refs. [3–
+11]. Furthermore, the new parameter space corresponds
+to an almost perfect alignment between the soft breaking
+vacuum and the θQCD vacuum. This provides a unique
+handle on the Axion Quality Problem [3, 12–17] allow-
+ing the introduction of a novel measure for quantifying
+the fine tuning. The Anarchic Axion can be made nat-
+ural given a Clockwork [18–20] inspired ultraviolet (UV)
+completion.
+In this Letter we first introduce the field content and
+the potential of an Anarchic Axion model. Given an ap-
+propriate basis choice, we compute the ma, fa and gaγγ
+relations, and present the new parameter space where
+experiments can hunt for the Anarchic Axion. We then
+discuss the quality of this solution to the Strong CP prob-
+lem and introduce a fine tuning measure to quantify the
+axion quality. We conclude by commenting on possible
+natural UV completions and future directions.
+The Anarchic Axion. — The particle content and
+charge assignments of the model, summarized in Table. I,
+consists of three complex scalars: H1 and H2 which can
+be identified with the Higgs doublet fields in DFSZ axion
+constructions [21, 22], and a gauge singlet Φ. Standard
+Model (SM) fermions coupling to H1 and H2 will medi-
+ate the requisite effective operator coupling the Anarchic
+Axion and the anomalous G ˜G QCD term.
+The scalar
+Field
+SU(3)c
+SU(2)L
+U(1)Y
+Z5
+U(1)P Q
+Qi
+L
+3
+2
+1/6
+0
+XQ
+ui
+R
+3
+1
+2/3
+1
+XQ-X1
+di
+R
+3
+1
+-1/3
+0
+XQ-X2
+Li
+L
+1
+2
+-1/2
+0
+XL
+ei
+R
+1
+1
+-1
+0
+XL-X2
+H1
+1
+2
+-1/2
+4
+X1
+H2
+1
+2
+1/2
+0
+X2
+Φ
+1
+1
+0
+1
+X3
+TABLE I. The field content of the Anarchic Axion model.
+potential is
+V =
+�
+i=1,2
+�
+µ2
+i |Hi|2 + λi|Hi|4�
++ λ|H1|2|H2|2 + λ′|H1H2|2
++ µ2
+3|Φ|2 + λ3|Φ|4 + λ13|H1|2|Φ|2 + λ23|H2|2|Φ|2 ,
+(1a)
+V Cλ
+break = −CλH1H2Φ + h.c. ,
+(1b)
+which is invariant under the global U(1)H1 × U(1)H2 ×
+U(1)Φ symmetry. Additional gauge symmetry preserving
+terms are forbidden by invoking a Z5 symmetry at high
+scales. The Z5 allows a term Eq. (1b) which breaks the
+global symmetry down to U(1)Y ×U(1)X, where U(1)Y is
+identified with SM hypercharge and U(1)X will be iden-
+tified with the accidentally arising PQ symmetry, with
+X3 = −X1 − X2.
+We choose the parameters of the potential such that all
+three complex scalar fields acquire a vacuum expectation
+value (vev) v1,2,3. Writing the electrically neutral fields
+in a non-linear representation, we have
+√
+2H0
+i = (vi +
+hi)eiai/vi and
+√
+2Φ = (v3+h3)eia3/v3, where hi define the
+CP even radial modes and ai define the CP odd angular
+modes.
+Given an appropriate choice of basis, the angular
+modes can be rewritten as two Goldstone fields a and
+A. We will then derive a basis-invariant anomalous CP-
+Violating (CPV) phase in the QCD sector, providing a
+mass for the Goldstone modes and allowing the identi-
+fication of one mode a with the axion which solves the
+strong CP problem while the other mode A is heavy.
+arXiv:2301.08760v1  [hep-ph]  20 Jan 2023
+
+2
+The interesting phenomenology of the Anarchic Axion
+is the deviation from the canonical QCD axion band in
+{ma, fa} parameter space (and similarly in the axion-
+photon effective coupling), which results from the intro-
+duction of soft PQ breaking at low scales. Specifically,
+V Bµ
+break = −BµH1H2 + h.c. ,
+(2)
+which further breaks the symmetry down to U(1)Y .
+We parameterize the symmetry breaking couplings as
+Bµ = |Bµ|e−iθµ and Cλ = |Cλ|e−iθλ. The original global
+symmetry can be used to render θλ unphysical, and hence
+Cλ is a real parameter.
+The Goldstone basis. — Following the procedure dis-
+cussed in the supplementary material, we perform a ba-
+sis transformation to align the Goldstone fields with the
+U(1)Y ×U(1)X symmetries, which isolates the Goldstone
+eaten by the gauging of hypercharge. In this new basis,
+the angular potential is
+Vang = −|Bµ|
+� 2
+�
+i=1
+(vi + hi)
+�
+cos
+� a
+va
++ A
+vA
+δ2 − θµ
+�
+(3)
+− |Cλ|
+√
+2
+� 3
+�
+i=1
+(vi + hi)
+�
+cos
+� A
+vA
+(1 + δ2) − θλ
+�
+,
+where δ
+= vA/va, v1v2
+= vva/
+√
+1 + δ2 and v3
+=
+vA/
+√
+1 + δ2, with v =
+�
+v2
+1 + v2
+2 ≈ 246 GeV is the elec-
+troweak vev.
+Next, we include the correction to the potential aris-
+ing from QCD instantons induced by the coupling of SM
+quarks to H1 and H2. The effective Lagrangian in the
+Anarchic Axion model is
+LG ˜
+G ⊃ g2
+s
+32π2
+�
+¯θSM − Ng
+� a
+va
++ δ2 A
+vA
+��
+Ga
+µν ˜Gaµν , (4)
+where Ng is the number of quark generations and ¯θSM ≡
+θQCD + arg det YuYd for the SM quark Yukawa matrices.
+By applying global U(1) transformations on H1, H2, Φ
+and the SM quarks, we can reshuffle the separate phases
+from Eq. (3) and Eq. (4) into a new ¯θ defined via ¯θSM −
+Ngθµ ≡ Ng ¯θ. We may choose U(1) phases such that ¯θ is
+only in the Bµ contribution to the potential, and hence
+below ΛQCD the corresponding a and A fields experience
+the instanton potential,
+LG ˜
+G ⊃ Λ4
+QCD cos
+�
+Ng
+� a
+va
++ δ2 A
+vA
+��
+,
+(5)
+where Λ4
+QCD ≡
+mumd
+(mu+md)2 m2
+πf 2
+π.
+Via the Peccei-Quinn
+mechanism, ¯θ is relaxed to the observable CPV parameter
+¯θeff, seen as the tadpoles effects of a and A in Eq. (5).
+Consequently, the total angular potential for a and A
+fields is now
+−Vang = Λ4
+QCD cos
+�
+Ng
+�
+α + α′δ2��
+(6)
++ Λ4
+QCD
+va
+vmax
+cos
+�
+α + α′δ2 + ¯θ
+�
++
+|Cλ|vv2
+A
+√
+2δ(1 + δ2) cos
+�
+α′(1 + δ2)
+�
+,
+where we have introduced α ≡ a/va, α′ ≡ A/vA as con-
+venient notation for the fields, and we have
+vmax ≡
+Λ4
+QCD
+|Bµ|v
+�
+1 + δ2 ,
+(7)
+as the extremal value of the PQ vev va.
+Relaxation and heavy A mass. — To ensure A is heavy,
+we will necessarily take |Cλ| ≫ |Bµ|1/2 as well as require
+δ ≪ 1, such that the mass of A arises dominantly from
+the Cλ contribution to the potential, yielding
+m2
+A = |Cλ|v
+√
+2
+�1
+δ + δ + O
+�
+δ2��
+,
+(8)
+setting the scale of A well above the electroweak scale.
+The vmax scale is the energy where the soft PQ breaking
+parameter must be nearly aligned to the ¯θSM to avoid
+neutron electric dipole moment (nEDM) constraints [23].
+Pragmatically, as will be shown below, vmax corresponds
+to the largest possible scale suppression in gaγγ for ¯θ ≈ π.
+The Anarchic Axion Parameters. — We now derive the
+ma, fa and gaγγ relations. After spontaneous breaking of
+the PQ symmetry by va, the physical degrees of freedom
+a and A acquire tadpoles α0 and α′
+0, respectively. Impor-
+tantly, the unphysical θλ also allows us to shift α′
+0 purely
+into α0, leaving α′
+0 unobservable, as seen in Eq. (6). Con-
+sequently, the tadpole α0 entirely generates |¯θeff| = α0,
+giving a potentially measurable nEDM. Note that in this
+basis, α0 entirely captures the deviation from the canon-
+ical DFSZ due to non-vanishing Bµ.
+Expanding Eq. (6) about the minimum and dropping
+constant terms and the heavy A field, yields
+− Vang
+Λ4
+QCD
+= α
+�
+Ng sin
+�
+Ng ¯θeff
+�
++
+va
+vmax
+sin
+�¯θ − ¯θeff
+��
++ 1
+2α2
+�
+N 2
+g cos
+�
+Ng ¯θeff
+�
++
+va
+vmax
+cos
+�¯θ − ¯θeff
+��
+. (9)
+For very small δ ≪ 1, a is already in its mass basis, where
+ma is given up to O
+�
+δ4�
+corrections by
+m2
+a =
+Λ4
+QCD
+v2a
+�
+N 2
+g cos
+�
+Ng ¯θeff
+�
++
+va
+vmax
+cos
+�¯θ − ¯θeff
+��
+.
+(10)
+
+3
+1/k = 10−10/(π − ¯θ)
+vmax/fa
+¯θeff
+= 10−9
+¯θeff
+= 10−11
+k = 10−8
+k = 10−4
+k = 1
+nEDM: ¯θeff
+≥ 10−10
+10−1
+100
+101
+102
+103
+104
+105
+106
+107
+108
+109
+10−1
+100
+101
+102
+FIG. 1. Contours correspond to values of physical CPV |¯θeff|,
+obtained from Eq. (13). The gray region corresponds to pa-
+rameter space constrained by the nEDM measurement.
+Using Eq. (10), the axion decay constant is
+1
+fa
+≡ Ng
+va
+= −
+cos
+�¯θ − ¯θeff
+�
+2Ngvmax cos
+�
+Ng ¯θeff
+�
+(11)
++
+�
+�
+�
+�
+m2a
+Λ4
+QCD cos
+�
+Ng ¯θeff
+� +
+�
+cos
+�¯θ − ¯θeff
+�
+2Ngvmax cos
+�
+Ng ¯θeff
+�
+�2
+.
+Note that in the limit va ≪ vmax, we recover the canon-
+ical relation m2
+af 2
+a = Λ4
+QCD.
+Finally, to evaluate the axion-diphoton coupling, we
+partition the irreducible U(1)em anomaly shared by a1
+and a2 into the mass eigenstate a, giving
+gaγγ = e2
+8π2
+� E
+N − 1.92
+� �
+1 + δ2
+2 + O
+�
+δ3�� 1
+fa
+,
+(12)
+where E/N = 8/3, analogous to the DFSZ case [24].
+CP Violation and nEDM. — We now return to the
+derivation of the tadpole α0 acquired by a, and the result-
+ing observable CPV ¯θeff constrained by measurements of
+the nEDM. To make contact with phenomenology, it will
+be useful to consider the leading order contribution to
+¯θeff. The first term of Eq. (9) encodes the residual CPV
+¯θeff in the Anarchic Axion model, where the leading con-
+tribution up to O((¯θ − π)2) is given by
+¯θeff =
+2(¯θ − π)
+�
+1 +
+4N 2
+g m2av2max
+Λ4
+QCD
+− 1
+.
+(13)
+Contours of ¯θeff are show in Fig. 1. We define k ≡ (¯θ −
+π)/10−10 to capture the sensitivity to the deviation of ¯θ
+from π, i.e. for k ≲ 1 a tuning will be required and we
+saturate at vmax/fa → 1/Ng. The white region is allowed
+by the nEDM bound. For k ≳ 1, we recover the DFSZ
+solution to strong CP, relaxing the required tuning.
+Results. — In Fig. 2, we display gaγγ vs. ma for the
+Anarchic Axion. The DFSZ axion line is shown in yel-
+low. Regions targeted by experimental searches or con-
+strained by astrophysical considerations are shaded out
+in gray [24]. For fixed values of ma and vmax, the blue
+contours are computed by plugging in 1/fa from Eq. (11)
+into Eq. (12) for gaγγ, and using Eq. (13) to fix ¯θeff as
+a function of k, ma and vmax. We also use Eq. (13) to
+enforce the nEDM constraint |¯θeff| ≤ 10−10. Choosing
+a specific k denoted by a red dotted line, we can access
+lighter axion masses along a given blue contour of fixed
+vmax up to the intersection point. Explicitly, accessing
+smaller axion masses requires a small k and hence tuning
+¯θ closer to π.
+As
+Eq.
+(11)
+suggests
+for
+sufficiently
+small
+ma
+(i.e., ma ≪
+��Λ2
+QCD cos
+�¯θ − ¯θeff
+�
+/(2Ngvmax)
+��), 1/fa be-
+comes insensitive to ma,
+and approaches 1/fa
+≃
+��cos
+�¯θ − ¯θeff
+�
+/(Ngvmax)
+��. Physically, the vev shift from
+the Bµ term begins to dominate in this regime; corre-
+sponding to the kink in the blue lines of
+Fig. 2 upon
+their intersection with the k = 1 line.
+In Fig. 2 we have enforced ¯θ ∈
+� π
+2 , π
+�
+leading to light
+Anarchic Axion masses populating the region to the left
+of the DFSZ band. Note that heavier masses can popu-
+late the region to the right of the DFSZ line for ¯θ < π/2.
+We leave the details of the heavy Anarchic Axion to fu-
+ture work [26].
+The Quality Problem. — All axion models suffer from
+a high scale quality problem, i.e. higher dimensional op-
+erators, which are generally present from gravity effects,
+break the PQ symmetry at high scales and shift the ax-
+ion vev. To preserve the quality of the PQ solution, we
+are forced to fine-tune parameters of the UV theory.
+The quality problem of the Anarchic Axion manifests
+as an alignment of ¯θ with π once the soft breaking Bµ
+term starts to dominate the vev shift, as is evident from
+the low ma plateau in Fig. 2. To quantify the quality
+problem, we introduce a measure ∆BG of fine tuning,
+following [27, 28]:
+∆BG(¯θeff) ≡
+���
+¯θ
+¯θeff
+∂¯θeff
+∂¯θ
+��� .
+(14)
+Note that a large value of ∆BG implies a large tuning.
+Indeed, in Fig. 3 we observe that ∆BG grows as ¯θ → π.
+We emphasize that the region where the Anarchic Axion
+exhibits a lighter than usual axion is characterized by
+a non-trivial fine tuning. This approach of quantifying
+the quality problem can be potentially applied to other
+axion models where the PQ symmetry breaking enters
+explicitly at high scales. Note that this is only possible
+since the residual CPV ¯θeff is calculable.
+We also mention the possibility that the soft break-
+ing Bµ term of the Anarchic Axion model can arise as
+the leading low energy operator matched to a Planck-
+suppressed PQ breaking term in canonical axion models.
+We will reserve a study of the matching requirements of
+soft PQ breaking terms in high-quality axion models for
+the future.
+Discussion. — In this Letter we have introduced the
+Anarchic Axion model which solves the QCD Strong
+CP problem while populating new regions of parameter
+
+4
+0.001
+1
+1000
+106
+10-15
+10-11
+ABRA
+SHAFT
+CAST
+MWD
+HB
+SN
+ν Solar
+Cosmology
+ma[eV]
+gaγγ [GeV−1]
+k = π − ¯θ
+10−10
+10−6
+¯θ ≥ π
+2 and
+¯θeff
+≤ 10−10
+Haloscopes
+10−9
+DFSZ
+k = 10−8
+k = 10−4
+k = 1
+vmax = 109 GeV
+vmax = 1011 GeV
+vmax = 1013 GeV
+vmax = 107 GeV
+FIG. 2. Parameter space for the axion-diphoton coupling in the Anarchic Axion model consistent with current nEDM con-
+straint [23]. Experimental limits, shown by the gray shaded regions are extracted from Ref. [25]. We show representative values
+of vmax and k that highlight the accessible light axion parameter space probed by ongoing haloscope and microwave cavity
+experiments.
+1.8
+2.0
+2.2
+2.5
+2.8
+3.0
+1
+2
+5
+10
+20
+50
+Δθ
+ΔBG
+¯θ
+ΔBG(¯θeff)
+1.8
+2.0
+2.2
+2.5
+2.8
+3.0
+1
+2
+5
+10
+20
+50
+FIG. 3.
+A measure of tuning for the variable ¯θ consistent
+with nEDM constraints on ¯θeff given in Eq. (13), fixing ma =
+10−6 eV and vmax = 107 GeV. As the figure demonstrates,
+the tuning exponentially increases as ¯θ → π, and this tuning
+is negligibly sensitive to alternate ma and vmax values.
+space. We close by mentioning that these regions with
+fine tuning can be motivated by, e.g. a clockwork-like
+ultraviolet model. For instance, consider a U(1)PQ bulk
+gauge symmetry in a 5D warped geometry with a bulk
+electroweak singlet scalar, where PQ charges will be car-
+ried by a brane-localized Higgs and right-handed up-type
+quarks. Given an appropriate choice of boundary condi-
+tions for the bulk field, the Anarchic Axion model then
+arises as an effective description with a global U(1)PQ
+symmetry.
+A discrete Z5 symmetry can be identified
+with a remnant of the bulk gauge symmetry. We leave
+the details of such UV completions to future work [26].
+While the interesting phenomenology of the Anarchic
+Axion model discussed in this Letter arose due to a soft
+PQ breaking term, other variations can produce similar
+phenomenology. For instance, replacing the soft breaking
+Bµ term with a Φ3 term would result in a potential which
+is protected by an accidental and global Z3 symmetry.
+We leave the exploration of variants of Anarchic Axion
+models to future work [26]. We expect the cosmological
+production of the Anarchic Axion to proceed through a
+variation of the canonical misalignment mechanisms and
+also leave the detailed implications of Anarchic Axion
+dark matter to future study.
+The experimental observation of an exceptionally light
+axion deviating from the canonical QCD axion band
+would be evidence for an Anarchic Axion solution to the
+Strong CP problem.
+Note added:. — When this work was in preparation,
+a related preprint appeared [29], focusing on generating
+high-quality axion solutions by suppressing Planck-scale
+operators using chiral gauged U(1) symmetries.
+We thank Prisco Lo Chiatto for useful conversations.
+We thank Raymond Co, Joshua Eby, and Alfredo Wal-
+ter Mario Guerrera for useful discussions and comments
+on the draft. F.E. and G.E. are grateful to CERN for
+their hospitality. This work is supported by the Cluster
+of Excellence Precision Physics, Fundamental Interac-
+
+5
+tions and Structure of Matter (PRISMA+ – EXC 2118/1)
+within the German Excellence Strategy (project ID
+39083149).
+FE is also funded by grant 05H18UMCA1
+of the German Federal Ministry for Education and Re-
+search (BMBF).
+∗ felahi@uni-mainz.de
+† gelor@uni-mainz.de
+‡ alkivel@uni-mainz.de
+§ jlaux01@uni-mainz.de
+¶ snajjari@uni-mainz.de
+∗∗ yu001@uni-mainz.de
+[1] R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440
+(1977).
+[2] R. D. Peccei and H. R. Quinn, Phys. Rev. D16, 1791
+(1977).
+[3] B. Holdom and M. E. Peskin, Nucl. Phys. B 208, 397
+(1982).
+[4] T. Gherghetta, N. Nagata, and M. Shifman, Phys. Rev.
+D 93, 115010 (2016), arXiv:1604.01127 [hep-ph].
+[5] P. Agrawal, G. Marques-Tavares,
+and W. Xue, JHEP
+03, 049 (2018), arXiv:1708.05008 [hep-ph].
+[6] P.
+Agrawal
+and
+K.
+Howe,
+JHEP 12,
+029
+(2018),
+arXiv:1710.04213 [hep-ph].
+[7] P.
+Agrawal
+and
+K.
+Howe,
+JHEP 12,
+035
+(2018),
+arXiv:1712.05803 [hep-ph].
+[8] A.
+Hook,
+Phys.
+Rev.
+Lett.
+120,
+261802
+(2018),
+arXiv:1802.10093 [hep-ph].
+[9] M. K. Gaillard, M. B. Gavela, R. Houtz, P. Quilez,
+and R. Del Rey, Eur. Phys. J. C 78, 972 (2018),
+arXiv:1805.06465 [hep-ph].
+[10] L. Di Luzio, B. Gavela, P. Quilez,
+and A. Ringwald,
+JHEP 05, 184 (2021), arXiv:2102.00012 [hep-ph].
+[11] A. Kivel, J. Laux,
+and F. Yu, JHEP 11, 088 (2022),
+arXiv:2207.08740 [hep-ph].
+[12] M. Kamionkowski and J. March-Russell, Phys. Lett. B
+282, 137 (1992), arXiv:hep-th/9202003.
+[13] J. E. Kim and G. Carosi, Rev. Mod. Phys. 82, 557
+(2010), [Erratum:
+Rev.Mod.Phys. 91, 049902 (2019)],
+arXiv:0807.3125 [hep-ph].
+[14] L. Darm´e and E. Nardi, Phys. Rev. D 104, 055013 (2021),
+arXiv:2102.05055 [hep-ph].
+[15] M. Dine, (2022), arXiv:2207.01068 [hep-ph].
+[16] A.
+Banerjee,
+J.
+Eby,
+and
+G.
+Perez,
+(2022),
+arXiv:2210.05690 [hep-ph].
+[17] Q. Bonnefoy, (2022), arXiv:2212.00102 [hep-ph].
+[18] K.
+Choi
+and
+S.
+H.
+Im,
+JHEP
+01,
+149
+(2016),
+arXiv:1511.00132 [hep-ph].
+[19] G. F. Giudice and M. McCullough, JHEP 02, 036 (2017),
+arXiv:1610.07962 [hep-ph].
+[20] A. Ahmed and B. M. Dillon, Phys. Rev. D 96, 115031
+(2017), arXiv:1612.04011 [hep-ph].
+[21] M. Dine, W. Fischler, and M. Srednicki, Physics Letters
+B 104, 199 (1981).
+[22] A. R. Zhitnitsky, Sov. J. Nucl. Phys. 31, 260 (1980).
+[23] C. Abel et al., Phys. Rev. Lett. 124, 081803 (2020),
+arXiv:2001.11966 [hep-ex].
+[24] R. L. Workman et al. (Particle Data Group), PTEP
+2022, 083C01 (2022).
+[25] C. O’Hare, “cajohare/axionlimits: Axionlimits,” https:
+//cajohare.github.io/AxionLimits/ (2020).
+[26] F. Elahi, G. Elor, A. Kivel, J. Laux, S. Najjari,
+and
+F. Yu, .
+[27] J. R. Ellis,
+K. Enqvist,
+D. V. Nanopoulos,
+and
+F. Zwirner, Mod. Phys. Lett. A 1, 57 (1986).
+[28] R. Barbieri and G. F. Giudice, Nucl. Phys. B 306, 63
+(1988).
+[29] Y.-C. Qiu, J.-W. Wang,
+and T. T. Yanagida,
+(2023),
+arXiv:2301.02345 [hep-ph].
+
+1
+Supplemental Material for: Lightening the Axion with Anarchy
+Fatemeh Elahi, Gilly Elor, Alexey Kivel, Julien Laux, Saereh Najjari and Felix Yu
+In this supplementary material, we first present the details of the Goldstone basis necessary for identifying the mass
+eigenstatates of the Anarchic Axion a and the heavy field A. We then present the details of the derivation of ¯θ.
+GOLDSTONE BASIS
+In order to identify the corresponding Goldstone bosons to the spontaneously broken U(1) symmetries of hyper-
+charge U(1)Y , Peccei-Quinn U(1)X and an orthogonal global U(1)Z, we perform an O(3) basis rotation on the initial
+U(1)H1 × U(1)H2 × U(1)Φ symmetries. We call the Goldstone bosons G for hypercharge, a for Peccei-Quinn, A for
+U(1)Z and the corresponding vevs v, va and vA, respectively. The rotation matrix reads
+�
+�
+G
+a
+A
+�
+� =
+�
+�
+sφcγ
+−cφcγ
+−sγ
+cφcβ − sφsβsγ sφcβ + cφsβsγ −sβcγ
+cφsβ + sφcβsγ sφsβ − cφcβsγ
+cβcγ
+�
+�
+�
+�
+a1
+a2
+a3
+�
+� ,
+(S1)
+with tan φ = v1/v2, tan β = vA/va and γ = 0, since Φ is not charged under U(1)Y and therefore a3 does not mix into
+G. The corresponding vev relations derived from orthogonality conditions are
+v1 = v sin φ ,
+v2 = v cos φ ,
+v3 = va sin β = vA cos β ,
+va cos β = v sin φ cos φ .
+(S2)
+Under this basis rotation the angular potential in our model transforms as
+Vang = − |Bµ|
+� 2
+�
+i=1
+(vi + hi)
+�
+cos
+� 2
+�
+i=1
+ai
+vi
+− θµ
+�
+− |Cλ|
+√
+2
+� 3
+�
+i=1
+(vi + hi)
+�
+cos
+� 3
+�
+i=1
+ai
+vi
+− θλ
+�
+O(3)
+−→ − |Bµ|
+� 2
+�
+i=1
+(vi + hi)
+�
+cos
+� a
+va
++ A
+vA
+tan2 β − θµ
+�
+− |Cλ|
+√
+2
+� 3
+�
+i=1
+(vi + hi)
+�
+cos
+� A
+vA
+sec2 β − θλ
+�
+.
+(S3)
+In this new basis the dependence of the angular potential on G and φ conveniently drops out. We can replace tan β
+by a small parameter δ ≡ vA/va, leading to
+tan2 β = δ2 ,
+sec2 β = 1 + δ2 ,
+v1v2 =
+vva
+√
+1 + δ2 ,
+v3 =
+vA
+√
+1 + δ2 .
+(S4)
+DERIVATION OF ¯θ
+We present the derivation of the Anarchic Axion strong CP-violating parameter ¯θ and discuss its relaxation. The
+overall observable strong CP-violating is basis independent and must be defined by a unique linear combination of
+the CP-violating phases, similar to the SM, where the quark phases and θQCD contribute to the unique observable
+¯θSM. The CPV of the Anarchic Axion can be reshuffled by applying a U(1) transformation on the fields H1, H2, Φ
+and the SM quarks, thereby redistributing the CP-violating phases θµ, θλ, and ¯θSM. Starting with the Lagrangian
+in Eq. (1a), the phases can be rotated into the quark masses by applying the transformations
+H2 → eiθµH2 ,
+Φ → ei(−θµ+θλ)Φ .
+(S5)
+This introduces real prefactors in all terms of Eq. (1a) and an additional phase factor eiθµ in the SM Yukawa couplings
+¯QLYdH2dR → ¯QLYdH2eiθµdR ≡ ¯QL(Y ′
+d)H2dR ,
+(S6)
+where QL are the left-handed quark doublets, dR are the right-handed down-type quarks, and Y ′
+d is the new Yukawa
+coupling matrix. Note that the unphysical θλ phase is absorbed by Φ. The resulting strong CPV is defined through
+(θQCD − arg(det(Y ′
+dYu))) G ˜G = (θQCD − arg(det(YdYu))) − Ngθµ) G ˜G
+= (¯θSM − Ngθµ) G ˜G ≡ Ng ¯θ G ˜G .
+(S7)
+Note that one can likewise choose to transform H1 in Eq. (S5) such that the phase factor appears in Yu, resulting in
+an identical ¯θ.
+
diff --git a/itFAT4oBgHgl3EQf-B4t/content/tmp_files/load_file.txt b/itFAT4oBgHgl3EQf-B4t/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c7d685ba99cd5875a05ec8717d67458599004fb6
--- /dev/null
+++ b/itFAT4oBgHgl3EQf-B4t/content/tmp_files/load_file.txt
@@ -0,0 +1,381 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf,len=380
+page_content='MITP-23-002  A Lighter QCD Axion from Anarchy  Fatemeh Elahi,1, ∗ Gilly Elor,1, † Alexey Kivel,1, ‡ Julien Laux,1, § Saereh Najjari,1, ¶ and Felix Yu1, ∗∗  1PRISMA+ Cluster of Excellence & Mainz Institute for Theoretical Physics  Johannes Gutenberg University, 55099 Mainz, Germany  We introduce the Anarchic Axion, a class of axion models which solves the Strong CP problem  with a lighter than usual QCD axion, thus populating new parameter space that ongoing and future  experiments target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The Anarchic Axion is driven light by a soft breaking of the Peccei-Quinn  symmetry, which also predicts a residual neutron electric dipole moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We introduce a novel  measure to quantify the tuning required for large deviations from the usual QCD axion band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' In  addition to motivating searches for unusually light axions, this work establishes a new target for  axion effective field theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The Peccei-Quinn (PQ) solution [1, 2] to the Strong  Charge-Parity (CP) problem of quantum chromodynam-  ics (QCD) predicts relationships between the axion mass  ma, decay constant fa and axion-photon coupling gaγγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  In this Letter, we introduce a new class of multi-scalar  axion models — The Anarchic Axion —so dubbed as to  emphasize that the PQ symmetry arises accidentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The U(1)PQ symmetry is softly broken leading to a so-  lution to the Strong CP problem that deviates from the  traditional QCD axion band, importantly populating a  region of parameter space targeted by many on-going ex-  periments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Related work to solving the strong CP prob-  lem departing from the canonical band include Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' [3–  11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Furthermore, the new parameter space corresponds  to an almost perfect alignment between the soft breaking  vacuum and the θQCD vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' This provides a unique  handle on the Axion Quality Problem [3, 12–17] allow-  ing the introduction of a novel measure for quantifying  the fine tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The Anarchic Axion can be made nat-  ural given a Clockwork [18–20] inspired ultraviolet (UV)  completion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  In this Letter we first introduce the field content and  the potential of an Anarchic Axion model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Given an ap-  propriate basis choice, we compute the ma, fa and gaγγ  relations, and present the new parameter space where  experiments can hunt for the Anarchic Axion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We then  discuss the quality of this solution to the Strong CP prob-  lem and introduce a fine tuning measure to quantify the  axion quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We conclude by commenting on possible  natural UV completions and future directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The Anarchic Axion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — The particle content and  charge assignments of the model, summarized in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' I,  consists of three complex scalars: H1 and H2 which can  be identified with the Higgs doublet fields in DFSZ axion  constructions [21, 22], and a gauge singlet Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Standard  Model (SM) fermions coupling to H1 and H2 will medi-  ate the requisite effective operator coupling the Anarchic  Axion and the anomalous G ˜G QCD term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The scalar  Field  SU(3)c  SU(2)L  U(1)Y  Z5  U(1)P Q  Qi  L  3  2  1/6  0  XQ  ui  R  3  1  2/3  1  XQ-X1  di  R  3  1  1/3  0  XQ-X2  Li  L  1  2  1/2  0  XL  ei  R  1  1  1  0  XL-X2  H1  1  2  1/2  4  X1  H2  1  2  1/2  0  X2  Φ  1  1  0  1  X3  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The field content of the Anarchic Axion model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  potential is  V =  �  i=1,2  �  µ2  i |Hi|2 + λi|Hi|4�  + λ|H1|2|H2|2 + λ′|H1H2|2  + µ2  3|Φ|2 + λ3|Φ|4 + λ13|H1|2|Φ|2 + λ23|H2|2|Φ|2 ,  (1a)  V Cλ  break = −CλH1H2Φ + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' ,  (1b)  which is invariant under the global U(1)H1 × U(1)H2 ×  U(1)Φ symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Additional gauge symmetry preserving  terms are forbidden by invoking a Z5 symmetry at high  scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The Z5 allows a term Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (1b) which breaks the  global symmetry down to U(1)Y ×U(1)X, where U(1)Y is  identified with SM hypercharge and U(1)X will be iden-  tified with the accidentally arising PQ symmetry, with  X3 = −X1 − X2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We choose the parameters of the potential such that all  three complex scalar fields acquire a vacuum expectation  value (vev) v1,2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Writing the electrically neutral fields  in a non-linear representation, we have  √  2H0  i = (vi +  hi)eiai/vi and  √  2Φ = (v3+h3)eia3/v3, where hi define the  CP even radial modes and ai define the CP odd angular  modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Given an appropriate choice of basis, the angular  modes can be rewritten as two Goldstone fields a and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We will then derive a basis-invariant anomalous CP-  Violating (CPV) phase in the QCD sector, providing a  mass for the Goldstone modes and allowing the identi-  fication of one mode a with the axion which solves the  strong CP problem while the other mode A is heavy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='08760v1  [hep-ph]  20 Jan 2023  2  The interesting phenomenology of the Anarchic Axion  is the deviation from the canonical QCD axion band in  {ma, fa} parameter space (and similarly in the axion-  photon effective coupling), which results from the intro-  duction of soft PQ breaking at low scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Specifically,  V Bµ  break = −BµH1H2 + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' ,  (2)  which further breaks the symmetry down to U(1)Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We parameterize the symmetry breaking couplings as  Bµ = |Bµ|e−iθµ and Cλ = |Cλ|e−iθλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The original global  symmetry can be used to render θλ unphysical, and hence  Cλ is a real parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The Goldstone basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — Following the procedure dis-  cussed in the supplementary material, we perform a ba-  sis transformation to align the Goldstone fields with the  U(1)Y ×U(1)X symmetries, which isolates the Goldstone  eaten by the gauging of hypercharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' In this new basis,  the angular potential is  Vang = −|Bµ|  � 2  �  i=1  (vi + hi)  �  cos  � a  va  + A  vA  δ2 − θµ  �  (3)  − |Cλ|  √  2  � 3  �  i=1  (vi + hi)  �  cos  � A  vA  (1 + δ2) − θλ  �  ,  where δ  = vA/va, v1v2  = vva/  √  1 + δ2 and v3  =  vA/  √  1 + δ2, with v =  �  v2  1 + v2  2 ≈ 246 GeV is the elec-  troweak vev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Next, we include the correction to the potential aris-  ing from QCD instantons induced by the coupling of SM  quarks to H1 and H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The effective Lagrangian in the  Anarchic Axion model is  LG ˜  G ⊃ g2  s  32π2  �  ¯θSM − Ng  � a  va  + δ2 A  vA  ��  Ga  µν ˜Gaµν , (4)  where Ng is the number of quark generations and ¯θSM ≡  θQCD + arg det YuYd for the SM quark Yukawa matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  By applying global U(1) transformations on H1, H2, Φ  and the SM quarks, we can reshuffle the separate phases  from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (3) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (4) into a new ¯θ defined via ¯θSM −  Ngθµ ≡ Ng ¯θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We may choose U(1) phases such that ¯θ is  only in the Bµ contribution to the potential, and hence  below ΛQCD the corresponding a and A fields experience  the instanton potential,  LG ˜  G ⊃ Λ4  QCD cos  �  Ng  � a  va  + δ2 A  vA  ��  ,  (5)  where Λ4  QCD ≡  mumd  (mu+md)2 m2  πf 2  π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Via the Peccei-Quinn  mechanism, ¯θ is relaxed to the observable CPV parameter  ¯θeff, seen as the tadpoles effects of a and A in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Consequently, the total angular potential for a and A  fields is now  −Vang = Λ4  QCD cos  �  Ng  �  α + α′δ2��  (6)  + Λ4  QCD  va  vmax  cos  �  α + α′δ2 + ¯θ  �  +  |Cλ|vv2  A  √  2δ(1 + δ2) cos  �  α′(1 + δ2)  �  ,  where we have introduced α ≡ a/va, α′ ≡ A/vA as con-  venient notation for the fields, and we have  vmax ≡  Λ4  QCD  |Bµ|v  �  1 + δ2 ,  (7)  as the extremal value of the PQ vev va.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Relaxation and heavy A mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — To ensure A is heavy,  we will necessarily take |Cλ| ≫ |Bµ|1/2 as well as require  δ ≪ 1, such that the mass of A arises dominantly from  the Cλ contribution to the potential, yielding  m2  A = |Cλ|v  √  2  �1  δ + δ + O  �  δ2��  ,  (8)  setting the scale of A well above the electroweak scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The vmax scale is the energy where the soft PQ breaking  parameter must be nearly aligned to the ¯θSM to avoid  neutron electric dipole moment (nEDM) constraints [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Pragmatically, as will be shown below, vmax corresponds  to the largest possible scale suppression in gaγγ for ¯θ ≈ π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The Anarchic Axion Parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — We now derive the  ma, fa and gaγγ relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' After spontaneous breaking of  the PQ symmetry by va, the physical degrees of freedom  a and A acquire tadpoles α0 and α′  0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Impor-  tantly, the unphysical θλ also allows us to shift α′  0 purely  into α0, leaving α′  0 unobservable, as seen in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Con-  sequently, the tadpole α0 entirely generates |¯θeff| = α0,  giving a potentially measurable nEDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Note that in this  basis, α0 entirely captures the deviation from the canon-  ical DFSZ due to non-vanishing Bµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Expanding Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (6) about the minimum and dropping  constant terms and the heavy A field, yields  − Vang  Λ4  QCD  = α  �  Ng sin  �  Ng ¯θeff  �  +  va  vmax  sin  �¯θ − ¯θeff  ��  + 1  2α2  �  N 2  g cos  �  Ng ¯θeff  �  +  va  vmax  cos  �¯θ − ¯θeff  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (9)  For very small δ ≪ 1, a is already in its mass basis, where  ma is given up to O  �  δ4�  corrections by  m2  a =  Λ4  QCD  v2a  �  N 2  g cos  �  Ng ¯θeff  �  +  va  vmax  cos  �¯θ − ¯θeff  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (10)  3  1/k = 10−10/(π − ¯θ)  vmax/fa  ¯θeff  = 10−9  ¯θeff  = 10−11  k = 10−8  k = 10−4  k = 1  nEDM: ¯θeff  ≥ 10−10  10−1  100  101  102  103  104  105  106  107  108  109  10−1  100  101  102  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Contours correspond to values of physical CPV |¯θeff|,  obtained from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The gray region corresponds to pa-  rameter space constrained by the nEDM measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (10), the axion decay constant is  1  fa  ≡ Ng  va  = −  cos  �¯θ − ¯θeff  �  2Ngvmax cos  �  Ng ¯θeff  �  (11)  +  �  �  �  �  m2a  Λ4  QCD cos  �  Ng ¯θeff  � +  �  cos  �¯θ − ¯θeff  �  2Ngvmax cos  �  Ng ¯θeff  �  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Note that in the limit va ≪ vmax, we recover the canon-  ical relation m2  af 2  a = Λ4  QCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Finally, to evaluate the axion-diphoton coupling, we  partition the irreducible U(1)em anomaly shared by a1  and a2 into the mass eigenstate a, giving  gaγγ = e2  8π2  � E  N − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='92  � �  1 + δ2  2 + O  �  δ3�� 1  fa  ,  (12)  where E/N = 8/3, analogous to the DFSZ case [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  CP Violation and nEDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — We now return to the  derivation of the tadpole α0 acquired by a, and the result-  ing observable CPV ¯θeff constrained by measurements of  the nEDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' To make contact with phenomenology, it will  be useful to consider the leading order contribution to  ¯θeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The first term of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (9) encodes the residual CPV  ¯θeff in the Anarchic Axion model, where the leading con-  tribution up to O((¯θ − π)2) is given by  ¯θeff =  2(¯θ − π)  �  1 +  4N 2  g m2av2max  Λ4  QCD  − 1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (13)  Contours of ¯θeff are show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We define k ≡ (¯θ −  π)/10−10 to capture the sensitivity to the deviation of ¯θ  from π, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' for k ≲ 1 a tuning will be required and we  saturate at vmax/fa → 1/Ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The white region is allowed  by the nEDM bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' For k ≳ 1, we recover the DFSZ  solution to strong CP, relaxing the required tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 2, we display gaγγ vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' ma for the  Anarchic Axion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The DFSZ axion line is shown in yel-  low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Regions targeted by experimental searches or con-  strained by astrophysical considerations are shaded out  in gray [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' For fixed values of ma and vmax, the blue  contours are computed by plugging in 1/fa from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (11)  into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (12) for gaγγ, and using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (13) to fix ¯θeff as  a function of k, ma and vmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We also use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (13) to  enforce the nEDM constraint |¯θeff| ≤ 10−10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Choosing  a specific k denoted by a red dotted line, we can access  lighter axion masses along a given blue contour of fixed  vmax up to the intersection point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Explicitly, accessing  smaller axion masses requires a small k and hence tuning  ¯θ closer to π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  As  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (11)  suggests  for  sufficiently  small  ma  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=', ma ≪  ��Λ2  QCD cos  �¯θ − ¯θeff  �  /(2Ngvmax)  ��), 1/fa be-  comes insensitive to ma,  and approaches 1/fa  ≃  ��cos  �¯θ − ¯θeff  �  /(Ngvmax)  ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Physically, the vev shift from  the Bµ term begins to dominate in this regime;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' corre-  sponding to the kink in the blue lines of  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 2 upon  their intersection with the k = 1 line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 2 we have enforced ¯θ ∈  � π  2 , π  �  leading to light  Anarchic Axion masses populating the region to the left  of the DFSZ band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Note that heavier masses can popu-  late the region to the right of the DFSZ line for ¯θ < π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We leave the details of the heavy Anarchic Axion to fu-  ture work [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The Quality Problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — All axion models suffer from  a high scale quality problem, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' higher dimensional op-  erators, which are generally present from gravity effects,  break the PQ symmetry at high scales and shift the ax-  ion vev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' To preserve the quality of the PQ solution, we  are forced to fine-tune parameters of the UV theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The quality problem of the Anarchic Axion manifests  as an alignment of ¯θ with π once the soft breaking Bµ  term starts to dominate the vev shift, as is evident from  the low ma plateau in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' To quantify the quality  problem, we introduce a measure ∆BG of fine tuning,  following [27, 28]:  ∆BG(¯θeff) ≡  ���  ¯θ  ¯θeff  ∂¯θeff  ∂¯θ  ��� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (14)  Note that a large value of ∆BG implies a large tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Indeed, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 3 we observe that ∆BG grows as ¯θ → π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We emphasize that the region where the Anarchic Axion  exhibits a lighter than usual axion is characterized by  a non-trivial fine tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' This approach of quantifying  the quality problem can be potentially applied to other  axion models where the PQ symmetry breaking enters  explicitly at high scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Note that this is only possible  since the residual CPV ¯θeff is calculable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We also mention the possibility that the soft break-  ing Bµ term of the Anarchic Axion model can arise as  the leading low energy operator matched to a Planck-  suppressed PQ breaking term in canonical axion models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We will reserve a study of the matching requirements of  soft PQ breaking terms in high-quality axion models for  the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — In this Letter we have introduced the  Anarchic Axion model which solves the QCD Strong  CP problem while populating new regions of parameter  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='001  1  1000  106  10-15  10-11  ABRA  SHAFT  CAST  MWD  HB  SN  ν Solar  Cosmology  ma[eV]  gaγγ [GeV−1]  k = π − ¯θ  10−10  10−6  ¯θ ≥ π  2 and  ¯θeff  ≤ 10−10  Haloscopes  10−9  DFSZ  k = 10−8  k = 10−4  k = 1  vmax = 109 GeV  vmax = 1011 GeV  vmax = 1013 GeV  vmax = 107 GeV  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Parameter space for the axion-diphoton coupling in the Anarchic Axion model consistent with current nEDM con-  straint [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Experimental limits, shown by the gray shaded regions are extracted from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We show representative values  of vmax and k that highlight the accessible light axion parameter space probed by ongoing haloscope and microwave cavity  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='0  1  2  5  10  20  50  Δθ  ΔBG  ¯θ  ΔBG(¯θeff)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='0  1  2  5  10  20  50  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  A measure of tuning for the variable ¯θ consistent  with nEDM constraints on ¯θeff given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (13), fixing ma =  10−6 eV and vmax = 107 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' As the figure demonstrates,  the tuning exponentially increases as ¯θ → π, and this tuning  is negligibly sensitive to alternate ma and vmax values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We close by mentioning that these regions with  fine tuning can be motivated by, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' a clockwork-like  ultraviolet model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' For instance, consider a U(1)PQ bulk  gauge symmetry in a 5D warped geometry with a bulk  electroweak singlet scalar, where PQ charges will be car-  ried by a brane-localized Higgs and right-handed up-type  quarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Given an appropriate choice of boundary condi-  tions for the bulk field, the Anarchic Axion model then  arises as an effective description with a global U(1)PQ  symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  A discrete Z5 symmetry can be identified  with a remnant of the bulk gauge symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We leave  the details of such UV completions to future work [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  While the interesting phenomenology of the Anarchic  Axion model discussed in this Letter arose due to a soft  PQ breaking term, other variations can produce similar  phenomenology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' For instance, replacing the soft breaking  Bµ term with a Φ3 term would result in a potential which  is protected by an accidental and global Z3 symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We leave the exploration of variants of Anarchic Axion  models to future work [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We expect the cosmological  production of the Anarchic Axion to proceed through a  variation of the canonical misalignment mechanisms and  also leave the detailed implications of Anarchic Axion  dark matter to future study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  The experimental observation of an exceptionally light  axion deviating from the canonical QCD axion band  would be evidence for an Anarchic Axion solution to the  Strong CP problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Note added:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' — When this work was in preparation,  a related preprint appeared [29], focusing on generating  high-quality axion solutions by suppressing Planck-scale  operators using chiral gauged U(1) symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We thank Prisco Lo Chiatto for useful conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  We thank Raymond Co, Joshua Eby, and Alfredo Wal-  ter Mario Guerrera for useful discussions and comments  on the draft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' are grateful to CERN for  their hospitality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' This work is supported by the Cluster  of Excellence Precision Physics, Fundamental Interac-  5  tions and Structure of Matter (PRISMA+ – EXC 2118/1)  within the German Excellence Strategy (project ID  39083149).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  FE is also funded by grant 05H18UMCA1  of the German Federal Ministry for Education and Re-  search (BMBF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  ∗ felahi@uni-mainz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='de  † gelor@uni-mainz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='de  ‡ alkivel@uni-mainz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='de  § jlaux01@uni-mainz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='de  ¶ snajjari@uni-mainz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='de  ∗∗ yu001@uni-mainz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='de  [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Peccei and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Quinn, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 38, 1440  (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [2] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Peccei and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Quinn, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' D16, 1791  (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [3] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Holdom and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Peskin, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' B 208, 397  (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Gherghetta, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Nagata, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Shifman, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  D 93, 115010 (2016), arXiv:1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='01127 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [5] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Agrawal, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Marques-Tavares,  and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Xue, JHEP  03, 049 (2018), arXiv:1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='05008 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [6] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Agrawal  and  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Howe,  JHEP 12,  029  (2018),  arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='04213 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Agrawal  and  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Howe,  JHEP 12,  035  (2018),  arXiv:1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='05803 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Hook,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  120,  261802  (2018),  arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='10093 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Gaillard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Gavela, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Houtz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Quilez,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Del Rey, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' C 78, 972 (2018),  arXiv:1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='06465 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Di Luzio, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Gavela, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Quilez,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Ringwald,  JHEP 05, 184 (2021), arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='00012 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Kivel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Laux,  and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Yu, JHEP 11, 088 (2022),  arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='08740 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Kamionkowski and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' March-Russell, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' B  282, 137 (1992), arXiv:hep-th/9202003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Kim and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Carosi, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 82, 557  (2010), [Erratum:  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 91, 049902 (2019)],  arXiv:0807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='3125 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [14] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Darm´e and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Nardi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' D 104, 055013 (2021),  arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='05055 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Dine, (2022), arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='01068 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Banerjee,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Eby,  and  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Perez,  (2022),  arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='05690 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [17] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Bonnefoy, (2022), arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='00102 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [18] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Choi  and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  Im,  JHEP  01,  149  (2016),  arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='00132 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [19] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Giudice and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' McCullough, JHEP 02, 036 (2017),  arXiv:1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='07962 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Ahmed and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Dillon, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' D 96, 115031  (2017), arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='04011 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Dine, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Fischler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Srednicki, Physics Letters  B 104, 199 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Zhitnitsky, Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 31, 260 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [23] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Abel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' 124, 081803 (2020),  arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='11966 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [24] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Workman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (Particle Data Group), PTEP  2022, 083C01 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [25] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' O’Hare, “cajohare/axionlimits: Axionlimits,” https:  //cajohare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='io/AxionLimits/ (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [26] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Elahi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Elor, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Kivel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Laux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Najjari,  and  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Yu, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Ellis,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Enqvist,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Nanopoulos,  and  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Zwirner, Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' A 1, 57 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [28] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Barbieri and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Giudice, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' B 306, 63  (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  [29] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Qiu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Wang,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Yanagida,  (2023),  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='02345 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  1  Supplemental Material for: Lightening the Axion with Anarchy  Fatemeh Elahi, Gilly Elor, Alexey Kivel, Julien Laux, Saereh Najjari and Felix Yu  In this supplementary material, we first present the details of the Goldstone basis necessary for identifying the mass  eigenstatates of the Anarchic Axion a and the heavy field A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We then present the details of the derivation of ¯θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  GOLDSTONE BASIS  In order to identify the corresponding Goldstone bosons to the spontaneously broken U(1) symmetries of hyper-  charge U(1)Y , Peccei-Quinn U(1)X and an orthogonal global U(1)Z, we perform an O(3) basis rotation on the initial  U(1)H1 × U(1)H2 × U(1)Φ symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We call the Goldstone bosons G for hypercharge, a for Peccei-Quinn, A for  U(1)Z and the corresponding vevs v, va and vA, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The rotation matrix reads  �  �  G  a  A  �  � =  �  �  sφcγ  −cφcγ  −sγ  cφcβ − sφsβsγ sφcβ + cφsβsγ −sβcγ  cφsβ + sφcβsγ sφsβ − cφcβsγ  cβcγ  �  �  �  �  a1  a2  a3  �  � ,  (S1)  with tan φ = v1/v2, tan β = vA/va and γ = 0, since Φ is not charged under U(1)Y and therefore a3 does not mix into  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The corresponding vev relations derived from orthogonality conditions are  v1 = v sin φ ,  v2 = v cos φ ,  v3 = va sin β = vA cos β ,  va cos β = v sin φ cos φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (S2)  Under this basis rotation the angular potential in our model transforms as  Vang = − |Bµ|  � 2  �  i=1  (vi + hi)  �  cos  � 2  �  i=1  ai  vi  − θµ  �  − |Cλ|  √  2  � 3  �  i=1  (vi + hi)  �  cos  � 3  �  i=1  ai  vi  − θλ  �  O(3)  −→ − |Bµ|  � 2  �  i=1  (vi + hi)  �  cos  � a  va  + A  vA  tan2 β − θµ  �  − |Cλ|  √  2  � 3  �  i=1  (vi + hi)  �  cos  � A  vA  sec2 β − θλ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (S3)  In this new basis the dependence of the angular potential on G and φ conveniently drops out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' We can replace tan β  by a small parameter δ ≡ vA/va, leading to  tan2 β = δ2 ,  sec2 β = 1 + δ2 ,  v1v2 =  vva  √  1 + δ2 ,  v3 =  vA  √  1 + δ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (S4)  DERIVATION OF ¯θ  We present the derivation of the Anarchic Axion strong CP-violating parameter ¯θ and discuss its relaxation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The  overall observable strong CP-violating is basis independent and must be defined by a unique linear combination of  the CP-violating phases, similar to the SM, where the quark phases and θQCD contribute to the unique observable  ¯θSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The CPV of the Anarchic Axion can be reshuffled by applying a U(1) transformation on the fields H1, H2, Φ  and the SM quarks, thereby redistributing the CP-violating phases θµ, θλ, and ¯θSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Starting with the Lagrangian  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (1a), the phases can be rotated into the quark masses by applying the transformations  H2 → eiθµH2 ,  Φ → ei(−θµ+θλ)Φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (S5)  This introduces real prefactors in all terms of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (1a) and an additional phase factor eiθµ in the SM Yukawa couplings  ¯QLYdH2dR → ¯QLYdH2eiθµdR ≡ ¯QL(Y ′  d)H2dR ,  (S6)  where QL are the left-handed quark doublets, dR are the right-handed down-type quarks, and Y ′  d is the new Yukawa  coupling matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' Note that the unphysical θλ phase is absorbed by Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' The resulting strong CPV is defined through  (θQCD − arg(det(Y ′  dYu))) G ˜G = (θQCD − arg(det(YdYu))) − Ngθµ) G ˜G  = (¯θSM − Ngθµ) G ˜G ≡ Ng ¯θ G ˜G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content='  (S7)  Note that one can likewise choose to transform H1 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
+page_content=' (S5) such that the phase factor appears in Yu, resulting in  an identical ¯θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/itFAT4oBgHgl3EQf-B4t/content/2301.08760v1.pdf'}
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+Proportional Fairness in Obnoxious Facility Location
+Haris Aziz*1, Alexander Lam†1(�), Bo Li‡2, Fahimeh Ramezani§1, and Toby
+Walsh¶1
+1UNSW Sydney
+2Hong Kong Polytechnic University
+Abstract
+We consider the obnoxious facility location problem (in which agents prefer the facility
+location to be far from them) and propose a hierarchy of distance-based proportional fairness
+concepts for the problem. These fairness axioms ensure that groups of agents at the same
+location are guaranteed to be a distance from the facility proportional to their group size. We
+consider deterministic and randomized mechanisms, and compute tight bounds on the price
+of proportional fairness. In the deterministic setting, not only are our proportional fairness
+axioms incompatible with strategyproofness, the Nash equilibria may not guarantee welfare
+within a constant factor of the optimal welfare. On the other hand, in the randomized setting,
+we identify proportionally fair and strategyproof mechanisms that give an expected welfare
+within a constant factor of the optimal welfare.
+1
+Introduction
+In the obnoxious facility location problem (OFLP), some undesirable facility such as a garbage
+dump or an oil refinery is to be located on a unit interval (i.e. the domain of locations is [0, 1]),
+and the agents along the interval wish to be as far from the facility as possible [Feigenbaum et
+al., 2020; Cheng et al., 2011; Ibara and Nagamochi, 2012; Cheng et al., 2019]. In this problem,
+agents have single-dipped preferences, contrasting with the single-peaked preferences of agents in
+the classic facility location problem (in which agents prefer to be located as close as possible to
+the facility).
+The obnoxious facility location problem models many real-world facility placements which
+negatively impact nearby agents, such as a prison or a power plant [Church and Drezner, 2022].
+Aside from the geographic placement of an obnoxious facility, the OFLP can also be applied to
+*haris.aziz@unsw.edu.au
+†alexander.lam1@unsw.edu.au
+‡comp-bo.li@polyu.edu.hk
+§ramezani81@googlemail.com
+¶t.walsh@unsw.edu.au
+1
+arXiv:2301.04340v1  [cs.GT]  11 Jan 2023
+
+various collective decision making problems. For instance, when agents are averse to their worst
+possible social outcomes (represented by their locations), the problem captures issues where a
+decision needs to be made on a social policy or a budget composition. When a socially sensitive
+or a politically undesirable policy needs to be implemented, the placements of such a policy in the
+space of outcomes may need to take equity considerations.
+It is known that placing the facility at one of the interval endpoints maximizes the sum of agent
+distances [Cheng et al., 2013], but such a solution may not be ‘proportionally fair’ for the agents.
+To build intuition, consider the instance depicted in Figure 1 where there are two agents at 0.1 and
+five agents at 0.8. The optimal utilitarian solution (which maximizes the sum of agent distances)
+places the facility at 0, disproportionately disadvantaging the agents at 0.1 who are located only
+0.1 distance from the facility. A facility location of 0.45 results in both groups of agents having the
+same distance from the facility, and would be considered to be more ‘fair’ in the egalitarian sense.
+However, it is not proportionally fair: despite having over twice as many agents, the group of agents
+at 0.8 have the same distance from the facility as the group of agents at 0.1. A proportionally fair
+solution places the facility at 0.3, and results in the distance between a group of agents and the
+facility being proportional to the size of the group.
+In this work, we pursue notions of proportional fairness as a central concern for the problem.
+Specifically, we formulate a hierarchy of proportional fairness axioms which guarantee that each
+group of agents at the same location are a distance from the facility proportional to the relative size
+of the group. While proportional fairness axioms have been formulated and studied in the classic
+facility location problem [Aziz et al., 2021], they have not yet been applied to the OFLP. Our pa-
+per provides a comprehensive overview of proportionally fair solutions for the obnoxious facility
+location problem, examining the interplay between proportional fairness and utilitarian/egalitarian
+welfare, and investigating concerns of agent strategic behaviour in both the deterministic and ran-
+domized settings.
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+xx
+xxxxx
+f∗
+UW
+2-UFS f∗
+EW
+Figure 1: OFLP with agent location profile (0.1, 0.1, 0.8, 0.8, 0.8, 0.8) represented by x. The facil-
+ity locations (represented by •) correspond to a utilitarian outcome, f ∗
+UW = 0; a proportionally fair
+outcome, 2-UFS = 0.3; and an egalitarian outcome, f ∗
+EW = 0.45.
+Contributions
+• We formalize (approximate) proportional fairness concepts such as 2-Individual Fair Share
+(2-IFS) and 2-Unanimous Fair Share (2-UFS) in the context of the obnoxious facility loca-
+tion problem. Several of the definitions are natural adaptations of axioms from fair division
+and participatory budgeting.
+• We find tight bounds on the price of 2-IFS and 2-UFS fairness for the objectives of egalitarian
+and utilitarian welfare, in both the deterministic and randomized settings.
+2
+
+Table 1: Table of price of fairness and welfare approximation results.
+Price of Fairness
+Best Known Approx.
+by 2-UFS SP Mech.
+2-IFS
+2-UFS
+Deterministic
+UW
+2
+2
+(Thm. 1)
+(Thm. 2)
+Incompatible
+EW
+1
+n-1
+(Prop. 4)
+(Prop. 3)
+(Thm. 3)
+Randomized
+UW
+12/11
+1.09384. . .
+1.5
+(Cor. 3)
+(Cor. 4)
+(Thm. 8)
+EW
+1
+1
+1
+(Prop. 3)
+(Cor. 2)
+(Prop. 6)
+• We prove that our proportional fairness axioms are incompatible with strategyproofness in
+the deterministic setting, and give strategyproof randomized mechanisms that satisfy these
+proportional fairness axioms in expectation and either have a constant approximation ratio
+for utilitarian welfare or are optimal for egalitarian welfare.
+• For the deterministic mechanisms that maximize utilitarian welfare under the constraints of
+2-IFS and 2-UFS, we prove that a pure ϵ-Nash equilibrium always exists and find linear
+bounds on the corresponding ϵ-prices of anarchy.
+• Finally, we give two possible extensions of our model: the fairness axiom of 2-Proportional
+Fairness (2-PF), which is stronger than 2-UFS as it captures proportional fairness concerns
+for groups of agents near but not necessarily at the same location, and the hybrid model,
+which additionally includes ‘classic’ agents which want to be near the facility (along with
+‘obnoxious’ agents which want to be far away from the facility). We give existence results
+for both extensions.
+Table 1 summarizes some of our results. Results lacking proofs are proven in the appendix.
+Related Work
+Facility location problems have been explored in the fields of computer science,
+economics and operations research. In the latter field, an optimization approach is usually taken,
+aiming to minimize transport costs. Summaries of results and approaches in the operations research
+literature are given by Hekmatfar [2009] and Melo et al. [2009]. On the other hand, research on
+the facility location problem at the intersection of computer science and economics often takes an
+approximate mechanism design approach, assuming that agent locations are private information
+and finding strategyproof mechanisms which approximate the optimal social cost. The seminal
+paper on this approach is written by Procaccia and Tennenholtz [2013], and for a recent and com-
+prehensive survey on facility location mechanism design, we refer the reader to a survey by Chan
+et al. [2021]. Our paper lies at the intersection of these two approaches, analyzing the agent strate-
+gic behaviour in the optimal mechanisms which satisfy our proportional fairness axioms as well as
+identifying a randomized strategyproof and proportionally fair mechanism.
+The papers most relevant to our research are those that treat the facility as obnoxious: agents
+prefer the facility to be as far as possible. Similar to the classical facility location problem, early
+operations research on the OFLP apply an optimization approach to compute solutions; a review
+3
+
+of these approaches is given by Church and Drezner [2022]. There have been several recent papers
+on the obnoxious facility location problem that assume agents’ location are private information,
+and thus aim to design strategyproof facility location mechanisms. Some of the earliest research
+applying a mechanism design approach was initiated by Cheng et al. [2011, 2013], in which they
+define an agent’s utility as its distance from the facility, and design strategyproof mechanisms
+which approximate the optimal utilitarian welfare on the path and network metrics, respectively.
+Other recent examples of related papers include [Cheng et al., 2019; Feigenbaum et al., 2020; Ibara
+and Nagamochi, 2012; Xu et al., 2021]. These papers do not pose or study the fairness concepts
+that we explore in this paper.
+Notions of fairness in various collective decision problems have been widely explored over
+the last few decades [Moulin, 2003; Nash, 1950; Shapley, 1953]. Fairness objectives specifically
+relevant to the facility location problem include maximum cost/egalitarian welfare (see, e.g. [Pro-
+caccia and Tennenholtz, 2013; Wang et al., 2021]) and maximum total/average group cost [Zhou
+et al., 2022]. Rather than optimize/approximate fairness objectives, we focus on solutions enforc-
+ing proportional fairness axioms, in which groups of agents with similar or identical preferences
+(represented in our setting as their location) have a minimum utility guarantee relative to the group
+size. The axioms of proportional fairness that we present stem from several related areas of social
+choice. Individual Fair Share (IFS) is closely related to the axiom of proportionality proposed by
+Steinhaus [1948], and appears in participatory budgeting along with Unanimous Fair Share (UFS)
+[Bogomolnaia et al., 2005; Aziz et al., 2019]. Most recently, all of our proportional fairness axioms
+have been studied in the classical facility location problem by Aziz et al. [2021].
+In our paper, we also analyse the loss of efficiency, defined as the price of fairness, of imple-
+menting the proportional fairness axioms that we have proposed. There have been many recent
+results on the price of fairness in various social choice contexts. For instance, Barman et al.
+[2020], Caragiannis et al. [2012] and Bei et al. [2021] find price of fairness bounds for axioms
+such as envy-freeness and equitability in fair division, Bertsimas et al. [2011] look at the price
+of proportional fairness in resource allocation, and Michorzewski et al. [2020] explore the areas
+of budget division and probabilistic social choice. There has also been work on price of fairness
+bounds for the facility location problem, such as when there is a lexicographic minimax objective
+[Buzna et al., 2014]. Wang and Zhang [2021] assume that facilities have preferences over subsets
+of agents, observing the concepts of fairness and efficiency from the facilities’ perspectives.
+As strategyproofness is impossible in our deterministic setting, we present results on the ex-
+istence of pure Nash equilibria and the price of anarchy. Similar models where such results are
+proven include a variation of the Hotelling-Downs model where clients have limited attraction
+ranges [Feldman et al., 2016], and two-stage facility location games where both facilities and
+clients act strategically [Krogmann et al., 2021]. In the classic facility location problem, Aziz et
+al. [2021] characterize the pure Nash equilibria of strictly monotonic facility location mechanisms
+satisfying UFS and show that the resulting facility location (under the pure Nash equilibria) is
+also guaranteed to satisfy UFS. In our setting, the price of anarchy is not well-defined for certain
+proportionally fair mechanisms, as a pure Nash equilibrium may not exist for a given location pro-
+file. As a result, we prove the existence of an approximate equilibrium notion, called pure ϵ-Nash
+equilibrium. Examples of papers applying this notion to other settings include [Chien and Sinclair,
+2011; Mylvaganam et al., 2015].
+The second half of our paper focuses on the randomized setting to overcome the incompatibility
+with strategyproofness. The use of randomized mechanisms to overcome impossibility results is
+4
+
+prevalent in many social choice contexts (see, e.g., [Brandt, 2017; Aziz, 2019]). Additionally, Aziz
+et al. [2022] use a randomized approach in the classic facility location problem to achieve stronger
+notions of proportional fairness, providing a unique characterization of universally anonymous
+and universally truthful mechanisms satisfying an axiom called Strong Proportionality. The use of
+randomized mechanisms also results in better approximation ratio/price of fairness bounds. This is
+common in many variants of the facility location problem, such as when agents have fractional or
+optional preferences [Fong et al., 2018; Chen et al., 2020], or in the hybrid facility location model
+[Feigenbaum et al., 2020].
+2
+Model
+Let N = {1, . . . , n} be a set of agents, and let X := [0, 1] be the domain of locations.1 Agent i’s
+location is denoted by xi ∈ X; the profile of agent locations is denoted by x = (x1, . . . , xn) ∈
+Xn. We also assume the agent locations are ordered such that x1 ≤ · · · ≤ xn. A deterministic
+mechanism is a mapping f : Xn → X from a location profile ˆx ∈ Xn to a facility location y ∈ X.
+We define a randomized mechanism as a probability distribution over deterministic mechanisms.
+Given a facility location y ∈ X, agent i’s utility2 is equal to its distance from the facility u(y, xi) :=
+|y − xi|. We are interested in maximizing the objectives of Utilitarian Welfare (UW), defined for a
+facility location y and location profile x as the sum of agent utilities �
+i u(y, xi), and Egalitarian
+Welfare (EW), defined as the minimum agent utility mini u(y, xi).
+Note that the preferences in OFLP can be viewed as single-dipped. In contrast, the classical
+facility location problem (FLP) concerns single-peaked preferences. The underlying model of both
+FLP and OFLP is the same except that the agents’ preferences have a different structure.
+Unless specified otherwise, we will state results for the obnoxious facility location problem
+(OFLP). For the first half of the paper, we will discuss the deterministic setting, and then move to
+the randomized setting for the second half.
+3
+Proportional Fairness Axioms
+In this section, we introduce proportional fairness axioms for the obnoxious facility location prob-
+lem.
+3.1
+Individual Fair Share
+We first present an adaptation of Individual Fair Share (IFS), the weakest of our proportional fair-
+ness axioms (as studied by Aziz et al. [2021] in the context of the classic facility location problem).
+IFS provides a minimum distance guarantee between each agent and the facility, requiring that each
+agent has at least 1
+n utility. By placing two agents at 1
+4 and 3
+4, it is easy to see that an IFS solution
+may not exist. As a result, we turn to approximations of IFS.
+1Our results can be naturally extended to any compact interval on R.
+2This definition is consistent with [Cheng et al., 2013].
+5
+
+Definition 1 (α-Individual Fair Share (IFS)). Given a profile of locations x, a facility location y
+satisfies α-Individual Fair Share (α-IFS) if
+u(y, xi) ≥ 1
+αn
+∀i ∈ N.
+We find that the lowest value of α such that an α−IFS solution always exists is α = 2. Intu-
+itively, with α = 2, each agent has a ball of radius
+1
+2n around its location. The sum of ball lengths
+is 1, meaning there will always be a 2-IFS solution. Furthermore, for any α < 2, the sum of ball
+lengths will exceed 1, so an α−IFS solution may not always exist.
+Proposition 1. The lowest value of α for which an α-IFS solution always exists is α = 2.
+A polynomial time mechanism (which we denote as f ∗
+2IFS) that maximizes the utilitarian wel-
+fare under the constraint of 2-IFS simply iterates through the endpoints of the intervals which sat-
+isfy the constraint and outputs the optimal facility location, breaking ties in favour of the leftmost
+optimal location.
+3.2
+Unanimous Fair Share
+We now present Unanimous Fair Share (UFS), a strengthening and generalization of IFS to groups
+of agents at the same location. Informally, if there are k agents at the same location, then UFS
+requires that the facility is placed at least k
+n distance from these agents. Again, we focus on ap-
+proximations of UFS as a UFS solution may not exist.
+Definition 2 (α-Unanimous Fair Share (UFS)). Given a profile of locations x, a facility location y
+satisfies α-Unanimous Fair Share (α-UFS) if for any set of agents S with identical location,
+u(y, xi) ≥ |S|
+αn
+∀i ∈ S.
+Note that α−UFS implies α−IFS. As with α−IFS, we find that the optimal value of α for which
+an α-UFS solution always exists is α = 2. The proof intuition is similar to that of Theorem 1, but
+the balls vary in size depending on the number of agents in the group.
+Proposition 2. The lowest value of α for which an α-UFS solution always exists is α = 2.
+Similar to f ∗
+2IFS, a polynomial time mechanism (which we denote as f ∗
+2UFS) that computes the
+optimal 2-UFS facility location for utilitarian welfare iterates through the endpoints of the intervals
+satisfying 2-UFS and outputs the optimal facility location, breaking ties in favour of the leftmost
+optimal location.
+4
+Deterministic Setting
+We begin with the deterministic setting, analyzing the price of proportional fairness and agent
+strategic behaviour. All results stated in this section are for the deterministic setting.
+6
+
+4.1
+Price of Fairness
+In this section, we analyze the price of fairness for our (approximate) fairness axioms.3 Informally,
+the price of fairness measures the loss of efficiency from imposing a certain fairness constraint.
+We focus on the objectives of utilitarian and egalitarian welfare, defined as the sum of utilities and
+the minimum agent utility, respectively.
+A fairness property P is a mapping from an agent location profile x ∈ Xn to a (possibly empty)
+set of facility locations P(x) ∈ X. Every facility location P(x) satisfies the fairness property P.
+The price of fairness for property P is the worst case ratio between the optimal welfare and the
+optimal welfare from a facility location satisfying P.
+4.1.1
+Utilitarian Welfare
+The utilitarian welfare of an instance is a standard measure of efficiency. Finding the price of our
+proportional fairness axioms for utilitarian welfare quantifies the impact on efficiency when the
+OFLP system is constrained to be proportionally fair.
+Definition 3 (Price of Fairness for Utilitarian Welfare). Let f ∗
+UW be the mechanism that returns
+the solution maximizing utilitarian welfare. For utilitarian welfare and fairness property P, we
+define the price of fairness as the worst case ratio (over all location profiles) between the optimal
+utilitarian welfare and the optimal utilitarian welfare achieved by a facility location satisfying
+fairness property P:
+max
+x∈[0,1]n
+�
+i u(f ∗
+UW(x), xi)
+maxy∈P(x)
+�
+i u(y, xi).
+We now move to compute the price of 2-IFS fairness for utilitarian welfare. Recall that the
+solution maximizing utilitarian welfare must be either 0 or 1 [Cheng et al., 2013].
+Lemma 1. The price of 2-IFS for utilitarian welfare is at least 2.
+Proof. Suppose n is even, and that the agents are located at 1
+2n −ϵ,
+3
+2n −2ϵ, . . . , n−1
+2n − n
+2ϵ, n+1
+2n + n
+2ϵ,
+. . . , 2n−3
+2n
++ 2ϵ, 2n−1
+2n
++ ϵ for some sufficiently small ϵ (see, e.g. Figure 2). Under this symmetric
+profile, either a facility location of 0 or 1 leads to the maximum utilitarian welfare of n
+2. The only
+facility locations satisfying 2-IFS are within the interval [ 1
+2 − n
+2ϵ, 1
+2 + n
+2ϵ]. Any location in this
+interval gives the same utilitarian welfare as there are an equal number of agents on both sides, so
+suppose the facility is at 1
+2. This corresponds to a utilitarian welfare of n
+2
+1
+2n(1 + 3 + · · · + n − 1) +
+2ϵ(1 + 2 + · · · + n
+2) = n
+4 + ϵn(1 + n
+2). Taking the limit ϵ → 0 gives a ratio of 2.
+Remark 1. The above example places the facility at the midpoint of the optimal median interval.
+The median is known for minimizing sum of distances.
+Theorem 1. The price of 2-IFS for utilitarian welfare is 2, and this bound is tight.
+We next compute bounds on the price of 2-UFS fairness for utilitarian welfare.
+Theorem 2. The price of 2-UFS for utilitarian welfare is 2, and this bound is tight.
+3The price of fairness can also be interpreted as the approximation ratio for the respective optimal mechanism
+satisfying the fairness constraint.
+7
+
+0
+1
+x1
+x2
+x3
+x4
+f ∗
+UW
+f ∗
+2IFS
+Figure 2: The instance in the proof of Lemma 1 for n = 4. f ∗
+UW represents the utilitarian wel-
+fare maximizing facility placement, whilst f ∗
+2IFS represents the facility that maximizes utilitarian
+welfare under the constraints of 2-IFS. The red intervals denote locations that are infeasible under
+2-IFS.
+As the price of fairness for utilitarian welfare is the same for both proportional fairness axioms,
+it may be desirable to implement 2-UFS in favour of 2-IFS when loss of utilitarian welfare is the
+primary concern.
+4.1.2
+Egalitarian Welfare
+The egalitarian welfare is an alternate measure of fairness frequently observed in the literature,
+focussing on the worst off agent. Our price of fairness analysis gives an insight into the tradeoff
+between egalitarian welfare/maximin fairness and proportional fairness in the OFLP.
+Definition 4 (Price of Fairness for Egalitarian Welfare). Let f ∗
+EW be the mechanism that returns
+the solution maximizing Egalitarian Welfare. For egalitarian welfare and fairness property P, we
+define the price of fairness as the worst case ratio (over all location profiles) between the optimal
+egalitarian welfare and the optimal egalitarian welfare achieved by a facility location satisfying
+fairness property P:
+max
+x∈[0,1]n
+mini u(f ∗
+EW(x), xi)
+maxy∈P(x) mini u(y, xi).
+Our first result is that the price of 2-IFS is 1, meaning that a mechanism that maximizes egali-
+tarian welfare is guaranteed to satisfy 2-IFS. The intuition is that since a 2-IFS solution (in which
+every agent obtains at least
+1
+2n utility) always exists, a solution which maximizes the worst off
+agent’s utility would therefore result in each agent obtaining at least
+1
+2n utility.
+Proposition 3. The price of 2-IFS for egalitarian welfare is 1.
+On the other hand, we find that the price of 2-UFS is noticeably worse, taking a linear factor of
+n − 1. The intuition behind this is that a coalition of n − 1 agents at one point can ensure that the
+facility is distant from their location (and closer to the remaining agent’s location) by a ‘factor’ of
+n − 1.
+Theorem 3. The price of 2-UFS for egalitarian welfare is n − 1.
+Proof. We first prove that the lower bound is n − 1. It suffices to consider n ≥ 3. Consider the
+location profile with 1 agent at
+1
+2n − ϵ and n − 1 agents at n+1
+2n + ϵ for sufficiently small ϵ > 0,
+(see, e.g. Figure 3). The optimal solution places the facility at 1 resulting in an egalitarian welfare
+of n−1
+2n − ϵ. The only 2-UFS solutions are in the interval [ 1
+n − ϵ, 1
+n + ϵ], and the solution of 1
+n + ϵ
+results in an egalitarian welfare of
+1
+2n + 2ϵ. As ϵ → 0, the ratio approaches n − 1.
+8
+
+0
+1
+x2...xn
+x1
+f ∗
+EW
+2UFS(x)
+Figure 3: The instance in the proof of Theorem 3. f ∗
+EW represents the egalitarian welfare maxi-
+mizing facility placement, whilst 2UFS(x) represents the interval of facility placements satisfying
+2-UFS. The red intervals denote locations that are infeasible under 2-UFS.
+We now prove that the upper bound is n − 1. Firstly, it clearly suffices to consider location
+profiles where groups contain at most n − 1 agents. Now suppose there exists such an x where
+mini u(f ∗
+EW(x), xi) ≥ n−1
+2n , i.e. there is a solution where every agent has at least n−1
+2n utility. Then
+this also satisfies 2-UFS and results in an egalitarian ratio of 1. Therefore the maximum ratio must
+have mini u(f ∗
+EW(x), xi) < n−1
+2n . Due to 2-UFS, we also have maxy∈2UFS(x) mini u(y, xi) ≥
+1
+2n.
+The theorem statement follows from dividing these two terms.
+4.2
+Incompatibility with Strategyproofness
+In mechanism design, the normative property of strategyproofness is often sought as it disincen-
+tivizes agents from misreporting their true location.
+Definition 5 (Strategyproofness). A (deterministic) mechanism f is strategyproof if for every agent
+i ∈ N, we have for every xi, x′
+i and ˆx−i,
+u(f(xi, ˆx−i), xi) ≥ u(f(x′
+i, ˆx−i), xi).
+We say that a randomized mechanism is strategyproof in expectation if no agent can improve
+its expected utility by misreporting its own location.
+We note that no strategyproof and deterministic mechanism can achieve any approximation of
+IFS (and therefore also UFS). This follows from the characterization of deterministic strategyproof
+mechanisms for the OFLP by Feigenbaum and Sethuraman [2015] which we describe below.
+Definition 6 (Feigenbaum and Sethuraman [2015]). Let f be a deterministic mechanism s.t. |Rf
+n| =
+|{fn(x) : x ∈ Xn}| ≤ 2 for all n ∈ N. For each n ∈ N, let Rf
+n = {αn, βn} s.t. βn ≥ αn, and
+let mn = αn+βn
+2
+. For any n ∈ N, for every profile x ∈ Xn, consider the partition of the agents
+Lx = {i ∈ N : xi < mn}, M x = {i ∈ N : xi = mn}, and Ex = {i ∈ N : xi > mn}. We say that
+f is a midpoint mechanism if it satisfies the following property: for any n ∈ N, let x, y ∈ Xn be
+any profiles s.t. f(x) = βn and f(y) = αn. If βn > αn, then there exists an agent i which satisfies
+one of the following:
+(D-1) i ∈ Lx and i ∈ M y
+(D-2) i ∈ Lx and i ∈ Ey
+(D-3) i ∈ M x and i ∈ Ey.
+9
+
+This definition has the following intuition: the mechanism can switch the facility location from
+right to left or from left to right only when an agent crosses the midpoint in the opposite direction.
+Proposition 4. There exists no strategyproof mechanism that achieves any approximation of IFS.
+Proof. Feigenbaum and Sethuraman [2015] proved that the midpoint mechanisms characterize all
+strategyproof mechanisms. Consider any profile which locates at least one agent at each point in
+Rf
+n. Such a mechanism does not satisfy any approximation of IFS.
+In other words, for every midpoint mechanism, there exists a location profile where the mech-
+anism places the facility at an agent’s location.
+Since strategyproofness is incompatible with our fairness axioms, we are interested in the per-
+formance of proportionally fair mechanisms in our model when accounting for agent strategic
+behaviour. Such performance can be quantified by the price of anarchy.
+4.3
+ϵ-Price of Anarchy
+In this section, we compute the worst case loss of efficiency by agents misreporting their location
+under the mechanisms f ∗
+2IFS and f ∗
+2UFS. Recall these are the mechanisms which maximize utilitar-
+ian welfare under the constraints of 2-IFS and 2-UFS, respectively. Typically, this efficiency loss
+is quantified by the price of anarchy [Koutsoupias and Papadimitriou, 1999; Nisan et al., 2007],
+defined as the worst case ratio between the utilitarian welfare corresponding to the truthful agent
+location profile, and the minimum utilitarian welfare corresponding to a pure Nash equilibrium of
+reports.
+Definition 7. Given a (truthful) profile of agent locations x and a deterministic mechanism f,
+a pure Nash equilibrium is a profile of reported agent locations x′ = (x′
+1, . . . , x′
+n) such that no
+single agent can improve its own utility (with respect to its true location) by changing its reported
+location.
+However, for f ∗
+2IFS and f ∗
+2UFS, a pure Nash equilibrium may not necessarily exist, and hence
+the price of anarchy is not well-defined.
+Proposition 5. A pure Nash equilibrium may not exist for f ∗
+2IFS or f ∗
+2UFS.
+As a result, we turn to proving existence of the approximate notion of pure ϵ-Nash equilibria,
+and computing the corresponding notion of ϵ-price of anarchy.
+Definition 8 (Tardos and Vazirani [2007]). A pure ϵ-Nash equilibrium is a profile of reported agent
+locations x′ = (x′
+1, . . . , x′
+n) such that no single agent can improve its own utility (with respect to its
+true location) by strictly more than ϵ by changing its reported location. A pure Nash equilibrium
+is a pure ϵ-Nash equilibrium where ϵ = 0.
+Theorem 4. For any ϵ > 0, a pure ϵ-Nash equilibrium always exists for f ∗
+2IFS.
+Theorem 5. For any ϵ > 0, a pure ϵ-Nash equilibrium always exists for f ∗
+2UFS.
+For a mechanism f, the ϵ-price of anarchy is defined as the worst case ratio (over all location
+profiles x) between the utilitarian welfare corresponding to all agents reporting truthfully and the
+minimum utilitarian welfare corresponding to agents reporting in a pure ϵ-Nash equilibrium.
+10
+
+Definition 9. Given f and x, define the set of pure ϵ-Nash equilibria location profiles as ϵ-
+Equil(f, x). The price of anarchy for utilitarian welfare is defined as:
+ϵ-PoA(f) := max
+x∈Xn
+�
+i u(f(x), xi)
+minx′∈ϵ-Equil(f,x)
+�
+i u(f(x′), xi).
+We must show that the price of anarchy is well-defined by proving that a pure Nash equilibrium
+always exists. However, we cannot simply apply the early theorems of [Debreu, 1952; Glicksberg,
+1952; Fan, 1952], which show existence of a pure Nash equilibrium when basic strategy space
+conditions are satisfied along with players having continuous and quasiconcave payoff functions.4
+This is because the payoff function is neither continuous nor quasiconcave.
+Nevertheless, we prove that a pure Nash equilibrium always exists for f ∗
+2IFS and f ∗
+2UFS.
+We now proceed to find ϵ-price of anarchy bounds for utilitarian welfare. The same proof
+arguments can be applied to find identical bounds for both f ∗
+2IFS and f ∗
+2UFS.
+Theorem 6. For any ϵ ∈ (0, 1
+n), the ϵ-price of anarchy for f ∗
+2IFS and f ∗
+2UFS of utilitarian welfare
+is at least 2n−1+nϵ
+1−nϵ . The price of anarchy is unbounded for ϵ ≥ 1
+n.
+Theorem 7. For any ϵ ∈ (0, 1
+2n), the ϵ−price of anarchy for f ∗
+2IFS and f ∗
+2UFS of utilitarian welfare
+is at most
+2n
+1−2nϵ.
+Proof. Firstly, we note that under a pure ϵ-Nash equilibrium, each agent must have at least
+1
+2n − ϵ
+utility. To see this, suppose there is a profile of reports x′ where some agent i has strictly less
+than
+1
+2n − ϵ utility. By switching its report to its truthful location, agent i can strictly improve
+its utility by greater than ϵ, as the facility must be at least
+1
+2n distance from the agent’s truthful
+location, hence x′ is not a pure ϵ-Nash equilibrium. Therefore the utilitarian welfare under a pure
+ϵ-Nash equilibrium must be at least 1
+2 − nϵ. Now the utilitarian welfare under any instance is at
+most n, from all agents being located at 0 and the facility being placed at 1. The theorem statement
+immediately follows.
+By setting ϵ = 0 in the ϵ-price of anarchy bounds of Theorems 6 and 7, we achieve the follow-
+ing result.
+Corollary 1. If a pure Nash equilibrium exists, the price of anarchy for f ∗
+2IFS and f ∗
+2UFS of utili-
+tarian welfare is between 2n − 1 and 2n.
+As the ϵ-price of anarchy of our proportional fairness axioms in the deterministic setting is
+linear, it may be desirable to use a randomized, strategyproof mechanism when the agent locations
+are private information. We give examples of such mechanisms in the upcoming section.
+5
+Randomized Mechanisms
+By using randomized mechanisms, we can achieve a better price of fairness for 2-IFS and 2-UFS,
+and overcome the incompatibility with strategyproofness. We define a randomized mechanism
+4A function f is quasiconcave if f(λx + (1 − λ)y) ≥ min{f(x), f(y)}.
+11
+
+as a probability distribution over deterministic mechanisms, and an agent’s utility as its expected
+distance from the facility.
+In the randomized setting, the optimal approximation of IFS and UFS for which a solution
+always exists is α = 2. This can be easily seen by setting 1 agent at 1
+2. Our fairness axioms are
+adapted as follows:
+Definition 10 (α-Individual Fair Share (IFS) in expectation). A mechanism f satisfies α-Individual
+Fair Share in expectation (α-IFS in expectation) if for any location profile x,
+E[u(f(x), xi)] ≥ 1
+αn
+∀i ∈ N.
+Definition 11 (α-Unanimous Fair Share (UFS) in expectation). A mechanism f satisfies α-Unanimous
+Fair Share in expectation (α-UFS in expectation) if for any location profile x and any set of agents
+S at the same location,
+E[u(f(x), xi)] ≥ |S|
+αn
+∀i ∈ S.
+5.1
+Strategyproofness
+From Proposition 4, we know that in the deterministic setting, strategyproofness is incompatible
+with our proportional fairness axioms. In the randomized setting, the space of mechanisms is much
+larger and hence we are able to overcome this impossibility.
+We first consider Mechanism 2 from [Cheng et al., 2013]. Denoting the numbers of agents
+located in [0, 1/2] and (1/2, 1] by n1 and n2 respectively, Mechanism 2 places the facility at 0 with
+probability α and at 1 with probability (1−α), where α =
+2n1n2+n2
+2
+n2
+1+n2
+2+4n1n2. This mechanism is known
+to be group strategy-proof (in expectation) and 3
+2−approximates the utilitarian welfare. As we will
+show, this mechanism satisfies 2-UFS (and therefore also 2-IFS).
+Theorem 8. Mechanism 2 satisfies 2-UFS in expectation.
+5.2
+Egalitarian Welfare
+We now provide some results on egalitarian welfare. Specifically, we give a randomized, strate-
+gyproof mechanism which maximizes egalitarian welfare subject to the constraints of 2-IFS and
+2-UFS in expectation.
+Randomized Egalitarian Welfare mechanism
+• If all agents are in [0, 1
+2], place the facility at 1.
+• If all agents are in ( 1
+2, 1], place the facility at 0.
+• Otherwise, place the facility at 0 with probability 1
+2 and at 1 with probability 1
+2.
+By considering cases, it is easy to see that this mechanism is strategyproof in expectation.
+Proposition 6. Randomized Egalitarian Welfare mechanism is strategyproof in expectation.
+12
+
+Before analyzing the optimality and approximation ratio of this mechanism, we prove a lemma
+that shows that in the randomized setting, it suffices to consider mechanisms which can only place
+the facility at 0 or 1.
+Lemma 2. Consider an arbitrary agent location profile x. For every 2-IFS/UFS randomized mech-
+anism that gives strictly positive probability to a facility placement between 0 and 1, there exists a
+2-IFS/UFS randomized mechanism that only gives positive support to a facility placement at 0 or
+1 that leads to weakly higher expected utility for each agent.
+We now proceed to prove that Randomized Egalitarian Welfare mechanism is egalitarian
+welfare-optimal.
+Proposition 7. The Randomized Egalitarian Welfare mechanism is optimal for egalitarian wel-
+fare and satisfies 2-UFS.
+Proof. The cases where all agents are in [0, 1
+2] and all agents are in ( 1
+2, 1] are trivial.
+We now examine the case where both intervals have at least one agent. An agent at xi has
+1
+2xi + 1
+2(1−xi) = 1/2 expected distance from the facility, hence this mechanism satisfies 2-UFS in
+expectation. By Lemma 2, it suffices to only consider mechanisms which can only place the facility
+at 0 or 1. Suppose that instead of having 1
+2 probability of placing the facility at either endpoint, we
+place the facility at 1 with 1
+2 + p probability and at 0 with 1
+2 − p probability, where p ∈ (0, 1
+2]. The
+expected utility of the rightmost agent is xn( 1
+2 − p) + (1 − xn)( 1
+2 + p) = 1
+2 + p(1 − 2xn) < 1
+2. By
+a symmetric argument, if the facility was placed at 1 with 1
+2 − p probability and at 0 with 1
+2 + p
+probability, the expected utility of the leftmost agent would be strictly less than 1
+2. Hence, our
+mechanism is optimal in this case.
+In other words, the approximation ratio of this mechanism for egalitarian welfare is 1. Recall
+that the price of fairness can be interpreted as the approximation ratio of the respective optimal
+mechanism that satisfies the fairness constraint. This leads us to the following corollary.
+Corollary 2. In the randomized setting, the price of fairness of 2-UFS for egalitarian welfare is 1.
+This is in stark contrast to the deterministic setting where the respective price of fairness is
+n − 1.
+5.3
+2-IFS
+We now analyze utilitarian welfare, beginning with the axiom of 2-IFS. Consider the randomized
+mechanism below which maximizes the utilitarian welfare subject to the 2-IFS constraint:
+2-IFS Randomized mechanism
+• If �n
+i=1 xi = n
+2, place the facility at 0 with probability 1
+2 and at 1 with probability 1
+2.
+• If �n
+i=1 xi > n
+2,
+– If x1 ≥
+1
+2n, place the facility at 0 with probability 1.
+– If x1 <
+1
+2n, place the facility at 0 with probability 1 − α, and at 1 with probability α,
+where α =
+1−2nx1
+2n(1−2x1).
+13
+
+• If �n
+i=1 xi < n
+2,
+– If xn ≤ 1 −
+1
+2n, place the facility at 1 with probability 1.
+– If xn > 1 −
+1
+2n, place the facility at 0 with probability 1 − β, and at 1 with probability
+β, where β =
+1−2nxn
+2n(1−2xn).
+The intuition behind this mechanism is as follows. When �n
+i=1 xi =
+n
+2, both facility locations
+of 0 and 1 are tied in terms of maximizing utilitarian welfare, and by placing the facility at either
+location with probability 1
+2, we achieve 2-IFS in expectation. When �n
+i=1 xi >
+n
+2, the optimal
+facility location is 0, so the mechanism places the facility there if it does not violate 2-IFS for
+any agent, else it also places the facility at 1 with the minimum probability that ensures 2-IFS is
+ensured for all agents. The case where �n
+i=1 xi < n
+2 is similar and symmetric.
+Our proof of the mechanism’s welfare-optimality is based on its intuition.
+Lemma 3. 2-IFS Randomized mechanism is optimal for utilitarian welfare amongst all random-
+ized mechanisms satisfying 2-IFS in expectation.
+We now prove a tight, constant approximation ratio for this mechanism.
+Theorem 9. 2-IFS Randomized mechanism has an approximation ratio for utilitarian welfare of
+12
+11 ≈ 1.091.
+This leads to the following price of fairness result for 2-IFS.
+Corollary 3. In the randomized setting, the price of fairness of 2-IFS for utilitarian welfare is
+12
+11 ≈ 1.091.
+5.4
+2-UFS
+We now move to analyze the axiom of 2-UFS in the context of utilitarian welfare. As in the previ-
+ous subsection, we begin by describing a randomized mechanism which maximizes the utilitarian
+welfare subject to the 2-UFS constraint:
+2-UFS Randomized mechanism
+• Order the m unique agent locations so that x1 is the smallest agent location and xm is the
+largest agent location.
+• Let S1, . . . , Sm denote the groups of agents at the m unique agent locations.
+• If �m
+i=1 |Si|xi = n
+2, place the facility at 0 with probability 1
+2 and at 1 with probability 1
+2.
+• If �m
+i=1 |Si|xi > n
+2,
+– Let k denote the index of the largest unique agent location satisfying xk < 1
+2.
+– For i in {1, . . . , k}, set αi = |Si|−2nxi
+2n(1−2xi).
+– Letting α = max{α1, . . . , αk}, place the facility at 0 with probability 1 − α and at 1
+with probability α.
+14
+
+• If �m
+i=1 |Si|xi < n
+2,
+– Let k denote the index of the smallest unique agent location satisfying xk > 1
+2.
+– For i in {k, . . . , m}, set αi = |Si|−2nxi
+2n(1−2xi).
+– Letting α = min{αk, . . . , αm}, place the facility at 0 with probability 1 − α and at 1
+with probability α.
+This mechanism is similar to the 2-IFS Randomized mechanism, but we must now iterate
+through the groups of agents to find the optimal value of α that guarantees 2-UFS for all agents.
+Specifically, if �m
+i=1 |Si|xi > n
+2, then αi denotes the smallest probability weight on location 1 such
+that 2-UFS is achieved for Si. Hence by setting α to be the largest αi, we achieve 2-UFS for all
+agents.
+Again, our proof of this mechanism’s optimality is based on the aforementioned intuition.
+Lemma 4. 2-UFS Randomized mechanism is optimal for utilitarian welfare amongst all random-
+ized mechanisms satisfying 2-UFS in expectation.
+Surprisingly, imposing the stronger fairness axiom of 2-UFS as opposed to 2-IFS has a minimal
+effect on the welfare-optimal mechanism’s approximation ratio.
+Theorem 10. 2-UFS Randomized mechanism has an approximation ratio of 2
+7(1 + 2
+√
+2) ≈
+1.09384.
+From Theorem 10, we have the following corollary.
+Corollary 4. In the randomized setting, the price of fairness of 2-UFS for utilitarian welfare is
+2
+7(1 + 2
+√
+2) ≈ 1.09384.
+6
+Extension 1: Proportional Fairness
+In our analyses of price of fairness and randomized mechanisms, we have considered 2-IFS and
+2-UFS, which give minimum distance guarantees for individual agents and groups of agents at the
+same location, respectively. One downside of the 2-UFS definition is that agents located near each
+other but not at the same location are considered to be in separate groups. An axiom which accounts
+for groups of agents located relatively close to each other is Proportional Fairness (PF), from [Aziz
+et al., 2021]. As with IFS and UFS, a PF solution may not exist so we define approximate α−PF
+as follows:
+Definition 12 (α-PF). Given a profile of locations x, a facility location y satisfies α-PF if for any
+set of agents S within range r := maxi∈S{xi} − mini∈S{xi},
+u(y, xi) ≥ 1
+α(|S|/(n)) − r
+∀i ∈ S.
+Note that α−PF implies α−UFS, and therefore also implies α−IFS.
+However, α−UFS does not imply α−PF, hence α−PF is a stronger notion than α−UFS.
+Lemma 5. For α = 2, there exists an α−UFS facility location y that does not satisfy α−PF.
+15
+
+It follows from Theorem 2 that the smallest value of α for which an α-PF solution exists for all
+location profiles is greater or equal than 2. We now show that a 2-PF solution always exists.
+Theorem 11. A 2-PF solution always exists.
+Proof Sketch. We prove the theorem by induction on the number of groups. Suppose we have m
+groups of agents where each group consists of agents at the same location. When m = 1, i.e, all
+the agents are at the same point, 2-PF existence follows from 2-UFS existence. Now, we assume
+for any k groups of agents where k ≤ m that there exists a 2-PF solution and we extend that for
+k = m + 1.
+Suppose we have m + 1 groups of agents placed at centers c1, c2, ..., cm+1 which are ordered
+from left to right. Set a ball Bi with radius |Si|
+2n around each center ci. We consider several cases
+based on the intersection of balls. If all the balls are disjoint, it can be shown there exists a point
+y ∈ [0, 1] which lies outside the union of balls B1 ∪ · · · ∪ Bm+1, satisfying the 2-PF inequality.
+If there exists two balls, say B1 and B2, intersecting each other, they are merged with the agents
+placed at a new center c′
+1. We then set a ball B′
+1 centered at c′
+1 with radius |S1|
+2n + |S2|
+2n . Now, we
+have m groups of agents placed at c′
+1, c3, . . . , cm+1, and from our inductive assumption, we know
+a 2-PF solution exists.
+Thus, 2-PF is the optimal approximation of PF for the obnoxious facility location problem.
+7
+Extension 2: Hybrid Model
+In the hybrid model, agents either want to be located close to the facility (as in the classic facility
+location model), or wish to be located far away from the facility (as in our obnoxious facility
+location model). Such a model has several real-world applications such as the placement of schools
+or religious places of worship; families with children or religious people would want to live near
+the facility for convenience, whilst others would want to be far from the facility due to the increased
+noise and traffic. In our model, we say an agent is type C if it is a classic agent and prefers to be
+closer to the facility, and an agent is type O if it is an obnoxious agent and prefers to be further
+away from the facility.5 We denote the set of classic agents as NC and the set of obnoxious agents
+as NO.
+A type C agent has utility u(y, xi) = 1 − d(y, xi) and a type O agent has utility u(y, xi) =
+d(y, xi).6
+When defining IFS and UFS in the hybrid model, we use definitions consistent with [Aziz
+et al., 2021] and this paper. Our definition of Hybrid-Individual Fair Share (H-IFS) provides an
+appropriate distance guarantee for each agent.
+Definition 13 (Hybrid-Individual Fair Share (H-IFS)). Given a profile of locations x, a facility
+location y satisfies Hybrid-Individual Fair Share (H-IFS) if for all i ∈ NC,
+u(y, xi) ≥ 1
+n
+or, equivalently,
+d(y, xi) ≤ 1 − 1
+n,
+5Our model is based on the model presented by Feigenbaum and Sethuraman [2015].
+6This choice of utility function is adapted from [Feigenbaum and Sethuraman, 2015; Aziz et al., 2021]. We refer
+the reader to those papers for a justification of the utility model.
+16
+
+and for all i ∈ NO,
+u(y, xi) ≥ 1
+2n
+or, equivalently,
+d(y, xi) ≥ 1
+2n.
+When defining UFS, we aim to capture proportional fairness guarantees for subsets of agents
+of the same type at the same location. Consider every subset S ⊆ N of agents at the same location,
+where S = SC ∪ SO. SC denotes the agents of S that are of type C, and SO denotes the agents of
+S that are of type O.
+Definition 14 (Hybrid-Unanimous Fair Share (H-UFS)). Given a profile of locations x such that a
+subset of Sj ⊆ N agents7 share the same type and location, a facility location y satisfies Hybrid-
+Unanimous Fair Share (H-UFS) if for all i ∈ SC,
+u(y, xi) ≥ |SC|
+n
+or, equivalently,
+d(y, xi) ≤ 1 − |SC|
+n ,
+and for all i ∈ SO,
+u(y, xi) ≥ |SO|
+2n
+or, equivalently,
+d(y, xi) ≥ |SO|
+2n .
+Example 1. Suppose there are n − k type C agents and k type O agents, all at the same location.
+The facility needs to be between
+k
+2n and k
+n distance from the group.
+Although our definitions have a discrepancy in utility functions between the classic and obnox-
+ious agents, we have specified them to be consistent with related literature and to be the optimal
+bounds such that a solution is guaranteed to exist. Furthermore, existence of a H-UFS solution
+under our definition implies existence of a solution under a weaker definition where a set SC of
+classic agents at the same location instead have a utility guarantee of |SC|
+2n .
+Theorem 12. Under the hybrid model, a H-UFS solution always exists.
+8
+Discussion
+In this paper we have formulated proportional fairness axioms for the obnoxious facility location
+problem, and given welfare-optimal deterministic and randomized mechanisms satisfying these
+axioms. In both the deterministic and randomized setting, we prove tight price of fairness bounds
+for 2-IFS and 2-UFS, for the objectives of utilitarian and egalitarian welfare. These correspond
+to the approximation ratios of the respective welfare-optimal mechanisms. For the deterministic
+utilitarian welfare-optimal mechanisms, we also prove existence of pure ϵ-Nash equilibria and
+linear ϵ-price of anarchy bounds. We also give a randomized, strategyproof mechanism satisfying
+2-UFS with a constant utilitarian approximation ratio.
+There are several future directions to this work, such as those stemming from our proposed ex-
+tensions of 2-PF and the hybrid model. For example, the price of anarchy and price of fairness for
+these two extensions could be computed. We could also supplement our price of anarchy results
+7j ∈ {C, O}
+17
+
+with bounds on the price of stability. Further extensions to the price of fairness results could in-
+volve different objective and utility functions. It is also worth analyzing the Nash equilibria of the
+randomized utilitarian welfare-optimal mechanisms, as they are not strategyproof in expectation.
+Although our proportional fairness axioms are incompatible with strategyproofness in the deter-
+ministic setting, we may consider weaker notions of strategyproofness which may be compatible
+with our fairness properties.
+Acknowledgements
+We would like to acknowledge the helpful feedback and suggestions from Minming Li.
+References
+H. Aziz, A. Bogomolnaia, and H. Moulin. Fair mixing: the case of dichotomous preferences.
+In Proceedings of the 2019 ACM Conference on Economics and Computation, pages 753–781,
+2019.
+H. Aziz, A. Lam, B. E. Lee, and T. Walsh. Strategyproof and proportionally fair facility location.
+CoRR, abs/2111.01566, 2021.
+H. Aziz, A. Lam, M. Suzuki, and T. Walsh. Random rank: The one and only strategyproof and
+proportionally fair randomized facility location mechanism. arXiv preprint arXiv:2205.14798,
+2022.
+H. Aziz. A probabilistic approach to voting, allocation, matching, and coalition formation. In The
+Future of Economic Design, pages 45–50. Springer, 2019.
+S. Barman, U. Bhaskar, and N. Shah. Optimal bounds on the price of fairness for indivisible goods.
+In International Conference on Web and Internet Economics, pages 356–369. Springer, 2020.
+X. Bei, X. Lu, P. Manurangsi, and W. Suksompong. The price of fairness for indivisible goods.
+Theory of Computing Systems, 65(7):1069–1093, 2021.
+D. Bertsimas, V. F. Farias, and N. Trichakis. The price of fairness. Operations research, 59(1):17–
+31, 2011.
+A. Bogomolnaia, H. Moulin, and R. Stong. Collective choice under dichotomous preferences.
+Journal of Economic Theory, 122(2):165–184, 2005.
+F. Brandt. Rolling the dice: Recent results in probabilistic social choice. Trends in computational
+social choice, pages 3–26, 2017.
+L. Buzna, M. Koháni, and J. Janáˇcek. An approximation algorithm for the facility location problem
+with lexicographic minimax objective. Journal of Applied Mathematics, 2014, 2014.
+I. Caragiannis, C. Kaklamanis, P. Kanellopoulos, and M. Kyropoulou. The efficiency of fair divi-
+sion. Theory of Computing Systems, 50(4):589–610, 2012.
+18
+
+H. Chan, A. Filos-Ratsikas, B. Li, M. Li, and C. Wang. Mechanism design for facility location
+problems: A survey. In 30th, 2021.
+Z. Chen, K. C. K. Fong, M. Li, K. Wang, H. Yuan, and Y. Zhang. Facility location games with
+optional preference. Theoretical Computer Science, 847:185–197, 2020.
+Y. Cheng, W. Yu, and G. Zhang. Mechanisms for obnoxious facility game on a path. In Combinato-
+rial Optimization and Applications - 5th International Conference, COCOA 2011, Zhangjiajie,
+China, August 4-6, 2011. Proceedings, pages 262–271, 2011.
+Y. Cheng, W. Yu, and G. Zhang. Strategy-proof approximation mechanisms for an obnoxious
+facility game on networks. Theor. Comput. Sci., 497:154–163, 2013.
+Y. Cheng, Q. Han, W. Yu, and G. Zhang. Strategy-proof mechanisms for obnoxious facility game
+with bounded service range. J. Comb. Optim., 37(2):737–755, 2019.
+S. Chien and A. Sinclair. Convergence to approximate nash equilibria in congestion games. Games
+and Economic Behavior, 71(2):315–327, 2011.
+R. L. Church and Z. Drezner. Review of obnoxious facilities location problems. Computers &
+Operations Research, 138:105468, 2022.
+G. Debreu. A social equilibrium existence theorem. Proceedings of the National Academy of
+Sciences, 38(10):886–893, 1952.
+K. Fan. Fixed-point and minimax theorems in locally convex topological linear spaces. Proceed-
+ings of the National Academy of Sciences of the United States of America, 38(2):121, 1952.
+I. Feigenbaum and J. Sethuraman. Strategyproof mechanisms for one-dimensional hybrid and
+obnoxious facility location models. In Incentive and Trust in E-Communities, Papers from the
+2015 AAAI Workshop, Austin, Texas, USA, January 25, 2015, 2015.
+I. Feigenbaum, M. Li, J. Sethuraman, F. Wang, and S. Zou. Strategic facility location problems
+with linear single-dipped and single-peaked preferences. Autonomous Agents and Multi-Agent
+Systems, 34(2):1–47, 2020.
+M. Feldman, A. Fiat, and S. Obraztsova. Variations on the hotelling-downs model. In Thirtieth
+AAAI Conference on Artificial Intelligence, 2016.
+K. C. K. Fong, M. Li, P. Lu, T. Todo, and M. Yokoo. Facility location games with fractional
+preferences. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 32, 2018.
+I. L. Glicksberg. A further generalization of the kakutani fixed point theorem, with application
+to nash equilibrium points. Proceedings of the American Mathematical Society, 3(1):170–174,
+1952.
+R. M. Hekmatfar. Facility location. Physica-Verlag, 2009.
+19
+
+K. Ibara and H. Nagamochi. Characterizing mechanisms in obnoxious facility game. In Combina-
+torial Optimization and Applications - 6th International Conference, COCOA 2012, Banff, AB,
+Canada, August 5-9, 2012. Proceedings, volume 7402 of Lecture Notes in Computer Science,
+pages 301–311. Springer, 2012.
+E. Koutsoupias and C. Papadimitriou. Worst-case equilibria. In Annual Symposium on Theoretical
+Aspects of Computer Science, pages 404–413. Springer, 1999.
+S. Krogmann, P. Lenzner, L. Molitor, and A. Skopalik. Two-stage facility location games with
+strategic clients and facilities. In Proceedings of the Thirtieth International Joint Conference on
+Artificial Intelligence, pages 292–298, 2021.
+M. T. Melo, S. Nickel, and F. Saldanha-Da-Gama. Facility location and supply chain management–
+a review. European Journal of Operational Research, 196(2):401–412, 2009.
+M. Michorzewski, D. Peters, and P. Skowron. Price of fairness in budget division and probabilistic
+social choice. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34,
+pages 2184–2191, 2020.
+H. Moulin. Fair division and collective welfare. MIT press, 2003.
+T. Mylvaganam, M. Sassano, and A. Astolfi. Constructive ϵ-nash equilibria for nonzero-sum dif-
+ferential games. IEEE Transactions on Automatic Control, 60(4):950–965, 2015.
+J. Nash. The bargaining problem. Econometrica, 18(2):155–162, 1950.
+N. Nisan, T. Roughgarden, É. Tardos, and V. Vazirani. Algorithmic Game Theory. Cambridge
+University Press, New York, NY, USA, 2007.
+A. D. Procaccia and M. Tennenholtz. Approximate mechanism design without money. In 14th,
+pages 1–26, 2013.
+L. S. Shapley. A Value for n-Person Games, pages 143–164. Princeton University Press, Princeton,
+NJ, 1953.
+H. Steinhaus. The problem of fair division. Econometrica, 16:101–104, 1948.
+E. Tardos and V. Vazirani.
+Basic solution concepts and computational issues.
+In N. Nisan,
+T. Roughgarden, É. Tardos, and V. Vazirani, editors, Algorithmic Game Theory, chapter 1, pages
+3–28. Cambridge University Press Cambridge, 2007.
+C. Wang and M. Zhang. Fairness and efficiency in facility location problems with continuous
+demands.
+In Proceedings of the 20th International Conference on Autonomous Agents and
+MultiAgent Systems, pages 1371–1379, 2021.
+C. Wang, X. Wu, M. Li, and H. Chan. Facility’s perspective to fair facility location problems. In
+Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI), pages 5734–5741,
+2021.
+20
+
+X. Xu, B. Li, M. Li, and L. Duan. Two-facility location games with minimum distance requirement.
+Journal of Artificial Intelligence Research, 70:719–756, 2021.
+H. Zhou, M. Li, and H. Chan. Strategyproof mechanisms for group-fair facility location prob-
+lems. In Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence,
+pages 613–619, 2022.
+21
+
+A
+Proof of Proposition 1
+Proposition 1. The lowest value of α for which an α-IFS solution always exists is α = 2.
+Proof. Consider n agents at ordered locations x1, . . . , xn. For each agent i, we construct an open
+ball Bi with center xi and radius
+1
+2n: Bi = {z|d(z, xi) < |1|
+2n}. Note that the sum of ball lengths is
+1.
+There are two cases:
+• Bi ∩ Bj = ∅ for all i ̸= j. As the sum of ball lengths is 1, the boundaries of two consecutive
+balls intersect, and thus the facility can be placed at the boundary of any ball.
+• Bi ∩ Bj ̸= ∅ for some i ̸= j. In this case, the length of B1 ∩ · · · ∩ Bn is less than 1, hence
+there must be an interval on [0, 1] that is not covered by any ball. The facility can be placed
+within this interval to achieve a 2−IFS solution.
+To see that an α−IFS solution may not exist for α < 2, consider for n = 2 the location profile
+( 1
+4, 3
+4), in which the intersection of the balls encompasses the entire unit interval.
+B
+Proof of Proposition 2
+Proposition 2. The lowest value of α for which an α-UFS solution always exists is α = 2.
+Proof. Consider n agents at m unique ordered locations x1, . . . , xm, and for i ∈ [m], let Si denote
+the group of agents at location xi. For each Si, we construct an open ball Bi with center xi and
+radius |Si|
+2n : Bi = {z|d(z, xi) < |Si|
+2n }. Note that the sum of ball lengths is �m
+i=1
+|Si|
+n = 1.
+There are two cases:
+• Bi ∩ Bj = ∅ for all i ̸= j. As the sum of ball lengths is 1, the boundaries of two consecutive
+balls intersect, and thus the facility can be placed at the boundary of any ball.
+• Bi ∩ Bj ̸= ∅ for some i ̸= j. In this case, the length of B1 ∩ · · · ∩ Bm is less than 1, hence
+there must be an interval on [0, 1] that is not covered by any ball. The facility can be placed
+within this interval to achieve a 2−UFS solution.
+To see that an α−UFS solution may not exist for α < 2, place all n agents at location 1
+2.
+C
+Proof of Theorem 1
+Theorem 1. The price of 2−IFS for utilitarian welfare is 2, and this bound is tight.
+Proof. Suppose without loss of generality that the optimal facility location is 0. We define a
+sufficiently small ϵ > 0 which will be used in specifying certain agent locations, but is negligible
+in the computation of the welfare ratio.
+Case 1: Suppose that the optimal 2−IFS facility location y∗ satisfies y∗ ∈ [xk, xk+1], where
+k ≤ n
+2.
+22
+
+Since y∗ is the optimal 2−IFS facility location, any facility location left of xk must violate
+2−IFS. To see this, suppose there exists some y′ < xk such that y′ satisfies 2−IFS. A facility
+placed at y′ corresponds to a higher utilitarian welfare than y∗ as it is more distant from a majority
+of agents, leading to a contradiction. Furthermore, the welfare ratio
+�
+i u(f ∗
+UW(x), xi)
+maxy∈2IFS(x)
+�
+i u(y, xi) =
+�n
+i=1 xi
+�k
+i=1(y∗ − xi) + �n
+i=k+1(xi − y∗)
+increases with �k
+i=1 xi, so we must maximize x1, . . . , xk whilst ensuring any facility location left
+of xk violates 2−IFS. We therefore deduce that xi = 2i−1
+2n −iϵ for i ∈ {1, . . . , k}, and we therefore
+have
+max
+x∈[0,1]n
+�
+i u(f ∗
+UW(x), xi)
+maxy∈2IFS(x)
+�
+i u(y, xi)
+= max
+x∈[0,1]n
+�n
+i=1 xi
+�k
+i=1(y∗ − xi) + �n
+i=k+1(xi − y∗)
+=
+max
+xk+1,...,xn∈[0,1]
+�k
+i=1( 2i−1
+2n − iϵ) + �n
+i=k+1 xi
+�k
+i=1(y∗ − ( 2i−1
+2n − iϵ)) + �n
+i=k+1(xi − y∗)
+.
+Now for the optimal facility location to be 0, we must have �
+i xi ≥ �
+i(1−xi), or �
+i xi ≥ n
+2. We
+rewrite this as �n
+i=k+1 xi ≥ n
+2 − �k
+i=1 xi. Now the welfare ratio increases as �n
+i=k+1 xi decreases,
+so it is maximized w.r.t xk+1, . . . , xn when we have �n
+i=k+1 xi = n
+2 − �k
+i=1 xi (which results in
+location 1 being tied with 0 as the optimal facility location).
+Substituting this into the welfare ratio, we have
+max
+x∈[0,1]n
+�
+i u(f ∗
+UW(x), xi)
+maxy∈2IFS(x)
+�
+i u(y, xi)
+=
+max
+xk+1,...,xn∈[0,1]
+�k
+i=1( 2i−1
+2n − iϵ) + �n
+i=k+1 xi
+�k
+i=1(y∗ − ( 2i−1
+2n − iϵ)) + �n
+i=k+1(xi − y∗)
+=
+�k
+i=1( 2i−1
+2n − iϵ) + n
+2 − �k
+i=1( 2i−1
+2n − iϵ)
+(2k − n)y∗ − �k
+i=1( 2i−1
+2n − iϵ) + n
+2 − �k
+i=1( 2i−1
+2n − iϵ)
+=
+n/2
+(2k − n)y∗ − 2( 1
+2n + · · · + 2k−1
+2n ) + n
+2 + 2 �k
+i=1 iϵ
+=
+n/2
+(2k − n)y∗ + n
+2 − k2
+n + 2 �k
+i=1 iϵ
+.
+Since k ≤
+n
+2, shifting a facility within (xk, xk+1) slightly to the left causes the total utility to
+weakly increase as there are a greater number of agents who gain utility than those who lose utility.
+Therefore as y∗ is the optimal 2−IFS facility, it must be as close to xk as possible, at y∗ = k
+n − kϵ.
+23
+
+Substituting this into the welfare ratio (and ignoring the negligible ϵ), we have
+max
+x∈[0,1]n
+�
+i u(f ∗
+UW(x), xi)
+maxy∈2IFS(x)
+�
+i u(y, xi) =
+n/2
+(2k − n)y∗ + n
+2 − k2
+n
+=
+n/2
+(2k − n) k
+n + n
+2 − k2
+n
+=
+n/2
+k2
+n − k + n
+2
+.
+Simple calculus shows that the denominator is minimized (w.r.t. k ∈ (0, n
+2]) when k =
+n
+2,
+resulting in a welfare ratio of 2. Therefore when the optimal 2−IFS facility location y∗ satisfies
+y∗ ∈ [xk, xk+1], where k ≤ n
+2, the price of 2−IFS for utilitarian welfare is at most 2.
+Case 2: Suppose that the unique optimal 2−IFS facility location y satisfies y∗ ∈ [xk, xk+1],
+where k > n
+2.8 We can assume uniqueness without loss of generality as a differing facility location
+y† with the same utilitarian welfare as y∗ must satisfy y† ∈ [xj, xj+1], where j ≤ n
+2. Similar to the
+previous case, any facility location right of xk+1 must violate 2−IFS as y∗ is the optimal facility
+location, and we have y∗ = xk+1 −
+1
+2n as it lies to the right of the majority of agents, so shifting it
+leftwards would decrease the utilitarian welfare. We also remark that xk ≤ xk+1 − 1
+n as y∗ satisfies
+2−IFS.
+We apply a sequence of transformations to the location profile where each transformation in-
+creases the welfare ratio. The transformations convert the location profile into an instance of Case
+1 (where the optimal 2−IFS facility location y∗ satisfies y∗ ∈ [xk, xk+1], where k ≤ n
+2).
+The transformations are as follows:
+• If xk−1 (and xk) are at y∗ −
+1
+2n(= xk+1 − 1
+n), shift xk rightwards to x′
+k = y∗ + (y∗ − xk),
+causing the optimal 2−IFS facility location y∗ to remain at the same location and/or satisfy
+Case 1.
+• If xk−1 ∈ (xk+1 − 2
+n, xk+1 − 1
+n), shift xk rightwards to x′
+k = xk−1 + 1
+n, causing the optimal
+2−IFS facility location y∗ to move leftwards to y′ = x′
+k −
+1
+2n(= xk−1 +
+1
+2n) and/or satisfy
+Case 1.
+• If xk−1 ≤ xk+1 − 2
+n, shift xk rightwards to x′
+k = xk+1 − 1
+n + ϵ, causing the optimal 2−IFS
+facility location y∗ to move leftwards to y′ = x′
+k − 1
+2n(= xk+1 − 3
+2n + ϵ) and/or satisfy Case
+1.
+To justify the effect on y∗ from shifting xk, recall that if y∗ still satisfies Case 2 after the shift, then
+it is still the rightmost location satisfying 2−IFS as the majority of agents lie left of y∗. Now if y∗
+changes to a location satisfying Case 1, then by our previous analysis the welfare ratio is at most
+2, so we can disregard this scenario. Suppose that the first dot point occurs i.e. y∗ remains at the
+same location. Recall that the welfare ratio is
+�
+i u(f ∗
+UW(x), xi)
+maxy∈2IFS(x)
+�
+i u(y, xi) =
+�n
+i=1 xi
+�n
+i=1 |y∗ − xi|.
+8We can disregard k = n as we would have y∗ = 1, and as 0 is the optimal facility location, we have �n
+i=1 xi ≥ n
+2 ,
+which corresponds to a welfare ratio under 2.
+24
+
+The optimal facility location is still 0 as the sum of agent locations increases, so the numerator
+strictly increases. The denominator remains the same as xk has moved to an equidistant location
+on the other side of y∗, and all other agents are at the same location. Thus this transformation
+increases the welfare ratio.
+Consider the second and third dot points, i.e., y∗ moves to y′ = x′
+k − 1
+2n. Clearly, the numerator
+increases, so we now show that the denominator decreases. The change in utilitarian welfare from
+the transformation is
+�k−1
+�
+i=1
+(y′ − xi) + (x′
+k − y′) +
+n
+�
+i=k+1
+(xi − y′)
+�
+−
+� k
+�
+i=1
+(y∗ − xi) +
+n
+�
+i=k+1
+(xi − y∗)
+�
+= (k − 1)(y′ − y∗) − (n − k)(y′ − y∗) + (x′
+k + xk) − (y∗ + y′)
+= (y′ − y∗)(2k − n − 1) + (x′
+k + xk) − (y∗ + y′) < 0.
+We know that (y′−y∗)(2k−n−1) < 0 as y′ < y∗ and k ≥ n+1
+2 . We also know that xk ≤ y∗− 1
+2n as
+y∗ satisfies 2−IFS and that y′ = x′
+k − 1
+2n, so from this we deduce that x′
+k +xk < y∗ +y′. Therefore
+the denominator of the welfare ratio decreases, and the transformation increases the welfare ratio.
+As the transformations only require that k > n
+2, we can repeatedly apply them (and update xk
+to be the rightmost agent left of y∗) until we have an instance of Case 1, which has been shown to
+have a maximum welfare ratio of 2. Therefore the theorem statement holds.
+D
+Proof of Theorem 2
+Theorem 2. The price of 2−UFS for utilitarian welfare is 2, and this bound is tight.
+Proof. Similar to the proof of Theorem 1, we suppose without loss of generality that the optimal
+facility location is 0 and define a sufficiently small ϵ > 0. We also divide the proof into two cases:
+Case 1: Suppose that the optimal 2−UFS facility location y∗ satisfies y∗ ∈ [xk, xk+1],
+where k ≤ n
+2. To avoid contradicting the 2−UFS optimality of y∗, the agent locations x1, . . . , xk
+must be arranged such that any location left of xk violates 2−UFS. Furthermore, those agents
+must be located such that �k
+i=1 xi is maximized, as the welfare ratio increases with �k
+i=1 xi. We
+claim that this occurs when all k agents are at the same location of
+k
+2n − ϵ. To see this, suppose
+that among agents {1, . . . , k} that there are m ≤ k unique agent locations, and construct an open
+ball at each unique agent location with radius
+c
+2n, where c is the number of agents at the location.
+Any location within an open ball fails to satisfy 2−UFS, so to maximize the welfare ratio and
+avoid a contradiction, the leftmost open ball must include 0, and the m balls should overlap by
+an ϵ distance (to prevent a 2−UFS facility being placed at the boundary between two balls). An
+example of this with m = k is for i ∈ {1, . . . , k}, xi = 2i−1
+2n − iϵ. Therefore we see that for m ≤ k
+unique agent locations, the sum of agent locations is �k
+i=1 xi =
+1
+2n + · · · + 2k−1
+2n − mϵ, which is
+maximized when all k agents are at
+k
+2n − ϵ.
+As in the 2−IFS proof, we require �n
+i=1 xi ≥
+n
+2 for the optimal facility location to be 0,
+and since the welfare ratio decreases with xk+1 + · · · + xn, we must have �n
+i=1 xi =
+n
+2 and
+25
+
+xk+1 + · · · + xn = n
+2 − (x1 + · · · + xk). Furthermore, as y is the optimal 2−UFS location, it must
+take the leftmost 2−UFS point within [xk, xk+1], which is at k
+n − ϵ. Substituting these expressions
+into the welfare ratio gives
+�
+i u(f ∗
+UW(x), xi)
+maxy∈2UFS(x)
+�
+i u(y, xi) =
+�n
+i=1 xi
+�n
+i=1 |y∗ − xi| =
+n/2
+k2
+n − k + n
+2
+,
+which has been shown in the proof of Theorem 1 to attain a maximum of 2. Therefore in this case,
+the price of 2−UFS for utilitarian welfare is at most 2.
+Case 2: Suppose that the unique optimal 2−UFS facility location y∗ satisfies y∗ ∈ [xk, xk+1],
+where k > n
+2. We can assume uniqueness without loss of generality as a differing facility location
+y† with the same utilitarian welfare as y∗ must satisfy y† ∈ [xj, xj+1], where j ≤ n
+2. We will apply
+a sequence of transformations which weakly increase the welfare ratio and result in a location pro-
+file satisfying Case 1. The transformation works as follows: shift xk rightwards to x′
+k = y∗ +
+1
+2n.
+If there is already an agent at y +
+1
+2n, then instead shift xk rightwards to x′
+k = y∗ +
+1
+2n + ϵk where
+ϵk > 0 is sufficiently small, such that there are no other agents at x′
+k.9 This causes y∗ to remain
+at the same location and/or satisfy Case 1, as if y∗ still satisfies Case 2, it is the rightmost location
+satisfying 2−UFS10, and the location y∗ still satisfies 2−UFS. Furthermore, the optimal facility
+location remains as 0 as the sum of agent locations strictly increases. If y∗ satisfies Case 1 then we
+know the welfare ratio is at most 2 so we disregard this scenario. We now show that otherwise the
+transformation increases the welfare ratio. Recall that the welfare ratio is
+�
+i u(f ∗
+UW(x), xi)
+maxy∈2UFS(x)
+�
+i u(y, xi) =
+�n
+i=1 xi
+�n
+i=1 |y∗ − xi|.
+We know that before the shift, y∗ ≥ xk +
+1
+2n, so the numerator increases by at least 1
+n. The
+denominator either decreases, remains the same, or increases by at most ϵk. Since ϵk is chosen
+to be sufficiently small, we conclude that this transformation causes the welfare ratio to weakly
+increase. By repeatedly applying these transformations and updating xk to be the rightmost agent
+left of y∗, we eventually arrive at a location profile satisfying Case 1, which we know has a welfare
+ratio of at most 2. Hence the price of 2−UFS for utilitarian welfare is at most 2. Lemma 1 also
+implies that the price of 2−UFS for utilitarian welfare is at least 2, and hence the theorem statement
+follows.
+E
+Proof of Proposition 3
+Proposition 3. The price of 2−IFS for egalitarian welfare is 1.
+Proof. We know a 2−IFS solution must always exist, meaning that under any agent location pro-
+file, there exists a facility location such that every agent is at least
+1
+2n distance from the facility. It
+follows immediately that a solution maximizes egalitarian welfare satisfies 2−IFS.
+9Such a location always exists unless xn = 1, y∗ = 1 −
+1
+2n and x1, . . . , xn−1 < y∗, but it can easily be shown
+using �n
+i=1 ≥ n
+2 that such a location profile corresponds to a welfare ratio less than 2.
+10The majority of agents are left of y∗, so shifting y∗ leftwards decreases the utilitarian welfare.
+26
+
+F
+Proof of Proposition 5
+Proposition 5. A pure Nash equilibrium may not exist for f ∗
+2IFS or f ∗
+2UFS.
+Proof. For simplicity, we prove this statement for f ∗
+2IFS. The same arguments hold verbatim for
+f ∗
+2UFS.
+We define a sufficiently small constant ϵ > 0, and consider the location profile x = ( 1
+4−ϵ, 3
+4+ϵ).
+We denote the reported location profile as x′ = (x′
+1, x′
+2), and prove this statement by considering
+cases on agent 1’s reported location x′
+1. Note that under a pure Nash equilibrium, f ∗
+2IFS cannot
+place the facility in the interval [0, 1
+2 − ϵ), as agent 1 can change its report to x′
+1 = 1
+4 − ϵ to strictly
+increase its utility. Similarly, under a pure Nash equilibrium, f ∗
+2IFS cannot place the facility in the
+interval ( 1
+2 + ϵ, 1], as agent 2 can change its report to x′
+2 = 3
+4 + ϵ to strictly increase its utility.
+Case 1 (x′
+1 < 1
+4 − ϵ): If x′
+2 ≤ 3
+4, then f ∗
+2IFS places the facility at 1, and thus this is not a pure
+Nash equilibrium. If x′
+2 > 3
+4, then f ∗
+2IFS places the facility at x′
+1 + 1
+4 < 1
+2 − ϵ, thus this is also not
+a pure Nash equilibrium.
+Case 2 (x′
+1 ≥ 1
+4): If f ∗
+2IFS places the facility at a location strictly right of 0, then this is not a
+pure Nash equilibrium as agent 2 can report x′
+2 = 1 to move the facility to 0, improving its utility.
+If f ∗
+2IFS places the facility at 0, then this is also not a pure Nash equilibrium as agent 1 can change
+its report to x′
+1 = 1
+4 − ϵ to strictly increase its utility.
+Case 3 (x′
+1 ∈ [ 1
+4 − ϵ, 1
+4)): Recall that under a pure Nash equilibrium, f ∗
+2IFS cannot place
+the facility in the interval ( 1
+2 + ϵ, 1]. Due to x′
+1, f ∗
+2IFS also cannot place the facility in the interval
+[0, x′
+1+ 1
+4). If x′
+2 ≤ 3
+4, then f ∗
+2IFS places the facility at 1, and thus this is not a pure Nash equilibrium.
+Suppose that x′
+2 > 3
+4, meaning the facility must be placed in the interval [x′
+1 + 1
+4, x′
+2 − 1
+4]. As f ∗
+2IFS
+places the facility at the leftmost point of the optimal interval, it places the facility at x′
+1 + 1
+4. Thus,
+for any x′
+1 ∈ [ 1
+4 − ϵ, 1
+4), there exists some sufficiently small δ > 0 such that agent 1 can instead
+report x′
+1 + δ to improve its utility, so by definition there does not exist a pure Nash equilibrium.
+In other words, agent 1 can continually shift its reported location asymptotically closer to 1
+4 to
+improve its utility, but from Case 2, we know that x′
+1 cannot reach 1
+4 as otherwise there is no pure
+Nash equilibrium.
+G
+Proof of Theorem 4
+Theorem 4. For any ϵ > 0, a pure ϵ-Nash equilibrium always exists for f ∗
+2IFS.
+Proof. Consider an arbitrary true agent location profile x = (x1, . . . , xn) and sufficiently small
+ϵ > 0. Note that a pure ϵ-Nash equilibrium is also a pure δ-Nash equilibrium, where δ > ϵ.
+Case 1 (n is even):
+Subcase 1a: We first show that if xi ≥
+2i−1
+2n
+for any i ∈ {1, . . . , n
+2}, then a pure ϵ-Nash
+equilibrium exists. Suppose this is the case, and let j = arg mini∈[ n
+2 ]{xi ≥ 2i−1
+2n }. If j = 1 (i.e.
+x1, . . . , xn ≥
+1
+2n), then the reported location profile (1, . . . , 1) is a pure ϵ-Nash equilibrium. This
+is because an agent can only influence the facility position by changing its report to a location in
+[0, 1
+2n), moving the facility from 0 to a point in (0, 1
+n) and reducing its utility.
+If j > 1, then we will show that the reported location profile x′ = (x′
+1, . . . , x′
+n) = ( 1
+2n −
+ϵ, . . . , 2(j−1)−1
+2n
+− (j − 1)ϵ, 1, . . . , 1) is a pure ϵ-Nash equilibrium. Under x′, the facility cannot be
+placed in [0, j−1
+n − (j − 1)ϵ) due to x′
+1, . . . , x′
+j−1, and hence it is placed at j−1
+n − (j − 1)ϵ.
+27
+
+Suppose that for some agent i ∈ {1, . . . , j − 1} changes its report to some x′
+i ̸= 2i−1
+2n − iϵ.
+Under the resulting location profile, the facility moves to a location in [0, 1
+n − 2ϵ] if i = 1 and
+[ i−1
+n − (i − 1)ϵ, i
+n − (i + 1)ϵ] if i ∈ {2, . . . , j − 2}, reducing the agent’s utility. As agent j − 2
+is located at 2(j−2)−1
+2n
+− (j − 2)ϵ, agent j − 1 (who is located at x′
+j−1 = 2(j−1)−1
+2n
+− (j − 1)ϵ) can
+improve its utility by reporting a new location x′′
+j−1 = x′
+j−1 + ϵ1, where ϵ1 < ϵ. This causes the
+facility to shift to the right. However, agent j − 1 cannot improve its utility by more than ϵ, as if it
+reports a location x′′
+j−1 ≥ x′
+j−1 + ϵ, the facility will be placed at j−2
+2n − (j − 2)ϵ, reducing its utility.
+Hence agents 1, . . . , j − 1 cannot improve their utility by more than ϵ by changing their reported
+location.
+Now consider agents j, . . . , n whose true locations satisfy xj, . . . , xn ≥ 2j−1
+2n and have reported
+locations x′
+j, . . . , x′
+n = 1. As at least half of the agents must lie to the right of the facility, the
+facility takes the leftmost location satisfying 2−IFS, even after any agent changes its report.11
+Hence an agent from {j, . . . , n} can only influence the facility location by changing its report to a
+location in ( 2(j−1)−1
+2n
+− (j − 1)ϵ, 2(j−1)+1
+2n
+− (j − 1)ϵ), causing the facility to move to a location in
+( j−1
+n − (j − 1)ϵ, j+1
+n − (j − 1)ϵ). It is easy to see that this strictly reduces the agent’s utility. We
+have shown that no deviation by a single agent can cause its utility to increase by more than ϵ, and
+hence x′ is a pure ϵ-Nash equilibrium. Therefore a pure ϵ-Nash equilibrium exists if xi ≥ 2i−1
+2n for
+any i ∈ {1, . . . , n
+2}.
+Subcase 1b: By symmetry, we see that a ϵ-Nash equilibrium also exists if xi ≤ 2i−1
+2n for any
+i ∈ {n
+2 + 2, . . . , n}. However, the exact symmetric argument does not work for i =
+n
+2 + 1 if
+x n
+2 +1 >
+n+3
+4n as under the reported location profile (0, . . . , 0, n+3
+2n + ( n
+2 − 1)ϵ, . . . , 1 −
+1
+2n + ϵ),
+agent n
+2 + 1 can change its report from x′n
+2 +1 = 0 to n+1
+2n + ( n
+2)ϵ, causing the facility to move from
+n+2
+2n + ( n
+2 − 1)ϵ to
+1
+2n. This is because f ∗
+2IFS breaks ties in favour of the leftmost optimal location,
+and results in increased utility as x n
+2 +1 ∈ ( n+3
+4n , n+1
+2n ].
+We now show that if xi >
+2i−1
+2n
+for all i ∈ {n
+2 + 2, . . . , n} and x n
+2 +1 ∈ ( n+3
+4n , n+1
+2n ], a pure
+ϵ-Nash equilibrium exists. It suffices to assume that xi < 2i−1
+2n for all i ∈ {1, . . . , n
+2}, as otherwise
+we know from Subcase 1a that a pure ϵ-Nash equilibrium exists. We divide this proof to two further
+subcases depending on where x n
+2 +1 is located.
+Subcase 1bi: In this subcase we consider x n
+2 +1 < 1
+2 +
+1
+2n. We claim that x′ = ( 1
+2n − ϵ, 3
+2n −
+2ϵ, . . . , n−1
+2n − ( n
+2)ϵ, 0, n+3
+2n + ( n
+2 − 1)ϵ, . . . , 1 − 1
+2n + ϵ) is a pure ϵ-Nash equilibrium. Under x′, the
+facility is placed at the rightmost point of the only feasible interval, at y′ = n+2
+2n + (n
+2 − 1)ϵ, as
+there is a majority of agents left of the point. If any agent i ∈ {1, . . . , n
+2 − 1} changes its report,
+the facility will move to a location in [ 1
+2n, 1
+n − 2ϵ] if i = 1, and in [ i−1
+n − (i − 1)ϵ, i
+n − (i + 1)ϵ] if
+i ∈ {2, . . . , n
+2 −1}. This reduces agent i’s utility as xi < 2i−1
+2n . We now consider agent n
+2 (reporting
+x′n
+2 = n−1
+2n − ( n
+2)ϵ). Any location right of y′ is not feasible and under x′, there are n
+2 + 2 agent
+reports, including x′n
+2 , left of the facility. Hence agent n
+2 can only influence the facility location by
+changing its report to a point in ( n+1
+2n + ( n
+2 − 1)ϵ, 1], causing the facility to move to the leftmost
+point of the feasible interval, at n−2
+2n − ( n
+2 − 1)ϵ. This reduces its utility as x n
+2 < n−1
+2n . Next we
+consider agent n
+2 + 1 (reporting x′n
+2 +1 = 0), whose report can only change the facility’s location
+within the feasible interval [ 1
+2 − ( n
+2)ϵ, n+2
+2n + ( n
+2 − 1)ϵ]. As we have x n
+2 +1 < 1
+2 +
+1
+2n, it is most
+optimal to have the facility at y′ = n+2
+2n + ( n
+2 − 1)ϵ, achieved by reporting x′n
+2 +1 = 0. Finally, we
+11Recall that f ∗
+2IF S selects the leftmost optimal location if there is a tie.
+28
+
+consider agents n
+2 + 2, . . . , n. Similar to Subcase 1a, agent n
+2 + 2 can improve its utility by strictly
+less than ϵ by reporting a location x′′n
+2 +2 = x′n
+2 +2 − ϵ1, where ϵ1 < ϵ. If ϵ1 ≥ ϵ, the facility is placed
+at n+4
+2n + ( n
+2 − 2)ϵ, reducing the agent’s utility. An agent i ∈ {n
+2 + 3, . . . , n} can only cause the
+facility to be in [ i−1
+n + (i − 1)ϵ, i+1
+n + (i − 2)ϵ]. This results in a reduction of utility as xi > 2i−1
+2n
+for all i ∈ {n
+2 + 2, . . . , n}. As no single agent can improve its utility by more than ϵ by changing
+its report, x′ is a pure ϵ-Nash equilibrium and hence one exists for this subcase.
+Subcase 1bii: In this subcase we consider x n
+2 +1 ≥ 1
+2 +
+1
+2n. We claim that x′ = ( 1
+2n − ϵ, 3
+2n −
+2ϵ, . . . , n−1
+2n −( n
+2)ϵ, n+1
+2n +( n
+2)ϵ, n+3
+2n +( n
+2 −1)ϵ, . . . , 1− 1
+2n +ϵ) is a pure Nash ϵ-equilibrium. Here
+the facility is placed at the leftmost point of the optimal interval, at 1
+2 − ( n
+2)ϵ. By using identical
+reasoning as in Subcase 1bi, it is easy to see that agents 1, . . . , n
+2, and agents n
+2 + 2, . . . , n cannot
+improve their utility by more than ϵ by misreporting. In this subcase, it is agent n
+2 rather than agent
+n
+2 + 2 who can improve its utility by less than ϵ by misreporting slightly to the right. Also, as
+in Subcase 1bi, agent n
+2 + 1 can only change the facility’s location to within the feasible interval
+[ 1
+2 − ( n
+2)ϵ, n+2
+2n + (n
+2 − 1)ϵ], but since we have x n
+2 +1 ≥ 1
+2 +
+1
+2n, their optimal facility location of
+1
+2 − ( n
+2)ϵ is achieved by their report of x′n
+2 +1 = n+1
+2n + ( n
+2)ϵ.
+Subcase 1c: It reminds to consider the subcase where xi < 2i−1
+2n for all i ∈ {1, . . . , n
+2} and
+xi > 2i−1
+2n for all i ∈ {n
+2 + 1, . . . , n}. Under this subcase, we claim that the location profile x′ =
+(x′
+1, . . . , x′
+n) = ( 1
+2n − ϵ, 3
+2n − 2ϵ, . . . , n−1
+2n − ( n
+2)ϵ, 1, . . . , 1) is a pure ϵ-Nash equilibrium. Here, the
+facility is placed at 1
+2 −( n
+2)ϵ. By using the same arguments as in the first subcase, we see that agents
+1, . . . , n
+2 −1 who have reported locations x′
+1 =
+1
+2n−ϵ, x′
+2 =
+3
+2n−2ϵ, . . . , x′n
+2 −1 = n−3
+2n −( n
+2 −1)ϵ have
+no incentive to change their report. Agent n
+2 who reports location x′n
+2 = n−1
+2n − ( n
+2)ϵ can improve
+its utility by strictly less than ϵ, by changing its report to x′′n
+2 = x′n
+2 + ϵ1, where ϵ1 < ϵ. Similar to
+Subcase 1a, if ϵ1 ≥ ϵ, then the facility is placed at n−2
+2n − ( n
+2 − 1)ϵ, reducing the agent’s utility. The
+agents n
+2 + 1, . . . , n who have reported their location as 1 under x′ can only move the facility to a
+location in ( 1
+2 −( n
+2)ϵ, 1
+2 + 1
+n −( n
+2)ϵ) by changing its report to a location in ( n−1
+2n −( n
+2)ϵ, n+1
+2n −( n
+2)ϵ).12
+However as we have x n
+2 +1, . . . , xn > n+1
+2n , this causes their utility to decrease. We have shown that
+under x′, no single agent can cause its utility to increase by more than ϵ by changing its report,
+and hence x′ is a ϵ-Nash equilibrium. By exhaustion of cases, we have shown that a pure ϵ-Nash
+equilibrium always exists under f ∗
+2IFS if n is even.
+Case 2 (n is odd): By using identical reasoning to the case where n is even, we can see that
+if xi ≥
+2i−1
+2n
+for any i ∈ {1, . . . , n−1
+2 , a pure ϵ-Nash equilibrium exists. Specifically, if we let
+j = arg mini∈[ n−1
+2 ]{xi ≥ 2i−1
+2n }, then the pure ϵ-Nash equilibrium is x′ = (1, . . . , 1) if j = 1, and
+x′ = ( 1
+2n − ϵ, . . . , 2(j−1)−1
+2n
+− (j − 1)ϵ, 1, . . . , 1) if j > 1. Furthermore, symmetric reasoning shows
+that if xi ≤ 2i−1
+2n for any i ∈ {n+3
+2 , . . . , n}, a pure ϵ-Nash equilibrium exists. It remains to consider
+the case where xi < 2i−1
+2n for all i ∈ {1, . . . , n−1
+2 } and xi > 2i−1
+2n for all i ∈ {n+3
+2 , . . . , n} (and x n+1
+2
+can be anywhere).
+Subcase 2a: Here we consider the subcase where x n+1
+2
+≥ 1
+2. We claim that x′ = ( 1
+2n − ϵ, 3
+2n −
+2ϵ, . . . , n−2
+2n − ( n−1
+2 )ϵ, 1, n+2
+2n + ( n+3
+2 )ϵ, . . . , 1 −
+1
+2n + ϵ) is a pure ϵ-Nash equilibrium. Here the
+interval of feasible agent locations is [ n−1
+2n − ( n−1
+2 )ϵ, n+1
+2n + ( n+3
+2 )ϵ], and the facility is placed at the
+leftmost point of the interval, at y′ = n−1
+2n − ( n−1
+2 )ϵ, as there is a majority of agents right of the
+interval. Any misreport by agent 1 will cause the facility to be placed in the interval [0, 1
+n − 2ϵ],
+12We note that �
+i x′
+i < n
+2 − 1 + n
+4 ( 1
+2n + n−1
+2n ) = 5n
+8 − 1, which is less than n
+2 if and only if n = 2. However if
+n = 2 it is trivial that x′ is a pure ϵ-Nash equilibrium.
+29
+
+which reduces their utility as x1 <
+1
+2n. Agent i ∈ {2, . . . , n−3
+2 } can only cause the facility to be
+placed in [ i−1
+n − (i − 1)ϵ, i
+n − (i + 1)ϵ], which reduces their utility. A symmetric argument can
+be applied to show that agents n+5
+2 , . . . , n cannot improve their utility by misreporting. Agent n−1
+2
+(who reports x′
+n−1
+2
+= n−2
+2n − ( n−1
+2 )ϵ) can improve its utility by strictly less than ϵ by changing its
+report to x′′
+n−1
+2
+= x′
+n−1
+2
++ ϵ1, where ϵ1 < ϵ. Similar to Subcase 1a, if ϵ1 ≥ ϵ, the agent’s utility will
+be decreased. As the facility takes the leftmost feasible point under x′, agent n+3
+2
+can only change
+the facility location to the rightmost feasible point (at n+3
+2n + ( n+5
+2 )ϵ), by misreporting such that
+there is a majority of agents left of the facility location. This reduces the agent’s utility. Finally,
+it is easy to see that agent n+1
+2
+cannot improve its utility by misreporting: the infeasible regions
+under x′ are a result of the other agent reports, and hence agent n+1
+2
+cannot cause the facility to be
+placed outside of the feasible interval. As x n+1
+2
+≥ 1
+2, the leftmost point of the interval is its most
+optimal facility placement over its possible reports. Therefore x′ is a pure ϵ-Nash equilibrium as no
+agent can improve its utility by more than ϵ by misreporting, and hence a pure ϵ-Nash equilibrium
+exists for this subcase.
+Subcase 2b: In this subcase, x n+1
+2
+< 1
+2 (and xi < 2i−1
+2n for all i ∈ {1, . . . , n−1
+2 } and xi > 2i−1
+2n
+for all i ∈ {n+3
+2 , . . . , n}). By using a symmetric argument as in Subcase 2a, x′ = ( 1
+2n − ϵ, 3
+2n −
+2ϵ, . . . , n−2
+2n −( n−1
+2 )ϵ, 0, n+2
+2n +( n+3
+2 )ϵ, . . . , 1− 1
+2n +ϵ), where the facility is placed at n+1
+2n +( n+3
+2 )ϵ,
+is a pure ϵ-Nash equilibrium.
+In this proof, we have provided a pure ϵ-Nash equilibrium for every possible location profile,
+and hence by exhaustion of cases, a ϵ-pure Nash equilibrium always exists for f ∗
+2IFS.
+H
+Proof of Theorem 5
+Theorem 5. For any ϵ > 0, a pure ϵ-Nash equilibrium always exists for f ∗
+2UFS.
+Proof. In the proof of Theorem 4, we divided all possible agent location profiles into several
+subcases, and provide a pure ϵ-Nash equilibrium for each subcase. We claim for every subcase, the
+pure ϵ-Nash equilibrium we describe in the proof of Theorem 4 is also a ϵ-Nash equilibrium for
+f ∗
+2UFS. First, we remark that every given pure ϵ-Nash equilibrium has the same facility placement
+under f ∗
+2UFS. This can be seen as every pure ϵ-Nash equilibrium has the n agents reporting n
+distinct locations, with the exception of the equilibria where multiple agents report 0 or 1. Under
+these equilibria, the facility takes the rightmost (resp. leftmost) location of the feasible interval, so
+the change to a 2−UFS constraint does not affect the facility placement.
+A simple case by case analysis shows that for each pure ϵ-Nash equilibrium x′ described in the
+proof of Theorem 4, no agent can improve its utility by more than ϵ by changing its report under
+f ∗
+2UFS. The same arguments hold verbatim for f ∗
+2UFS and the constraint of 2−UFS, even when
+accounting for agents being able to change their report to the same location as another agent’s
+report (to widen the ‘infeasible’ ball around the report). We give the following intuition: if agent i
+makes such a report change from x′
+i, this either causes the facility to move to some location near
+x′
+i which has consequently become feasible, or it ‘pushes’ the facility towards xi (such as if the
+facility takes the leftmost feasible location under x′ and agent i changes its report from x′
+i = 1 to
+the rightmost reported location left of the facility). Hence every possible agent location profile has
+a pure ϵ-Nash equilibrium under f ∗
+2UFS.
+30
+
+I
+Proof of Theorem 6
+Theorem 6. For any ϵ ∈ (0, 1
+n), the ϵ-price of anarchy for f ∗
+2IFS and f ∗
+2UFS of utilitarian welfare
+is at least 2n−1+nϵ
+1−nϵ . The price of anarchy is unbounded for ϵ ≥ 1
+n.
+Proof. Suppose for any ϵ ∈ (0, 1
+n) that we have the (true) agent location profile x = ( 1
+2n − ϵ
+2, 1
+2n −
+ϵ
+2, . . . , 1
+2n − ϵ
+2). We show that the location profile x′ = (1, . . . , 1) is a pure ϵ-Nash equilibrium for
+x. Under x′, both f ∗
+2IFS and f ∗
+2UFS place the facility at 0, causing each agent to have
+1
+2n − ϵ
+2 utility.
+An agent can only change the facility position by deviating to a reported location in [0, 1
+2n), causing
+the facility to instead be placed somewhere in (0, 1
+n). This results in the agent receiving a utility
+of u(xi) <
+1
+2n + ϵ
+2, which is an increase of at most ϵ. Since no agent can improve its utility by
+greater than ϵ by misreporting, x′ is a pure ϵ-Nash equilibrium. Now the utilitarian welfare under x
+is n − 1
+2 + nϵ
+2 , whilst under x′ it is 1
+2 − nϵ
+2 (w.r.t. x). Hence the ϵ-price of anarchy is at least 2n−1+nϵ
+1−nϵ
+for ϵ ∈ (0, 1
+n).
+For ϵ ≥
+1
+n, the (true) agent location profile x = (0, . . . , 0) has a corresponding pure ϵ-Nash
+equilibrium of x′ = (1, . . . , 1) which results in each agent having 0 utility. This can be seen as no
+agent can improve its utility by 1
+n or greater, as an agent can only change the facility to a location
+in (0, 1
+n) by changing its report to a location in (0, 1
+2n). As each agent has 0 utility under the pure
+ϵ-Nash equilibrium, the ϵ-price of anarchy is unbounded for ϵ ≥ 1
+n.
+J
+Proof of Theorem 8
+Theorem 8. Mechanism 2 satisfies 2−UFS in expectation.
+Proof. Consider a coalition of |S| agents at location xi and suppose there are n1 agents in [0, 1
+2]
+and n2 agents in ( 1
+2, 1]. The expected distance from the facility is
+E(d(y, xi)) =
+2n1n2 + n2
+2
+n2
+1 + n2
+2 + 4n1n2
+xi +
+n2
+1 + 2n1n2
+n2
+1 + n2
+2 + 4n1n2
+(1 − xi)
+=
+n2
+1 + 2n1n2
+n2
+1 + n2
+2 + 4n1n2
++ xi
+�
+n2
+2 − n2
+1
+n2
+1 + n2
+2 + 4n1n2
+�
+.
+Due to symmetry it suffices to only consider xi ∈ [0, 1
+2], and since E(d(y, xi)) is a linear function
+of x, we further restrict our attention to xi ∈ {0, 1
+2}.
+When xi = 1
+2, E(d(y, xi)) = 1
+2 and hence 2−UFS is satisfied for any coalition of agents at 1
+2.
+31
+
+When xi = 0,
+E(d(y, xi)) =
+n2
+1 + 2n1n2
+n2
+1 + n2
+2 + 4n1n2
+=
+n1(2n2
+1 + 6n1n2 + 4n2
+2)
+2(n2
+1 + n2
+2 + 4n1n2)(n1 + n2)
+>
+n1(n2
+1 + 4n1n2 + n2
+2)
+2(n2
+1 + n2
+2 + 4n1n2)(n1 + n2)
+=
+n1
+2(n1 + n2)
+≥ |S|
+2n .
+Therefore Mechanism 2 satisfies 2−UFS.
+K
+Proof of Lemma 2
+Lemma 2. Consider an arbitrary agent location profile x. For every 2−IFS/UFS randomized
+mechanism that gives positive support to a facility placement between 0 and 1, there exists a
+2−IFS/UFS randomized mechanism that only gives positive support to a facility placement at 0 or
+1 that leads to weakly higher expected utility for each agent.
+Proof. Consider an arbitrary location profile x = (x1, . . . , xn), and suppose for this profile that
+some (2−IFS/UFS) mechanism places the facility at location c ∈ (0, 1) with probability p. If
+instead the mechanism placed the facility at location 1 with probability cp and at location 0 with
+probability p − cp, each agent’s expected distance from the facility would increase. This can be
+seen as for any xi ≤ c,
+cp(1 − xi) + (p − cp)xi = pxi − 2cpxi + cp
+= cp + pxi(1 − c) − cpxi
+≥ cp − cpxi
+≥ p(c − xi),
+and for any xj > c,
+cp(1 − xj) + (p − cp)xj = pxj + cp(1 − xj) − cpxj
+≥ pxj − cpxj
+≥ p(xj − c).
+Therefore this modified mechanism also satisfies 2−IFS/UFS and results in weakly higher ex-
+pected utility for each agent than the original mechanism. By repeatedly applying this modifica-
+tion, any 2−IFS/UFS mechanism that places positive probability on any location between 0 and 1
+can be modified to a 2−IFS/UFS mechanism that only places positive probability on locations 0
+and 1.
+32
+
+L
+Proof of Lemma 3
+Lemma 3. 2-IFS Randomized mechanism is optimal amongst all randomized mechanisms sat-
+isfying 2-IFS in expectation.
+Proof. We first prove by cases that the mechanism satisfies 2-IFS in expectation. Recall that for
+the OFLP, the utilitarian welfare maximizing solution places the facility at either 0 or 1.
+Case 1 (�n
+i=1 xi = n
+2)
+In this case, the facility locations of 0 and 1 are tied for maximizing utilitarian welfare, so
+placing the facility at either location with probability 1
+2 is optimal. The mechanism also satisfies
+2-IFS in expectation as the expected distance of any agent from the facility is 1
+2xi + 1
+2(1 − xi) =
+1
+2 ≥
+1
+2n.
+Case 2 (�n
+i=1 xi > n
+2)
+In this case, the optimal facility location is 0. It is trivial that placing the facility at 0 with
+probability 1 when x1 ≥
+1
+2n is optimal and satisfies 2-IFS, so we consider the subcase where
+x1 <
+1
+2n.
+We first show that the mechanism satisfies 2-IFS in this case. The expected distance between
+x1 and the facility is
+(1 − α)x1 + α(1 − x1) = 2n − 1 − 2nx1
+2n(1 − 2x1) x1 +
+1 − 2nx1
+2n(1 − 2x1)(1 − x1)
+= 2nx1 − x1 − 2nx2
+1 + 1 − x1 − 2nx1 + 2nx2
+1
+2n(1 − 2x1)
+= 1
+2n.
+2-IFS is therefore satisfied for agents x2, . . . , xn as α ≤ 1
+2.
+We now show for this case that the mechanism is optimal amongst all randomized mechanisms
+satisfying 2-IFS in expectation. By Lemma 2, it suffices to only consider mechanisms that can
+only place the facility at 0 or 1.
+Now consider the 2-IFS Randomized mechanism. If α were increased, the utilitarian welfare
+would decrease, and if α were decreased, 2−IFS would be violated for x1, hence α =
+1−2nx1
+2n(1−2x1) is
+optimal and therefore the mechanism is optimal under the constraint of 2-IFS in expectation.
+Case 3 (�n
+i=1 xi > n
+2)
+This case is similar and symmetric to Case 2.
+M
+Proof of Proposition 6
+Proposition 6. Randomized Egalitarian Welfare mechanism is strategyproof in expectation.
+Proof. If all agents are in [0, 1
+2] or all agents are in ( 1
+2, 1], then each agent has at least 1
+2 expected
+utility. Any misreport either causes their expected utility to either stay the same or be reduced to
+1
+2 from the facility being placed at 0 or 1 with probability 1
+2 each. If there is at least one agent
+in each interval, then an agent can only affect the outcome if it is the only agent in its interval
+and it misreports its location to be in the other interval. However this weakly reduces the agent’s
+expected utility, which consequently has an upper bound of 1
+2.
+33
+
+N
+Proof of Theorem 9
+Theorem 9. 2-IFS Randomized mechanism has an approximation ratio of 12
+11 ≈ 1.091.
+Proof. It suffices to consider the case where �n
+i=1 xi >
+n
+2 and x1 <
+1
+2n as the case where
+�n
+i=1 xi >
+n
+2 is symmetric, and the mechanism is optimal for the cases of �n
+i=1 xi =
+n
+2, and
+�n
+i=1 xi > n
+2 and x1 ≥
+1
+2n.
+The approximation ratio of the mechanism is
+max
+x∈Xn
+�
+φ∗(x)
+φ2IFS(x)
+�
+= max
+x∈Xn
+�
+i xi
+(1 − α) �
+i xi + α �
+i(1 − xi)
+= max
+x∈Xn
+�
+i xi
+2n−1−2nx1
+2n(1−2x1)
+�
+i xi +
+1−2nx1
+2n(1−2x1)
+�
+i(1 − xi)
+= max
+x∈Xn
+�
+i xi
+1−2nx1
+2(1−2x1) +
+n−1
+n(1−2x1)
+�
+i xi
+= max
+x∈Xn
+1
+1−2nx1
+2(1−2x1) �
+i xi +
+n−1
+n(1−2x1)
+=
+max
+x1∈[0, 1
+2n )
+1
+1−2nx1
+2(1−2x1)(n−1+x1) +
+n−1
+n(1−2x1)
+=
+max
+x1∈[0, 1
+2n )
+2n(1 − 2x1)(n − 1 + x1)
+n − 2n2x1 + 2(n − 1)(n − 1 + x1).
+In the second last line, we substitute x2, . . . , xn = 1 as the ratio is monotonic increasing with
+�
+i xi. Some optimization programming shows that when n ≥ 3, the ratio is maximized when
+x1 = 0. Substituting x1 = 0 into the ratio gives
+2n2 − 2n
+2n2 − 3n + 2,
+which has a derivative of − 2(n2−4n+2)
+(2n2−3n+2)2. We therefore see our ratio has a maximum turning point at
+x = 2+
+√
+2 and is monotonic decreasing after this point. For integer n ≥ 3, the ratio is maximized
+when either n = 3 or n = 4, and the ratio is equal to 12
+11 ≈ 1.091 for both of these points.
+We now consider the case where n = 2 (and x1 < 1
+4). The ratio becomes
+max
+x1∈[0, 1
+4 )
+2 − 2x1 − 4x2
+1
+2 − 3x1
+= 1
+9(22 − 4
+√
+10)
+≈ 1.039.
+Therefore the mechanism’s welfare ratio is maximized when x1 = 0 and either n = 3 or n = 4,
+taking a value of 12
+11 ≈ 1.091.
+O
+Proof of Lemma 4
+Lemma 3. 2-UFS Randomized mechanism is optimal amongst all randomized mechanisms sat-
+isfying 2−UFS in expectation.
+34
+
+Proof. Similar to the proof of Lemma 3, we prove this statement by cases.
+Case 1 (�m
+i=1 |Si|xi = n
+2)
+When �m
+i=1 |Si|xi =
+n
+2, the facility locations of 0 and 1 are tied for maximizing utilitarian
+welfare, so placing the facility at either location with probability 1
+2 is optimal. The mechanism
+also satisfies 2−UFS in expectation as the expected distance of any agent from the facility is
+1
+2xi + 1
+2(1 − xi) = 1
+2.
+Case 2 (�m
+i=1 |Si|xi > n
+2)
+Note that in this case the optimal facility location is 0. We first show that the mechanism
+satisfies 2−UFS in this case. For a group of agents Si at xi < 1
+2, the expected distance from the
+facility is
+α(1 − xi) + xi(1 − α) ≥ αi(1 − xi) + xi(1 − αi)
+= |Si| − 2nxi
+2n(1 − 2xi)(1 − xi) + 2n − 2nxi − |Si|
+2n(1 − 2xi)
+xi
+= |Si|(1 − 2xi)
+2n(1 − 2xi) = |Si|
+2n .
+By setting |Si| = n, we also see that α ≤ 1
+2, hence 2−UFS is satisfied for any group of agents at
+xj ≥ 1
+2.
+We now show for this case that the mechanism is optimal amongst all randomized mechanisms
+satisfying 2-UFS in expectation. By Lemma 2, it suffices to only consider mechanisms that can
+only place the facility at 0 or 1. Now under the 2−UFS Randomized mechanism, increasing α
+would decrease the utilitarian welfare, and decreasing α would violate 2−UFS for some group of
+agents. Hence the mechanism is optimal under the constraint of 2−UFS in expectation.
+Case 3 (�m
+i=1 |Si|xi < n
+2)
+This case is similar and symmetric to Case 2.
+P
+Proof of Theorem 10
+Theorem 10. 2-UFS Randomized mechanism has an approximation ratio of 2
+7(1 + 2
+√
+2) ≈
+1.09384.
+Proof. Without loss of generality we suppose that �n
+i=1 > n
+2. Let j be the index of the group of
+agents corresponding to α (i.e. αj = max{α1, . . . , αk}).
+35
+
+The approximation ratio of the mechanism is
+max
+x∈Xn
+�
+φ∗(x)
+φ2UFS(x)
+�
+= max
+x∈Xn
+�
+i xi
+(1 − α) �
+i xi + α �
+i(1 − xi)
+= max
+x∈Xn
+�
+i xi
+2n−|Sj|−2nxj
+2n(1−2xj)
+�
+i xi + |Sj|−2nxj
+2n(1−2xj)
+�
+i(1 − xi)
+= max
+x∈Xn
+�
+i xi
+|Sj|−2nxj
+2(1−2xj) +
+n−|Sj|
+n(1−2xj)
+�
+i xi
+= max
+x∈Xn
+1
+|Sj|−2nxj
+2(1−2xj) �
+i xi +
+n−|Sj|
+n(1−2xj)
+=
+max
+xj∈[0, 1
+2 )
+|Sj|∈{1,...,n−1}
+1
+|Sj|−2nxj
+2(1−2xj)(n−|Sj|+|Sj|xj) +
+n−|Sj|
+n(1−2xj)
+=
+max
+xj∈[0, 1
+2 )
+|Sj|∈{1,...,n−1}
+2n(1 − 2xj)(n − |Sj| + |Sj|xj)
+n|Sj| − 2n2xj + 2(n − |Sj|)(n − |Sj| + |Sj|xj)
+= max
+xj∈[0, 1
+2 )
+r∈(0,1)
+2(1 − 2xj)(1 − r + rxj)
+r − 2xj + 2(1 − r)(1 − r + rxj) where r = |Sj|
+n .
+Some optimization programming shows that this ratio is maximized at r = 1 −
+1
+√
+2 and xj = 0,
+taking a value of 2
+7(1 + 2
+√
+2).
+Q
+Proof of Lemma 5
+Lemma 5. For α = 2, there exists an α−UFS facility location y that does not satisfy α−PF.
+Proof. Assume that n = 10 and that we have 2 groups of agents, with the first group of 7 agents
+located at the point c1 = 0.35, and the second group of 3 agents located at the point c2 = 0.55. We
+consider two balls B1 and B2 respectively with centers c1 and c2 and radius |S1|
+2n =
+7
+20 = 0.35 and
+|S2|
+2n =
+3
+20 = 0.15. We set the facility location y at the point 0.71. Since point y is outside of the
+two balls, it satisfies 2-UFS. However, it does not satisfy the 2-PF inequality: d(y, c2) = 0.16 ≱
+|S1|
+20 + |S2|
+20 − r = 0.3.
+R
+Lemma 6 and Proof of Lemma 6
+Here we introduce an auxiliary lemma which will be used in the proof of Theorem 11.
+Lemma 6. The intersection of (I − Bi)’s is not empty.
+36
+
+Proof. We consider two cases:
+• Every open ball Bi, i ∈ [m] lies completely in interval I = [0, 1]. Hence, the boundary
+points of interval I are not in each Bi’s and therefore {0, 1} ∈ ∩m
+i=1(I − Bi).
+• There exists an open ball which does not completely lie in the interval I. Assuming the
+points x1, x2, ..., xm are ordered from left to right, let k be the smallest index such that Bk
+does not completely lie in I. So either 0 ∈ Bk or 1 ∈ Bk. Both end points 0 and 1 can
+not be in Bk, since in this case |Bk| = |Sk|
+n
+> 1. Let us assume 0 ∈ Bk and 1 /∈ Bk, i.e,
+1 ∈ (I − Bk). Now if for every i ∈ [m], we have 1 ∈ (I − Bi), the lemma statement holds.
+Now suppose there exists an open ball Bj such that 1 /∈ (I − Bj), i.e, 1 ∈ Bj. Without
+loss of generality let j be the largest index in which the aforementioned statement holds. We
+consider two cases:
+– Bk ∩ Bj is not an empty set. In this case [0, 1] ⊆ Bk ∪ Bj and |Sk|
+n + |Sj|
+n > 1, which
+can not happen.
+– Bk ∩ Bj is an empty set. We consider the set A := I − (Bk ∪ Bj) and consider two
+cases:
+* A ⊆ ∪j−1
+i=k+1Bi: in this case [0, 1] ⊆ ∪m
+i=1Bi and �m
+i=1
+|Si|
+n
+> 1, which can not
+happen.
+* A ⊈ ∪j−1
+i=k+1Bi. Therefore there exists y ∈ A such that y /∈ ∪j−1
+i=k+1Bi. Also by the
+definition of A, y /∈ (Bk ∪ Bj). For every 1 ≤ i ≤ k − 1, Bi ⊂ Bk holds as i is
+the smallest index such that its corresponding ball contains the point 0. Similarly,
+we have for every j + 1 ≤ i ≤ m, Bi ⊂ Bj. Hence y /∈ Bi for every i ∈ [m], i.e,
+y ∈ (I − Bi) for every i ∈ [m] and y ∈ ∩m
+i=1(I − Bi).
+S
+Proof of Theorem 11
+Theorem 11. A 2-PF solution always exists.
+Proof. Suppose we have m unique agent locations, i.e. m groups of agents. We prove the theorem
+by induction on the number of groups. When all the agents have the same location, i.e, m = 1,
+we can allocate the facility y at the furthest boundary point. This trivially satisfies 2-PF. Now, we
+assume for any k groups of agents where k ≤ m that there exists a 2-PF solution, and we extend
+that for k = m + 1.
+Suppose we have m + 1 groups of agents placed at points c1, c2, . . . , cm+1, which are ordered
+such that c1 ≤ c2 ≤ · · · ≤ cm+1. Let Si denote the group of agents at ci. We set an open ball Bi
+with radius |Si|
+2n , around each center ci. To prove the theorem, we consider several cases.
+• Case 1 (There is no overlap between any two balls, i.e. Bi∩Bj = ∅∀i, j ∈ {1, 2, . . . , m+1}).
+In Lemma 6, we have shown that the intersection of (I − Bi)’s is not empty, so there exists
+a point y outside of every ball Bi where the facility can be placed. Here r is the distance
+between centers ci and cj. If r = 0, then 2-PF is satisfied since we have d(y, ci) ≥
+|Si|
+2n .
+37
+
+Otherwise, since all the balls are disjoint, r is larger than the sum of the radii of Bi and Bj,
+so |Si|
+2n + |Sj|
+2n − r < 0. Hence,
+d(y, ck) ≥ |Si|
+2n + |Sj|
+2n − r
+for k = i, j,
+and thus y satisfies the 2-PF inequality.
+• Case 2 (There exists at least two overlapping balls, i.e., ∃ i, j ∈ {1, 2, . . . , m + 1} s.t.
+Bi ∩ Bj ̸= ∅).
+– Case 2a (There exists one ball that is contained within another ball, i.e., ∃ i, j ∈
+{1, 2, . . . , m + 1} s.t.Bi ⊆ Bj). Without loss of generality, we assume B2 ⊆ B1. Now
+we place all the agents at c2 and c1 together at c1. We set a new ball B
+′ centered at
+c1 with radius |S1|
+2n + |S2|
+2n , which is the summation of the radii of B1 and B2. Now, we
+have m new groups of agents located at the centers c1, c3, . . . , cm+1. By induction, a
+2-PF solution y exists. We claim that y is also a 2-PF solution for m + 1 groups of
+agents located c1, c2, . . . , cm+1. Since y is a 2-PF solution for the m groups of agents
+located at c1, c3, ..., cm+1, y lies outside of every ball, satisfying the 2-PF inequality for
+r = 0. Since y is outside the ball B′, y is outside of balls B1 and B2, therefore we have
+d(y, c1) ≥ |S1|
+2n and d(y, c2) ≥ |S2|
+2n . So y satisfies 2-PF inequalities for r = 0. We now
+set r to be the distance between two centers c1 and c2 (i.e., r = c2 − c1). Since y is
+outside the ball B′ we have d(y, c1) ≥ |S1|
+2n + |S2|
+2n ≥ |S1|
+2n + |S2|
+2n − r, so c1 satisfies the
+PF inequality. To show that the agents at c2 also satisfy the PF inequality, we consider
+2 cases:
+* Case 2ai (Ball B2 does not contain center c1 (see Figure 4)). We denote a :=
+(c2 − c1) − |S2|
+2n as the distance between c1 and the left boundary of B2, b := |S2|
+2n
+as the radius of B2 and c := c1 + |S1|
+2n − c2 − |S2|
+2n as the distance between the right
+boundaries of B1 and B2. In this case, we have
+|S1|
+2n + |S2|
+2n − r = a + 2b + c + b − a − b = 2b + c.
+(1)
+Since y is outside of ball B′, we have d(y, c2) ≥ 2b + c and by (1), d(y, c2) ≥
+|S1|
+2n + |S2|
+2n − r and thus the 2-PF inequality is satisfied.
+* Case 2aii (Ball B2 contains center c1 (see Figure 5)). In this case, the range r is
+smaller than the diameter of B2. We denote a := c2 − c1 as the distance between
+the two centers, b := |S2|
+2n as the radius of B2 and c := c1 + |S1|
+2n − c2 − |S2|
+2n as the
+distance between the right boundaries of B1 and B2. We have
+|S1|
+2n + |S2|
+2n − r = a + b + c + b − a = 2b + c.
+(2)
+Since y is outside of ball B′, we have d(y, c2) ≥ 2b + c and by (2), d(y, c2) ≥
+|S1|
+2n + |S2|
+2n − r and thus the 2-PF inequality is satisfied.
+38
+
+Figure 4: B1 and B′ are open balls centered at c1 and B2 is an open ball centered at c2. The
+variables a, b and c denote the distances between the boundaries of the balls and the centers.
+Figure 5: B1 and B′ are open balls centered at c1 and B2 is an open ball centered at c2. The
+variables a, b and c denote the distances between the boundaries of the balls and the centers.
+39
+
+– Case 2b (There exist two overlapping balls, i.e. ∃ i, j ∈ {1, 2, . . . , m+1} s.t. Bi∩Bj ̸=
+∅, but they are not contained within each other.) Without loss of generality, we assume
+B1 ∩ B2 ̸= ∅. Consider the line segment that connects the left border of B1 to the right
+border of ball B2 and denote the midpoint of this line as c′
+1 := 1
+2(c1 − |S1|
+2n + c2 + |S2|
+2n ).
+We move all the agents at c1 and c2 to point c′
+1 and set a new ball B′ around it with
+radius |S1|
+2n + |S2|
+2n , which is the summation of radii of B1 and B2. Similar to the previous
+subcase, by our inductive assumption there exists a 2-PF solution y for the new m
+groups of agents placed at c′
+1, c3, ..., cm, cm+1. Now we claim that y is a 2-PF solution
+for c1, c2, ..., cm+1 as well. Since y is outside of the ball B′, y is also outside of the
+balls B1 and B2, therefore d(y, c1) ≥ |S1|
+2n and d(y, c2) ≥ |S2|
+2n . So y satisfies the 2-PF
+inequalities for r = 0. We now set r to be the distance between two centers c1 and c2
+(i.e., r = c2 − c1) and consider 3 cases which depend on whether the intersections of
+the balls also contain a center. In each case we show that |S1|
+2n + |S2|
+2n − r is equal to
+the length of intersection of B1 and B2 which denote as |intersection| (and hence the
+2-PF inequality is satisfied).
+* Case 2bi (The intersection between B1 and B2 does not contain centers c1 and c2
+(see Figure 6)). We denote a := c2 − |S2|
+2n − c1 as the distance between c1 and the
+left boundary of B2, b := c1 + |S1|
+2n − (c2 − |S2|
+2n ) as the length of the intersection,
+and c := c2 − |S1|
+2n − c1 as the distance between c2 and the right boundary of B1.
+We have |S1|
+2n + |S2|
+2n − r = a + b + b + c − a − b − c = b = |intersection|.
+Since y is placed outside of ball B′, it is outside of balls B1 and B2. We have
+d(y, ci) ≥ |Si|
+2n ≥ |intersection| = |S1|
+2 + |S2|
+2 − r and thus 2-PF is satisfied.
+Figure 6: B1, B2 and B′ are open balls centered at c1, c2 and c′ respectively. The terms a, b, c and
+|intersection|
+2
+denote the distances between the boundaries of the balls and the centers.
+* Case 2bii (The intersection between B1 and B2 contains one of the centers c1 and
+c2 (see Figure 7)). Without loss of generality suppose the contained center is c2.
+We denote a := c2 − |S2|
+2n − c1 as the distance between c1 and the left boundary of
+B2, b := |S2|
+2n as the radius of B2, and c := c2 − |S1|
+2n − c1 as the distance between
+c2 and the right boundary of B1. We have |S1|
+2n + |S2|
+2n − r = a + b + c + b − a − b =
+40
+
+b + c = |intersection|. Since y is outside of B1, we have
+d(y, c1) ≥ |S1|
+2n = a + b + c ≥ b + c
+= |intersection| = |S1|
+2n + |S2|
+2n − r.
+Now we show d(y, c2) satisfies the 2-PF inequality. Recall B′ is a ball centered
+at the midpoint of the left boundary of B1 and right boundary of B2, with radius
+|S1|
+2n + |S2|
+2n . Also, y lies outside of B′, so the right boundary of B2 has a distance of
+length |intersection|
+2
+from the right boundary of B′. We therefore have
+d(y, c2) ≥ |S2|
+2n + |intersection|
+2
+= b + b + c
+2
+Also, since b ≥ c, we have
+b + b + c
+2
+≥ b + c = |intersection| = |S1|
+2n + |S2|
+2n − r.
+Figure 7: B1, B2 and B′ are open balls centered at c1, c2 and c′ respectively. The terms a, b, c and
+|intersection|
+2
+denote the distances between the boundaries of the balls and the centers.
+* Case 2biii (The intersection between B1 and B2 contains both centers c1 and c2
+(see Figure 8)). We denote a := c2 − |S2|
+2n − c1 as the distance between c1 and the
+left boundary of B2, b := c2 − c1 as the distance between the two centers, and
+c := c2 − |S1|
+2n − c1 as the distance between c2 and the right boundary of B1. We
+have |S1|
+2n + |S2|
+2n −r = b+c+b+a−b = a+b+c = |intersection|. In this case, b+c
+is the radius of ball B1 and a+b is the radius of ball B2. Since the balls B1 and B2
+are not contained within each other, we have b + c > a and a + b > c (see Figure
+8). Like before, B′ is a ball with a center at the midpoint of the left boundary of
+B1 and right boundary of B2 and radius |S1|
+2n + |S2|
+2n , and y lies outside of this ball,
+41
+
+so the boundaries of each ball B1 and B2 have a distance of length |intersection|
+2
+with
+the boundary of B′. We therefore have
+d(y, c1) ≥ b + c + |intersection|
+2
+= b + c + a + b + c
+2
+≥ b + c + a = |intersection| = |S1|
+2n + |S2|
+2n − r.
+Similarly, we can show that y satisfies the 2-PF inequality for center c2.
+d(y, c2) ≥ a + b + |intersection|
+2
+= a + b + a + b + c
+2
+≥ a + b + c = |intersection| = |S1|
+2n + |S2|
+2n − r.
+Hence the facility placement of y satisfies the 2-PF inequalities.
+Figure 8: B1, B2 and B′ are open balls centered at c1, c2 and c′ respectively. The terms a, b, c and
+|intersection|
+2
+denote the distances between the boundaries of the balls and the centers.
+By exhaustion of cases, we have proven the inductive statement, and thus a facility placement that
+satisfies 2-PF always exists.
+T
+Proof of Theorem 12
+Theorem 12. Under the hybrid model, a H-UFS solution always exists.
+Proof. Let nC denote the number of classic agents and nO denote the number of obnoxious agents
+(such that nC + nO = n). Consider an arbitrary agent location profile with m unique classic
+agent locations x1, . . . , xm, and suppose they are ordered such that x1 ≤ . . . xm. We first focus on
+the region of feasible facility locations pertaining to the classic agents’ distance constraints. For
+42
+
+i ∈ [m], let SCi denote the group of classic agents at location xi, and construct a closed ball with
+center xi and radius 1 −
+|SCi|
+n : Bi = {z|d(z, xi) ≤ 1 −
+|SCi|
+n }. By definition, the intersection of the
+closed balls ∩i∈[m]Bi denotes the (continuous) region of feasible facility locations pertaining to the
+classic agents’ distance constraints. From [Aziz et al., 2021], we know this region is non-empty.
+We show that the length of the feasible region ∩i∈[m]Bi is at least n−nC
+n
+by iteratively trans-
+forming the agent location profile to one where all classic agents are at 0 or 1, and showing that
+each transformation weakly decreases the feasible region length. For each ball Bi, there is a (pos-
+sibly empty) left interval of infeasible points Li and a (possibly empty) right interval of infeasible
+points Ri such that Bi = [0, 1] − Li − Ri. We denote the left infeasible interval of points as
+Li = [0, xi − (1 −
+|SCi|
+n )) if xi − (1 −
+|SCi|
+n ) > 0 and as Li = ∅ otherwise. Similarly, we denote the
+right infeasible interval of points as Ri = (xi +(1−
+|SCi|
+n ), 1]. The union of left infeasible intervals
+is therefore ∪i∈[m]Li = [0, maxi∈[m] xi − (1 −
+|SCi|
+n )) if there exists a nonempty Li, and is empty
+otherwise. The union of right infeasible intervals is ∪i∈[m]Ri = (mini∈[m] xi + (1 −
+|SCi|
+n ), 1] if
+there exists a nonempty Ri, and is empty otherwise. Therefore the length of the feasible region is
+min
+�
+min
+i∈[m]
+�
+xi + (1 − |SCi|
+n )
+�
+, 1
+�
+− max
+�
+0, max
+i∈[m]
+�
+xi − (1 − |SCi|
+n )
+��
+.
+By symmetry, we suppose without loss of generality that
+min
+i∈[m]
+�
+xi + (1 − |SCi|
+n )
+�
+≤ 1.
+We consider the following transformation. Let j correspond to the agent location with the largest
+right infeasible interval, i.e.
+j := arg min
+i∈[m]
+�
+xi + (1 − |SCi|
+n )
+�
+,
+and we have xj < 1. If xj > 0, move all agents at xj to 0. We show that this transformation
+weakly decreases the feasible region length: in mini∈[m]
+�
+xi + (1 −
+|SCi|
+n )
+�
+, xi decreases to 0
+and |SCi| weakly increases (it strictly increases if there are already agents at 0). Furthermore,
+the maxi∈[m]
+�
+xi − (1 −
+|SCi|
+n )
+�
+term is unaffected unless the shifted group of agents originally
+corresponded to the maximum value, in which case the xi term decreases by at most the length
+of the shift, and the (1 −
+|SCi|
+n ) term weakly decreases as |SCi| weakly increases. Therefore this
+transformation weakly decreases the feasible region length. Now the agent location with the largest
+right infeasible interval is 0, so our feasible region length is
+(1 −
+|SCj′|
+n
+) − max
+�
+0, max
+i∈[m]
+�
+xi − (1 − |SCi|
+n )
+��
+,
+where j′ corresponds to the location xj′ = 0. If the right boundary of the largest left infeasible
+interval maxi∈[m]
+�
+xi − (1 −
+|SCi|
+n )
+�
+corresponds to the agents at xj′ = 0, then it is at most 0, and
+the feasible region length is (1 −
+|SCj′ |
+n
+) which is at least n−nC
+n
+. We now suppose that this is not the
+case.
+43
+
+We have
+max
+i∈[m]
+�
+xi − (1 − |SCi|
+n )
+�
+≤ max
+i∈[m]
+�
+1 − (1 − |SCi|
+n )
+�
+,
+so the feasible region length is at least
+(1 −
+|SCj′|
+n
+) − max
+�
+0, max
+i∈[m]
+�|SCi|
+n
+��
+.
+Since arg maxi∈[m]
+� |SCi|
+n
+�
+̸= j′, the feasible region length is at least
+1 −
+|SCj′| + |SCk|
+n
+≥ n − nC
+n
+where k ̸= j′.
+We now know the length of the (continuous) feasible region corresponding to the classic agents
+is at least n−nC
+n
+= nO
+n . We now consider the obnoxious agents. Suppose we construct an open ball
+of radius
+|SOi|
+2n
+around each group of obnoxious agents at the same location. Any location within
+one of these open balls is infeasible. The sum of ball lengths is nO
+n , so using a similar argument
+to that in the proof of Proposition 2, we see that a feasible solution with respect to both the classic
+agents’ and obnoxious agents’ distance inequalities always exists.
+44
+
diff --git a/jNE3T4oBgHgl3EQfJAm8/content/tmp_files/load_file.txt b/jNE3T4oBgHgl3EQfJAm8/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18cde5e2932000c5dbcd7623798afb103880d0ff
--- /dev/null
+++ b/jNE3T4oBgHgl3EQfJAm8/content/tmp_files/load_file.txt
@@ -0,0 +1,1650 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf,len=1649
+page_content='Proportional Fairness in Obnoxious Facility Location  Haris Aziz*1, Alexander Lam†1(�), Bo Li‡2, Fahimeh Ramezani§1, and Toby  Walsh¶1  1UNSW Sydney  2Hong Kong Polytechnic University  Abstract  We consider the obnoxious facility location problem (in which agents prefer the facility  location to be far from them) and propose a hierarchy of distance-based proportional fairness  concepts for the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' These fairness axioms ensure that groups of agents at the same  location are guaranteed to be a distance from the facility proportional to their group size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We  consider deterministic and randomized mechanisms, and compute tight bounds on the price  of proportional fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In the deterministic setting, not only are our proportional fairness  axioms incompatible with strategyproofness, the Nash equilibria may not guarantee welfare  within a constant factor of the optimal welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' On the other hand, in the randomized setting,  we identify proportionally fair and strategyproof mechanisms that give an expected welfare  within a constant factor of the optimal welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  1  Introduction  In the obnoxious facility location problem (OFLP), some undesirable facility such as a garbage  dump or an oil refinery is to be located on a unit interval (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' the domain of locations is [0, 1]),  and the agents along the interval wish to be as far from the facility as possible [Feigenbaum et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Ibara and Nagamochi, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2019].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In this problem,  agents have single-dipped preferences, contrasting with the single-peaked preferences of agents in  the classic facility location problem (in which agents prefer to be located as close as possible to  the facility).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The obnoxious facility location problem models many real-world facility placements which  negatively impact nearby agents, such as a prison or a power plant [Church and Drezner, 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Aside from the geographic placement of an obnoxious facility, the OFLP can also be applied to  haris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='aziz@unsw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='au  †alexander.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='lam1@unsw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='au  ‡comp-bo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='li@polyu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='hk  §ramezani81@googlemail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='com  ¶t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='walsh@unsw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='au  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='04340v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='GT]  11 Jan 2023  various collective decision making problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For instance, when agents are averse to their worst  possible social outcomes (represented by their locations), the problem captures issues where a  decision needs to be made on a social policy or a budget composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' When a socially sensitive  or a politically undesirable policy needs to be implemented, the placements of such a policy in the  space of outcomes may need to take equity considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  It is known that placing the facility at one of the interval endpoints maximizes the sum of agent  distances [Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2013], but such a solution may not be ‘proportionally fair’ for the agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  To build intuition, consider the instance depicted in Figure 1 where there are two agents at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1 and  five agents at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The optimal utilitarian solution (which maximizes the sum of agent distances)  places the facility at 0, disproportionately disadvantaging the agents at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1 who are located only  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1 distance from the facility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A facility location of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='45 results in both groups of agents having the  same distance from the facility, and would be considered to be more ‘fair’ in the egalitarian sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  However, it is not proportionally fair: despite having over twice as many agents, the group of agents  at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='8 have the same distance from the facility as the group of agents at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A proportionally fair  solution places the facility at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='3, and results in the distance between a group of agents and the  facility being proportional to the size of the group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In this work, we pursue notions of proportional fairness as a central concern for the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Specifically, we formulate a hierarchy of proportional fairness axioms which guarantee that each  group of agents at the same location are a distance from the facility proportional to the relative size  of the group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' While proportional fairness axioms have been formulated and studied in the classic  facility location problem [Aziz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2021], they have not yet been applied to the OFLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Our pa-  per provides a comprehensive overview of proportionally fair solutions for the obnoxious facility  location problem, examining the interplay between proportional fairness and utilitarian/egalitarian  welfare, and investigating concerns of agent strategic behaviour in both the deterministic and ran-  domized settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='9  1  xx  xxxxx  f∗  UW  2-UFS f∗  EW  Figure 1: OFLP with agent location profile (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='8) represented by x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The facil-  ity locations (represented by •) correspond to a utilitarian outcome, f ∗  UW = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' a proportionally fair  outcome, 2-UFS = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' and an egalitarian outcome, f ∗  EW = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Contributions  We formalize (approximate) proportional fairness concepts such as 2-Individual Fair Share  (2-IFS) and 2-Unanimous Fair Share (2-UFS) in the context of the obnoxious facility loca-  tion problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Several of the definitions are natural adaptations of axioms from fair division  and participatory budgeting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We find tight bounds on the price of 2-IFS and 2-UFS fairness for the objectives of egalitarian  and utilitarian welfare, in both the deterministic and randomized settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  2  Table 1: Table of price of fairness and welfare approximation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Price of Fairness  Best Known Approx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  by 2-UFS SP Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  2-IFS  2-UFS  Deterministic  UW  2  2  (Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 1)  (Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2)  Incompatible  EW  1  n-1  (Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 4)  (Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 3)  (Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 3)  Randomized  UW  12/11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='09384.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='5  (Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 3)  (Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 4)  (Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 8)  EW  1  1  1  (Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 3)  (Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2)  (Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 6)  We prove that our proportional fairness axioms are incompatible with strategyproofness in  the deterministic setting, and give strategyproof randomized mechanisms that satisfy these  proportional fairness axioms in expectation and either have a constant approximation ratio  for utilitarian welfare or are optimal for egalitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  For the deterministic mechanisms that maximize utilitarian welfare under the constraints of  2-IFS and 2-UFS, we prove that a pure ϵ-Nash equilibrium always exists and find linear  bounds on the corresponding ϵ-prices of anarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Finally, we give two possible extensions of our model: the fairness axiom of 2-Proportional  Fairness (2-PF), which is stronger than 2-UFS as it captures proportional fairness concerns  for groups of agents near but not necessarily at the same location, and the hybrid model,  which additionally includes ‘classic’ agents which want to be near the facility (along with  ‘obnoxious’ agents which want to be far away from the facility).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We give existence results  for both extensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Table 1 summarizes some of our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Results lacking proofs are proven in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Related Work  Facility location problems have been explored in the fields of computer science,  economics and operations research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In the latter field, an optimization approach is usually taken,  aiming to minimize transport costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Summaries of results and approaches in the operations research  literature are given by Hekmatfar [2009] and Melo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2009].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' On the other hand, research on  the facility location problem at the intersection of computer science and economics often takes an  approximate mechanism design approach, assuming that agent locations are private information  and finding strategyproof mechanisms which approximate the optimal social cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The seminal  paper on this approach is written by Procaccia and Tennenholtz [2013], and for a recent and com-  prehensive survey on facility location mechanism design, we refer the reader to a survey by Chan  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Our paper lies at the intersection of these two approaches, analyzing the agent strate-  gic behaviour in the optimal mechanisms which satisfy our proportional fairness axioms as well as  identifying a randomized strategyproof and proportionally fair mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The papers most relevant to our research are those that treat the facility as obnoxious: agents  prefer the facility to be as far as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar to the classical facility location problem, early  operations research on the OFLP apply an optimization approach to compute solutions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' a review  3  of these approaches is given by Church and Drezner [2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' There have been several recent papers  on the obnoxious facility location problem that assume agents’ location are private information,  and thus aim to design strategyproof facility location mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Some of the earliest research  applying a mechanism design approach was initiated by Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2011, 2013], in which they  define an agent’s utility as its distance from the facility, and design strategyproof mechanisms  which approximate the optimal utilitarian welfare on the path and network metrics, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Other recent examples of related papers include [Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Feigenbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Ibara  and Nagamochi, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' These papers do not pose or study the fairness concepts  that we explore in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Notions of fairness in various collective decision problems have been widely explored over  the last few decades [Moulin, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Nash, 1950;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Shapley, 1953].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fairness objectives specifically  relevant to the facility location problem include maximum cost/egalitarian welfare (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [Pro-  caccia and Tennenholtz, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2021]) and maximum total/average group cost [Zhou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Rather than optimize/approximate fairness objectives, we focus on solutions enforc-  ing proportional fairness axioms, in which groups of agents with similar or identical preferences  (represented in our setting as their location) have a minimum utility guarantee relative to the group  size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The axioms of proportional fairness that we present stem from several related areas of social  choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Individual Fair Share (IFS) is closely related to the axiom of proportionality proposed by  Steinhaus [1948], and appears in participatory budgeting along with Unanimous Fair Share (UFS)  [Bogomolnaia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Aziz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2019].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Most recently, all of our proportional fairness axioms  have been studied in the classical facility location problem by Aziz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In our paper, we also analyse the loss of efficiency, defined as the price of fairness, of imple-  menting the proportional fairness axioms that we have proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' There have been many recent  results on the price of fairness in various social choice contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For instance, Barman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  [2020], Caragiannis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2012] and Bei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2021] find price of fairness bounds for axioms  such as envy-freeness and equitability in fair division, Bertsimas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2011] look at the price  of proportional fairness in resource allocation, and Michorzewski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2020] explore the areas  of budget division and probabilistic social choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' There has also been work on price of fairness  bounds for the facility location problem, such as when there is a lexicographic minimax objective  [Buzna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Wang and Zhang [2021] assume that facilities have preferences over subsets  of agents, observing the concepts of fairness and efficiency from the facilities’ perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  As strategyproofness is impossible in our deterministic setting, we present results on the ex-  istence of pure Nash equilibria and the price of anarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar models where such results are  proven include a variation of the Hotelling-Downs model where clients have limited attraction  ranges [Feldman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2016], and two-stage facility location games where both facilities and  clients act strategically [Krogmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In the classic facility location problem, Aziz et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2021] characterize the pure Nash equilibria of strictly monotonic facility location mechanisms  satisfying UFS and show that the resulting facility location (under the pure Nash equilibria) is  also guaranteed to satisfy UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In our setting, the price of anarchy is not well-defined for certain  proportionally fair mechanisms, as a pure Nash equilibrium may not exist for a given location pro-  file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As a result, we prove the existence of an approximate equilibrium notion, called pure ϵ-Nash  equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Examples of papers applying this notion to other settings include [Chien and Sinclair,  2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Mylvaganam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2015].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The second half of our paper focuses on the randomized setting to overcome the incompatibility  with strategyproofness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The use of randomized mechanisms to overcome impossibility results is  4  prevalent in many social choice contexts (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', [Brandt, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Aziz, 2019]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Additionally, Aziz  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2022] use a randomized approach in the classic facility location problem to achieve stronger  notions of proportional fairness, providing a unique characterization of universally anonymous  and universally truthful mechanisms satisfying an axiom called Strong Proportionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The use of  randomized mechanisms also results in better approximation ratio/price of fairness bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This is  common in many variants of the facility location problem, such as when agents have fractional or  optional preferences [Fong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2020], or in the hybrid facility location model  [Feigenbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  2  Model  Let N = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n} be a set of agents, and let X := [0, 1] be the domain of locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1 Agent i’s  location is denoted by xi ∈ X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' the profile of agent locations is denoted by x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn) ∈  Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We also assume the agent locations are ordered such that x1 ≤ · · · ≤ xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A deterministic  mechanism is a mapping f : Xn → X from a location profile ˆx ∈ Xn to a facility location y ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We define a randomized mechanism as a probability distribution over deterministic mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Given a facility location y ∈ X, agent i’s utility2 is equal to its distance from the facility u(y, xi) :=  |y − xi|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We are interested in maximizing the objectives of Utilitarian Welfare (UW), defined for a  facility location y and location profile x as the sum of agent utilities �  i u(y, xi), and Egalitarian  Welfare (EW), defined as the minimum agent utility mini u(y, xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Note that the preferences in OFLP can be viewed as single-dipped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In contrast, the classical  facility location problem (FLP) concerns single-peaked preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The underlying model of both  FLP and OFLP is the same except that the agents’ preferences have a different structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Unless specified otherwise, we will state results for the obnoxious facility location problem  (OFLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For the first half of the paper, we will discuss the deterministic setting, and then move to  the randomized setting for the second half.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  3  Proportional Fairness Axioms  In this section, we introduce proportional fairness axioms for the obnoxious facility location prob-  lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1  Individual Fair Share  We first present an adaptation of Individual Fair Share (IFS), the weakest of our proportional fair-  ness axioms (as studied by Aziz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' [2021] in the context of the classic facility location problem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  IFS provides a minimum distance guarantee between each agent and the facility, requiring that each  agent has at least 1  n utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By placing two agents at 1  4 and 3  4, it is easy to see that an IFS solution  may not exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As a result, we turn to approximations of IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  1Our results can be naturally extended to any compact interval on R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  2This definition is consistent with [Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2013].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  5  Definition 1 (α-Individual Fair Share (IFS)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Given a profile of locations x, a facility location y  satisfies α-Individual Fair Share (α-IFS) if  u(y, xi) ≥ 1  αn  ∀i ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We find that the lowest value of α such that an α−IFS solution always exists is α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Intu-  itively, with α = 2, each agent has a ball of radius  1  2n around its location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The sum of ball lengths  is 1, meaning there will always be a 2-IFS solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Furthermore, for any α < 2, the sum of ball  lengths will exceed 1, so an α−IFS solution may not always exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The lowest value of α for which an α-IFS solution always exists is α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  A polynomial time mechanism (which we denote as f ∗  2IFS) that maximizes the utilitarian wel-  fare under the constraint of 2-IFS simply iterates through the endpoints of the intervals which sat-  isfy the constraint and outputs the optimal facility location, breaking ties in favour of the leftmost  optimal location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='2  Unanimous Fair Share  We now present Unanimous Fair Share (UFS), a strengthening and generalization of IFS to groups  of agents at the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Informally, if there are k agents at the same location, then UFS  requires that the facility is placed at least k  n distance from these agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Again, we focus on ap-  proximations of UFS as a UFS solution may not exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 2 (α-Unanimous Fair Share (UFS)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Given a profile of locations x, a facility location y  satisfies α-Unanimous Fair Share (α-UFS) if for any set of agents S with identical location,  u(y, xi) ≥ |S|  αn  ∀i ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Note that α−UFS implies α−IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As with α−IFS, we find that the optimal value of α for which  an α-UFS solution always exists is α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The proof intuition is similar to that of Theorem 1, but  the balls vary in size depending on the number of agents in the group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The lowest value of α for which an α-UFS solution always exists is α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Similar to f ∗  2IFS, a polynomial time mechanism (which we denote as f ∗  2UFS) that computes the  optimal 2-UFS facility location for utilitarian welfare iterates through the endpoints of the intervals  satisfying 2-UFS and outputs the optimal facility location, breaking ties in favour of the leftmost  optimal location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  4  Deterministic Setting  We begin with the deterministic setting, analyzing the price of proportional fairness and agent  strategic behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' All results stated in this section are for the deterministic setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1  Price of Fairness  In this section, we analyze the price of fairness for our (approximate) fairness axioms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='3 Informally,  the price of fairness measures the loss of efficiency from imposing a certain fairness constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We focus on the objectives of utilitarian and egalitarian welfare, defined as the sum of utilities and  the minimum agent utility, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  A fairness property P is a mapping from an agent location profile x ∈ Xn to a (possibly empty)  set of facility locations P(x) ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Every facility location P(x) satisfies the fairness property P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The price of fairness for property P is the worst case ratio between the optimal welfare and the  optimal welfare from a facility location satisfying P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1  Utilitarian Welfare  The utilitarian welfare of an instance is a standard measure of efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Finding the price of our  proportional fairness axioms for utilitarian welfare quantifies the impact on efficiency when the  OFLP system is constrained to be proportionally fair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 3 (Price of Fairness for Utilitarian Welfare).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Let f ∗  UW be the mechanism that returns  the solution maximizing utilitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For utilitarian welfare and fairness property P, we  define the price of fairness as the worst case ratio (over all location profiles) between the optimal  utilitarian welfare and the optimal utilitarian welfare achieved by a facility location satisfying  fairness property P:  max  x∈[0,1]n  �  i u(f ∗  UW(x), xi)  maxy∈P(x)  �  i u(y, xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now move to compute the price of 2-IFS fairness for utilitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Recall that the  solution maximizing utilitarian welfare must be either 0 or 1 [Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2013].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of 2-IFS for utilitarian welfare is at least 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose n is even, and that the agents are located at 1  2n −ϵ,  3  2n −2ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−1  2n − n  2ϵ, n+1  2n + n  2ϵ,  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 2n−3  2n  + 2ϵ, 2n−1  2n  + ϵ for some sufficiently small ϵ (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Under this symmetric  profile, either a facility location of 0 or 1 leads to the maximum utilitarian welfare of n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The only  facility locations satisfying 2-IFS are within the interval [ 1  2 − n  2ϵ, 1  2 + n  2ϵ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Any location in this  interval gives the same utilitarian welfare as there are an equal number of agents on both sides, so  suppose the facility is at 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This corresponds to a utilitarian welfare of n  2  1  2n(1 + 3 + · · · + n − 1) +  2ϵ(1 + 2 + · · · + n  2) = n  4 + ϵn(1 + n  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Taking the limit ϵ → 0 gives a ratio of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The above example places the facility at the midpoint of the optimal median interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The median is known for minimizing sum of distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of 2-IFS for utilitarian welfare is 2, and this bound is tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We next compute bounds on the price of 2-UFS fairness for utilitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of 2-UFS for utilitarian welfare is 2, and this bound is tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  3The price of fairness can also be interpreted as the approximation ratio for the respective optimal mechanism  satisfying the fairness constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  7  0  1  x1  x2  x3  x4  f ∗  UW  f ∗  2IFS  Figure 2: The instance in the proof of Lemma 1 for n = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' f ∗  UW represents the utilitarian wel-  fare maximizing facility placement, whilst f ∗  2IFS represents the facility that maximizes utilitarian  welfare under the constraints of 2-IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The red intervals denote locations that are infeasible under  2-IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  As the price of fairness for utilitarian welfare is the same for both proportional fairness axioms,  it may be desirable to implement 2-UFS in favour of 2-IFS when loss of utilitarian welfare is the  primary concern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='2  Egalitarian Welfare  The egalitarian welfare is an alternate measure of fairness frequently observed in the literature,  focussing on the worst off agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Our price of fairness analysis gives an insight into the tradeoff  between egalitarian welfare/maximin fairness and proportional fairness in the OFLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 4 (Price of Fairness for Egalitarian Welfare).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Let f ∗  EW be the mechanism that returns  the solution maximizing Egalitarian Welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For egalitarian welfare and fairness property P, we  define the price of fairness as the worst case ratio (over all location profiles) between the optimal  egalitarian welfare and the optimal egalitarian welfare achieved by a facility location satisfying  fairness property P:  max  x∈[0,1]n  mini u(f ∗  EW(x), xi)  maxy∈P(x) mini u(y, xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Our first result is that the price of 2-IFS is 1, meaning that a mechanism that maximizes egali-  tarian welfare is guaranteed to satisfy 2-IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The intuition is that since a 2-IFS solution (in which  every agent obtains at least  1  2n utility) always exists, a solution which maximizes the worst off  agent’s utility would therefore result in each agent obtaining at least  1  2n utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of 2-IFS for egalitarian welfare is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  On the other hand, we find that the price of 2-UFS is noticeably worse, taking a linear factor of  n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The intuition behind this is that a coalition of n − 1 agents at one point can ensure that the  facility is distant from their location (and closer to the remaining agent’s location) by a ‘factor’ of  n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of 2-UFS for egalitarian welfare is n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We first prove that the lower bound is n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' It suffices to consider n ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider the  location profile with 1 agent at  1  2n − ϵ and n − 1 agents at n+1  2n + ϵ for sufficiently small ϵ > 0,  (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The optimal solution places the facility at 1 resulting in an egalitarian welfare  of n−1  2n − ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The only 2-UFS solutions are in the interval [ 1  n − ϵ, 1  n + ϵ], and the solution of 1  n + ϵ  results in an egalitarian welfare of  1  2n + 2ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As ϵ → 0, the ratio approaches n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  8  0  1  x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='xn  x1  f ∗  EW  2UFS(x)  Figure 3: The instance in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' f ∗  EW represents the egalitarian welfare maxi-  mizing facility placement, whilst 2UFS(x) represents the interval of facility placements satisfying  2-UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The red intervals denote locations that are infeasible under 2-UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now prove that the upper bound is n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Firstly, it clearly suffices to consider location  profiles where groups contain at most n − 1 agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now suppose there exists such an x where  mini u(f ∗  EW(x), xi) ≥ n−1  2n , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' there is a solution where every agent has at least n−1  2n utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Then  this also satisfies 2-UFS and results in an egalitarian ratio of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore the maximum ratio must  have mini u(f ∗  EW(x), xi) < n−1  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Due to 2-UFS, we also have maxy∈2UFS(x) mini u(y, xi) ≥  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The theorem statement follows from dividing these two terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='2  Incompatibility with Strategyproofness  In mechanism design, the normative property of strategyproofness is often sought as it disincen-  tivizes agents from misreporting their true location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 5 (Strategyproofness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A (deterministic) mechanism f is strategyproof if for every agent  i ∈ N, we have for every xi, x′  i and ˆx−i,  u(f(xi, ˆx−i), xi) ≥ u(f(x′  i, ˆx−i), xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We say that a randomized mechanism is strategyproof in expectation if no agent can improve  its expected utility by misreporting its own location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We note that no strategyproof and deterministic mechanism can achieve any approximation of  IFS (and therefore also UFS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This follows from the characterization of deterministic strategyproof  mechanisms for the OFLP by Feigenbaum and Sethuraman [2015] which we describe below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 6 (Feigenbaum and Sethuraman [2015]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Let f be a deterministic mechanism s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' |Rf  n| =  |{fn(x) : x ∈ Xn}| ≤ 2 for all n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For each n ∈ N, let Rf  n = {αn, βn} s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' βn ≥ αn, and  let mn = αn+βn  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For any n ∈ N, for every profile x ∈ Xn, consider the partition of the agents  Lx = {i ∈ N : xi < mn}, M x = {i ∈ N : xi = mn}, and Ex = {i ∈ N : xi > mn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We say that  f is a midpoint mechanism if it satisfies the following property: for any n ∈ N, let x, y ∈ Xn be  any profiles s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' f(x) = βn and f(y) = αn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If βn > αn, then there exists an agent i which satisfies  one of the following:  (D-1) i ∈ Lx and i ∈ M y  (D-2) i ∈ Lx and i ∈ Ey  (D-3) i ∈ M x and i ∈ Ey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  9  This definition has the following intuition: the mechanism can switch the facility location from  right to left or from left to right only when an agent crosses the midpoint in the opposite direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' There exists no strategyproof mechanism that achieves any approximation of IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Feigenbaum and Sethuraman [2015] proved that the midpoint mechanisms characterize all  strategyproof mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider any profile which locates at least one agent at each point in  Rf  n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Such a mechanism does not satisfy any approximation of IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In other words, for every midpoint mechanism, there exists a location profile where the mech-  anism places the facility at an agent’s location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Since strategyproofness is incompatible with our fairness axioms, we are interested in the per-  formance of proportionally fair mechanisms in our model when accounting for agent strategic  behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Such performance can be quantified by the price of anarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='3  ϵ-Price of Anarchy  In this section, we compute the worst case loss of efficiency by agents misreporting their location  under the mechanisms f ∗  2IFS and f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Recall these are the mechanisms which maximize utilitar-  ian welfare under the constraints of 2-IFS and 2-UFS, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Typically, this efficiency loss  is quantified by the price of anarchy [Koutsoupias and Papadimitriou, 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Nisan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2007],  defined as the worst case ratio between the utilitarian welfare corresponding to the truthful agent  location profile, and the minimum utilitarian welfare corresponding to a pure Nash equilibrium of  reports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Given a (truthful) profile of agent locations x and a deterministic mechanism f,  a pure Nash equilibrium is a profile of reported agent locations x′ = (x′  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , x′  n) such that no  single agent can improve its own utility (with respect to its true location) by changing its reported  location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  However, for f ∗  2IFS and f ∗  2UFS, a pure Nash equilibrium may not necessarily exist, and hence  the price of anarchy is not well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A pure Nash equilibrium may not exist for f ∗  2IFS or f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  As a result, we turn to proving existence of the approximate notion of pure ϵ-Nash equilibria,  and computing the corresponding notion of ϵ-price of anarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 8 (Tardos and Vazirani [2007]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A pure ϵ-Nash equilibrium is a profile of reported agent  locations x′ = (x′  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , x′  n) such that no single agent can improve its own utility (with respect to its  true location) by strictly more than ϵ by changing its reported location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A pure Nash equilibrium  is a pure ϵ-Nash equilibrium where ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For any ϵ > 0, a pure ϵ-Nash equilibrium always exists for f ∗  2IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For any ϵ > 0, a pure ϵ-Nash equilibrium always exists for f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  For a mechanism f, the ϵ-price of anarchy is defined as the worst case ratio (over all location  profiles x) between the utilitarian welfare corresponding to all agents reporting truthfully and the  minimum utilitarian welfare corresponding to agents reporting in a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  10  Definition 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Given f and x, define the set of pure ϵ-Nash equilibria location profiles as ϵ-  Equil(f, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of anarchy for utilitarian welfare is defined as:  ϵ-PoA(f) := max  x∈Xn  �  i u(f(x), xi)  minx′∈ϵ-Equil(f,x)  �  i u(f(x′), xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We must show that the price of anarchy is well-defined by proving that a pure Nash equilibrium  always exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' However, we cannot simply apply the early theorems of [Debreu, 1952;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Glicksberg,  1952;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fan, 1952], which show existence of a pure Nash equilibrium when basic strategy space  conditions are satisfied along with players having continuous and quasiconcave payoff functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='4  This is because the payoff function is neither continuous nor quasiconcave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Nevertheless, we prove that a pure Nash equilibrium always exists for f ∗  2IFS and f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now proceed to find ϵ-price of anarchy bounds for utilitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The same proof  arguments can be applied to find identical bounds for both f ∗  2IFS and f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For any ϵ ∈ (0, 1  n), the ϵ-price of anarchy for f ∗  2IFS and f ∗  2UFS of utilitarian welfare  is at least 2n−1+nϵ  1−nϵ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of anarchy is unbounded for ϵ ≥ 1  n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For any ϵ ∈ (0, 1  2n), the ϵ−price of anarchy for f ∗  2IFS and f ∗  2UFS of utilitarian welfare  is at most  2n  1−2nϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Firstly, we note that under a pure ϵ-Nash equilibrium, each agent must have at least  1  2n − ϵ  utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' To see this, suppose there is a profile of reports x′ where some agent i has strictly less  than  1  2n − ϵ utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By switching its report to its truthful location, agent i can strictly improve  its utility by greater than ϵ, as the facility must be at least  1  2n distance from the agent’s truthful  location, hence x′ is not a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore the utilitarian welfare under a pure  ϵ-Nash equilibrium must be at least 1  2 − nϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now the utilitarian welfare under any instance is at  most n, from all agents being located at 0 and the facility being placed at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The theorem statement  immediately follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  By setting ϵ = 0 in the ϵ-price of anarchy bounds of Theorems 6 and 7, we achieve the follow-  ing result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If a pure Nash equilibrium exists, the price of anarchy for f ∗  2IFS and f ∗  2UFS of utili-  tarian welfare is between 2n − 1 and 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  As the ϵ-price of anarchy of our proportional fairness axioms in the deterministic setting is  linear, it may be desirable to use a randomized, strategyproof mechanism when the agent locations  are private information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We give examples of such mechanisms in the upcoming section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  5  Randomized Mechanisms  By using randomized mechanisms, we can achieve a better price of fairness for 2-IFS and 2-UFS,  and overcome the incompatibility with strategyproofness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We define a randomized mechanism  4A function f is quasiconcave if f(λx + (1 − λ)y) ≥ min{f(x), f(y)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  11  as a probability distribution over deterministic mechanisms, and an agent’s utility as its expected  distance from the facility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In the randomized setting, the optimal approximation of IFS and UFS for which a solution  always exists is α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This can be easily seen by setting 1 agent at 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Our fairness axioms are  adapted as follows:  Definition 10 (α-Individual Fair Share (IFS) in expectation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A mechanism f satisfies α-Individual  Fair Share in expectation (α-IFS in expectation) if for any location profile x,  E[u(f(x), xi)] ≥ 1  αn  ∀i ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 11 (α-Unanimous Fair Share (UFS) in expectation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A mechanism f satisfies α-Unanimous  Fair Share in expectation (α-UFS in expectation) if for any location profile x and any set of agents  S at the same location,  E[u(f(x), xi)] ≥ |S|  αn  ∀i ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='1  Strategyproofness  From Proposition 4, we know that in the deterministic setting, strategyproofness is incompatible  with our proportional fairness axioms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In the randomized setting, the space of mechanisms is much  larger and hence we are able to overcome this impossibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We first consider Mechanism 2 from [Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2013].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Denoting the numbers of agents  located in [0, 1/2] and (1/2, 1] by n1 and n2 respectively, Mechanism 2 places the facility at 0 with  probability α and at 1 with probability (1−α), where α =  2n1n2+n2  2  n2  1+n2  2+4n1n2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This mechanism is known  to be group strategy-proof (in expectation) and 3  2−approximates the utilitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As we will  show, this mechanism satisfies 2-UFS (and therefore also 2-IFS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Mechanism 2 satisfies 2-UFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='2  Egalitarian Welfare  We now provide some results on egalitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Specifically, we give a randomized, strate-  gyproof mechanism which maximizes egalitarian welfare subject to the constraints of 2-IFS and  2-UFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Randomized Egalitarian Welfare mechanism  If all agents are in [0, 1  2], place the facility at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If all agents are in ( 1  2, 1], place the facility at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Otherwise, place the facility at 0 with probability 1  2 and at 1 with probability 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  By considering cases, it is easy to see that this mechanism is strategyproof in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Randomized Egalitarian Welfare mechanism is strategyproof in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  12  Before analyzing the optimality and approximation ratio of this mechanism, we prove a lemma  that shows that in the randomized setting, it suffices to consider mechanisms which can only place  the facility at 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider an arbitrary agent location profile x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For every 2-IFS/UFS randomized mech-  anism that gives strictly positive probability to a facility placement between 0 and 1, there exists a  2-IFS/UFS randomized mechanism that only gives positive support to a facility placement at 0 or  1 that leads to weakly higher expected utility for each agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now proceed to prove that Randomized Egalitarian Welfare mechanism is egalitarian  welfare-optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The Randomized Egalitarian Welfare mechanism is optimal for egalitarian wel-  fare and satisfies 2-UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The cases where all agents are in [0, 1  2] and all agents are in ( 1  2, 1] are trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now examine the case where both intervals have at least one agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' An agent at xi has  1  2xi + 1  2(1−xi) = 1/2 expected distance from the facility, hence this mechanism satisfies 2-UFS in  expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By Lemma 2, it suffices to only consider mechanisms which can only place the facility  at 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose that instead of having 1  2 probability of placing the facility at either endpoint, we  place the facility at 1 with 1  2 + p probability and at 0 with 1  2 − p probability, where p ∈ (0, 1  2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The  expected utility of the rightmost agent is xn( 1  2 − p) + (1 − xn)( 1  2 + p) = 1  2 + p(1 − 2xn) < 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By  a symmetric argument, if the facility was placed at 1 with 1  2 − p probability and at 0 with 1  2 + p  probability, the expected utility of the leftmost agent would be strictly less than 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence, our  mechanism is optimal in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In other words, the approximation ratio of this mechanism for egalitarian welfare is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Recall  that the price of fairness can be interpreted as the approximation ratio of the respective optimal  mechanism that satisfies the fairness constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This leads us to the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In the randomized setting, the price of fairness of 2-UFS for egalitarian welfare is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  This is in stark contrast to the deterministic setting where the respective price of fairness is  n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='3  2-IFS  We now analyze utilitarian welfare, beginning with the axiom of 2-IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider the randomized  mechanism below which maximizes the utilitarian welfare subject to the 2-IFS constraint:  2-IFS Randomized mechanism  If �n  i=1 xi = n  2, place the facility at 0 with probability 1  2 and at 1 with probability 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If �n  i=1 xi > n  2,  – If x1 ≥  1  2n, place the facility at 0 with probability 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  – If x1 <  1  2n, place the facility at 0 with probability 1 − α, and at 1 with probability α,  where α =  1−2nx1  2n(1−2x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  13  If �n  i=1 xi < n  2,  – If xn ≤ 1 −  1  2n, place the facility at 1 with probability 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  – If xn > 1 −  1  2n, place the facility at 0 with probability 1 − β, and at 1 with probability  β, where β =  1−2nxn  2n(1−2xn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The intuition behind this mechanism is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' When �n  i=1 xi =  n  2, both facility locations  of 0 and 1 are tied in terms of maximizing utilitarian welfare, and by placing the facility at either  location with probability 1  2, we achieve 2-IFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' When �n  i=1 xi >  n  2, the optimal  facility location is 0, so the mechanism places the facility there if it does not violate 2-IFS for  any agent, else it also places the facility at 1 with the minimum probability that ensures 2-IFS is  ensured for all agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The case where �n  i=1 xi < n  2 is similar and symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Our proof of the mechanism’s welfare-optimality is based on its intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2-IFS Randomized mechanism is optimal for utilitarian welfare amongst all random-  ized mechanisms satisfying 2-IFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now prove a tight, constant approximation ratio for this mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2-IFS Randomized mechanism has an approximation ratio for utilitarian welfare of  12  11 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='091.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  This leads to the following price of fairness result for 2-IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In the randomized setting, the price of fairness of 2-IFS for utilitarian welfare is  12  11 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='091.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='4  2-UFS  We now move to analyze the axiom of 2-UFS in the context of utilitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As in the previ-  ous subsection, we begin by describing a randomized mechanism which maximizes the utilitarian  welfare subject to the 2-UFS constraint:  2-UFS Randomized mechanism  Order the m unique agent locations so that x1 is the smallest agent location and xm is the  largest agent location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Let S1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , Sm denote the groups of agents at the m unique agent locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If �m  i=1 |Si|xi = n  2, place the facility at 0 with probability 1  2 and at 1 with probability 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If �m  i=1 |Si|xi > n  2,  – Let k denote the index of the largest unique agent location satisfying xk < 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  – For i in {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , k}, set αi = |Si|−2nxi  2n(1−2xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  – Letting α = max{α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , αk}, place the facility at 0 with probability 1 − α and at 1  with probability α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  14  If �m  i=1 |Si|xi < n  2,  – Let k denote the index of the smallest unique agent location satisfying xk > 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  – For i in {k, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , m}, set αi = |Si|−2nxi  2n(1−2xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  – Letting α = min{αk, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , αm}, place the facility at 0 with probability 1 − α and at 1  with probability α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  This mechanism is similar to the 2-IFS Randomized mechanism, but we must now iterate  through the groups of agents to find the optimal value of α that guarantees 2-UFS for all agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Specifically, if �m  i=1 |Si|xi > n  2, then αi denotes the smallest probability weight on location 1 such  that 2-UFS is achieved for Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence by setting α to be the largest αi, we achieve 2-UFS for all  agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Again, our proof of this mechanism’s optimality is based on the aforementioned intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2-UFS Randomized mechanism is optimal for utilitarian welfare amongst all random-  ized mechanisms satisfying 2-UFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Surprisingly, imposing the stronger fairness axiom of 2-UFS as opposed to 2-IFS has a minimal  effect on the welfare-optimal mechanism’s approximation ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2-UFS Randomized mechanism has an approximation ratio of 2  7(1 + 2  √  2) ≈  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='09384.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  From Theorem 10, we have the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In the randomized setting, the price of fairness of 2-UFS for utilitarian welfare is  2  7(1 + 2  √  2) ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='09384.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  6  Extension 1: Proportional Fairness  In our analyses of price of fairness and randomized mechanisms, we have considered 2-IFS and  2-UFS, which give minimum distance guarantees for individual agents and groups of agents at the  same location, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' One downside of the 2-UFS definition is that agents located near each  other but not at the same location are considered to be in separate groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' An axiom which accounts  for groups of agents located relatively close to each other is Proportional Fairness (PF), from [Aziz  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As with IFS and UFS, a PF solution may not exist so we define approximate α−PF  as follows:  Definition 12 (α-PF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Given a profile of locations x, a facility location y satisfies α-PF if for any  set of agents S within range r := maxi∈S{xi} − mini∈S{xi},  u(y, xi) ≥ 1  α(|S|/(n)) − r  ∀i ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Note that α−PF implies α−UFS, and therefore also implies α−IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  However, α−UFS does not imply α−PF, hence α−PF is a stronger notion than α−UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For α = 2, there exists an α−UFS facility location y that does not satisfy α−PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  15  It follows from Theorem 2 that the smallest value of α for which an α-PF solution exists for all  location profiles is greater or equal than 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We now show that a 2-PF solution always exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A 2-PF solution always exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof Sketch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We prove the theorem by induction on the number of groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose we have m  groups of agents where each group consists of agents at the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' When m = 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e, all  the agents are at the same point, 2-PF existence follows from 2-UFS existence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now, we assume  for any k groups of agents where k ≤ m that there exists a 2-PF solution and we extend that for  k = m + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Suppose we have m + 1 groups of agents placed at centers c1, c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', cm+1 which are ordered  from left to right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Set a ball Bi with radius |Si|  2n around each center ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We consider several cases  based on the intersection of balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If all the balls are disjoint, it can be shown there exists a point  y ∈ [0, 1] which lies outside the union of balls B1 ∪ · · · ∪ Bm+1, satisfying the 2-PF inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If there exists two balls, say B1 and B2, intersecting each other, they are merged with the agents  placed at a new center c′  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We then set a ball B′  1 centered at c′  1 with radius |S1|  2n + |S2|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now, we  have m groups of agents placed at c′  1, c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , cm+1, and from our inductive assumption, we know  a 2-PF solution exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Thus, 2-PF is the optimal approximation of PF for the obnoxious facility location problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  7  Extension 2: Hybrid Model  In the hybrid model, agents either want to be located close to the facility (as in the classic facility  location model), or wish to be located far away from the facility (as in our obnoxious facility  location model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Such a model has several real-world applications such as the placement of schools  or religious places of worship;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' families with children or religious people would want to live near  the facility for convenience, whilst others would want to be far from the facility due to the increased  noise and traffic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In our model, we say an agent is type C if it is a classic agent and prefers to be  closer to the facility, and an agent is type O if it is an obnoxious agent and prefers to be further  away from the facility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='5 We denote the set of classic agents as NC and the set of obnoxious agents  as NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  A type C agent has utility u(y, xi) = 1 − d(y, xi) and a type O agent has utility u(y, xi) =  d(y, xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='6  When defining IFS and UFS in the hybrid model, we use definitions consistent with [Aziz  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2021] and this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Our definition of Hybrid-Individual Fair Share (H-IFS) provides an  appropriate distance guarantee for each agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 13 (Hybrid-Individual Fair Share (H-IFS)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Given a profile of locations x, a facility  location y satisfies Hybrid-Individual Fair Share (H-IFS) if for all i ∈ NC,  u(y, xi) ≥ 1  n  or, equivalently,  d(y, xi) ≤ 1 − 1  n,  5Our model is based on the model presented by Feigenbaum and Sethuraman [2015].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  6This choice of utility function is adapted from [Feigenbaum and Sethuraman, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Aziz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We refer  the reader to those papers for a justification of the utility model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  16  and for all i ∈ NO,  u(y, xi) ≥ 1  2n  or, equivalently,  d(y, xi) ≥ 1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  When defining UFS, we aim to capture proportional fairness guarantees for subsets of agents  of the same type at the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider every subset S ⊆ N of agents at the same location,  where S = SC ∪ SO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' SC denotes the agents of S that are of type C, and SO denotes the agents of  S that are of type O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Definition 14 (Hybrid-Unanimous Fair Share (H-UFS)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Given a profile of locations x such that a  subset of Sj ⊆ N agents7 share the same type and location, a facility location y satisfies Hybrid-  Unanimous Fair Share (H-UFS) if for all i ∈ SC,  u(y, xi) ≥ |SC|  n  or, equivalently,  d(y, xi) ≤ 1 − |SC|  n ,  and for all i ∈ SO,  u(y, xi) ≥ |SO|  2n  or, equivalently,  d(y, xi) ≥ |SO|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Example 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose there are n − k type C agents and k type O agents, all at the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The facility needs to be between  k  2n and k  n distance from the group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Although our definitions have a discrepancy in utility functions between the classic and obnox-  ious agents, we have specified them to be consistent with related literature and to be the optimal  bounds such that a solution is guaranteed to exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Furthermore, existence of a H-UFS solution  under our definition implies existence of a solution under a weaker definition where a set SC of  classic agents at the same location instead have a utility guarantee of |SC|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theorem 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Under the hybrid model, a H-UFS solution always exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  8  Discussion  In this paper we have formulated proportional fairness axioms for the obnoxious facility location  problem, and given welfare-optimal deterministic and randomized mechanisms satisfying these  axioms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In both the deterministic and randomized setting, we prove tight price of fairness bounds  for 2-IFS and 2-UFS, for the objectives of utilitarian and egalitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' These correspond  to the approximation ratios of the respective welfare-optimal mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For the deterministic  utilitarian welfare-optimal mechanisms, we also prove existence of pure ϵ-Nash equilibria and  linear ϵ-price of anarchy bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We also give a randomized, strategyproof mechanism satisfying  2-UFS with a constant utilitarian approximation ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  There are several future directions to this work, such as those stemming from our proposed ex-  tensions of 2-PF and the hybrid model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For example, the price of anarchy and price of fairness for  these two extensions could be computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We could also supplement our price of anarchy results  7j ∈ {C, O}  17  with bounds on the price of stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Further extensions to the price of fairness results could in-  volve different objective and utility functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' It is also worth analyzing the Nash equilibria of the  randomized utilitarian welfare-optimal mechanisms, as they are not strategyproof in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Although our proportional fairness axioms are incompatible with strategyproofness in the deter-  ministic setting, we may consider weaker notions of strategyproofness which may be compatible  with our fairness properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Acknowledgements  We would like to acknowledge the helpful feedback and suggestions from Minming Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  References  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Aziz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Bogomolnaia, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Moulin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fair mixing: the case of dichotomous preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In Proceedings of the 2019 ACM Conference on Economics and Computation, pages 753–781,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Aziz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Lam, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Lee, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Walsh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Strategyproof and proportionally fair facility location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  CoRR, abs/2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='01566, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Aziz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Lam, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suzuki, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Walsh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Random rank: The one and only strategyproof and  proportionally fair randomized facility location mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='14798,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Aziz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A probabilistic approach to voting, allocation, matching, and coalition formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In The  Future of Economic Design, pages 45–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Springer, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Barman, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Bhaskar, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Optimal bounds on the price of fairness for indivisible goods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In International Conference on Web and Internet Economics, pages 356–369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Bei, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Lu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Manurangsi, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suksompong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of fairness for indivisible goods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Theory of Computing Systems, 65(7):1069–1093, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Bertsimas, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Farias, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Trichakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Operations research, 59(1):17–  31, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Bogomolnaia, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Moulin, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Stong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Collective choice under dichotomous preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Journal of Economic Theory, 122(2):165–184, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Brandt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Rolling the dice: Recent results in probabilistic social choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Trends in computational  social choice, pages 3–26, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Buzna, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Koháni, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Janáˇcek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' An approximation algorithm for the facility location problem  with lexicographic minimax objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Journal of Applied Mathematics, 2014, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Caragiannis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Kaklamanis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Kanellopoulos, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Kyropoulou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The efficiency of fair divi-  sion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Theory of Computing Systems, 50(4):589–610, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  18  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Chan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Filos-Ratsikas, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Mechanism design for facility location  problems: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In 30th, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Yuan, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Facility location games with  optional preference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Theoretical Computer Science, 847:185–197, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Cheng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Yu, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Mechanisms for obnoxious facility game on a path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Combinato-  rial Optimization and Applications - 5th International Conference, COCOA 2011, Zhangjiajie,  China, August 4-6, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Proceedings, pages 262–271, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Cheng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Yu, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Strategy-proof approximation mechanisms for an obnoxious  facility game on networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 497:154–163, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Cheng, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Han, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Yu, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Strategy-proof mechanisms for obnoxious facility game  with bounded service range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Comb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 37(2):737–755, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Chien and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Sinclair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Convergence to approximate nash equilibria in congestion games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Games  and Economic Behavior, 71(2):315–327, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Church and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Drezner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Review of obnoxious facilities location problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Computers &  Operations Research, 138:105468, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Debreu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A social equilibrium existence theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Proceedings of the National Academy of  Sciences, 38(10):886–893, 1952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fixed-point and minimax theorems in locally convex topological linear spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Proceed-  ings of the National Academy of Sciences of the United States of America, 38(2):121, 1952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Feigenbaum and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Sethuraman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Strategyproof mechanisms for one-dimensional hybrid and  obnoxious facility location models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Incentive and Trust in E-Communities, Papers from the  2015 AAAI Workshop, Austin, Texas, USA, January 25, 2015, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Feigenbaum, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Sethuraman, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Wang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Zou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Strategic facility location problems  with linear single-dipped and single-peaked preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Autonomous Agents and Multi-Agent  Systems, 34(2):1–47, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Feldman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fiat, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Obraztsova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Variations on the hotelling-downs model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Thirtieth  AAAI Conference on Artificial Intelligence, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Lu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Todo, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Yokoo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Facility location games with fractional  preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Proceedings of the AAAI Conference on Artificial Intelligence, volume 32, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Glicksberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A further generalization of the kakutani fixed point theorem, with application  to nash equilibrium points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Proceedings of the American Mathematical Society, 3(1):170–174,  1952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hekmatfar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Facility location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Physica-Verlag, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  19  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Ibara and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Nagamochi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Characterizing mechanisms in obnoxious facility game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Combina-  torial Optimization and Applications - 6th International Conference, COCOA 2012, Banff, AB,  Canada, August 5-9, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Proceedings, volume 7402 of Lecture Notes in Computer Science,  pages 301–311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Springer, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Koutsoupias and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Papadimitriou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Worst-case equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Annual Symposium on Theoretical  Aspects of Computer Science, pages 404–413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Springer, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Krogmann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Lenzner, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Molitor, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Skopalik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Two-stage facility location games with  strategic clients and facilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Proceedings of the Thirtieth International Joint Conference on  Artificial Intelligence, pages 292–298, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Melo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Nickel, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Saldanha-Da-Gama.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Facility location and supply chain management–  a review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' European Journal of Operational Research, 196(2):401–412, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Michorzewski, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Peters, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Skowron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Price of fairness in budget division and probabilistic  social choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34,  pages 2184–2191, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Moulin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fair division and collective welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' MIT press, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Mylvaganam, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Sassano, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Astolfi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Constructive ϵ-nash equilibria for nonzero-sum dif-  ferential games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' IEEE Transactions on Automatic Control, 60(4):950–965, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Nash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The bargaining problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Econometrica, 18(2):155–162, 1950.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Nisan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Roughgarden, É.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Tardos, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Vazirani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Algorithmic Game Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Cambridge  University Press, New York, NY, USA, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Procaccia and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Tennenholtz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Approximate mechanism design without money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In 14th,  pages 1–26, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Shapley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A Value for n-Person Games, pages 143–164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Princeton University Press, Princeton,  NJ, 1953.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Steinhaus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The problem of fair division.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Econometrica, 16:101–104, 1948.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Tardos and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Vazirani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Basic solution concepts and computational issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Nisan,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Roughgarden, É.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Tardos, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Vazirani, editors, Algorithmic Game Theory, chapter 1, pages  3–28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Cambridge University Press Cambridge, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Wang and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Fairness and efficiency in facility location problems with continuous  demands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In Proceedings of the 20th International Conference on Autonomous Agents and  MultiAgent Systems, pages 1371–1379, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Wu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Chan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Facility’s perspective to fair facility location problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In  Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI), pages 5734–5741,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  20  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Xu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Duan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Two-facility location games with minimum distance requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Journal of Artificial Intelligence Research, 70:719–756, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Zhou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Li, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Chan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Strategyproof mechanisms for group-fair facility location prob-  lems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence,  pages 613–619, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  21  A  Proof of Proposition 1  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The lowest value of α for which an α-IFS solution always exists is α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider n agents at ordered locations x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For each agent i, we construct an open  ball Bi with center xi and radius  1  2n: Bi = {z|d(z, xi) < |1|  2n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Note that the sum of ball lengths is  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  There are two cases:  Bi ∩ Bj = ∅ for all i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As the sum of ball lengths is 1, the boundaries of two consecutive  balls intersect, and thus the facility can be placed at the boundary of any ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Bi ∩ Bj ̸= ∅ for some i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In this case, the length of B1 ∩ · · · ∩ Bn is less than 1, hence  there must be an interval on [0, 1] that is not covered by any ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The facility can be placed  within this interval to achieve a 2−IFS solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  To see that an α−IFS solution may not exist for α < 2, consider for n = 2 the location profile  ( 1  4, 3  4), in which the intersection of the balls encompasses the entire unit interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  B  Proof of Proposition 2  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The lowest value of α for which an α-UFS solution always exists is α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider n agents at m unique ordered locations x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xm, and for i ∈ [m], let Si denote  the group of agents at location xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For each Si, we construct an open ball Bi with center xi and  radius |Si|  2n : Bi = {z|d(z, xi) < |Si|  2n }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Note that the sum of ball lengths is �m  i=1  |Si|  n = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  There are two cases:  Bi ∩ Bj = ∅ for all i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As the sum of ball lengths is 1, the boundaries of two consecutive  balls intersect, and thus the facility can be placed at the boundary of any ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Bi ∩ Bj ̸= ∅ for some i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In this case, the length of B1 ∩ · · · ∩ Bm is less than 1, hence  there must be an interval on [0, 1] that is not covered by any ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The facility can be placed  within this interval to achieve a 2−UFS solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  To see that an α−UFS solution may not exist for α < 2, place all n agents at location 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  C  Proof of Theorem 1  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of 2−IFS for utilitarian welfare is 2, and this bound is tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose without loss of generality that the optimal facility location is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We define a  sufficiently small ϵ > 0 which will be used in specifying certain agent locations, but is negligible  in the computation of the welfare ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 1: Suppose that the optimal 2−IFS facility location y∗ satisfies y∗ ∈ [xk, xk+1], where  k ≤ n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  22  Since y∗ is the optimal 2−IFS facility location, any facility location left of xk must violate  2−IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' To see this, suppose there exists some y′ < xk such that y′ satisfies 2−IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A facility  placed at y′ corresponds to a higher utilitarian welfare than y∗ as it is more distant from a majority  of agents, leading to a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Furthermore, the welfare ratio  �  i u(f ∗  UW(x), xi)  maxy∈2IFS(x)  �  i u(y, xi) =  �n  i=1 xi  �k  i=1(y∗ − xi) + �n  i=k+1(xi − y∗)  increases with �k  i=1 xi, so we must maximize x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xk whilst ensuring any facility location left  of xk violates 2−IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We therefore deduce that xi = 2i−1  2n −iϵ for i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , k}, and we therefore  have  max  x∈[0,1]n  �  i u(f ∗  UW(x), xi)  maxy∈2IFS(x)  �  i u(y, xi)  = max  x∈[0,1]n  �n  i=1 xi  �k  i=1(y∗ − xi) + �n  i=k+1(xi − y∗)  =  max  xk+1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=',xn∈[0,1]  �k  i=1( 2i−1  2n − iϵ) + �n  i=k+1 xi  �k  i=1(y∗ − ( 2i−1  2n − iϵ)) + �n  i=k+1(xi − y∗)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Now for the optimal facility location to be 0, we must have �  i xi ≥ �  i(1−xi), or �  i xi ≥ n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We  rewrite this as �n  i=k+1 xi ≥ n  2 − �k  i=1 xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now the welfare ratio increases as �n  i=k+1 xi decreases,  so it is maximized w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t xk+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn when we have �n  i=k+1 xi = n  2 − �k  i=1 xi (which results in  location 1 being tied with 0 as the optimal facility location).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Substituting this into the welfare ratio, we have  max  x∈[0,1]n  �  i u(f ∗  UW(x), xi)  maxy∈2IFS(x)  �  i u(y, xi)  =  max  xk+1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=',xn∈[0,1]  �k  i=1( 2i−1  2n − iϵ) + �n  i=k+1 xi  �k  i=1(y∗ − ( 2i−1  2n − iϵ)) + �n  i=k+1(xi − y∗)  =  �k  i=1( 2i−1  2n − iϵ) + n  2 − �k  i=1( 2i−1  2n − iϵ)  (2k − n)y∗ − �k  i=1( 2i−1  2n − iϵ) + n  2 − �k  i=1( 2i−1  2n − iϵ)  =  n/2  (2k − n)y∗ − 2( 1  2n + · · · + 2k−1  2n ) + n  2 + 2 �k  i=1 iϵ  =  n/2  (2k − n)y∗ + n  2 − k2  n + 2 �k  i=1 iϵ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Since k ≤  n  2, shifting a facility within (xk, xk+1) slightly to the left causes the total utility to  weakly increase as there are a greater number of agents who gain utility than those who lose utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Therefore as y∗ is the optimal 2−IFS facility, it must be as close to xk as possible, at y∗ = k  n − kϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  23  Substituting this into the welfare ratio (and ignoring the negligible ϵ), we have  max  x∈[0,1]n  �  i u(f ∗  UW(x), xi)  maxy∈2IFS(x)  �  i u(y, xi) =  n/2  (2k − n)y∗ + n  2 − k2  n  =  n/2  (2k − n) k  n + n  2 − k2  n  =  n/2  k2  n − k + n  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Simple calculus shows that the denominator is minimized (w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' k ∈ (0, n  2]) when k =  n  2,  resulting in a welfare ratio of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore when the optimal 2−IFS facility location y∗ satisfies  y∗ ∈ [xk, xk+1], where k ≤ n  2, the price of 2−IFS for utilitarian welfare is at most 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2: Suppose that the unique optimal 2−IFS facility location y satisfies y∗ ∈ [xk, xk+1],  where k > n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='8 We can assume uniqueness without loss of generality as a differing facility location  y† with the same utilitarian welfare as y∗ must satisfy y† ∈ [xj, xj+1], where j ≤ n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar to the  previous case, any facility location right of xk+1 must violate 2−IFS as y∗ is the optimal facility  location, and we have y∗ = xk+1 −  1  2n as it lies to the right of the majority of agents, so shifting it  leftwards would decrease the utilitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We also remark that xk ≤ xk+1 − 1  n as y∗ satisfies  2−IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We apply a sequence of transformations to the location profile where each transformation in-  creases the welfare ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The transformations convert the location profile into an instance of Case  1 (where the optimal 2−IFS facility location y∗ satisfies y∗ ∈ [xk, xk+1], where k ≤ n  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The transformations are as follows:  If xk−1 (and xk) are at y∗ −  1  2n(= xk+1 − 1  n), shift xk rightwards to x′  k = y∗ + (y∗ − xk),  causing the optimal 2−IFS facility location y∗ to remain at the same location and/or satisfy  Case 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If xk−1 ∈ (xk+1 − 2  n, xk+1 − 1  n), shift xk rightwards to x′  k = xk−1 + 1  n, causing the optimal  2−IFS facility location y∗ to move leftwards to y′ = x′  k −  1  2n(= xk−1 +  1  2n) and/or satisfy  Case 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If xk−1 ≤ xk+1 − 2  n, shift xk rightwards to x′  k = xk+1 − 1  n + ϵ, causing the optimal 2−IFS  facility location y∗ to move leftwards to y′ = x′  k − 1  2n(= xk+1 − 3  2n + ϵ) and/or satisfy Case  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  To justify the effect on y∗ from shifting xk, recall that if y∗ still satisfies Case 2 after the shift, then  it is still the rightmost location satisfying 2−IFS as the majority of agents lie left of y∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now if y∗  changes to a location satisfying Case 1, then by our previous analysis the welfare ratio is at most  2, so we can disregard this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose that the first dot point occurs i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' y∗ remains at the  same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Recall that the welfare ratio is  �  i u(f ∗  UW(x), xi)  maxy∈2IFS(x)  �  i u(y, xi) =  �n  i=1 xi  �n  i=1 |y∗ − xi|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  8We can disregard k = n as we would have y∗ = 1, and as 0 is the optimal facility location, we have �n  i=1 xi ≥ n  2 ,  which corresponds to a welfare ratio under 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  24  The optimal facility location is still 0 as the sum of agent locations increases, so the numerator  strictly increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The denominator remains the same as xk has moved to an equidistant location  on the other side of y∗, and all other agents are at the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Thus this transformation  increases the welfare ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Consider the second and third dot points, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', y∗ moves to y′ = x′  k − 1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Clearly, the numerator  increases, so we now show that the denominator decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The change in utilitarian welfare from  the transformation is  �k−1  �  i=1  (y′ − xi) + (x′  k − y′) +  n  �  i=k+1  (xi − y′)  �  −  � k  �  i=1  (y∗ − xi) +  n  �  i=k+1  (xi − y∗)  �  = (k − 1)(y′ − y∗) − (n − k)(y′ − y∗) + (x′  k + xk) − (y∗ + y′)  = (y′ − y∗)(2k − n − 1) + (x′  k + xk) − (y∗ + y′) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We know that (y′−y∗)(2k−n−1) < 0 as y′ < y∗ and k ≥ n+1  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We also know that xk ≤ y∗− 1  2n as  y∗ satisfies 2−IFS and that y′ = x′  k − 1  2n, so from this we deduce that x′  k +xk < y∗ +y′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore  the denominator of the welfare ratio decreases, and the transformation increases the welfare ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  As the transformations only require that k > n  2, we can repeatedly apply them (and update xk  to be the rightmost agent left of y∗) until we have an instance of Case 1, which has been shown to  have a maximum welfare ratio of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore the theorem statement holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  D  Proof of Theorem 2  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of 2−UFS for utilitarian welfare is 2, and this bound is tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar to the proof of Theorem 1, we suppose without loss of generality that the optimal  facility location is 0 and define a sufficiently small ϵ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We also divide the proof into two cases:  Case 1: Suppose that the optimal 2−UFS facility location y∗ satisfies y∗ ∈ [xk, xk+1],  where k ≤ n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' To avoid contradicting the 2−UFS optimality of y∗, the agent locations x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xk  must be arranged such that any location left of xk violates 2−UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Furthermore, those agents  must be located such that �k  i=1 xi is maximized, as the welfare ratio increases with �k  i=1 xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We  claim that this occurs when all k agents are at the same location of  k  2n − ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' To see this, suppose  that among agents {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , k} that there are m ≤ k unique agent locations, and construct an open  ball at each unique agent location with radius  c  2n, where c is the number of agents at the location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Any location within an open ball fails to satisfy 2−UFS, so to maximize the welfare ratio and  avoid a contradiction, the leftmost open ball must include 0, and the m balls should overlap by  an ϵ distance (to prevent a 2−UFS facility being placed at the boundary between two balls).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' An  example of this with m = k is for i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , k}, xi = 2i−1  2n − iϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore we see that for m ≤ k  unique agent locations, the sum of agent locations is �k  i=1 xi =  1  2n + · · · + 2k−1  2n − mϵ, which is  maximized when all k agents are at  k  2n − ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  As in the 2−IFS proof, we require �n  i=1 xi ≥  n  2 for the optimal facility location to be 0,  and since the welfare ratio decreases with xk+1 + · · · + xn, we must have �n  i=1 xi =  n  2 and  25  xk+1 + · · · + xn = n  2 − (x1 + · · · + xk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Furthermore, as y is the optimal 2−UFS location, it must  take the leftmost 2−UFS point within [xk, xk+1], which is at k  n − ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Substituting these expressions  into the welfare ratio gives  �  i u(f ∗  UW(x), xi)  maxy∈2UFS(x)  �  i u(y, xi) =  �n  i=1 xi  �n  i=1 |y∗ − xi| =  n/2  k2  n − k + n  2  ,  which has been shown in the proof of Theorem 1 to attain a maximum of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore in this case,  the price of 2−UFS for utilitarian welfare is at most 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2: Suppose that the unique optimal 2−UFS facility location y∗ satisfies y∗ ∈ [xk, xk+1],  where k > n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We can assume uniqueness without loss of generality as a differing facility location  y† with the same utilitarian welfare as y∗ must satisfy y† ∈ [xj, xj+1], where j ≤ n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We will apply  a sequence of transformations which weakly increase the welfare ratio and result in a location pro-  file satisfying Case 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The transformation works as follows: shift xk rightwards to x′  k = y∗ +  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If there is already an agent at y +  1  2n, then instead shift xk rightwards to x′  k = y∗ +  1  2n + ϵk where  ϵk > 0 is sufficiently small, such that there are no other agents at x′  k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='9 This causes y∗ to remain  at the same location and/or satisfy Case 1, as if y∗ still satisfies Case 2, it is the rightmost location  satisfying 2−UFS10, and the location y∗ still satisfies 2−UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Furthermore, the optimal facility  location remains as 0 as the sum of agent locations strictly increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If y∗ satisfies Case 1 then we  know the welfare ratio is at most 2 so we disregard this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We now show that otherwise the  transformation increases the welfare ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Recall that the welfare ratio is  �  i u(f ∗  UW(x), xi)  maxy∈2UFS(x)  �  i u(y, xi) =  �n  i=1 xi  �n  i=1 |y∗ − xi|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We know that before the shift, y∗ ≥ xk +  1  2n, so the numerator increases by at least 1  n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The  denominator either decreases, remains the same, or increases by at most ϵk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since ϵk is chosen  to be sufficiently small, we conclude that this transformation causes the welfare ratio to weakly  increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By repeatedly applying these transformations and updating xk to be the rightmost agent  left of y∗, we eventually arrive at a location profile satisfying Case 1, which we know has a welfare  ratio of at most 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence the price of 2−UFS for utilitarian welfare is at most 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Lemma 1 also  implies that the price of 2−UFS for utilitarian welfare is at least 2, and hence the theorem statement  follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  E  Proof of Proposition 3  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of 2−IFS for egalitarian welfare is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We know a 2−IFS solution must always exist, meaning that under any agent location pro-  file, there exists a facility location such that every agent is at least  1  2n distance from the facility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' It  follows immediately that a solution maximizes egalitarian welfare satisfies 2−IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  9Such a location always exists unless xn = 1, y∗ = 1 −  1  2n and x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn−1 < y∗, but it can easily be shown  using �n  i=1 ≥ n  2 that such a location profile corresponds to a welfare ratio less than 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  10The majority of agents are left of y∗, so shifting y∗ leftwards decreases the utilitarian welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  26  F  Proof of Proposition 5  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A pure Nash equilibrium may not exist for f ∗  2IFS or f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For simplicity, we prove this statement for f ∗  2IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The same arguments hold verbatim for  f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We define a sufficiently small constant ϵ > 0, and consider the location profile x = ( 1  4−ϵ, 3  4+ϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We denote the reported location profile as x′ = (x′  1, x′  2), and prove this statement by considering  cases on agent 1’s reported location x′  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Note that under a pure Nash equilibrium, f ∗  2IFS cannot  place the facility in the interval [0, 1  2 − ϵ), as agent 1 can change its report to x′  1 = 1  4 − ϵ to strictly  increase its utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similarly, under a pure Nash equilibrium, f ∗  2IFS cannot place the facility in the  interval ( 1  2 + ϵ, 1], as agent 2 can change its report to x′  2 = 3  4 + ϵ to strictly increase its utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 1 (x′  1 < 1  4 − ϵ): If x′  2 ≤ 3  4, then f ∗  2IFS places the facility at 1, and thus this is not a pure  Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If x′  2 > 3  4, then f ∗  2IFS places the facility at x′  1 + 1  4 < 1  2 − ϵ, thus this is also not  a pure Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2 (x′  1 ≥ 1  4): If f ∗  2IFS places the facility at a location strictly right of 0, then this is not a  pure Nash equilibrium as agent 2 can report x′  2 = 1 to move the facility to 0, improving its utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If f ∗  2IFS places the facility at 0, then this is also not a pure Nash equilibrium as agent 1 can change  its report to x′  1 = 1  4 − ϵ to strictly increase its utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 3 (x′  1 ∈ [ 1  4 − ϵ, 1  4)): Recall that under a pure Nash equilibrium, f ∗  2IFS cannot place  the facility in the interval ( 1  2 + ϵ, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Due to x′  1, f ∗  2IFS also cannot place the facility in the interval  [0, x′  1+ 1  4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If x′  2 ≤ 3  4, then f ∗  2IFS places the facility at 1, and thus this is not a pure Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Suppose that x′  2 > 3  4, meaning the facility must be placed in the interval [x′  1 + 1  4, x′  2 − 1  4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As f ∗  2IFS  places the facility at the leftmost point of the optimal interval, it places the facility at x′  1 + 1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Thus,  for any x′  1 ∈ [ 1  4 − ϵ, 1  4), there exists some sufficiently small δ > 0 such that agent 1 can instead  report x′  1 + δ to improve its utility, so by definition there does not exist a pure Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In other words, agent 1 can continually shift its reported location asymptotically closer to 1  4 to  improve its utility, but from Case 2, we know that x′  1 cannot reach 1  4 as otherwise there is no pure  Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  G  Proof of Theorem 4  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For any ϵ > 0, a pure ϵ-Nash equilibrium always exists for f ∗  2IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider an arbitrary true agent location profile x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn) and sufficiently small  ϵ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Note that a pure ϵ-Nash equilibrium is also a pure δ-Nash equilibrium, where δ > ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 1 (n is even):  Subcase 1a: We first show that if xi ≥  2i−1  2n  for any i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n  2}, then a pure ϵ-Nash  equilibrium exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose this is the case, and let j = arg mini∈[ n  2 ]{xi ≥ 2i−1  2n }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If j = 1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn ≥  1  2n), then the reported location profile (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1) is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This  is because an agent can only influence the facility position by changing its report to a location in  [0, 1  2n), moving the facility from 0 to a point in (0, 1  n) and reducing its utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  If j > 1, then we will show that the reported location profile x′ = (x′  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , x′  n) = ( 1  2n −  ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 2(j−1)−1  2n  − (j − 1)ϵ, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1) is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Under x′, the facility cannot be  placed in [0, j−1  n − (j − 1)ϵ) due to x′  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , x′  j−1, and hence it is placed at j−1  n − (j − 1)ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  27  Suppose that for some agent i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , j − 1} changes its report to some x′  i ̸= 2i−1  2n − iϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Under the resulting location profile, the facility moves to a location in [0, 1  n − 2ϵ] if i = 1 and  [ i−1  n − (i − 1)ϵ, i  n − (i + 1)ϵ] if i ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , j − 2}, reducing the agent’s utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As agent j − 2  is located at 2(j−2)−1  2n  − (j − 2)ϵ, agent j − 1 (who is located at x′  j−1 = 2(j−1)−1  2n  − (j − 1)ϵ) can  improve its utility by reporting a new location x′′  j−1 = x′  j−1 + ϵ1, where ϵ1 < ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This causes the  facility to shift to the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' However, agent j − 1 cannot improve its utility by more than ϵ, as if it  reports a location x′′  j−1 ≥ x′  j−1 + ϵ, the facility will be placed at j−2  2n − (j − 2)ϵ, reducing its utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Hence agents 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , j − 1 cannot improve their utility by more than ϵ by changing their reported  location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Now consider agents j, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n whose true locations satisfy xj, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn ≥ 2j−1  2n and have reported  locations x′  j, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , x′  n = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As at least half of the agents must lie to the right of the facility, the  facility takes the leftmost location satisfying 2−IFS, even after any agent changes its report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='11  Hence an agent from {j, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n} can only influence the facility location by changing its report to a  location in ( 2(j−1)−1  2n  − (j − 1)ϵ, 2(j−1)+1  2n  − (j − 1)ϵ), causing the facility to move to a location in  ( j−1  n − (j − 1)ϵ, j+1  n − (j − 1)ϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' It is easy to see that this strictly reduces the agent’s utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We  have shown that no deviation by a single agent can cause its utility to increase by more than ϵ, and  hence x′ is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore a pure ϵ-Nash equilibrium exists if xi ≥ 2i−1  2n for  any i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n  2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Subcase 1b: By symmetry, we see that a ϵ-Nash equilibrium also exists if xi ≤ 2i−1  2n for any  i ∈ {n  2 + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' However, the exact symmetric argument does not work for i =  n  2 + 1 if  x n  2 +1 >  n+3  4n as under the reported location profile (0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 0, n+3  2n + ( n  2 − 1)ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1 −  1  2n + ϵ),  agent n  2 + 1 can change its report from x′n  2 +1 = 0 to n+1  2n + ( n  2)ϵ, causing the facility to move from  n+2  2n + ( n  2 − 1)ϵ to  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This is because f ∗  2IFS breaks ties in favour of the leftmost optimal location,  and results in increased utility as x n  2 +1 ∈ ( n+3  4n , n+1  2n ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now show that if xi >  2i−1  2n  for all i ∈ {n  2 + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n} and x n  2 +1 ∈ ( n+3  4n , n+1  2n ], a pure  ϵ-Nash equilibrium exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' It suffices to assume that xi < 2i−1  2n for all i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n  2}, as otherwise  we know from Subcase 1a that a pure ϵ-Nash equilibrium exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We divide this proof to two further  subcases depending on where x n  2 +1 is located.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Subcase 1bi: In this subcase we consider x n  2 +1 < 1  2 +  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We claim that x′ = ( 1  2n − ϵ, 3  2n −  2ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−1  2n − ( n  2)ϵ, 0, n+3  2n + ( n  2 − 1)ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1 − 1  2n + ϵ) is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Under x′, the  facility is placed at the rightmost point of the only feasible interval, at y′ = n+2  2n + (n  2 − 1)ϵ, as  there is a majority of agents left of the point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If any agent i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n  2 − 1} changes its report,  the facility will move to a location in [ 1  2n, 1  n − 2ϵ] if i = 1, and in [ i−1  n − (i − 1)ϵ, i  n − (i + 1)ϵ] if  i ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n  2 −1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This reduces agent i’s utility as xi < 2i−1  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We now consider agent n  2 (reporting  x′n  2 = n−1  2n − ( n  2)ϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Any location right of y′ is not feasible and under x′, there are n  2 + 2 agent  reports, including x′n  2 , left of the facility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence agent n  2 can only influence the facility location by  changing its report to a point in ( n+1  2n + ( n  2 − 1)ϵ, 1], causing the facility to move to the leftmost  point of the feasible interval, at n−2  2n − ( n  2 − 1)ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This reduces its utility as x n  2 < n−1  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Next we  consider agent n  2 + 1 (reporting x′n  2 +1 = 0), whose report can only change the facility’s location  within the feasible interval [ 1  2 − ( n  2)ϵ, n+2  2n + ( n  2 − 1)ϵ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As we have x n  2 +1 < 1  2 +  1  2n, it is most  optimal to have the facility at y′ = n+2  2n + ( n  2 − 1)ϵ, achieved by reporting x′n  2 +1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Finally, we  11Recall that f ∗  2IF S selects the leftmost optimal location if there is a tie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  28  consider agents n  2 + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar to Subcase 1a, agent n  2 + 2 can improve its utility by strictly  less than ϵ by reporting a location x′′n  2 +2 = x′n  2 +2 − ϵ1, where ϵ1 < ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If ϵ1 ≥ ϵ, the facility is placed  at n+4  2n + ( n  2 − 2)ϵ, reducing the agent’s utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' An agent i ∈ {n  2 + 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n} can only cause the  facility to be in [ i−1  n + (i − 1)ϵ, i+1  n + (i − 2)ϵ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This results in a reduction of utility as xi > 2i−1  2n  for all i ∈ {n  2 + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As no single agent can improve its utility by more than ϵ by changing  its report, x′ is a pure ϵ-Nash equilibrium and hence one exists for this subcase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Subcase 1bii: In this subcase we consider x n  2 +1 ≥ 1  2 +  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We claim that x′ = ( 1  2n − ϵ, 3  2n −  2ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−1  2n −( n  2)ϵ, n+1  2n +( n  2)ϵ, n+3  2n +( n  2 −1)ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1− 1  2n +ϵ) is a pure Nash ϵ-equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Here  the facility is placed at the leftmost point of the optimal interval, at 1  2 − ( n  2)ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By using identical  reasoning as in Subcase 1bi, it is easy to see that agents 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n  2, and agents n  2 + 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n cannot  improve their utility by more than ϵ by misreporting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In this subcase, it is agent n  2 rather than agent  n  2 + 2 who can improve its utility by less than ϵ by misreporting slightly to the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Also, as  in Subcase 1bi, agent n  2 + 1 can only change the facility’s location to within the feasible interval  [ 1  2 − ( n  2)ϵ, n+2  2n + (n  2 − 1)ϵ], but since we have x n  2 +1 ≥ 1  2 +  1  2n, their optimal facility location of  1  2 − ( n  2)ϵ is achieved by their report of x′n  2 +1 = n+1  2n + ( n  2)ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Subcase 1c: It reminds to consider the subcase where xi < 2i−1  2n for all i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n  2} and  xi > 2i−1  2n for all i ∈ {n  2 + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Under this subcase, we claim that the location profile x′ =  (x′  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , x′  n) = ( 1  2n − ϵ, 3  2n − 2ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−1  2n − ( n  2)ϵ, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1) is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Here, the  facility is placed at 1  2 −( n  2)ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By using the same arguments as in the first subcase, we see that agents  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n  2 −1 who have reported locations x′  1 =  1  2n−ϵ, x′  2 =  3  2n−2ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , x′n  2 −1 = n−3  2n −( n  2 −1)ϵ have  no incentive to change their report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Agent n  2 who reports location x′n  2 = n−1  2n − ( n  2)ϵ can improve  its utility by strictly less than ϵ, by changing its report to x′′n  2 = x′n  2 + ϵ1, where ϵ1 < ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar to  Subcase 1a, if ϵ1 ≥ ϵ, then the facility is placed at n−2  2n − ( n  2 − 1)ϵ, reducing the agent’s utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The  agents n  2 + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n who have reported their location as 1 under x′ can only move the facility to a  location in ( 1  2 −( n  2)ϵ, 1  2 + 1  n −( n  2)ϵ) by changing its report to a location in ( n−1  2n −( n  2)ϵ, n+1  2n −( n  2)ϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='12  However as we have x n  2 +1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn > n+1  2n , this causes their utility to decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We have shown that  under x′, no single agent can cause its utility to increase by more than ϵ by changing its report,  and hence x′ is a ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By exhaustion of cases, we have shown that a pure ϵ-Nash  equilibrium always exists under f ∗  2IFS if n is even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2 (n is odd): By using identical reasoning to the case where n is even, we can see that  if xi ≥  2i−1  2n  for any i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−1  2 , a pure ϵ-Nash equilibrium exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Specifically, if we let  j = arg mini∈[ n−1  2 ]{xi ≥ 2i−1  2n }, then the pure ϵ-Nash equilibrium is x′ = (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1) if j = 1, and  x′ = ( 1  2n − ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 2(j−1)−1  2n  − (j − 1)ϵ, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1) if j > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Furthermore, symmetric reasoning shows  that if xi ≤ 2i−1  2n for any i ∈ {n+3  2 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n}, a pure ϵ-Nash equilibrium exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' It remains to consider  the case where xi < 2i−1  2n for all i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−1  2 } and xi > 2i−1  2n for all i ∈ {n+3  2 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n} (and x n+1  2  can be anywhere).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Subcase 2a: Here we consider the subcase where x n+1  2  ≥ 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We claim that x′ = ( 1  2n − ϵ, 3  2n −  2ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−2  2n − ( n−1  2 )ϵ, 1, n+2  2n + ( n+3  2 )ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1 −  1  2n + ϵ) is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Here the  interval of feasible agent locations is [ n−1  2n − ( n−1  2 )ϵ, n+1  2n + ( n+3  2 )ϵ], and the facility is placed at the  leftmost point of the interval, at y′ = n−1  2n − ( n−1  2 )ϵ, as there is a majority of agents right of the  interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Any misreport by agent 1 will cause the facility to be placed in the interval [0, 1  n − 2ϵ],  12We note that �  i x′  i < n  2 − 1 + n  4 ( 1  2n + n−1  2n ) = 5n  8 − 1, which is less than n  2 if and only if n = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' However if  n = 2 it is trivial that x′ is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  29  which reduces their utility as x1 <  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Agent i ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−3  2 } can only cause the facility to be  placed in [ i−1  n − (i − 1)ϵ, i  n − (i + 1)ϵ], which reduces their utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A symmetric argument can  be applied to show that agents n+5  2 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n cannot improve their utility by misreporting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Agent n−1  2  (who reports x′  n−1  2  = n−2  2n − ( n−1  2 )ϵ) can improve its utility by strictly less than ϵ by changing its  report to x′′  n−1  2  = x′  n−1  2  + ϵ1, where ϵ1 < ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar to Subcase 1a, if ϵ1 ≥ ϵ, the agent’s utility will  be decreased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As the facility takes the leftmost feasible point under x′, agent n+3  2  can only change  the facility location to the rightmost feasible point (at n+3  2n + ( n+5  2 )ϵ), by misreporting such that  there is a majority of agents left of the facility location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This reduces the agent’s utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Finally,  it is easy to see that agent n+1  2  cannot improve its utility by misreporting: the infeasible regions  under x′ are a result of the other agent reports, and hence agent n+1  2  cannot cause the facility to be  placed outside of the feasible interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As x n+1  2  ≥ 1  2, the leftmost point of the interval is its most  optimal facility placement over its possible reports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore x′ is a pure ϵ-Nash equilibrium as no  agent can improve its utility by more than ϵ by misreporting, and hence a pure ϵ-Nash equilibrium  exists for this subcase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Subcase 2b: In this subcase, x n+1  2  < 1  2 (and xi < 2i−1  2n for all i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−1  2 } and xi > 2i−1  2n  for all i ∈ {n+3  2 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By using a symmetric argument as in Subcase 2a, x′ = ( 1  2n − ϵ, 3  2n −  2ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , n−2  2n −( n−1  2 )ϵ, 0, n+2  2n +( n+3  2 )ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1− 1  2n +ϵ), where the facility is placed at n+1  2n +( n+3  2 )ϵ,  is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In this proof, we have provided a pure ϵ-Nash equilibrium for every possible location profile,  and hence by exhaustion of cases, a ϵ-pure Nash equilibrium always exists for f ∗  2IFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  H  Proof of Theorem 5  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For any ϵ > 0, a pure ϵ-Nash equilibrium always exists for f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In the proof of Theorem 4, we divided all possible agent location profiles into several  subcases, and provide a pure ϵ-Nash equilibrium for each subcase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We claim for every subcase, the  pure ϵ-Nash equilibrium we describe in the proof of Theorem 4 is also a ϵ-Nash equilibrium for  f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' First, we remark that every given pure ϵ-Nash equilibrium has the same facility placement  under f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This can be seen as every pure ϵ-Nash equilibrium has the n agents reporting n  distinct locations, with the exception of the equilibria where multiple agents report 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Under  these equilibria, the facility takes the rightmost (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' leftmost) location of the feasible interval, so  the change to a 2−UFS constraint does not affect the facility placement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  A simple case by case analysis shows that for each pure ϵ-Nash equilibrium x′ described in the  proof of Theorem 4, no agent can improve its utility by more than ϵ by changing its report under  f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The same arguments hold verbatim for f ∗  2UFS and the constraint of 2−UFS, even when  accounting for agents being able to change their report to the same location as another agent’s  report (to widen the ‘infeasible’ ball around the report).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We give the following intuition: if agent i  makes such a report change from x′  i, this either causes the facility to move to some location near  x′  i which has consequently become feasible, or it ‘pushes’ the facility towards xi (such as if the  facility takes the leftmost feasible location under x′ and agent i changes its report from x′  i = 1 to  the rightmost reported location left of the facility).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence every possible agent location profile has  a pure ϵ-Nash equilibrium under f ∗  2UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  30  I  Proof of Theorem 6  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For any ϵ ∈ (0, 1  n), the ϵ-price of anarchy for f ∗  2IFS and f ∗  2UFS of utilitarian welfare  is at least 2n−1+nϵ  1−nϵ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The price of anarchy is unbounded for ϵ ≥ 1  n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose for any ϵ ∈ (0, 1  n) that we have the (true) agent location profile x = ( 1  2n − ϵ  2, 1  2n −  ϵ  2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1  2n − ϵ  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We show that the location profile x′ = (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1) is a pure ϵ-Nash equilibrium for  x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Under x′, both f ∗  2IFS and f ∗  2UFS place the facility at 0, causing each agent to have  1  2n − ϵ  2 utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  An agent can only change the facility position by deviating to a reported location in [0, 1  2n), causing  the facility to instead be placed somewhere in (0, 1  n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This results in the agent receiving a utility  of u(xi) <  1  2n + ϵ  2, which is an increase of at most ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since no agent can improve its utility by  greater than ϵ by misreporting, x′ is a pure ϵ-Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now the utilitarian welfare under x  is n − 1  2 + nϵ  2 , whilst under x′ it is 1  2 − nϵ  2 (w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence the ϵ-price of anarchy is at least 2n−1+nϵ  1−nϵ  for ϵ ∈ (0, 1  n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  For ϵ ≥  1  n, the (true) agent location profile x = (0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 0) has a corresponding pure ϵ-Nash  equilibrium of x′ = (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , 1) which results in each agent having 0 utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This can be seen as no  agent can improve its utility by 1  n or greater, as an agent can only change the facility to a location  in (0, 1  n) by changing its report to a location in (0, 1  2n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' As each agent has 0 utility under the pure  ϵ-Nash equilibrium, the ϵ-price of anarchy is unbounded for ϵ ≥ 1  n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  J  Proof of Theorem 8  Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Mechanism 2 satisfies 2−UFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider a coalition of |S| agents at location xi and suppose there are n1 agents in [0, 1  2]  and n2 agents in ( 1  2, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The expected distance from the facility is  E(d(y, xi)) =  2n1n2 + n2  2  n2  1 + n2  2 + 4n1n2  xi +  n2  1 + 2n1n2  n2  1 + n2  2 + 4n1n2  (1 − xi)  =  n2  1 + 2n1n2  n2  1 + n2  2 + 4n1n2  + xi  �  n2  2 − n2  1  n2  1 + n2  2 + 4n1n2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Due to symmetry it suffices to only consider xi ∈ [0, 1  2], and since E(d(y, xi)) is a linear function  of x, we further restrict our attention to xi ∈ {0, 1  2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  When xi = 1  2, E(d(y, xi)) = 1  2 and hence 2−UFS is satisfied for any coalition of agents at 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  31  When xi = 0,  E(d(y, xi)) =  n2  1 + 2n1n2  n2  1 + n2  2 + 4n1n2  =  n1(2n2  1 + 6n1n2 + 4n2  2)  2(n2  1 + n2  2 + 4n1n2)(n1 + n2)  >  n1(n2  1 + 4n1n2 + n2  2)  2(n2  1 + n2  2 + 4n1n2)(n1 + n2)  =  n1  2(n1 + n2)  ≥ |S|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Therefore Mechanism 2 satisfies 2−UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  K  Proof of Lemma 2  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider an arbitrary agent location profile x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For every 2−IFS/UFS randomized  mechanism that gives positive support to a facility placement between 0 and 1, there exists a  2−IFS/UFS randomized mechanism that only gives positive support to a facility placement at 0 or  1 that leads to weakly higher expected utility for each agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider an arbitrary location profile x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn), and suppose for this profile that  some (2−IFS/UFS) mechanism places the facility at location c ∈ (0, 1) with probability p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If  instead the mechanism placed the facility at location 1 with probability cp and at location 0 with  probability p − cp, each agent’s expected distance from the facility would increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This can be  seen as for any xi ≤ c,  cp(1 − xi) + (p − cp)xi = pxi − 2cpxi + cp  = cp + pxi(1 − c) − cpxi  ≥ cp − cpxi  ≥ p(c − xi),  and for any xj > c,  cp(1 − xj) + (p − cp)xj = pxj + cp(1 − xj) − cpxj  ≥ pxj − cpxj  ≥ p(xj − c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Therefore this modified mechanism also satisfies 2−IFS/UFS and results in weakly higher ex-  pected utility for each agent than the original mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By repeatedly applying this modifica-  tion, any 2−IFS/UFS mechanism that places positive probability on any location between 0 and 1  can be modified to a 2−IFS/UFS mechanism that only places positive probability on locations 0  and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  32  L  Proof of Lemma 3  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2-IFS Randomized mechanism is optimal amongst all randomized mechanisms sat-  isfying 2-IFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We first prove by cases that the mechanism satisfies 2-IFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Recall that for  the OFLP, the utilitarian welfare maximizing solution places the facility at either 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 1 (�n  i=1 xi = n  2)  In this case, the facility locations of 0 and 1 are tied for maximizing utilitarian welfare, so  placing the facility at either location with probability 1  2 is optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The mechanism also satisfies  2-IFS in expectation as the expected distance of any agent from the facility is 1  2xi + 1  2(1 − xi) =  1  2 ≥  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2 (�n  i=1 xi > n  2)  In this case, the optimal facility location is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' It is trivial that placing the facility at 0 with  probability 1 when x1 ≥  1  2n is optimal and satisfies 2-IFS, so we consider the subcase where  x1 <  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We first show that the mechanism satisfies 2-IFS in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The expected distance between  x1 and the facility is  (1 − α)x1 + α(1 − x1) = 2n − 1 − 2nx1  2n(1 − 2x1) x1 +  1 − 2nx1  2n(1 − 2x1)(1 − x1)  = 2nx1 − x1 − 2nx2  1 + 1 − x1 − 2nx1 + 2nx2  1  2n(1 − 2x1)  = 1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  2-IFS is therefore satisfied for agents x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn as α ≤ 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now show for this case that the mechanism is optimal amongst all randomized mechanisms  satisfying 2-IFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By Lemma 2, it suffices to only consider mechanisms that can  only place the facility at 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Now consider the 2-IFS Randomized mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If α were increased, the utilitarian welfare  would decrease, and if α were decreased, 2−IFS would be violated for x1, hence α =  1−2nx1  2n(1−2x1) is  optimal and therefore the mechanism is optimal under the constraint of 2-IFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 3 (�n  i=1 xi > n  2)  This case is similar and symmetric to Case 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  M  Proof of Proposition 6  Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Randomized Egalitarian Welfare mechanism is strategyproof in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If all agents are in [0, 1  2] or all agents are in ( 1  2, 1], then each agent has at least 1  2 expected  utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Any misreport either causes their expected utility to either stay the same or be reduced to  1  2 from the facility being placed at 0 or 1 with probability 1  2 each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If there is at least one agent  in each interval, then an agent can only affect the outcome if it is the only agent in its interval  and it misreports its location to be in the other interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' However this weakly reduces the agent’s  expected utility, which consequently has an upper bound of 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  33  N  Proof of Theorem 9  Theorem 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2-IFS Randomized mechanism has an approximation ratio of 12  11 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='091.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' It suffices to consider the case where �n  i=1 xi >  n  2 and x1 <  1  2n as the case where  �n  i=1 xi >  n  2 is symmetric, and the mechanism is optimal for the cases of �n  i=1 xi =  n  2, and  �n  i=1 xi > n  2 and x1 ≥  1  2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  The approximation ratio of the mechanism is  max  x∈Xn  �  φ∗(x)  φ2IFS(x)  �  = max  x∈Xn  �  i xi  (1 − α) �  i xi + α �  i(1 − xi)  = max  x∈Xn  �  i xi  2n−1−2nx1  2n(1−2x1)  �  i xi +  1−2nx1  2n(1−2x1)  �  i(1 − xi)  = max  x∈Xn  �  i xi  1−2nx1  2(1−2x1) +  n−1  n(1−2x1)  �  i xi  = max  x∈Xn  1  1−2nx1  2(1−2x1) �  i xi +  n−1  n(1−2x1)  =  max  x1∈[0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 1  2n )  1  1−2nx1  2(1−2x1)(n−1+x1) +  n−1  n(1−2x1)  =  max  x1∈[0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 1  2n )  2n(1 − 2x1)(n − 1 + x1)  n − 2n2x1 + 2(n − 1)(n − 1 + x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In the second last line, we substitute x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xn = 1 as the ratio is monotonic increasing with  �  i xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Some optimization programming shows that when n ≥ 3, the ratio is maximized when  x1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Substituting x1 = 0 into the ratio gives  2n2 − 2n  2n2 − 3n + 2,  which has a derivative of − 2(n2−4n+2)  (2n2−3n+2)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We therefore see our ratio has a maximum turning point at  x = 2+  √  2 and is monotonic decreasing after this point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For integer n ≥ 3, the ratio is maximized  when either n = 3 or n = 4, and the ratio is equal to 12  11 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='091 for both of these points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now consider the case where n = 2 (and x1 < 1  4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The ratio becomes  max  x1∈[0, 1  4 )  2 − 2x1 − 4x2  1  2 − 3x1  = 1  9(22 − 4  √  10)  ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='039.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Therefore the mechanism’s welfare ratio is maximized when x1 = 0 and either n = 3 or n = 4,  taking a value of 12  11 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='091.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  O  Proof of Lemma 4  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2-UFS Randomized mechanism is optimal amongst all randomized mechanisms sat-  isfying 2−UFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  34  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar to the proof of Lemma 3, we prove this statement by cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 1 (�m  i=1 |Si|xi = n  2)  When �m  i=1 |Si|xi =  n  2, the facility locations of 0 and 1 are tied for maximizing utilitarian  welfare, so placing the facility at either location with probability 1  2 is optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The mechanism  also satisfies 2−UFS in expectation as the expected distance of any agent from the facility is  1  2xi + 1  2(1 − xi) = 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2 (�m  i=1 |Si|xi > n  2)  Note that in this case the optimal facility location is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We first show that the mechanism  satisfies 2−UFS in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For a group of agents Si at xi < 1  2, the expected distance from the  facility is  α(1 − xi) + xi(1 − α) ≥ αi(1 − xi) + xi(1 − αi)  = |Si| − 2nxi  2n(1 − 2xi)(1 − xi) + 2n − 2nxi − |Si|  2n(1 − 2xi)  xi  = |Si|(1 − 2xi)  2n(1 − 2xi) = |Si|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  By setting |Si| = n, we also see that α ≤ 1  2, hence 2−UFS is satisfied for any group of agents at  xj ≥ 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now show for this case that the mechanism is optimal amongst all randomized mechanisms  satisfying 2-UFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By Lemma 2, it suffices to only consider mechanisms that can  only place the facility at 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now under the 2−UFS Randomized mechanism, increasing α  would decrease the utilitarian welfare, and decreasing α would violate 2−UFS for some group of  agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence the mechanism is optimal under the constraint of 2−UFS in expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 3 (�m  i=1 |Si|xi < n  2)  This case is similar and symmetric to Case 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  P  Proof of Theorem 10  Theorem 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' 2-UFS Randomized mechanism has an approximation ratio of 2  7(1 + 2  √  2) ≈  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='09384.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Without loss of generality we suppose that �n  i=1 > n  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Let j be the index of the group of  agents corresponding to α (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' αj = max{α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , αk}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  35  The approximation ratio of the mechanism is  max  x∈Xn  �  φ∗(x)  φ2UFS(x)  �  = max  x∈Xn  �  i xi  (1 − α) �  i xi + α �  i(1 − xi)  = max  x∈Xn  �  i xi  2n−|Sj|−2nxj  2n(1−2xj)  �  i xi + |Sj|−2nxj  2n(1−2xj)  �  i(1 − xi)  = max  x∈Xn  �  i xi  |Sj|−2nxj  2(1−2xj) +  n−|Sj|  n(1−2xj)  �  i xi  = max  x∈Xn  1  |Sj|−2nxj  2(1−2xj) �  i xi +  n−|Sj|  n(1−2xj)  =  max  xj∈[0, 1  2 )  |Sj|∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=',n−1}  1  |Sj|−2nxj  2(1−2xj)(n−|Sj|+|Sj|xj) +  n−|Sj|  n(1−2xj)  =  max  xj∈[0, 1  2 )  |Sj|∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=',n−1}  2n(1 − 2xj)(n − |Sj| + |Sj|xj)  n|Sj| − 2n2xj + 2(n − |Sj|)(n − |Sj| + |Sj|xj)  = max  xj∈[0, 1  2 )  r∈(0,1)  2(1 − 2xj)(1 − r + rxj)  r − 2xj + 2(1 − r)(1 − r + rxj) where r = |Sj|  n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Some optimization programming shows that this ratio is maximized at r = 1 −  1  √  2 and xj = 0,  taking a value of 2  7(1 + 2  √  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Q  Proof of Lemma 5  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For α = 2, there exists an α−UFS facility location y that does not satisfy α−PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Assume that n = 10 and that we have 2 groups of agents, with the first group of 7 agents  located at the point c1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='35, and the second group of 3 agents located at the point c2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We  consider two balls B1 and B2 respectively with centers c1 and c2 and radius |S1|  2n =  7  20 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='35 and  |S2|  2n =  3  20 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We set the facility location y at the point 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since point y is outside of the  two balls, it satisfies 2-UFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' However, it does not satisfy the 2-PF inequality: d(y, c2) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='16 ≱  |S1|  20 + |S2|  20 − r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  R  Lemma 6 and Proof of Lemma 6  Here we introduce an auxiliary lemma which will be used in the proof of Theorem 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The intersection of (I − Bi)’s is not empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  36  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We consider two cases:  Every open ball Bi, i ∈ [m] lies completely in interval I = [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence, the boundary  points of interval I are not in each Bi’s and therefore {0, 1} ∈ ∩m  i=1(I − Bi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  There exists an open ball which does not completely lie in the interval I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Assuming the  points x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', xm are ordered from left to right, let k be the smallest index such that Bk  does not completely lie in I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' So either 0 ∈ Bk or 1 ∈ Bk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Both end points 0 and 1 can  not be in Bk, since in this case |Bk| = |Sk|  n  > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Let us assume 0 ∈ Bk and 1 /∈ Bk, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e,  1 ∈ (I − Bk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now if for every i ∈ [m], we have 1 ∈ (I − Bi), the lemma statement holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Now suppose there exists an open ball Bj such that 1 /∈ (I − Bj), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e, 1 ∈ Bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Without  loss of generality let j be the largest index in which the aforementioned statement holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We  consider two cases:  – Bk ∩ Bj is not an empty set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In this case [0, 1] ⊆ Bk ∪ Bj and |Sk|  n + |Sj|  n > 1, which  can not happen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  – Bk ∩ Bj is an empty set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We consider the set A := I − (Bk ∪ Bj) and consider two  cases:  A ⊆ ∪j−1  i=k+1Bi: in this case [0, 1] ⊆ ∪m  i=1Bi and �m  i=1  |Si|  n  > 1, which can not  happen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  A ⊈ ∪j−1  i=k+1Bi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore there exists y ∈ A such that y /∈ ∪j−1  i=k+1Bi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Also by the  definition of A, y /∈ (Bk ∪ Bj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For every 1 ≤ i ≤ k − 1, Bi ⊂ Bk holds as i is  the smallest index such that its corresponding ball contains the point 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similarly,  we have for every j + 1 ≤ i ≤ m, Bi ⊂ Bj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence y /∈ Bi for every i ∈ [m], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e,  y ∈ (I − Bi) for every i ∈ [m] and y ∈ ∩m  i=1(I − Bi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  S  Proof of Theorem 11  Theorem 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' A 2-PF solution always exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose we have m unique agent locations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' m groups of agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We prove the theorem  by induction on the number of groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' When all the agents have the same location, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e, m = 1,  we can allocate the facility y at the furthest boundary point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' This trivially satisfies 2-PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now, we  assume for any k groups of agents where k ≤ m that there exists a 2-PF solution, and we extend  that for k = m + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Suppose we have m + 1 groups of agents placed at points c1, c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , cm+1, which are ordered  such that c1 ≤ c2 ≤ · · · ≤ cm+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Let Si denote the group of agents at ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We set an open ball Bi  with radius |Si|  2n , around each center ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' To prove the theorem, we consider several cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 1 (There is no overlap between any two balls, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Bi∩Bj = ∅∀i, j ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , m+1}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  In Lemma 6, we have shown that the intersection of (I − Bi)’s is not empty, so there exists  a point y outside of every ball Bi where the facility can be placed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Here r is the distance  between centers ci and cj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If r = 0, then 2-PF is satisfied since we have d(y, ci) ≥  |Si|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  37  Otherwise, since all the balls are disjoint, r is larger than the sum of the radii of Bi and Bj,  so |Si|  2n + |Sj|  2n − r < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Hence,  d(y, ck) ≥ |Si|  2n + |Sj|  2n − r  for k = i, j,  and thus y satisfies the 2-PF inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2 (There exists at least two overlapping balls, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', ∃ i, j ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , m + 1} s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Bi ∩ Bj ̸= ∅).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  – Case 2a (There exists one ball that is contained within another ball, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', ∃ i, j ∈  {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , m + 1} s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='Bi ⊆ Bj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Without loss of generality, we assume B2 ⊆ B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now  we place all the agents at c2 and c1 together at c1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We set a new ball B  ′ centered at  c1 with radius |S1|  2n + |S2|  2n , which is the summation of the radii of B1 and B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now, we  have m new groups of agents located at the centers c1, c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , cm+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By induction, a  2-PF solution y exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We claim that y is also a 2-PF solution for m + 1 groups of  agents located c1, c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , cm+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since y is a 2-PF solution for the m groups of agents  located at c1, c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', cm+1, y lies outside of every ball, satisfying the 2-PF inequality for  r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since y is outside the ball B′, y is outside of balls B1 and B2, therefore we have  d(y, c1) ≥ |S1|  2n and d(y, c2) ≥ |S2|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' So y satisfies 2-PF inequalities for r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We now  set r to be the distance between two centers c1 and c2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', r = c2 − c1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since y is  outside the ball B′ we have d(y, c1) ≥ |S1|  2n + |S2|  2n ≥ |S1|  2n + |S2|  2n − r, so c1 satisfies the  PF inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' To show that the agents at c2 also satisfy the PF inequality, we consider  2 cases:  Case 2ai (Ball B2 does not contain center c1 (see Figure 4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We denote a :=  (c2 − c1) − |S2|  2n as the distance between c1 and the left boundary of B2, b := |S2|  2n  as the radius of B2 and c := c1 + |S1|  2n − c2 − |S2|  2n as the distance between the right  boundaries of B1 and B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In this case, we have  |S1|  2n + |S2|  2n − r = a + 2b + c + b − a − b = 2b + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  (1)  Since y is outside of ball B′, we have d(y, c2) ≥ 2b + c and by (1), d(y, c2) ≥  |S1|  2n + |S2|  2n − r and thus the 2-PF inequality is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2aii (Ball B2 contains center c1 (see Figure 5)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In this case, the range r is  smaller than the diameter of B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We denote a := c2 − c1 as the distance between  the two centers, b := |S2|  2n as the radius of B2 and c := c1 + |S1|  2n − c2 − |S2|  2n as the  distance between the right boundaries of B1 and B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We have  |S1|  2n + |S2|  2n − r = a + b + c + b − a = 2b + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  (2)  Since y is outside of ball B′, we have d(y, c2) ≥ 2b + c and by (2), d(y, c2) ≥  |S1|  2n + |S2|  2n − r and thus the 2-PF inequality is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  38  Figure 4: B1 and B′ are open balls centered at c1 and B2 is an open ball centered at c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The  variables a, b and c denote the distances between the boundaries of the balls and the centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Figure 5: B1 and B′ are open balls centered at c1 and B2 is an open ball centered at c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The  variables a, b and c denote the distances between the boundaries of the balls and the centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  39  – Case 2b (There exist two overlapping balls, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' ∃ i, j ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , m+1} s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Bi∩Bj ̸=  ∅, but they are not contained within each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=') Without loss of generality, we assume  B1 ∩ B2 ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider the line segment that connects the left border of B1 to the right  border of ball B2 and denote the midpoint of this line as c′  1 := 1  2(c1 − |S1|  2n + c2 + |S2|  2n ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We move all the agents at c1 and c2 to point c′  1 and set a new ball B′ around it with  radius |S1|  2n + |S2|  2n , which is the summation of radii of B1 and B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similar to the previous  subcase, by our inductive assumption there exists a 2-PF solution y for the new m  groups of agents placed at c′  1, c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', cm, cm+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now we claim that y is a 2-PF solution  for c1, c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', cm+1 as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since y is outside of the ball B′, y is also outside of the  balls B1 and B2, therefore d(y, c1) ≥ |S1|  2n and d(y, c2) ≥ |S2|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' So y satisfies the 2-PF  inequalities for r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We now set r to be the distance between two centers c1 and c2  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', r = c2 − c1) and consider 3 cases which depend on whether the intersections of  the balls also contain a center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In each case we show that |S1|  2n + |S2|  2n − r is equal to  the length of intersection of B1 and B2 which denote as |intersection| (and hence the  2-PF inequality is satisfied).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2bi (The intersection between B1 and B2 does not contain centers c1 and c2  (see Figure 6)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We denote a := c2 − |S2|  2n − c1 as the distance between c1 and the  left boundary of B2, b := c1 + |S1|  2n − (c2 − |S2|  2n ) as the length of the intersection,  and c := c2 − |S1|  2n − c1 as the distance between c2 and the right boundary of B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We have |S1|  2n + |S2|  2n − r = a + b + b + c − a − b − c = b = |intersection|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Since y is placed outside of ball B′, it is outside of balls B1 and B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We have  d(y, ci) ≥ |Si|  2n ≥ |intersection| = |S1|  2 + |S2|  2 − r and thus 2-PF is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Figure 6: B1, B2 and B′ are open balls centered at c1, c2 and c′ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The terms a, b, c and  |intersection|  2  denote the distances between the boundaries of the balls and the centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2bii (The intersection between B1 and B2 contains one of the centers c1 and  c2 (see Figure 7)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Without loss of generality suppose the contained center is c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We denote a := c2 − |S2|  2n − c1 as the distance between c1 and the left boundary of  B2, b := |S2|  2n as the radius of B2, and c := c2 − |S1|  2n − c1 as the distance between  c2 and the right boundary of B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We have |S1|  2n + |S2|  2n − r = a + b + c + b − a − b =  40  b + c = |intersection|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since y is outside of B1, we have  d(y, c1) ≥ |S1|  2n = a + b + c ≥ b + c  = |intersection| = |S1|  2n + |S2|  2n − r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Now we show d(y, c2) satisfies the 2-PF inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Recall B′ is a ball centered  at the midpoint of the left boundary of B1 and right boundary of B2, with radius  |S1|  2n + |S2|  2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Also, y lies outside of B′, so the right boundary of B2 has a distance of  length |intersection|  2  from the right boundary of B′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We therefore have  d(y, c2) ≥ |S2|  2n + |intersection|  2  = b + b + c  2  Also, since b ≥ c, we have  b + b + c  2  ≥ b + c = |intersection| = |S1|  2n + |S2|  2n − r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Figure 7: B1, B2 and B′ are open balls centered at c1, c2 and c′ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The terms a, b, c and  |intersection|  2  denote the distances between the boundaries of the balls and the centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Case 2biii (The intersection between B1 and B2 contains both centers c1 and c2  (see Figure 8)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We denote a := c2 − |S2|  2n − c1 as the distance between c1 and the  left boundary of B2, b := c2 − c1 as the distance between the two centers, and  c := c2 − |S1|  2n − c1 as the distance between c2 and the right boundary of B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We  have |S1|  2n + |S2|  2n −r = b+c+b+a−b = a+b+c = |intersection|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' In this case, b+c  is the radius of ball B1 and a+b is the radius of ball B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Since the balls B1 and B2  are not contained within each other, we have b + c > a and a + b > c (see Figure  8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Like before, B′ is a ball with a center at the midpoint of the left boundary of  B1 and right boundary of B2 and radius |S1|  2n + |S2|  2n , and y lies outside of this ball,  41  so the boundaries of each ball B1 and B2 have a distance of length |intersection|  2  with  the boundary of B′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We therefore have  d(y, c1) ≥ b + c + |intersection|  2  = b + c + a + b + c  2  ≥ b + c + a = |intersection| = |S1|  2n + |S2|  2n − r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Similarly, we can show that y satisfies the 2-PF inequality for center c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  d(y, c2) ≥ a + b + |intersection|  2  = a + b + a + b + c  2  ≥ a + b + c = |intersection| = |S1|  2n + |S2|  2n − r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Hence the facility placement of y satisfies the 2-PF inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Figure 8: B1, B2 and B′ are open balls centered at c1, c2 and c′ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The terms a, b, c and  |intersection|  2  denote the distances between the boundaries of the balls and the centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  By exhaustion of cases, we have proven the inductive statement, and thus a facility placement that  satisfies 2-PF always exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  T  Proof of Theorem 12  Theorem 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Under the hybrid model, a H-UFS solution always exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Let nC denote the number of classic agents and nO denote the number of obnoxious agents  (such that nC + nO = n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Consider an arbitrary agent location profile with m unique classic  agent locations x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' , xm, and suppose they are ordered such that x1 ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' xm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We first focus on  the region of feasible facility locations pertaining to the classic agents’ distance constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For  42  i ∈ [m], let SCi denote the group of classic agents at location xi, and construct a closed ball with  center xi and radius 1 −  |SCi|  n : Bi = {z|d(z, xi) ≤ 1 −  |SCi|  n }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' By definition, the intersection of the  closed balls ∩i∈[m]Bi denotes the (continuous) region of feasible facility locations pertaining to the  classic agents’ distance constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' From [Aziz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=', 2021], we know this region is non-empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We show that the length of the feasible region ∩i∈[m]Bi is at least n−nC  n  by iteratively trans-  forming the agent location profile to one where all classic agents are at 0 or 1, and showing that  each transformation weakly decreases the feasible region length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' For each ball Bi, there is a (pos-  sibly empty) left interval of infeasible points Li and a (possibly empty) right interval of infeasible  points Ri such that Bi = [0, 1] − Li − Ri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We denote the left infeasible interval of points as  Li = [0, xi − (1 −  |SCi|  n )) if xi − (1 −  |SCi|  n ) > 0 and as Li = ∅ otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Similarly, we denote the  right infeasible interval of points as Ri = (xi +(1−  |SCi|  n ), 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The union of left infeasible intervals  is therefore ∪i∈[m]Li = [0, maxi∈[m] xi − (1 −  |SCi|  n )) if there exists a nonempty Li, and is empty  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The union of right infeasible intervals is ∪i∈[m]Ri = (mini∈[m] xi + (1 −  |SCi|  n ), 1] if  there exists a nonempty Ri, and is empty otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore the length of the feasible region is  min  �  min  i∈[m]  �  xi + (1 − |SCi|  n )  �  , 1  �  − max  �  0, max  i∈[m]  �  xi − (1 − |SCi|  n )  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  By symmetry, we suppose without loss of generality that  min  i∈[m]  �  xi + (1 − |SCi|  n )  �  ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We consider the following transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Let j correspond to the agent location with the largest  right infeasible interval, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  j := arg min  i∈[m]  �  xi + (1 − |SCi|  n )  �  ,  and we have xj < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If xj > 0, move all agents at xj to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We show that this transformation  weakly decreases the feasible region length: in mini∈[m]  �  xi + (1 −  |SCi|  n )  �  , xi decreases to 0  and |SCi| weakly increases (it strictly increases if there are already agents at 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Furthermore,  the maxi∈[m]  �  xi − (1 −  |SCi|  n )  �  term is unaffected unless the shifted group of agents originally  corresponded to the maximum value, in which case the xi term decreases by at most the length  of the shift, and the (1 −  |SCi|  n ) term weakly decreases as |SCi| weakly increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Therefore this  transformation weakly decreases the feasible region length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Now the agent location with the largest  right infeasible interval is 0, so our feasible region length is  (1 −  |SCj′|  n  ) − max  �  0, max  i∈[m]  �  xi − (1 − |SCi|  n )  ��  ,  where j′ corresponds to the location xj′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' If the right boundary of the largest left infeasible  interval maxi∈[m]  �  xi − (1 −  |SCi|  n )  �  corresponds to the agents at xj′ = 0, then it is at most 0, and  the feasible region length is (1 −  |SCj′ |  n  ) which is at least n−nC  n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We now suppose that this is not the  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  43  We have  max  i∈[m]  �  xi − (1 − |SCi|  n )  �  ≤ max  i∈[m]  �  1 − (1 − |SCi|  n )  �  ,  so the feasible region length is at least  (1 −  |SCj′|  n  ) − max  �  0, max  i∈[m]  �|SCi|  n  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  Since arg maxi∈[m]  � |SCi|  n  �  ̸= j′, the feasible region length is at least  1 −  |SCj′| + |SCk|  n  ≥ n − nC  n  where k ̸= j′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  We now know the length of the (continuous) feasible region corresponding to the classic agents  is at least n−nC  n  = nO  n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' We now consider the obnoxious agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Suppose we construct an open ball  of radius  |SOi|  2n  around each group of obnoxious agents at the same location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' Any location within  one of these open balls is infeasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content=' The sum of ball lengths is nO  n , so using a similar argument  to that in the proof of Proposition 2, we see that a feasible solution with respect to both the classic  agents’ and obnoxious agents’ distance inequalities always exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
+page_content='  44' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE3T4oBgHgl3EQfJAm8/content/2301.04340v1.pdf'}
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+Sub-Planck structures and sensitivity of the superposed photon-added or
+photon-subtracted squeezed-vacuum states
+Naeem Akhtar,1, ∗ Jizhou Wu,2, † Jia-Xin Peng,3 Wu-Ming Liu,4, 5, 6 and Gao Xianlong1, ‡
+1Department of Physics, Zhejiang Normal University, Jinhua 321004, China
+2Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
+3State Key Laboratory of Precision Spectroscopy, Quantum Institute for Light and
+Atoms, Department of Physics, East China Normal University, Shanghai 200062, China
+4Beijing National Laboratory for Condensed Matter Physics, Institute
+of Physics, Chinese Academy of Sciences, Beijing 100190, China
+5School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
+6Songshan Lake Materials Laboratory, Dongguan 523808, Guangdong, China
+(Dated: January 3, 2023)
+The Wigner function of the compass state (a superposition of four coherent states) develops phase-
+space structures of dimension much less than the Planck scale ℏ, which are crucial in determining the
+sensitivity of these states to phase-space displacements. In the present work, we introduce compass-
+like states that may have connection to the contemporary experiments, which are obtained by either
+adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We
+show that, when a significant quantity of photons is added (or subtracted), the Wigner function of
+these states are shown to have phase-space structures of an area that is substantially smaller than
+the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher
+than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures
+and the sensitivity of our states are strongly influenced by the average photon number, with the
+photon addition case having a higher average photon number leading to the smaller sub-Planck
+structures and, consequently, being more sensitive to displacement than the photon subtraction
+case. Our states offer unprecedented resolution to the external perturbations, making them suitable
+for quantum sensing applications.
+I.
+INTRODUCTION
+Quantum mechanical states can be visualized in the
+phase space via the Wigner quasiprobability distribu-
+tion [1–5]. The term “Gaussian state” refers to a state
+having the Gaussian Wigner function [6, 7]. The coher-
+ent state [8] is an example of a Gaussian state.
+The
+Wigner function of the coherent state exhibits the Planck
+limit [9, 10] in the phase space, which is also known as
+the standard quantum limit (SQL) or shot-noise limit.
+The Wigner function of certain non-Gaussian states
+may attain negative values [11–14], indicating that these
+states are nonclassical.
+The quantum superposition is
+the source of intriguing non-classical properties of quan-
+tum states, such as quantum coherence [11, 15], squeez-
+ing [16], and entanglement [17–19]. Non-classical quan-
+tum states play a significant role in quantum-information
+processing [20], tests of fundamental of physics [21–23],
+and applications in sensing and metrology [24, 25].
+Non-classical states are not always non-Gaussian, how-
+ever, non-classical states can be Gaussian in some cases.
+For example, a squeezed-vacuum state (SVS) is a com-
+mon non-classical state, but it possesses a Gaussian
+Wigner function [12, 13]. The Wigner function of the
+superposition of SVS is non-Gaussian and may have
+∗ naeem abbasi@zjnu.edu.cn
+† wujz3@sustech.edu.cn (Corresponding author)
+‡ gaoxl@zjnu.edu.cn
+negative amplitudes [26, 27]. Squeezed quantum states
+play an important role in performing enhanced quan-
+tum metrology [16, 28].
+Squeezed light has been uti-
+lized experimentally to carry out improved measure-
+ments [29, 30].
+The superpositions of two coherent states with op-
+posite phases (cat states) also possess non-Gaussian
+Wigner functions [31, 32].
+Moreover, the superposi-
+tion of four coherent states, which is known as the
+“compass state” [33] exhibits nonclassical features in the
+Wigner function with dimensions far smaller than the
+SQL. The quantum states with sub-Planck structures are
+found very sensitive to environmental decoherence [34]
+and have achieved prominent theoretical attentions in
+quantum metrology [34–38].
+The connection between
+sub-Planck structures and teleportation fidelity has been
+established [39].
+Sub-Fourier sensitivity is a classical
+analogue of the sub-Planck structures [40]. Compass-like
+states have been thoroughly investigated in several situa-
+tions [41–56]. Both theoretical [57–62] and experimental
+study [63–66] have been taken to achieve the controlled
+generation of such states.
+In recent years, there has been a lot of focus on sub-
+tracting photons from or adding photons to the quantum
+states [67–79]. A non-Gaussian state can also be gen-
+erated by adding or subtracting photons from a Gaus-
+sian state. For example, when photons are added to
+or subtracted from the Gaussian SVS, one may ob-
+tain two non-Gaussian squeezed states that have non-
+positive Wigner functions [72–75, 77, 79, 80]: photon-
+arXiv:2301.00195v1  [quant-ph]  31 Dec 2022
+
+2
+added squeezed-vacuum states (PASVS) [69] and photon-
+subtracted squeezed-vacuum states (PSSVS) [75]. Both
+PASVS and PSSVS have attracted theoretical interest in
+quantum metrology [81–83].
+The first theoretical investigation into the photon-
+addition operation is accomplished by adding photons to
+the coherent states [84]. Later, the photon-addition op-
+eration was successfully proved in experiments by using
+a non-degenerate parametric amplifier with a weak cou-
+pling [85]. The PSSVS is currently the most successfully
+experimentally observed non-Gaussian SVS in quantum
+optics [86, 87].
+Schr¨odinger cat-like states with higher amplitude can
+be used as qubits in quantum computing or as re-
+sources for quantum error-correcting coding [88, 89].
+Conventional methods are unable to produce Schr¨odinger
+cat-like states with the necessary amplitudes [90–92].
+Numerous theoretical [93–95] and experimental [96, 97]
+research involving the photons addition or subtractions
+from the SVS have been carried out to achieve such
+states.
+In the present work, we introduce a few non-Gaussian
+SVSs that may also hold the properties of the com-
+pass state. In particular, we show that the Wigner func-
+tion of the superpositions of two PASVSs (or PSSVSs)
+exhibit phase-space structures of an area, which vary
+inversely with the number of photons added (or sub-
+tracted). When a large amount of the photons are added
+to or subtracted from our states the support area of these
+structures is substantially smaller than that found for
+coherent states. Similar sub-Planck structures are also
+found in the phase space of the mixed states related to
+the PASVSs and PSSVSs. We demonstrate that the av-
+erage photon number in the states significantly influences
+the size of these sub-Planck structures, with photon ad-
+dition case having higher average photon number leading
+to smaller sub-Planck structures in the phase space than
+photon subtraction case.
+To investigate the potential applications of these non-
+Gaussian states in quantum metrology, we analyze the
+overlap between these states and their slightly shifted
+analogues [98].
+The degree to which the state is sen-
+sitive against perturbations in the phase space can be
+determined from this overlap.
+The sensitivity associ-
+ated with coherent states cannot be improved by increas-
+ing the number of photons. Techniques using probes pre-
+pared in such states have the sensitivity at the SQL [99,
+100]. Here, we show that the sensitivity of our states is
+much higher than the SQL when the quantity of added
+(or subtracted) photons is relatively high. Furthermore,
+our superpositions exhibit this enhanced sensitivity in all
+phase-space directions, whereas the mixtures only do so
+for specific displacements. The varying average photon
+number in the states also contributed to the variation in
+the sensitivities between the photon addition and sub-
+traction cases; it is shown that the photon addition cases
+have higher sensitivity than the subtracted ones.
+The structure of our paper is as follows.
+In §II, we
+review the concept of the sub-Planck structures associ-
+ated to the compass state. In §III, we review the Wigner
+functions of PASVS and PSSVS. In §IV, we introduce
+our states and analyze their phase space by using the
+Wigner function. Here, we also discuss the sensitivity of
+our states against the phase-space perturbations. In §V,
+we provide our conclusion.
+II.
+THEORY OF SUB-PLANCK STRUCTURES
+This section provides the background of the sub-Planck
+structures and is organized as follows. §II A introduces
+the basic concepts that will be used in this article. In
+§II B, we review the sub-Planck structures that build
+in the phase space of the compass state. §II C explains
+the sensitivity to phase-space displacements associated
+to this compass state.
+A.
+Basic concepts
+The position operator ˆx and the momentum operator
+ˆp acts on an infinite-dimensional Hilbert space, forming
+the so-called Heisenberg-Weyl (HW) algebra hw(1) [101–
+103] for a single degree of freedom. The quantum uncer-
+tainty principle [9, 10], arising from commutator relations
+[ˆx, ˆp] = i (with ℏ being scaled to unity throughout) lim-
+its the size of a phase-space structure [10], for example,
+represented by the Wigner function [1] for hw(1) algebra
+and, more generally, by Moyal symbols [104] for other
+symmetries [102]. For convenience, we use the vector
+ζ := (x, p)⊤,
+(1)
+to represent the position-momentum pair in the follow-
+ing.
+A Schr¨odinger coherent state is a non-spreading wave
+packet of the quantum harmonic oscillator [8] and is an
+eigenstate of the annihilation operator:
+ˆa |α⟩ = α |α⟩
+with α ∈ C. The coherent states are obtained by dis-
+placing the vacuum state |0⟩, i.e.,
+|α⟩ = ˆD(α) |0⟩ ,
+(2)
+where
+ˆD(α) := exp(αˆa† − α∗ˆa),
+(3)
+is the displacement operator [103].
+The overlap between two coherent states |α⟩ and |β⟩
+is [105]
+|⟨α | β⟩|2 = e−|α|2−|β|2+2β∗α = e−|α−β|2,
+(4)
+which implies that two different coherent states are not
+orthogonal.
+The Wigner function for a generic quantum state ˆρ is
+written as an expectation value of the parity kernel [4, 6]
+Wˆρ (ζ) := tr
+�
+ˆρ ˆ∆(α)
+�
+,
+(5)
+
+3
+(a)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(b)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(c)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+FIG. 1: Wigner distribution of the compass state with (a) x0 = 4 (b) x0 = 8 and (c) x0 = 12. Insets represent the
+central interference pattern of each case.
+10-1
+100
+101
+x0
+10-3
+10-2
+10-1
+100
+101
+102
+"x"p
+FIG. 2: Variation of the area of the central phase-space
+structure of the compass state versus x0.
+where
+ˆ∆(α) := 2 ˆD(α)ˆΠ ˆD†(α), ˆΠ := (−1)ˆa†ˆa ,
+(6)
+being the displaced parity operator.
+The Wigner function for a coherent state is a strictly
+positive function, and appeared as a Gaussian of the
+form [5] (we omit the normalization of states and their
+Wigner functions throughout the paper)
+G(ζ; ±x0, ±p0) = e−(x∓x0)2−(p∓p0)2,
+(7)
+where (x0, p0) is the location of the coherent state in
+phase space.
+The product of uncertainties of position
+and momentum for a coherent state has a lower limit
+∆x∆p = 1/2 [5, 9, 10, 105], which is also known as the
+Planck action in the phase space.
+It is a common belief that phase-space structures with
+areas smaller than the Planck scale either do not exist
+or have no observational consequences for physical quan-
+tum states. In fact, this is true for all Gaussian states
+(coherent, squeezed, thermal, etc.) [6, 7] and even for
+other non-Gaussian states like cat states [31, 32] that ex-
+hibit rapid oscillations in one direction of phase space
+but an infinite Gaussian profile in the orthogonal direc-
+tion [54]. However, this notion was refuted by Zurek [33],
+who demonstrated that the Wigner function of compass
+states develops phase-space structures with dimensions
+far smaller than the Planck scale, arguing that these
+structures play a vital role in determining the sensitivity
+of these states against perturbations.
+B.
+Zurek compass state
+The Zurek compass state [33] is obtained from the su-
+perposition of the following four coherent states
+|ψ⟩ := |x0/
+√
+2⟩ + |−x0/
+√
+2⟩ + |ix0/
+√
+2⟩ + |−ix0/
+√
+2⟩ ,
+(8)
+with x0 ∈ R. Fig. 1 depicts the Wigner function for this
+compass state for the cases of x0 = 4, 8 and 12. Note
+that we normalize the Wigner functions throughout by
+using their maximum amplitudes, |Wˆρ(0)|. The Wigner
+function of the compass state (8) can be represented as
+
+4
+(a)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(b)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(c)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+0
+0.2
+0.4
+0.6
+0.8
+1
+FIG. 3: Overlap of the compass state with its δα-displaced part with δα = (δx + iδp)/
+√
+2: (a) x0 = 4 (b) x0 = 8 and
+(c) x0 = 12.
+follows
+W|ψ⟩(ζ) = W◦(ζ) + WΞ(ζ) + W⊞(ζ),
+(9)
+where the first term
+W◦(ζ) :=G(ζ; x0, 0) + G(ζ; −x0, 0) + G(ζ; 0, x0)+
+G(ζ; 0, −x0),
+(10)
+represents the Wigner function of four coherent states
+that appear in the phase space as Gaussian lobes. The
+second term in Eq. (9) is
+WΞ(ζ) := 1
+2
+�
+i1,i2=±1
+I(i1x, i2p),
+(11)
+with
+I(ζ) := G(ζ; x0/2, x0/2) cos
+�
+x0
+�
+x + p − x0
+2
+� �
+,
+(12)
+reflecting the Gaussian-modulated oscillations that ap-
+pear far away from the phase-space origin.
+The central pattern resembles a chessboard as shown
+in the insets of Fig. 1 and is generated by
+W⊞(ζ) := 1
+2G(ζ; 0, 0)
+�
+cos(2x0x) + cos(2x0p)
+�
+.
+(13)
+This pattern consists of tiles with alternate signs (central
+chessboardlike pattern). The extension of each tile can
+be roughly estimated by calculating zeros of Eq. (13),
+and it is found that it is proportional to x−1
+0
+in all di-
+rections of phase space. As a result, the support area of
+each tile in the chessboardlike pattern is proportional to
+x−2
+0
+as shown in the log-log plot of the central support
+area versus x0 in Fig. 2, which is much smaller than the
+area of the coherent state for x0 ≫ 1. Note that the mix-
+ture of two cat states also contains the same sub-Planck
+structures that are found in the compass state [54].
+The sub-Planck structures also emerge in the Wigner
+functions of non-Gaussian states with the SU(1,1) [53]
+and SU(2) symmetries [54].
+In particular, it has been
+found that the Wigner function of the superposition of
+four SU(1,1) (or SU(2)) coherent states also have sub-
+Planck structures similar to the compass state when rep-
+resented on the Poincar´e disk [53] (or the sphere [54]).
+The two-mode bosonic realization of the SU(1,1) im-
+plies that the sub-Planck structures in the phase space
+of the SU(1,1) compass state can be associated to the
+number of photons added to one of the modes of the
+two-mode squeezed number states [53], and they arise
+at greater numbers of these added photons. The exis-
+tence of the sub-Planck structures in the Wigner func-
+tion of the SU(2) compass state can similarly be linked
+to the angular momentum; the higher value of the angu-
+lar momentum causes sub-Planck structures in the phase
+space [54]. In the subsequent sections, we will demon-
+strate how adding or subtracting photons from superpo-
+sitions related to the one-mode non-Gaussian SVS can
+also cause the emergence of sub-Planck structures in the
+phase space of those states.
+C.
+Sensitivity of compass state
+The sensitivity of a quantum state to displacements
+can be determined by calculating the overlap between it
+and its slightly displaced version [98]. The overlap be-
+tween a state ˆρ and its displaced version ˆD(δα)ˆρ ˆD†(δα)
+is
+Oˆρ(δα) := tr{ˆρ ˆD(δα)ˆρ ˆD†(δα)} =
+���⟨ψ| ˆD(δα)|ψ⟩
+���
+2
+,
+(14)
+where δα ∈ C is an arbitrary displacement. Note that the
+last equality of above expression holds when the state is
+pure, ˆρ = |ψ⟩⟨ψ|. The smaller the displacement δα needs
+to be in order to bring the overlap to zero, the more sensi-
+tive the state is claimed to be against displacements [37].
+This overlap results in
+O|α⟩(δα) = e−|δα|2,
+(15)
+for a coherent state |α⟩, indicating that the smallest no-
+ticeable displacement that vanishes this overlap is above
+
+05
+(a)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(b)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(c)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+FIG. 4: Wigner distribution of the PASVS with (a) n = 10 (b) n = 15 and (c) n = 20. In all cases r = 0.5. Insets
+represent the central interference pattern of each case.
+(a)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(b)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(c)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+FIG. 5: Wigner distribution of the PSSVS with (a) n = 10 (b) n = 15 and (c) n = 20. In all cases r = 0.5. Insets
+represent the central interference pattern of each case.
+the Planck scale, |δα| > 1. It is interesting to note that
+the sensitivity to displacements in coherent states is inde-
+pendent of the quantity of quanta contained in the state,
+¯n = ⟨ˆa†ˆa⟩ = |α|2. Therefore, increasing ¯n will not im-
+prove the sensitivity and is solely limited by the shot
+noise introduced by vacuum fluctuations [99, 100].
+We now discuss the sensitivity of the compass state
+(8) to phase-space displacements. Assuming x0 ≫ 1 and
+|δα| ≪ 1 , the overlap (14) for this compass state results
+in
+O|ψ⟩(δα) = 1
+4e− 1
+2 |δα|2�
+cos (x0δx) + cos (x0δp)
+�2,
+(16)
+
+6
+with
+δα = δx + iδp,
+δj ∈ R.
+(17)
+It can be concluded that O|ψ⟩(δα) becomes zero when
+either of the conditions is satisfied
+δx ± δp = 2m + 1
+x0
+π, m ∈ Z.
+(18)
+As illustrated in Fig. 3 for O|ψ⟩(δα) of cases when x0
+is increased from 4 to 12, the overlap vanishes for the
+displacements |δα| ∼ x−1
+0
+and the arbitrary directions in
+the phase space. As a result, it can be inferred that this
+sensitivity is proportional to x−1
+0
+and that ¯n = x2
+0/2 ties it
+to the number of excitations ¯n. Therefore, in comparison
+to coherent states, a compass state with ¯n excitations has
+shown √¯n-enhanced sensitivity to displacements of any
+arbitrary directions in the phase space. Weak force mea-
+surements have been performed with Heisenberg-limited
+sensitivity using compass states [36, 37]. In contrast, cat
+states have shown the sensitivity to displacements along
+the specific direction in the phase space [54]. It has been
+found that cat-state mixtures only exhibit this enhanced
+sensitivity for displacements along particular phase-space
+directions [53, 54]. Hence, cat-state mixtures with sub-
+Planck structures in the Wigner function do not have
+the potential for metrology of compass states, for which
+the additional quantum coherence of the cat-state super-
+position provided by the second term in Eq. (9) plays a
+crucial role.
+The SU(1,1) and SU(2) compass states have shown the
+same sensitivity to displacements as their HW counter-
+parts [53, 54]. The sensitivity of the SU(1,1) compass
+state can be connected with the amount of the number
+of photons added to one of the modes of the two-mode
+squeezed number state, and this sensitivity improves as
+the quantity of added photons increases [53]. Similarly,
+the sensitivity of the SU(2) compass state improves as
+the angular momentum goes higher [54].
+This addition
+of the photons increases the average photon number in
+the states, and it can be understood in a way similar to
+that for compass states of the harmonic oscillator, i.e.,
+injecting more photons in the states improves its sensi-
+tivity.
+III.
+NON-GAUSSIAN SVS
+The non-Gaussian Wigner functions of the PASVS
+and PSSVS illustrate the non-Gaussian nature of these
+states [72–75, 77, 79]. In this section, we first provide
+a brief review of two non-Gaussian SVS, the PASVS
+and the PSSVS, in §III A and §III B, respectively. These
+two states are heavily used in our construction of non-
+Gaussian states that manifest the sub-Planck structures
+in §IV. The Wigner functions of both PASVS and PSSVS
+are discussed in relation to the amount of photons added
+or subtracted in the following subsections.
+A.
+PASVS
+First, we review the Wigner function of the PASVS.
+The creation operator ˆa† is repeatedly applied to SVS
+ˆS(±r) |0⟩ to obtain a single-mode PASVS [69]
+|ψ±
+PA⟩ := ˆa†n ˆS(±r) |0⟩ with n ∈ N.
+(19)
+The subscript “PA” is the shorthand for “PASVS”, and
+we introduce“±” in the squeezing operator ˆS(±r) with
+the definition [106]
+ˆS(±r) := exp
+�
+± r
+2
+�
+ˆa†2 − ˆa2� �
+.
+(20)
+which allows us to preserve part of the expressions intro-
+duced in this section for later uses in §IV.
+Using Eq. (5), the Wigner function of PASVS is easily
+found to be [72, 73, 77, 79]
+W|ψ±
+PA⟩(ζ) =exp (χ±) [± sinh(2r)]n
+π4n
+n
+�
+l=0
+(n!)2 [∓2 coth(r)]l
+l! [(n − l)!]2
+���Hn−l
+�
+−i
+�
+±2 coth(r)¯α±
+����
+2
+,
+(21)
+where Hm represents the Hermite polynomial, and
+χ± := ± sinh(2r)
+�
+α∗2 + α2�
+− 2|α|2 cosh(2r),
+(22)
+with
+¯α± := α cosh(r) ∓ α∗ sinh(r).
+(23)
+The
+non-Gaussian
+shape
+of
+the
+Wigner
+function
+W|ψ+
+PA⟩(ζ), which is shown in Fig. 4 for the cases when
+n is chosen as 10, 15 and 20, indicates that PASVS is a
+non-Gaussian state. We can clearly see the interference
+pattern that emerge in the form of an oscillating pattern
+in the p direction in the phase space. As the number of
+photons n rises, this pattern gets more pronounced (the
+frequency of the oscillations is increased). Moreover, the
+existence of these negative peaks in the Wigner function
+shows that the PASVS is a non-classical state as well.
+Another indication of the nonclassicality of this state is
+the squeezing effect in one of the quadratures, which is
+visible in the plots. Note that the PASVS is the Gaussian
+SVS when n = 0.
+B.
+PSSVS
+Now, we review the Wigner function of the PSSVS.
+The PSSVS [74, 75] is obtained by repeatedly applying
+the annihilation operator ˆa to the SVS as
+|ψ±
+PS⟩ := ˆan ˆS(±r) |0⟩ ,
+(24)
+
+7
+(a)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(b)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(c)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+FIG. 6: Wigner distribution of the pure SPASVS with (a) n = 10 (b) n = 15 and (c) n = 20. In all cases r = 0.5.
+Insets represent the central interference pattern of each case.
+101
+102
+n
+10-2
+"x"p
+FIG. 7: Variation of the area of the central phase-space
+structure versus the photon number n of the SPASVS
+state with n chosen from 5 to 100.
+where the subscript “PS” is the shorthand for “PSSVS”.
+The Wigner function of this state is also in a non-
+Gaussian form, and is written as
+W|ψ±
+PS⟩(ζ) =exp (χ±) [± sinh(2r)]n
+π4n
+n
+�
+l=0
+(n!)2 [∓2 tanh(r)]l
+l! [(n − l)!]2
+���Hn−l
+�
+−i
+�
+±2 tanh(r)¯α±
+����
+2
+.
+(25)
+We plot the Wigner function W|ψ+
+PS⟩(ζ) in Fig. 5 with r
+being 0.5 and n being 10, 15, and 20. This Wigner func-
+tion exhibit the interference pattern around the origin of
+the phase space and oscillates along the p direction in
+the phase space. As n grows, the frequency of this os-
+cillating pattern increases. The simpliest case n = 0 of
+the PSSVS corresponds to the Gaussian SVS. Another
+indicator of the non-classical nature of this state is the
+squeezing effect in one of the quadratures, which is in-
+dicative of the nonclassicality of state.
+In summary, for non-zero values of n, the Wigner func-
+tion of PASVS and PSSVS maintains non-Gaussianity. It
+is interesting to note that both PASVS and PSSVS ex-
+hibit similar phase-space features as cat-like states. The
+addition or subtraction of photons from the Gaussian
+SVS has been employed both theoretically [93–95] and
+experimentally [96, 97] to produce cat-like states. Both
+PASVS and PSSVS have been found very useful for the
+quantum metrology [81–83]. When photons are added to
+or subtracted from the Gaussian SVS, the average photon
+number of the resulting state grows [82, 83]. It has been
+shown that for the same number of photons applied on
+the Gaussian SVS, the subsequent PASVS has a higher
+average photon number than the PSSVS [82, 83]. This
+means that the PASVS has a better potential for metrol-
+ogy than the PSSVS [82].
+IV.
+SUPERPOSITION OF NONGAUSSIAN SVS
+In this section, we introduce the quantum states of our
+interest and present their phase-space analysis by using
+the Wigner function [1–5]. The photon-number distribu-
+tion [27] and the Wigner function [26] have both been
+used to discuss the nonclassicality in the superpositions
+
+8
+(a)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(b)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(c)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+FIG. 8: Wigner distribution of the mixed-state SPASVS with (a) n = 10 (b) n = 15 and (c) n = 20. In all cases
+r = 0.5. Insets represent the central interference pattern of each case.
+of two SVSs. Theoretically, a non-linear harmonic oscil-
+lator can be used to create some specified superpositions
+of two SVSs [27]. Here, we focus on the superposition of
+two Gaussian SVSs with opposite phases given by
+|ψSSV⟩ := ˆS(r) |0⟩ + ˆS(−r) |0⟩ ,
+(26)
+with “SSV” in the subscript for the “superposition of
+SVSs”.
+The Wigner function corresponding to this
+state exhibit non-Gaussian and non-classical proper-
+ties [26, 27].
+The addition of n photons to the superposed state (26)
+leads to the superposition of two photon-added squeezed-
+vacuum states (SPASVS), that is,
+|ψSPA⟩ := ˆa†n |ψSSV⟩ = |ψ+
+PA⟩ + |ψ−
+PA⟩
+(27)
+with the subscript “SPA” a shorthand for “SPASVS”.
+Similarly, the subtraction of n photons from the super-
+position (26) results in the superposition of two photon-
+subtracted squeezed-vacuum states (SPSVS) of the fol-
+lowing form:
+|ψSPS⟩ := ˆan |ψSSV⟩ = |ψ+
+PS⟩ + |ψ−
+PS⟩ ,
+(28)
+where
+the
+subscript
+“SPS”
+is
+the
+short
+form
+of
+“SPSSVS”.
+Following subsections cover the discussion about these
+two superpositions, which are structured as follows. In
+§IV A, we discuss Wigner functions corresponding to
+|ψSPA⟩ and |ψSPS⟩. Here, we describe how the addition
+and subtraction of photons lead to the sub-Planck struc-
+tures in the phase space. In §IV B, we discuss the sensi-
+tivity to displacements associated with these two super-
+positions.
+A.
+Photons addition versus photons subtraction
+The Wigner function of the SPASVS (27) can be ob-
+tained by using Eq. (5) as (see Appendix A for detailed
+derivations)
+W|SPA⟩(ζ) = 2 Re [IΞ(ζ)] + W⊞(ζ),
+(29)
+and is shown in Fig. 6 for the cases when n = 10, 15 and
+20. The first term in (29)
+IΞ(ζ) :=
+exp (ξ) [−i tanh(2r)]n
+π4n cosh(r)
+�
+1 + tanh2(r)
+n
+�
+l=0
+(n!)2 [−2i coth(r)]l
+[(n − l)!]2
+Hn−l [iΩα−] Hn−l
+�
+−Ωα∗
++
+�
+,
+(30)
+provides the interference pattern that appears far away
+from the phase-space origin, where
+Ω :=
+�
+tanh(2r)
+sinh(r)
+,
+(31)
+and
+ξ := − tanh(2r)
+�
+α2 − α2∗�
+− 2|α|2 sech(2r),
+(32)
+with
+α± := α∗ sinh(r) ± α cosh(r)
+(33)
+being the hyperbolic-rotated α.
+For our purposes, we concentrate on the second term in
+Eq. 29, which contributes to the chessboardlike pattern
+that is visible at the phase-space origin for n ≫ 1. This
+
+9
+(a)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(b)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(c)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+FIG. 9: Wigner distribution of the pure SPSSVS with (a) n = 10 (b) n = 15 and (c) n = 20. In all cases r = 0.5.
+Insets represent the central interference pattern of each case.
+101
+102
+n
+10-2
+"x"p
+FIG. 10: Variation of the area of the central
+phase-space structure versus the photon number n of
+the SPSSVS state with n chosen from 5 to 100.
+central interference pattern is equal to the sum of the
+individual Wigner functions of PASVSs as
+W⊞(ζ) := W|ψ+
+PA⟩(ζ) + W|ψ−
+PA⟩(ζ).
+(34)
+The extension of a single tile in the chessboardlike pat-
+tern is inversely proportional to n along any arbitrary
+direction in the phase space.
+This is demonstrated in
+Fig. 6, where we see that as n increases, the support area
+of a fundamental tile in the chessboardlike pattern de-
+creases. The area of a fundamental tile can be roughly
+estimated by calculating the zeros of the Eq. (34). For
+n ≫ 1, the support area of a fundamental tile may be
+considerably lower than the area of the coherent state.
+This is depicted in Fig. 7, where we plot the area of the
+center tile against n using a log-log plot. Thus, the sub-
+Planck structures that Zurek discovered for the compass
+state [33] are also present in SPASVS.
+The same sub-Planck structures are also contained by
+following mixed state
+ˆρPA := |ψ+
+PA⟩⟨ψ−
+PA| + |ψ−
+PA⟩⟨ψ+
+PA| ,
+(35)
+and its Wigner function, which is the same as the one
+given in Eq. (34), is shown in Fig. 8.
+Similarly, for the SPSSVS (28), the Wigner function is
+also written into two terms (see Appendix A for detailed
+derivations):
+W|SPS⟩(ζ) = 2 Re [IΞ(ζ)] + W⊞(ζ),
+(36)
+which is plotted in Fig. 9. With
+ω :=
+�
+tanh(2r)
+cosh(r)
+,
+(37)
+the term that contains
+IΞ(ζ) :=
+exp (ξ) [i tanh(2r)]n
+π4n cosh(r)
+�
+1 + tanh2(r)
+n
+�
+l=0
+(n!)2 [2i tanh(r)]l
+[(n − l)!]2
+Hn−l [−ωα−] Hn−l
+�
+−iωα∗
++
+�
+(38)
+causes the interference pattern that manifests as oscil-
+lating peaks far from the phase-space origin. Again, we
+concentrate on the second term of Eq. (36), which results
+in the chessboardlike pattern at the phase-space origin.
+
+10
+(a)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(b)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+(c)
+-12
+-8
+-4
+0
+4
+8
+12
+x
+-12
+-8
+-4
+0
+4
+8
+12
+p
+-1.6
+-0.8
+0
+0.8
+1.6
+-1.6
+-0.8
+0
+0.8
+1.6
+-1
+-0.5
+0
+0.5
+1
+FIG. 11: Wigner distribution of the mixed-state SPSSVS with (a) n = 10 (b) n = 15 and (c) n = 20. In all cases
+r = 0.5. Insets represent the central interference pattern of each case.
+This term is the sum of the Wigner functions (25) of
+PSSVSs, that is,
+W⊞(ζ) := W|ψ+
+PS⟩(ζ) + W|ψ−
+PS⟩(ζ).
+(39)
+This pattern manifests sub-Planck oscillations around
+the origin of the phase space. It is similar to the pattern
+identified for the case of SPASVS. Again, the extension of
+a fundamental tile can be estimated by calculating zeros
+of Eq. (39). As shown in Fig. 9, the extensions of these
+alternating-sign tiles decrease isotropically as n increases,
+and the support area of these tiles in the phase is signif-
+icantly less than the coherent state for n ≫ 1. This is
+also shown in Fig. 10, which is a log-log plot showing the
+extension of the central tile. It is interesting to note that
+for a given r and n, the central tile in the chessboardlike
+pattern is larger than that of the SPASVS.
+Additionally, we demonstrate that the following mixed
+state likewise has the same sub-Planck structures
+ˆρPS := |ψ+
+PS⟩⟨ψ−
+PS| + |ψ−
+PS⟩⟨ψ+
+PS| .
+(40)
+Similar to the case of the mixture of PASVSs (35), the
+Wigner function of ˆρPS shown in Fig. 11 is identical to
+Eq. (39).
+Thus, the photon-addition or photon-subtraction op-
+erations on the superpositions of the Gaussian SVS may
+produce the sub-Planck structures in the phase space.
+The average photon number of the resulting states is ac-
+tually increased by either adding or subtracting photons
+from the superposition of the Gaussian SVS [82], with the
+addition of photons producing a higher average photon
+number than the subtraction of photons. This difference
+in holding the photons number in the states also effects
+the size of the sub-Planck structures of such states. As an
+illustration, the photons addition case has demonstrated
+to hold smaller sub-Planck structures in the phase space
+than the photons subtraction for the same amount of
+photons utilized in the Gaussian SVS. Hence, the idea
+of the sub-Planck structures connected to our states can
+be understood in a manner similar to that of the com-
+pass state [33], i.e., a higher average photon number in
+the states leads to the smaller tiles in the chessboardlike
+pattern.
+In summary, the sub-Planck structures of the compass
+state are present in the Wigner functions of both SPASVS
+and SPSSVS. The mixtures associated to PASVSs or
+PSSVSs likewise contain the same sub-Planck structures.
+Additionally, for the available average photon number,
+the SPASVS and its associated mixture show smaller sub-
+Planck structures than their counterparts in the photon-
+subtracted case.
+B.
+Sub-shot noise sensitivity of our states
+In this subsection, we discuss the susceptibility of our
+proposed states to phase-space displacement. Let us first
+consider SPASVS (27). The overlap (14) for this state un-
+der the approximation |δα| ≪ 1 and n ≫ 1 leads to (see
+Appendix A 2 for the detailed derivations)
+OSPA(δα) =
+�
+⟨ψ+
+PA| ˆD(δα) |ψ+
+PA⟩ + ⟨ψ−
+PA| ˆD(δα) |ψ−
+PA⟩
+�2
+.
+(41)
+
+11
+(a)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(b)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(c)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+0
+0.2
+0.4
+0.6
+0.8
+1
+FIG. 12: Overlap of the pure SPASVS state with its δα-displaced part with δα = (δx + iδp)/
+√
+2: (a) n = 10
+(b) n = 15 and (c) n = 20. In all cases r = 0.5.
+(a)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(b)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(c)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+0
+0.2
+0.4
+0.6
+0.8
+1
+FIG. 13: Overlap of the mixed-state SPASVS with its δα-displaced part with δα = (δx + iδp)/
+√
+2: (a) n = 10
+(b) n = 15 and (c) n = 20. In all cases r = 0.5.
+Each term of this overlap is calculated as
+⟨ψ±
+PA| ˆD(δα) |ψ±
+PA⟩ =[∓ sinh(2r)]n e−|η±|2/2
+4n
+n
+�
+l=0
+(n!)2
+l![(n − l)!]2
+[∓2coth(r)]lHn−l [Θ±] Hn−l
+�
+Θ∗
+±
+�
+,
+(42)
+where
+Θ± = i
+�
+±coth(r)
+2
+η±,
+(43)
+and
+η± = δαcosh(r) ∓ δα∗sinh(r),
+(44)
+with
+δα = δx + iδp.
+(45)
+In Fig. 12, we plot this overlap for n=10, 15, and 20. For
+the large n, a small displacement |δα| ≪ 1 can turn the
+SPASVS into an state orthogonal to its original state,
+and this orthogonality occurs in all phase-space direc-
+tions. We have normalized overlaps to their maximum
+amplitudes, Oˆρ(0).
+Let us now consider the mixture of PASVSs (19), for
+which the overlap (14) is calculated as
+OˆρPA(δα) =
+���⟨ψ+
+PA| ˆD(δα) |ψ+
+PA⟩
+���
+2
++
+���⟨ψ−
+PA| ˆD(δα) |ψ−
+PA⟩
+���
+2
+.
+(46)
+We plot this overlap with n=10, 15, and 20 in Fig. 13.
+Again, we see that the overlap OˆρPA(δα) disappears for
+the displacement |δα| ≪ 1, but unlike the SPASVS, this
+orthogonality now take place when δx = ±δp in the phase
+space.
+Similarly, overlap (14) for SPSSVS is obtained as
+OSPS(δα) =
+�
+⟨ψ+
+PS| ˆD(δα) |ψ+
+PS⟩ + ⟨ψ−
+PS| ˆD(δα) |ψ−
+PS⟩
+�2
+,
+(47)
+where
+⟨ψ±
+PS| ˆD(δα) |ψ±
+PS⟩ =[∓ sinh(2r)]n e−|η±|2/2
+4n
+n
+�
+l=0
+(n!)2
+l![(n − l)!]2
+[∓2tanh(r)]lHn−l [θ±] Hn−l
+�
+θ∗
+±
+�
+,
+(48)
+with
+θ± = i
+�
+±tanh(r)
+2
+η±.
+(49)
+
+12
+(a)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(b)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(c)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+0
+0.2
+0.4
+0.6
+0.8
+1
+FIG. 14: Overlap of the pure SPSSVS state with its δα-displaced part with δα = (δx + iδp)/
+√
+2: (a) n = 10
+(b) n = 15 and (c) n = 20. In all cases r = 0.5.
+(a)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(b)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+(c)
+-1.6
+-0.8
+0
+0.8
+1.6
+/x
+-1.6
+-0.8
+0
+0.8
+1.6
+/p
+0
+0.2
+0.4
+0.6
+0.8
+1
+FIG. 15: Overlap of the mixed-state SPSSVS with its δα-displaced part with δα = (δx + iδp)/
+√
+2: (a) n = 10
+(b) n = 15 and (c) n = 20. In all cases r = 0.5.
+In Fig. 14, we plot this overlap with n equal to 10, 15, and
+20. The SPSSVS overlap plot exhibits the same behavior
+as the SPASVS: the overlap disappears in any direction in
+phase space when |δα| ≪ 1. The only distinction is that,
+for the same n and r, the central pattern of the overlap of
+the SPSSVS is larger than that of the SPASVS, showing
+that the SPSSVS is less sensitive than the SPASVS.
+Finally, we consider mixtures of PSSVSs (24).
+The
+overlap (14) for this state leads to
+OˆρPS(δα) =
+���⟨ψ+
+PS| ˆD(δα) |ψ+
+PS⟩
+���
+2
++
+���⟨ψ−
+PS| ˆD(δα) |ψ−
+PS⟩
+���
+2
+.
+(50)
+In Fig. 15, we plot the overlap OˆρPS(δα) using the same
+parameter values as that of the SPSSVS. We observe that
+the overlap of the mixture of the PSSVSs looks similar
+to the mixture of the PASVSs, with the distinction being
+that the mixture of PSSVSs appears to be less sensitive
+for a given number of n and r, which is manifested as the
+larger chessboardlike pattern in the center of the phase
+space than that of the mixture of PASVSs.
+In summary, we have demonstrated that the sensitivity
+associated to our proposed states depends on the quan-
+tity of photons added (or subtracted), and it drops con-
+siderably below the sensitivity of the coherent state when
+there are excessive amount of photons added (or sub-
+tracted). For both SPASVS and SPSSVS, the enhanced
+sensitivity is unaffected by the directions of phase-space
+displacements.
+However, for the mixtures related to
+PASVSs or PSSVSs, this enhancement only takes place
+in particular phase-space directions. This implies that
+compared to mixed states, our superposition states have
+more potential for quantum sensing applications. More-
+over, it has been found that the quantum states associ-
+ated with photon addition cases are more sensitive than
+their counterparts of the photon subtraction cases.
+V.
+SUMMARY AND OUTLOOK
+We have shown that the Wigner function of the
+SPASVS (or SPSSVS) contains the chessboardlike pat-
+tern around the origin of the phase space. Similar chess-
+boardlike pattern is also emerged by the mixtures related
+to PASVSs and PSSVSs. The support area of the phase-
+space structures contained by this chessboardlike pattern
+varies inversely with the photon number added (or sub-
+tracted). When a sizable number of photons are added
+(or subtracted), the support area of these structures is
+noticeably smaller than that of the coherent state, and
+these are the same sub-Planck structures, as shown by
+compass states.
+The average photon numbers of our states, which
+are increased either by photon-addition or photon-
+
+13
+subtraction actions on the Gaussian SVS, have an im-
+pact on the size of the sub-Planck structures in the phase
+space.
+The sub-Planck structures associated with the
+SPASVS are smaller than those of the SPSSVS for the
+same number of photons added or subtracted. This is be-
+cause the photon-addition operation always leads to the
+higher average photon number in the resultant states.
+The association of the average photon number with the
+sub-Planck structures in our states is much similar to
+that of the compass states, i.e., higher average photon
+number in the compass state correspond to the smaller
+sub-Planck structures in the phase space.
+We have demonstrated that the sensitivity of our pro-
+posed states is noticeably higher than that of the coherent
+state when a significant number of photons are added (or
+subtracted). Both the SPASVS and SPSSVS exhibit the
+enhanced sensitivity, which is independent of the phase-
+space directions, indicating that they hold more promise
+for quantum metrology. In addition, the difference in the
+sensitivities between the photon addition and subtraction
+cases is arose from the different average photon numbers
+in the states; photon addition cases are demonstrated to
+have greater sensitivity than the subtracted cases.
+It is incredibly exciting that sub-Planck structures can
+possibly build from photons being added to or subtracted
+from states. As a result, it will be able to apply a va-
+riety of ways to engineer compass-like states in associa-
+tion with contemporary experiments [94–97]. For exam-
+ple, the theoretical research in [94] shows that subtract-
+ing a photon from the Gaussian SVS results in an odd
+Schr¨odinger cat state.
+Another subsequent theoretical
+approach introduces the idea of photon subtraction from
+the Gaussian SVS to produce the compass-like states [61].
+Additionally, theoretical research to construct the cat-
+like states advocated in [94] is subsequently applied in
+actual experiments [96, 97]. These illustrations unequiv-
+ocally demonstrate that it is possible to add or subtract
+photons from states in both theory and experiments to
+produce compass-like states. It may possible that some
+of these techniques can be modified to produce SPASVS
+and SPSSVS, which are entirely new research avenues
+that can be adapted in the future.
+ACKNOWLEDGMENTS
+NA acknowledges the support of postdoctoral fund
+of
+the
+Zhejiang
+Normal
+University
+under
+Grant
+No. ZC304021937. GX acknowledges support by the Na-
+tional Natural Science Foundation of China (Grants Nos.
+11835011 and No. 12174346). WML acknowledges the
+support from the National Key R&D Program of China
+under grants No. 2021YFA1400900, 2021YFA0718300,
+2021YFA1402100, NSFC under grants Nos. 61835013,
+12174461, 12234012, and Space Application System of
+China Manned Space Program.
+Appendix A: Wigner functions of SPASVS and SPSSVS
+This section provides the main steps to drive the Wigner functions of SPASVS and SPSSVS.
+1.
+Derivations of the Wigner function of SPASVS
+Let us first consider the Wigner function of SPASVS given by Eq. (29). First term of this Wigner function is given
+by
+IΞ(ζ) =
+�
+ψ+
+PA
+��� ˆ∆(α)
+��� ψ−
+PA
+�
+,
+(A1)
+where the alternative form of the displaced parity operator ˆ∆(α) is [77]
+ˆ∆(α) := 1
+π2 e2|α|2 � ∞
+−∞
+d2βe−2α∗β+2αβ∗ |β⟩⟨−β| .
+(A2)
+Eq. (A1) can be rewritten as
+IΞ(ζ) = (−1)ne2|α|2
+π2 cosh(r)
+� ∞
+−∞
+d2β|β|2n exp
+�
+− |β|2 − tanh(r)
+2
+�
+β2 + β∗2�
+− 2βα∗ + 2β∗α
+�
+.
+(A3)
+We incorporate the factor |β|2n into a differential equation as
+IΞ(ζ) = (−1)ne2|α|2
+π2 cosh(r)
+∂2n
+∂sn∂tn
+� ∞
+−∞
+d2β exp
+�
+− |β|2 − tanh(r)
+2
+�
+β2 − β∗2�
+− 2βα∗ + 2β∗α + sβ + tβ∗
+�����
+s=t=0
+.
+(A4)
+
+14
+Consider the integral formula [107]
+� ∞
+−∞
+d2β exp
+�
+a|β|2 + bβ + cβ∗ + dβ2 + kβ∗2
+�
+=
+π
+√
+a2 − 4dk
+exp
+�−abc + b2k + c2d
+a2 − 4dk
+�
+,
+(A5)
+whose convergent conditions are Re [a ± d ± k] < 0 and Re
+�
+(a2−4dk)/a±d±k
+�
+< 0. By using this integral Eq. (A4) leads
+to
+IΞ(ζ) =
+(−1)neξ
+π cosh(r)
+�
+1 + tanh2(r)
+∂2n
+∂sn∂tn exp
+�
+tanh(2r)
+4
+s2 − tanh(2r)
+4
+t2 +
+�
+1 + tanh2(r)
+�−1st − 2 cosh(r)sech(2r)α−s
+− 2 cosh(r)sech(2r)α∗
++t
+������
+s=t=0
+,
+(A6)
+with
+ξ := −(α2 − α∗2) tanh(2r) − 2|α|2sech(2r).
+(A7)
+It is challenging to solve Eq. (A6) because it has eγst terms. We employ the following sum series [73] to get rid of it.
+exp(Cs + Dt + Est) =
+∞
+�
+l=0
+El
+l!
+∂2l
+∂Cl∂Dl [exp (Cs + Dt)] .
+(A8)
+Using this formula Eq. (A6) modifies as
+IΞ(ζ) =
+(−1)neξ
+π cosh(r)
+�
+1 + tanh2(r)
+∞
+�
+l=0
+1
+l! 22l
+�
+1 + tanh2(r)
+�−l
+cosh2l(r)sech2l(2r)
+∂2l
+∂α∗l
++αl
+−
+∂2n
+∂sn∂tn exp
+�tanh(2r)
+4
+s2 − tanh(2r)
+4
+t2
+− 2 cosh(r)sech(2r)(α−s + α∗
++t)
+�����
+s=t=0
+.
+(A9)
+Noticing the generating function of Hermite polynomial
+Hn(x) = ∂n
+∂sn exp
+�
+2xs − s2� ��
+s=0,
+(A10)
+and its recursive relation
+dl
+dxl Hn(x) =
+2ln!
+(n − l)!Hn−l(x).
+(A11)
+The preceding equation can then be simplified in the form of Eq. (30) by applying the relationships (A10) and (A11).
+Let us now calculate second term of the Wigner function (29). This term can be written as
+W⊞(ζ) =
+�
+ψ+
+PA
+��� ˆ∆(α)
+��� ψ+
+PA
+�
++
+�
+ψ−
+PA
+��� ˆ∆(α)
+��� ψ−
+PA
+�
+,
+(A12)
+where
+�
+ψ±
+PA
+��� ˆ∆(α)
+��� ψ±
+PA
+�
+=(−1)n
+π2
+e2|α|2
+cosh(r)
+∂2n
+∂sn∂tn
+� ∞
+−∞
+d2β exp
+�
+− |β|2 ± 1
+2 tanh(r)(β2 + β∗2) − 2βα∗ + 2β∗α + sβ + tβ∗���
+s=t=0.
+Using the integral (A5), we get
+�
+ψ±
+PA
+��� ˆ∆(α)
+��� ψ±
+PA
+�
+=(−1)n
+π
+exp
+�
+± sinh(2r)(α∗2 + α2) − 4 cosh2(r)|α|2�
+∂2n
+∂sn∂tn exp
+�
+± 1
+4 sinh(2r)(s2 + t2)
++ 2 cosh(r)(¯α±s − ¯α∗
+±t) + cosh2(r)st
+�����
+s=t=0
+.
+(A13)
+Again, use of sum series (A8) eliminates the factors eγst, that is,
+�
+ψ±
+PA
+��� ˆ∆(α)
+��� ψ±
+PA
+�
+=
+∞
+�
+l=0
+(−1)l
+22ll!
+∂2l
+∂ ¯αl
+±∂ ¯α∗l
+±
+∂2n
+∂sn∂tn exp
+�
+±sinh(2r)
+4
+�
+s2 + t2�
++ 2 cosh r
+�
+¯α±s − ¯α∗
+±t
+������
+s=t=0
+.
+(A14)
+Then, by using the relations (A10) and (A11), the expression (39) is obtained.
+
+15
+2.
+Derivations of the Wigner function of SPSSVS
+This section presents the detailed derivation of the Eq. (36), for which the first term gets form as below
+IΞ(ζ) =
+�
+ψ+
+PS
+��� ˆ∆(α)
+��� ψ−
+PS
+�
+.
+(A15)
+This term is calculated as
+IΞ(ζ) = 1
+π2
+e2|α|2
+cosh(r)
+∂2n
+∂sn∂tn exp
+�
+− tanh(r)
+2
+�
+t2 − s2�� � ∞
+−∞
+d2β exp
+�
+− |β|2 −
+�
+tanh(r)t + 2α∗�
+β −
+�
+tanh(r)s
+− 2α
+�
+β∗ − tanh(r)
+2
+(β2 − β∗2)
+�����
+s=t=0
+.
+(A16)
+Using the integral (A5), we obtain
+IΞ(ζ) =
+eξ
+π cosh(r)
+�
+1 + tanh2(r)
+∂2n
+∂sn∂tn exp
+�tanh(2r)
+4
+s2 − tanh(2r)
+4
+t2 + 2sech(2r) sinh(r)(α∗
++s − α−t)
++ sech(2r) sinh2(r)st
+�����
+s=t=0
+.
+(A17)
+Now, we eliminate eγst terms by using Eq. (A8)
+IΞ(ζ) =
+eξ
+π cosh(r)
+�
+1 + tanh2(r)
+∞
+�
+l=0
+1
+l!22lsechl(2r)
+∂2l
+∂α∗l
++∂αl
+−
+∂2
+∂sn∂tn exp
+�tanh(2r)
+4
+s2 − tanh(2r)
+4
+t2
++ 2sech(2r) sinh(r)(α∗
++s + α−t)
+�����
+s=t=0
+.
+(A18)
+Then, using the relations (A10) and (A11) we obtain expression (38).
+Finally, we derive the second term of the Eq. (36). This term can be written as
+W⊞(ζ) =
+�
+ψ+
+PS
+��� ˆ∆(α)
+��� ψ+
+PS
+�
++
+�
+ψ−
+PS
+��� ˆ∆(α)
+��� ψ−
+PS
+�
+,
+(A19)
+where
+�
+ψ±
+PS
+��� ˆ∆(α)
+��� ψ±
+PS
+�
+= 1
+π exp
+�
+± sinh(2r)(α2 + α∗2) − 2 cosh(2r)|α|2� ∂2n
+∂sntn exp
+�
+± 1
+4 sinh(2r)(s2 + t2)
+± 2 sinh(r)(¯α±t + ¯α∗
+±s) − sinh2(r)st
+�����
+s,t=0
+.
+(A20)
+Again, we use Eq. (A8) to get rid of all eγst factors, obtaining
+�
+ψ±
+PS
+��� ˆ∆(α)
+��� ψ±
+PS
+�
+= 1
+π exp
+�
+± sinh(2r)(α2 + α∗2) − 2 cosh(2r)|α|2� ∞
+�
+l=0
+(−1)l
+22ll!
+∂2l
+∂ ¯αl
+±¯α∗l
+±
+∂2n
+∂sntn exp
+�
+± sinh(2r)
+4
+�
+s2 + t2�
+± 2 sinh(r)
+�
+¯α±t + ¯α∗
+±s
+������
+s=t=0
+.
+(A21)
+Finally, this equation can be simplified to expression (39) by utilizing the relations (A10) and (A11).
+OVERLAPS OF SPASV AND SPSSV
+In this section, we calculate the overlap (14) of SPASVS and SPSSVS. Note that, for n ≫ 1 and |δα| ≪ 1, the
+contribution of the cross terms between the states to the overlap is negligible, that is,
+⟨ψ+
+PA| ˆD(δα) |ψ−
+PA⟩ = 0 and ⟨ψ+
+PS| ˆD(δα) |ψ−
+PS⟩ = 0.
+(A22)
+
+16
+First, we drive each term of Eq. (41). PASV (19) can be rewritten as [73]
+|ψ±
+PA⟩ = ˆS(±r)
+�
+ˆa† cosh(r) ± ˆa sinh(r)
+�n |0⟩ .
+(A23)
+Then, considering relation given by [73]
+(fˆa + gˆa†) :=
+�
+− i
+�
+fg
+2
+�n
+Hn
+�
+i
+�
+f
+2g ˆa + i
+� g
+2f ˆa†
+�
+,
+(A24)
+which leads to
+[ˆa† cosh(r) + ˆa sinh(r)]n =
+�
+− i
+�
+sinh(2r)
+4
+�n
+Hn
+�
+i
+�
+tanh(r)
+2
+ˆa + i
+�
+coth(r)
+2
+ˆa†
+�
+,
+(A25)
+[ˆa cosh(r) + ˆa† sinh(r)]n =
+�
+− i
+�
+sinh(2r)
+4
+�n
+Hn
+�
+i
+�
+tanh(r)
+2
+ˆa† + i
+�
+coth(r)
+2
+ˆa
+�
+.
+(A26)
+By using these relations, we obtain
+⟨ψ±
+PA| ˆD(δα)|ψ±
+PA⟩ =
+�
+∓ sinh(2r)
+4
+�n �
+0
+����� Hn
+�
+i
+�
+±coth(r)
+2
+ˆa
+�
+ˆD(η±)Hn
+�
+i
+�
+±coth(r)
+2
+ˆa†
+� ����� 0
+�
+,
+=
+�
+∓ sinh(2r)
+4
+�n � ∞
+−∞
+d2α
+π
+exp
+�
+− |α|2
+2
+− α
+2 η∗
+± + α∗
+2 η± − |α − η±|2
+2
+�
+Hn
+�
+i
+�
+±coth(r)
+2
+α
+�
+Hn
+�
+i
+�
+±coth(r)
+2
+(α∗ − η∗
+±)
+�
+,
+(A27)
+where
+ˆD(η±) = ˆS†(±r) ˆD(δα) ˆS(±r) with η± = δα cosh(r) ∓ δα∗ sinh(r).
+(A28)
+By using (A10), we get
+⟨ψ±
+PA| ˆD(δα)|ψ±
+PA⟩ =
+�
+∓ sinh(2r)
+4
+�n
+∂2n
+∂τ n∂tn exp
+�
+− i
+�
+±2 coth(r) η∗
+±τ
+�
+exp
+�
+− τ 2 − t2�
+� ∞
+−∞
+d2α
+π
+exp
+�
+− |α|2
+2
+− α
+2 η∗
+± + α∗
+2 η± − |α − η±|2
+2
++ i
+�
+±2 coth(r) αt + i
+�
+±2 coth(r) α∗τ
+�����
+τ=t=0
+.
+(A29)
+Using the integral (A5), the previous equation yields
+⟨ψ±
+PA| ˆD(δα)|ψ±
+PA⟩ =
+�
+∓ sinh(2r)
+4
+�n
+exp
+�
+− |η±|2
+2
+�
+∂2n
+∂τ n∂tn exp
+�
+− t2 + i
+�
+±2 coth(r) η±t − τ 2 − i
+�
+±2 coth(r) η∗
+±τ
+(A30)
+∓ 2 coth(r) tτ
+�����
+t=τ=0
+.
+(A31)
+First, we rid out the factors eγτt from above equation by using (A8). Then, by using (A10) and (A11), the preceding
+equation is simplified to (42).
+Similarly, PSSVS can be rewritten as [73]
+|ψ±
+PS⟩ = ˆS(±r)
+�
+ˆa cosh(r) ± ˆa† sinh(r)
+�n |0⟩ .
+(A32)
+The overlap
+⟨ψ±
+PS| ˆD(δα)|ψ±
+PS⟩ =
+�
+∓ sinh(2r)
+4
+�n �
+0
+����� Hn
+�
+i
+�
+±tanh(r)
+2
+ˆa
+�
+ˆD(η±)Hn
+�
+i
+�
+±tanh(r)
+2
+ˆa†
+� ����� 0
+�
+,
+=
+�
+∓ sinh(2r)
+4
+�n � ∞
+−∞
+d2α
+π
+exp
+�
+− |α|2
+2
+− α
+2 η∗
+± + α∗
+2 η± − |α − η±|2
+2
+�
+Hn
+�
+i
+�
+±tanh(r)
+2
+α
+�
+Hn
+�
+i
+�
+±tanh(r)
+2
+(α∗ − η∗
+±)
+�
+,
+(A33)
+
+17
+can be easily simplified to (48).
+[1] E. Wigner, On the quantum correction for thermody-
+namic equilibrium, Phys. Rev. 40, 749 (1932).
+[2] C. Gerry and P. Knight, Introductory Quantum Op-
+tics (Cambridge University Press, England, Cambridge,
+2005).
+[3] W. P. Schleich, Quantum Optics in Phase Space (Wiley-
+VCH, Weinheim, 2001).
+[4] R. P. Rundle and M. J. Everitt, Overview of the phase
+space formulation of quantum mechanics with applica-
+tion to quantum technologies, Adv. Quantum Technol.
+4, 2100016 (2021).
+[5] U. Leonhardt, Measuring the quantum state of light,
+Vol. 22 (Cambridge university press, United Kingdom,
+1997).
+[6] C. Navarrete-Benlloch, An Introduction to the Formal-
+ism of
+Quantum Information with Continuous Variables (Mor-
+gan & Claypool/IOP, Bristol, 2015).
+[7] B. L. Schumaker, Quantum mechanical pure states with
+Gaussian wave functions, Phys. Rep. 135, 317 (1986).
+[8] E. Schr¨odinger, Der stetige ¨ubergang von der mikro- zur
+makromechanik, Sci. Nat. 14, 664 (1926).
+[9] H. P. Robertson, The uncertainty principle, Phys. Rev.
+34, 163 (1929).
+[10] J. A. Wheeler and W. H. Zurek, Quantum Theory and
+Measurement (Princeton University Press, Princeton,
+NJ, 1983).
+[11] V. Buˇzek and P. L. Knight, I: Quantum interference, su-
+perposition states of light, and nonclassical effects (El-
+sevier, 1995) pp. 1–158.
+[12] M. Walschaers, Non-Gaussian quantum states and
+where to find them, PRX Quantum 2, 030204 (2021).
+[13] M. C. de Freitas and V. V. Dodonov, Non-Gaussianity
+of four-photon superpositions of fock states, Quantum
+Reports 3, 350 (2021).
+[14] V. V. Dodonov, ‘Nonclassical’ states in quantum op-
+tics: a ‘squeezed’ review of the first 75 years, J. Opt. B:
+Quantum Semiclassical Opt. 4, R1 (2002).
+[15] A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium:
+Quantum coherence as a resource, Rev. Mod. Phys. 89,
+041003 (2017).
+[16] P. D. Drummond and Z. Ficek, Quantum Squeezing
+(Springer-Verlag, Berlin, 2004).
+[17] B. C. Sanders, Entangled coherent states, Phys. Rev. A
+45, 6811 (1992).
+[18] B. C. Sanders, Erratum:
+Entangled coherent states
+[Phys. Rev. A 45, 6811 (1992)], Phys. Rev. A 46, 2966
+(1992).
+[19] B. C. Sanders, Review of entangled coherent states, J.
+Phys. A: Math. Theor. 45, 244002 (2012).
+[20] M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard,
+R. J. Schoelkopf, L. Jiang, and M. H. Devoret, Dynami-
+cally protected cat-qubits: a new paradigm for universal
+quantum computation, New J. Phys. 16, 045014 (2014).
+[21] S. Bose, K. Jacobs, and P. L. Knight, Scheme to probe
+the decoherence of a macroscopic object, Phys. Rev. A
+59, 3204 (1999).
+[22] W.
+Marshall,
+C.
+Simon,
+R.
+Penrose,
+and
+D.
+Bouwmeester,
+Towards
+quantum
+superpositions
+of a mirror, Phys. Rev. Lett. 91, 130401 (2003).
+[23] W.
+Marshall,
+C.
+Simon,
+R.
+Penrose,
+and
+D. Bouwmeester, Publisher’s note:
+Towards quan-
+tum superpositions of a mirror [Phys. Rev. Lett. 91,
+130401 (2003)], Phys. Rev. Lett. 91, 159903 (2003).
+[24] P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin,
+S. Gasparoni, and A. Zeilinger, De Broglie wavelength of
+a non-local four-photon state, Nature 429, 158 (2004).
+[25] M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg,
+Super-resolving phase measurements with a multipho-
+ton entangled state, Nature 429, 161 (2004).
+[26] L. Happ, M. A. Efremov, H. Nha, and W. P. Schle-
+ich, Sufficient condition for a quantum state to be gen-
+uinely quantum non-Gaussian, New J. Phys. 20, 023046
+(2018).
+[27] B. C. Sanders, Superposition of two squeezed vacuum
+states and interference effects, Phys. Rev. A 39, 4284
+(1989).
+[28] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum-
+enhanced measurements: Beating the standard quan-
+tum limit, Science 306, 1330 (2004).
+[29] A gravitational wave observatory operating beyond the
+quantum shot-noise limit, Nat. Physics 7, 962 (2011).
+[30] Enhancing the sensitivity of the ligo gravitational wave
+detector by using squeezed states of light, Nat. Physics
+7, 962 (2013).
+[31] G. J. Milburn, Quantum and classical Liouville dynam-
+ics of the anharmonic oscillator, Phys. Rev. A 33, 674
+(1986).
+[32] B. Yurke and D. Stoler, Generating Quantum Mechan-
+ical Superpositions of Macroscopically Distinguishable
+States via Amplitude Dispersion, Phys. Rev. Lett. 57,
+13 (1986).
+[33] W. H. Zurek, Sub-Planck structure in phase space and
+its relevance for quantum decoherence, Nature 412, 712
+(2001).
+[34] W. H. Zurek, Decoherence, einselection, and the quan-
+tum origins of the classical, Rev. Mod. Phys. 75, 715
+(2003).
+[35] A. K. Pan and P. K. Panigrahi, Cat state, sub-Planck
+structure and weak measurement, Eur. Phys. J. D 67,
+1 (2013).
+[36] D. A. R. Dalvit, R. L. de Matos Filho, and F. Toscano,
+Quantum metrology at the heisenberg limit with ion
+trap motional compass states, New J. Phys. 8, 276
+(2006).
+[37] F. Toscano, D. A. R. Dalvit, L. Davidovich, and
+W. H. Zurek, Sub-Planck phase-space structures and
+Heisenberg-limited measurements, Phys. Rev. A 73,
+023803 (2006).
+[38] S. Ghosh, J. Bera, P. K. Panigrahi, and U. Roy,
+Sub-fourier quantum metrology through bright solitary
+trains in Bose–Einstein condensate, Int. J. Quantum Inf.
+17, 1950019 (2019).
+[39] A. J. Scott and C. M. Caves, Teleportation fidelity as a
+probe of sub-Planck phase-space structure, Ann. Phys.
+(NY) 323, 2685 (2008).
+
+18
+[40] L.
+Praxmeyer,
+P.
+Wasylczyk,
+C.
+Radzewicz,
+and
+K. W´odkiewicz, Time-Frequency Domain Analogues of
+Phase Space Sub-Planck Structures, Phys. Rev. Lett.
+98, 063901 (2007).
+[41] P. Jacquod, I. Adagideli, and C. W. J. Beenakker, Decay
+of the Loschmidt Echo for Quantum States with Sub-
+Planck-scale Structures, Phys. Rev. Lett. 89, 154103
+(2002).
+[42] D. A. Wisniacki, Short-time decay of the Loschmidt
+echo, Phys. Rev. E 67, 016205 (2003).
+[43] S. Ghosh, A. Chiruvelli, J. Banerji, and P. K. Pan-
+igrahi, Mesoscopic superposition and sub-Planck-scale
+structure in molecular wave packets, Phys. Rev. A 73,
+013411 (2006).
+[44] J.
+R.
+Bhatt,
+P.
+K.
+Panigrahi,
+and
+M.
+Vyas,
+Entanglement-induced sub-Planck phase-space struc-
+tures, Phys. Rev. A 78, 034101 (2008).
+[45] M. Stobi´nska, G. J. Milburn, and K. W´odkiewicz,
+Wigner function evolution of quantum states in the pres-
+ence of self-Kerr interaction, Phys. Rev. A 78, 013810
+(2008).
+[46] S. Ghosh, U. Roy, C. Genes, and D. Vitali, Sub-Planck-
+scale structures in a vibrating molecule in the presence
+of decoherence, Phys. Rev. A 79, 052104 (2009).
+[47] U. Roy, S. Ghosh, P. K. Panigrahi, and D. Vitali, Sub-
+Planck-scale structures in the P¨oschl-teller potential
+and their sensitivity to perturbations, Phys. Rev. A 80,
+052115 (2009).
+[48] S. Ghosh, Coherent control of mesoscopic superpositions
+in a diatomic molecule, Int. J. Quantum Inf. 10, 1250014
+(2012).
+[49] A. Kumari, A. K. Pan, and P. K. Panigrahi, Sub-Planck
+structure in a mixed state, Eur. Phys. D 69, 248 (2015).
+[50] V. Dodonov, C. Valverde, L. Souza, and B. Baseia, De-
+coherence of odd compass states in the phase-sensitive
+amplifying/dissipating environment, Ann. Phys. (NY)
+371, 296 (2016).
+[51] P. Kumar and R.-K. Lee, Sensitivity of sub-Planck
+structures of mesoscopically superposed coherent states
+to the thermal reservoirs induced decoherence, Opt.
+Commun. 394, 23 (2017).
+[52] L.
+A.
+Howard,
+T.
+J.
+Weinhold,
+F.
+Shahandeh,
+J. Combes, M. R. Vanner, A. G. White, and M. Ring-
+bauer, Quantum Hypercube States, Phys. Rev. Lett.
+123, 020402 (2019).
+[53] N. Akhtar, B. C. Sanders, and G. Xianlong, Sub-Planck
+phase-space structure and sensitivity for SU(1,1) com-
+pass states, Phys. Rev. A 106, 043704 (2022).
+[54] N.
+Akhtar,
+B.
+C.
+Sanders,
+and
+C.
+Navarrete-
+Benlloch, Sub-Planck structures: Analogies between the
+Heisenberg-Weyl and SU(2) groups, Phys. Rev. A 103,
+053711 (2021).
+[55] N. Shukla, N. Akhtar, and B. C. Sanders, Quantum
+tetrachotomous states: Superposition of four coherent
+states on a line in phase space, Phys. Rev. A 99, 063813
+(2019).
+[56] P. K. Panigrahi et al., Compass state: Effect of squeez-
+ing and displacement on the Fock space, arXiv preprint
+arXiv:2211.10374 (2022).
+[57] G. S. Agarwal and P. K. Pathak, Mesoscopic superposi-
+tion of states with sub-Planck structures in phase space,
+Phys. Rev. A 70, 053813 (2004).
+[58] P. K. Pathak and G. S. Agarwal, Generation of a super-
+position of multiple mesoscopic states of radiation in a
+resonant cavity, Phys. Rev. A 71, 043823 (2005).
+[59] M. Stobi´nska, A. S. Villar, and G. Leuchs, Generation
+of Kerr non-Gaussian motional states of trapped ions,
+Europhys. Lett. 94, 54002 (2011).
+[60] Z. Leghtas, G. Kirchmair, B. Vlastakis, M. H. Devoret,
+R. J. Schoelkopf, and M. Mirrahimi, Deterministic pro-
+tocol for mapping a qubit to coherent state superposi-
+tions in a cavity, Phys. Rev. A 87, 042315 (2013).
+[61] L. C. G. Govia, E. J. Pritchett, and F. K. Wilhelm,
+Generating nonclassical states from classical radiation
+by subtraction measurements, New J. Phys. 16, 045011
+(2014).
+[62] J. Hastrup, J. S. Neergaard-Nielsen, and U. L. Ander-
+sen, Deterministic generation of a four-component opti-
+cal cat state, Opt. Lett. 45, 640 (2020).
+[63] N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Legh-
+tas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin,
+L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J.
+Schoelkopf, Extending the lifetime of a quantum bit
+with error correction in superconducting circuits, Na-
+ture 536, 441 (2016).
+[64] B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg,
+L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. De-
+voret, and R. J. Schoelkopf, Deterministically encoding
+quantum information using 100-photon Schr¨odinger cat
+states, Science 342, 607 (2013).
+[65] G. B. Lemos, R. M. Gomes, S. P. Walborn, P. H.
+S. Ribeiro, and F. Toscano, Experimental observation
+of quantum chaos in a beam of light, Nat. Commun. 3,
+2041 (2012).
+[66] D. R. Austin, T. Witting, A. S. Wyatt, and I. A.
+Walmsley, Measuring sub-Planck structural analogues
+in chronocyclic phase space, Opt. Commun. 283, 855
+(2010).
+[67] H. Nha and H. J. Carmichael, Proposed test of quantum
+nonlocality for continuous variables, Phys. Rev. Lett.
+93, 020401 (2004).
+[68] H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi,
+M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki,
+Entanglement distillation from Gaussian input states,
+Nat. Photonics 4, 178 (2010).
+[69] Z. Zhang and H. Fan, Properties of states generated by
+excitations on a squeezed vacuum state, Phys. Lett. A
+165, 14 (1992).
+[70] C. Hughes, M. G. Genoni, T. Tufarelli, M. G. A. Paris,
+and M. S. Kim, Quantum non-Gaussianity witnesses in
+phase space, Phys. Rev. A 90, 013810 (2014).
+[71] C. Quesne, Completeness of photon-added squeezed
+vacuum and one-photon states and of photon-added co-
+herent states on a circle, Phys. Lett. A 288, 241 (2001).
+[72] K. Si, X.-H. Ji, and H.-Y. Jia, Nonclassicality of photon-
+added squeezed vacuum states, Chin. Phys. B 19,
+064205 (2010).
+[73] L.-Y. Hu and H.-Y. Fan, Nonclassicality of photon-
+added squeezed vacuum and its decoherence in thermal
+environment, J. Mod. Opt. 57, 1344 (2010).
+[74] S. Dey and S. S. Nair, Generalized photon-subtracted
+squeezed vacuum states, J. Phys. A: Math. Theor. 53,
+385305 (2020).
+[75] X.-G. Meng, Z. Wang, H.-Y. Fan, and J.-S. Wang,
+Nonclassicality and decoherence of photon-subtracted
+squeezed vacuum states, J. Opt. Soc. Am. B 29, 3141
+(2012).
+[76] A. Biswas and G. S. Agarwal, Nonclassicality and de-
+
+19
+coherence of photon-subtracted squeezed states, Phys.
+Rev. A 75, 032104 (2007).
+[77] S.-J. Ma and W.-W. Luo, Comparison of nonclassicality
+between photon-added and photon-subtracted squeezed
+vacuum states, Chin. Phys. B 21, 024203 (2012).
+[78] B. K¨uhn and W. Vogel, Quantum non-Gaussianity
+and quantification of nonclassicality, Phys. Rev. A 97,
+053823 (2018).
+[79] X.-B.
+Tang,
+F.
+Gao,
+Y.-X.
+Wang,
+J.-G.
+Wu,
+and F. Shuang, Non-Gaussian features from excited
+squeezed vacuum state, Opt. Commun. 345, 86 (2015).
+[80] S. M. Barnett, G. Ferenczi, C. R. Gilson, and F. C.
+Speirits, Statistics of photon-subtracted and photon-
+added states, Phys. Rev. A 98, 013809 (2018).
+[81] M. D. Lang and C. M. Caves, Optimal quantum-
+enhanced interferometry using a laser power source,
+Phys. Rev. Lett. 111, 173601 (2013).
+[82] S. Wang, X. Xu, Y. Xu, and L. Zhang, Quantum in-
+terferometry via a coherent state mixed with a photon-
+added squeezed vacuum state, Opt. Commun. 444, 102
+(2019).
+[83] R. Birrittella and C. C. Gerry, Quantum optical in-
+terferometry via the mixing of coherent and photon-
+subtracted squeezed vacuum states of light, J. Opt. Soc.
+Am. B 31, 586 (2014).
+[84] G. S. Agarwal and K. Tara, Nonclassical properties of
+states generated by the excitations on a coherent state,
+Phys. Rev. A 43, 492 (1991).
+[85] A. Zavatta, S. Viciani, and M. Bellini, Quantum-to-
+classical transition with single-photon-added coherent
+states of light, Science 306, 660 (2004).
+[86] J. Wenger, R. Tualle-Brouri, and P. Grangier, Non-
+gaussian statistics from individual pulses of squeezed
+light, Phys. Rev. Lett. 92, 153601 (2004).
+[87] A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and
+P. Grangier, Increasing entanglement between Gaussian
+states by coherent photon subtraction, Phys. Rev. Lett.
+98, 030502 (2007).
+[88] P. T. Cochrane, G. J. Milburn, and W. J. Munro,
+Macroscopically distinct quantum-superposition states
+as a bosonic code for amplitude damping, Phys. Rev. A
+59, 2631 (1999).
+[89] T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro,
+and S. Glancy, Quantum computation with optical co-
+herent states, Phys. Rev. A 68, 042319 (2003).
+[90] K. Huang, H. Le Jeannic, J. Ruaudel, V. B. Verma,
+M. D. Shaw, F. Marsili, S. W. Nam, E. Wu, H. Zeng,
+Y.-C. Jeong, R. Filip, O. Morin, and J. Laurat, Opti-
+cal synthesis of large-amplitude squeezed coherent-state
+superpositions with minimal resources, Phys. Rev. Lett.
+115, 023602 (2015).
+[91] D. V. Sychev, A. E. Ulanov, A. A. Pushkina, M. W.
+Richards, I. A. Fedorov, and A. I. Lvovsky, Enlargement
+of optical Schr¨odinger’s cat states, Nat. Photonics 11,
+379 (2017).
+[92] A. E. Ulanov, I. A. Fedorov, D. Sychev, P. Grang-
+ier, and A. Lvovsky, Loss-tolerant state engineering for
+quantum-enhanced metrology via the reverse hong–ou–
+mandel effect, Nat. commun. 7, 1 (2016).
+[93] K. Wakui, H. Takahashi, A. Furusawa, and M. Sasaki,
+Photon subtracted squeezed states generated with peri-
+odically poled ktiopo4, Opt. Express 15, 3568 (2007).
+[94] M. Dakna, T. Anhut, T. Opatrn´y, L. Kn¨oll, and D.-
+G. Welsch, Generating Schr¨odinger-cat-like states by
+means of conditional measurements on a beam splitter,
+Phys. Rev. A 55, 3184 (1997).
+[95] K. Takase, J.-i. Yoshikawa, W. Asavanant, M. Endo,
+and A. Furusawa, Generation of optical Schr¨odinger cat
+states by generalized photon subtraction, Phys. Rev. A
+103, 013710 (2021).
+[96] J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich,
+K. Mølmer, and E. S. Polzik, Generation of a super-
+position of odd photon number states for quantum in-
+formation networks, Phys. Rev. Lett. 97, 083604 (2006).
+[97] A. Ourjoumtsev,
+R. Tualle-Brouri,
+J. Laurat, and
+P. Grangier, Generating optical Schr¨odinger kittens
+for quantum information processing, Science 312, 83
+(2006).
+[98] K. M. R. Audenaert, Comparisons between quantum
+state distinguishability measures, Quantum Inf. Com-
+put. 14, 31 (2014).
+[99] D. Braun, G. Adesso, F. Benatti, R. Floreanini, U. Mar-
+zolino, M. W. Mitchell, and S. Pirandola, Quantum-
+enhanced measurements without entanglement, Rev.
+Mod. Phys. 90, 035006 (2018).
+[100] A. Luis, Quantum-limited metrology with nonlinear de-
+tection schemes, SPIE Reviews 1, 018006 (2010).
+[101] H. Weyl, The Theory of Groups and Quantum Mechan-
+ics (Dover, New York, 1950).
+[102] A. Perelomov, Generalized Coherent States and Their
+Applications, Theoretical and Mathematical Physics
+(Springer-Verlag, Berlin, 1986).
+[103] J.-P. Gazeau, Coherent States in Quantum Physics
+(Wiley-VCH, Berlin, 2009).
+[104] J. E. Moyal, Quantum mechanics as a statistical theory,
+Math. Proc. Cambridge Philos. Soc. 45, 99 (1949).
+[105] R. Gilmore, Properties of coherent states, Rev. Mex.
+Fis. 23, 143 (1974).
+[106] P. Kok and B. W. Lovett, Introduction to Optical Quan-
+tum Information Processing, 1st ed. (Cambridge Univer-
+sity Press, 2010).
+[107] R. R. Puri, Mathematical methods of quantum optics
+(Springer-Verlag, Berlin, 2001).
+
diff --git a/jdAyT4oBgHgl3EQfX_es/content/tmp_files/load_file.txt b/jdAyT4oBgHgl3EQfX_es/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf,len=1582
+page_content='Sub-Planck structures and sensitivity of the superposed photon-added or  photon-subtracted squeezed-vacuum states  Naeem Akhtar,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ∗ Jizhou Wu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' † Jia-Xin Peng,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='3 Wu-Ming Liu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 6 and Gao Xianlong1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ‡  1Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zhejiang Normal University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Jinhua 321004,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' China  2Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Southern University of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Shenzhen 518055,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' China  3State Key Laboratory of Precision Spectroscopy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Quantum Institute for Light and  Atoms,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' East China Normal University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Shanghai 200062,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' China  4Beijing National Laboratory for Condensed Matter Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Institute  of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Beijing 100190,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' China  5School of Physical Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' University of Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Beijing 100190,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' China  6Songshan Lake Materials Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dongguan 523808,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Guangdong,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' China  (Dated: January 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 2023)  The Wigner function of the compass state (a superposition of four coherent states) develops phase-  space structures of dimension much less than the Planck scale ℏ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' which are crucial in determining the  sensitivity of these states to phase-space displacements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In the present work, we introduce compass-  like states that may have connection to the contemporary experiments, which are obtained by either  adding photons to or subtracting photons from the superposition of two squeezed-vacuum states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' We  show that, when a significant quantity of photons is added (or subtracted), the Wigner function of  these states are shown to have phase-space structures of an area that is substantially smaller than  the Planck scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In addition, these states exhibit sensitivity to displacements that is much higher  than the standard quantum limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Finally, we show that both the size of the sub-Planck structures  and the sensitivity of our states are strongly influenced by the average photon number, with the  photon addition case having a higher average photon number leading to the smaller sub-Planck  structures and, consequently, being more sensitive to displacement than the photon subtraction  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Our states offer unprecedented resolution to the external perturbations, making them suitable  for quantum sensing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  INTRODUCTION  Quantum mechanical states can be visualized in the  phase space via the Wigner quasiprobability distribu-  tion [1–5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The term “Gaussian state” refers to a state  having the Gaussian Wigner function [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The coher-  ent state [8] is an example of a Gaussian state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The  Wigner function of the coherent state exhibits the Planck  limit [9, 10] in the phase space, which is also known as  the standard quantum limit (SQL) or shot-noise limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The Wigner function of certain non-Gaussian states  may attain negative values [11–14], indicating that these  states are nonclassical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The quantum superposition is  the source of intriguing non-classical properties of quan-  tum states, such as quantum coherence [11, 15], squeez-  ing [16], and entanglement [17–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Non-classical quan-  tum states play a significant role in quantum-information  processing [20], tests of fundamental of physics [21–23],  and applications in sensing and metrology [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Non-classical states are not always non-Gaussian, how-  ever, non-classical states can be Gaussian in some cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  For example, a squeezed-vacuum state (SVS) is a com-  mon non-classical state, but it possesses a Gaussian  Wigner function [12, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The Wigner function of the  superposition of SVS is non-Gaussian and may have  ∗ naeem abbasi@zjnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='cn  † wujz3@sustech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='cn (Corresponding author)  ‡ gaoxl@zjnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='cn  negative amplitudes [26, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Squeezed quantum states  play an important role in performing enhanced quan-  tum metrology [16, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Squeezed light has been uti-  lized experimentally to carry out improved measure-  ments [29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The superpositions of two coherent states with op-  posite phases (cat states) also possess non-Gaussian  Wigner functions [31, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Moreover, the superposi-  tion of four coherent states, which is known as the  “compass state” [33] exhibits nonclassical features in the  Wigner function with dimensions far smaller than the  SQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The quantum states with sub-Planck structures are  found very sensitive to environmental decoherence [34]  and have achieved prominent theoretical attentions in  quantum metrology [34–38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The connection between  sub-Planck structures and teleportation fidelity has been  established [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Sub-Fourier sensitivity is a classical  analogue of the sub-Planck structures [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Compass-like  states have been thoroughly investigated in several situa-  tions [41–56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Both theoretical [57–62] and experimental  study [63–66] have been taken to achieve the controlled  generation of such states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  In recent years, there has been a lot of focus on sub-  tracting photons from or adding photons to the quantum  states [67–79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A non-Gaussian state can also be gen-  erated by adding or subtracting photons from a Gaus-  sian state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' For example, when photons are added to  or subtracted from the Gaussian SVS, one may ob-  tain two non-Gaussian squeezed states that have non-  positive Wigner functions [72–75, 77, 79, 80]: photon-  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='00195v1  [quant-ph]  31 Dec 2022  2  added squeezed-vacuum states (PASVS) [69] and photon-  subtracted squeezed-vacuum states (PSSVS) [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Both  PASVS and PSSVS have attracted theoretical interest in  quantum metrology [81–83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The first theoretical investigation into the photon-  addition operation is accomplished by adding photons to  the coherent states [84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Later, the photon-addition op-  eration was successfully proved in experiments by using  a non-degenerate parametric amplifier with a weak cou-  pling [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The PSSVS is currently the most successfully  experimentally observed non-Gaussian SVS in quantum  optics [86, 87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Schr¨odinger cat-like states with higher amplitude can  be used as qubits in quantum computing or as re-  sources for quantum error-correcting coding [88, 89].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Conventional methods are unable to produce Schr¨odinger  cat-like states with the necessary amplitudes [90–92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Numerous theoretical [93–95] and experimental [96, 97]  research involving the photons addition or subtractions  from the SVS have been carried out to achieve such  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  In the present work, we introduce a few non-Gaussian  SVSs that may also hold the properties of the com-  pass state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In particular, we show that the Wigner func-  tion of the superpositions of two PASVSs (or PSSVSs)  exhibit phase-space structures of an area, which vary  inversely with the number of photons added (or sub-  tracted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' When a large amount of the photons are added  to or subtracted from our states the support area of these  structures is substantially smaller than that found for  coherent states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Similar sub-Planck structures are also  found in the phase space of the mixed states related to  the PASVSs and PSSVSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' We demonstrate that the av-  erage photon number in the states significantly influences  the size of these sub-Planck structures, with photon ad-  dition case having higher average photon number leading  to smaller sub-Planck structures in the phase space than  photon subtraction case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  To investigate the potential applications of these non-  Gaussian states in quantum metrology, we analyze the  overlap between these states and their slightly shifted  analogues [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The degree to which the state is sen-  sitive against perturbations in the phase space can be  determined from this overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The sensitivity associ-  ated with coherent states cannot be improved by increas-  ing the number of photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Techniques using probes pre-  pared in such states have the sensitivity at the SQL [99,  100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Here, we show that the sensitivity of our states is  much higher than the SQL when the quantity of added  (or subtracted) photons is relatively high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Furthermore,  our superpositions exhibit this enhanced sensitivity in all  phase-space directions, whereas the mixtures only do so  for specific displacements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The varying average photon  number in the states also contributed to the variation in  the sensitivities between the photon addition and sub-  traction cases;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' it is shown that the photon addition cases  have higher sensitivity than the subtracted ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The structure of our paper is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  In §II, we  review the concept of the sub-Planck structures associ-  ated to the compass state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In §III, we review the Wigner  functions of PASVS and PSSVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In §IV, we introduce  our states and analyze their phase space by using the  Wigner function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Here, we also discuss the sensitivity of  our states against the phase-space perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In §V,  we provide our conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  THEORY OF SUB-PLANCK STRUCTURES  This section provides the background of the sub-Planck  structures and is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' §II A introduces  the basic concepts that will be used in this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In  §II B, we review the sub-Planck structures that build  in the phase space of the compass state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' §II C explains  the sensitivity to phase-space displacements associated  to this compass state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Basic concepts  The position operator ˆx and the momentum operator  ˆp acts on an infinite-dimensional Hilbert space, forming  the so-called Heisenberg-Weyl (HW) algebra hw(1) [101–  103] for a single degree of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The quantum uncer-  tainty principle [9, 10], arising from commutator relations  [ˆx, ˆp] = i (with ℏ being scaled to unity throughout) lim-  its the size of a phase-space structure [10], for example,  represented by the Wigner function [1] for hw(1) algebra  and, more generally, by Moyal symbols [104] for other  symmetries [102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' For convenience, we use the vector  ζ := (x, p)⊤,  (1)  to represent the position-momentum pair in the follow-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  A Schr¨odinger coherent state is a non-spreading wave  packet of the quantum harmonic oscillator [8] and is an  eigenstate of the annihilation operator:  ˆa |α⟩ = α |α⟩  with α ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The coherent states are obtained by dis-  placing the vacuum state |0⟩, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=',  |α⟩ = ˆD(α) |0⟩ ,  (2)  where  ˆD(α) := exp(αˆa† − α∗ˆa),  (3)  is the displacement operator [103].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The overlap between two coherent states |α⟩ and |β⟩  is [105]  |⟨α | β⟩|2 = e−|α|2−|β|2+2β∗α = e−|α−β|2,  (4)  which implies that two different coherent states are not  orthogonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The Wigner function for a generic quantum state ˆρ is  written as an expectation value of the parity kernel [4, 6]  Wˆρ (ζ) := tr  �  ˆρ ˆ∆(α)  �  ,  (5)  3  (a)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (b)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (c)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 1: Wigner distribution of the compass state with (a) x0 = 4 (b) x0 = 8 and (c) x0 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Insets represent the  central interference pattern of each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  10-1  100  101  x0  10-3  10-2  10-1  100  101  102  "x"p  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 2: Variation of the area of the central phase-space  structure of the compass state versus x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  where  ˆ∆(α) := 2 ˆD(α)ˆΠ ˆD†(α), ˆΠ := (−1)ˆa†ˆa ,  (6)  being the displaced parity operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The Wigner function for a coherent state is a strictly  positive function, and appeared as a Gaussian of the  form [5] (we omit the normalization of states and their  Wigner functions throughout the paper)  G(ζ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ±x0, ±p0) = e−(x∓x0)2−(p∓p0)2,  (7)  where (x0, p0) is the location of the coherent state in  phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The product of uncertainties of position  and momentum for a coherent state has a lower limit  ∆x∆p = 1/2 [5, 9, 10, 105], which is also known as the  Planck action in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  It is a common belief that phase-space structures with  areas smaller than the Planck scale either do not exist  or have no observational consequences for physical quan-  tum states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In fact, this is true for all Gaussian states  (coherent, squeezed, thermal, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=') [6, 7] and even for  other non-Gaussian states like cat states [31, 32] that ex-  hibit rapid oscillations in one direction of phase space  but an infinite Gaussian profile in the orthogonal direc-  tion [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' However, this notion was refuted by Zurek [33],  who demonstrated that the Wigner function of compass  states develops phase-space structures with dimensions  far smaller than the Planck scale, arguing that these  structures play a vital role in determining the sensitivity  of these states against perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Zurek compass state  The Zurek compass state [33] is obtained from the su-  perposition of the following four coherent states  |ψ⟩ := |x0/  √  2⟩ + |−x0/  √  2⟩ + |ix0/  √  2⟩ + |−ix0/  √  2⟩ ,  (8)  with x0 ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 1 depicts the Wigner function for this  compass state for the cases of x0 = 4, 8 and 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Note  that we normalize the Wigner functions throughout by  using their maximum amplitudes, |Wˆρ(0)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The Wigner  function of the compass state (8) can be represented as  4  (a)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  /x  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  /p  (b)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  /x  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  /p  (c)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  /x  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  /p  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 3: Overlap of the compass state with its δα-displaced part with δα = (δx + iδp)/  √  2: (a) x0 = 4 (b) x0 = 8 and  (c) x0 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  follows  W|ψ⟩(ζ) = W◦(ζ) + WΞ(ζ) + W⊞(ζ),  (9)  where the first term  W◦(ζ) :=G(ζ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' x0, 0) + G(ζ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' −x0, 0) + G(ζ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 0, x0)+  G(ζ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 0, −x0),  (10)  represents the Wigner function of four coherent states  that appear in the phase space as Gaussian lobes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The  second term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (9) is  WΞ(ζ) := 1  2  �  i1,i2=±1  I(i1x, i2p),  (11)  with  I(ζ) := G(ζ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' x0/2, x0/2) cos  �  x0  �  x + p − x0  2  � �  ,  (12)  reflecting the Gaussian-modulated oscillations that ap-  pear far away from the phase-space origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The central pattern resembles a chessboard as shown  in the insets of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 1 and is generated by  W⊞(ζ) := 1  2G(ζ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 0, 0)  �  cos(2x0x) + cos(2x0p)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (13)  This pattern consists of tiles with alternate signs (central  chessboardlike pattern).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The extension of each tile can  be roughly estimated by calculating zeros of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (13),  and it is found that it is proportional to x−1  0  in all di-  rections of phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' As a result, the support area of  each tile in the chessboardlike pattern is proportional to  x−2  0  as shown in the log-log plot of the central support  area versus x0 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 2, which is much smaller than the  area of the coherent state for x0 ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Note that the mix-  ture of two cat states also contains the same sub-Planck  structures that are found in the compass state [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The sub-Planck structures also emerge in the Wigner  functions of non-Gaussian states with the SU(1,1) [53]  and SU(2) symmetries [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  In particular, it has been  found that the Wigner function of the superposition of  four SU(1,1) (or SU(2)) coherent states also have sub-  Planck structures similar to the compass state when rep-  resented on the Poincar´e disk [53] (or the sphere [54]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The two-mode bosonic realization of the SU(1,1) im-  plies that the sub-Planck structures in the phase space  of the SU(1,1) compass state can be associated to the  number of photons added to one of the modes of the  two-mode squeezed number states [53], and they arise  at greater numbers of these added photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The exis-  tence of the sub-Planck structures in the Wigner func-  tion of the SU(2) compass state can similarly be linked  to the angular momentum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' the higher value of the angu-  lar momentum causes sub-Planck structures in the phase  space [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In the subsequent sections, we will demon-  strate how adding or subtracting photons from superpo-  sitions related to the one-mode non-Gaussian SVS can  also cause the emergence of sub-Planck structures in the  phase space of those states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Sensitivity of compass state  The sensitivity of a quantum state to displacements  can be determined by calculating the overlap between it  and its slightly displaced version [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The overlap be-  tween a state ˆρ and its displaced version ˆD(δα)ˆρ ˆD†(δα)  is  Oˆρ(δα) := tr{ˆρ ˆD(δα)ˆρ ˆD†(δα)} =  ���⟨ψ| ˆD(δα)|ψ⟩  ���  2  ,  (14)  where δα ∈ C is an arbitrary displacement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Note that the  last equality of above expression holds when the state is  pure, ˆρ = |ψ⟩⟨ψ|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The smaller the displacement δα needs  to be in order to bring the overlap to zero, the more sensi-  tive the state is claimed to be against displacements [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  This overlap results in  O|α⟩(δα) = e−|δα|2,  (15)  for a coherent state |α⟩, indicating that the smallest no-  ticeable displacement that vanishes this overlap is above  05  (a)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (b)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (c)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 4: Wigner distribution of the PASVS with (a) n = 10 (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Insets  represent the central interference pattern of each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (a)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (b)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (c)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 5: Wigner distribution of the PSSVS with (a) n = 10 (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Insets  represent the central interference pattern of each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  the Planck scale, |δα| > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' It is interesting to note that  the sensitivity to displacements in coherent states is inde-  pendent of the quantity of quanta contained in the state,  ¯n = ⟨ˆa†ˆa⟩ = |α|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Therefore, increasing ¯n will not im-  prove the sensitivity and is solely limited by the shot  noise introduced by vacuum fluctuations [99, 100].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  We now discuss the sensitivity of the compass state  (8) to phase-space displacements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Assuming x0 ≫ 1 and  |δα| ≪ 1 , the overlap (14) for this compass state results  in  O|ψ⟩(δα) = 1  4e− 1  2 |δα|2�  cos (x0δx) + cos (x0δp)  �2,  (16)  6  with  δα = δx + iδp,  δj ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (17)  It can be concluded that O|ψ⟩(δα) becomes zero when  either of the conditions is satisfied  δx ± δp = 2m + 1  x0  π, m ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (18)  As illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 3 for O|ψ⟩(δα) of cases when x0  is increased from 4 to 12, the overlap vanishes for the  displacements |δα| ∼ x−1  0  and the arbitrary directions in  the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' As a result, it can be inferred that this  sensitivity is proportional to x−1  0  and that ¯n = x2  0/2 ties it  to the number of excitations ¯n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Therefore, in comparison  to coherent states, a compass state with ¯n excitations has  shown √¯n-enhanced sensitivity to displacements of any  arbitrary directions in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Weak force mea-  surements have been performed with Heisenberg-limited  sensitivity using compass states [36, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In contrast, cat  states have shown the sensitivity to displacements along  the specific direction in the phase space [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' It has been  found that cat-state mixtures only exhibit this enhanced  sensitivity for displacements along particular phase-space  directions [53, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Hence, cat-state mixtures with sub-  Planck structures in the Wigner function do not have  the potential for metrology of compass states, for which  the additional quantum coherence of the cat-state super-  position provided by the second term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (9) plays a  crucial role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The SU(1,1) and SU(2) compass states have shown the  same sensitivity to displacements as their HW counter-  parts [53, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The sensitivity of the SU(1,1) compass  state can be connected with the amount of the number  of photons added to one of the modes of the two-mode  squeezed number state, and this sensitivity improves as  the quantity of added photons increases [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Similarly,  the sensitivity of the SU(2) compass state improves as  the angular momentum goes higher [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  This addition  of the photons increases the average photon number in  the states, and it can be understood in a way similar to  that for compass states of the harmonic oscillator, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=',  injecting more photons in the states improves its sensi-  tivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  NON-GAUSSIAN SVS  The non-Gaussian Wigner functions of the PASVS  and PSSVS illustrate the non-Gaussian nature of these  states [72–75, 77, 79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In this section, we first provide  a brief review of two non-Gaussian SVS, the PASVS  and the PSSVS, in §III A and §III B, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' These  two states are heavily used in our construction of non-  Gaussian states that manifest the sub-Planck structures  in §IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The Wigner functions of both PASVS and PSSVS  are discussed in relation to the amount of photons added  or subtracted in the following subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  PASVS  First, we review the Wigner function of the PASVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The creation operator ˆa† is repeatedly applied to SVS  ˆS(±r) |0⟩ to obtain a single-mode PASVS [69]  |ψ±  PA⟩ := ˆa†n ˆS(±r) |0⟩ with n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (19)  The subscript “PA” is the shorthand for “PASVS”, and  we introduce“±” in the squeezing operator ˆS(±r) with  the definition [106]  ˆS(±r) := exp  �  ± r  2  �  ˆa†2 − ˆa2� �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (20)  which allows us to preserve part of the expressions intro-  duced in this section for later uses in §IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (5), the Wigner function of PASVS is easily  found to be [72, 73, 77, 79]  W|ψ±  PA⟩(ζ) =exp (χ±) [± sinh(2r)]n  π4n  n  �  l=0  (n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' )2 [∓2 coth(r)]l  l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' [(n − l)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ]2  ���Hn−l  �  −i  �  ±2 coth(r)¯α±  ����  2  ,  (21)  where Hm represents the Hermite polynomial, and  χ± := ± sinh(2r)  �  α∗2 + α2�  − 2|α|2 cosh(2r),  (22)  with  ¯α± := α cosh(r) ∓ α∗ sinh(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (23)  The  non-Gaussian  shape  of  the  Wigner  function  W|ψ+  PA⟩(ζ), which is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 4 for the cases when  n is chosen as 10, 15 and 20, indicates that PASVS is a  non-Gaussian state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' We can clearly see the interference  pattern that emerge in the form of an oscillating pattern  in the p direction in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' As the number of  photons n rises, this pattern gets more pronounced (the  frequency of the oscillations is increased).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Moreover, the  existence of these negative peaks in the Wigner function  shows that the PASVS is a non-classical state as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Another indication of the nonclassicality of this state is  the squeezing effect in one of the quadratures, which is  visible in the plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Note that the PASVS is the Gaussian  SVS when n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  PSSVS  Now, we review the Wigner function of the PSSVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The PSSVS [74, 75] is obtained by repeatedly applying  the annihilation operator ˆa to the SVS as  |ψ±  PS⟩ := ˆan ˆS(±r) |0⟩ ,  (24)  7  (a)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (b)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (c)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 6: Wigner distribution of the pure SPASVS with (a) n = 10 (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Insets represent the central interference pattern of each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  101  102  n  10-2  "x"p  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 7: Variation of the area of the central phase-space  structure versus the photon number n of the SPASVS  state with n chosen from 5 to 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  where the subscript “PS” is the shorthand for “PSSVS”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The Wigner function of this state is also in a non-  Gaussian form, and is written as  W|ψ±  PS⟩(ζ) =exp (χ±) [± sinh(2r)]n  π4n  n  �  l=0  (n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' )2 [∓2 tanh(r)]l  l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' [(n − l)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ]2  ���Hn−l  �  −i  �  ±2 tanh(r)¯α±  ����  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (25)  We plot the Wigner function W|ψ+  PS⟩(ζ) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 5 with r  being 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5 and n being 10, 15, and 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This Wigner func-  tion exhibit the interference pattern around the origin of  the phase space and oscillates along the p direction in  the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' As n grows, the frequency of this os-  cillating pattern increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The simpliest case n = 0 of  the PSSVS corresponds to the Gaussian SVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Another  indicator of the non-classical nature of this state is the  squeezing effect in one of the quadratures, which is in-  dicative of the nonclassicality of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  In summary, for non-zero values of n, the Wigner func-  tion of PASVS and PSSVS maintains non-Gaussianity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' It  is interesting to note that both PASVS and PSSVS ex-  hibit similar phase-space features as cat-like states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The  addition or subtraction of photons from the Gaussian  SVS has been employed both theoretically [93–95] and  experimentally [96, 97] to produce cat-like states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Both  PASVS and PSSVS have been found very useful for the  quantum metrology [81–83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' When photons are added to  or subtracted from the Gaussian SVS, the average photon  number of the resulting state grows [82, 83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' It has been  shown that for the same number of photons applied on  the Gaussian SVS, the subsequent PASVS has a higher  average photon number than the PSSVS [82, 83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This  means that the PASVS has a better potential for metrol-  ogy than the PSSVS [82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  SUPERPOSITION OF NONGAUSSIAN SVS  In this section, we introduce the quantum states of our  interest and present their phase-space analysis by using  the Wigner function [1–5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The photon-number distribu-  tion [27] and the Wigner function [26] have both been  used to discuss the nonclassicality in the superpositions  8  (a)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (b)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
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+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (c)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 8: Wigner distribution of the mixed-state SPASVS with (a) n = 10 (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases  r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Insets represent the central interference pattern of each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  of two SVSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Theoretically, a non-linear harmonic oscil-  lator can be used to create some specified superpositions  of two SVSs [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Here, we focus on the superposition of  two Gaussian SVSs with opposite phases given by  |ψSSV⟩ := ˆS(r) |0⟩ + ˆS(−r) |0⟩ ,  (26)  with “SSV” in the subscript for the “superposition of  SVSs”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The Wigner function corresponding to this  state exhibit non-Gaussian and non-classical proper-  ties [26, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The addition of n photons to the superposed state (26)  leads to the superposition of two photon-added squeezed-  vacuum states (SPASVS), that is,  |ψSPA⟩ := ˆa†n |ψSSV⟩ = |ψ+  PA⟩ + |ψ−  PA⟩  (27)  with the subscript “SPA” a shorthand for “SPASVS”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Similarly, the subtraction of n photons from the super-  position (26) results in the superposition of two photon-  subtracted squeezed-vacuum states (SPSVS) of the fol-  lowing form:  |ψSPS⟩ := ˆan |ψSSV⟩ = |ψ+  PS⟩ + |ψ−  PS⟩ ,  (28)  where  the  subscript  “SPS”  is  the  short  form  of  “SPSSVS”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Following subsections cover the discussion about these  two superpositions, which are structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In  §IV A, we discuss Wigner functions corresponding to  |ψSPA⟩ and |ψSPS⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Here, we describe how the addition  and subtraction of photons lead to the sub-Planck struc-  tures in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In §IV B, we discuss the sensi-  tivity to displacements associated with these two super-  positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Photons addition versus photons subtraction  The Wigner function of the SPASVS (27) can be ob-  tained by using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (5) as (see Appendix A for detailed  derivations)  W|SPA⟩(ζ) = 2 Re [IΞ(ζ)] + W⊞(ζ),  (29)  and is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 6 for the cases when n = 10, 15 and  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The first term in (29)  IΞ(ζ) :=  exp (ξ) [−i tanh(2r)]n  π4n cosh(r)  �  1 + tanh2(r)  n  �  l=0  (n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' )2 [−2i coth(r)]l  [(n − l)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ]2  Hn−l [iΩα−] Hn−l  �  −Ωα∗  +  �  ,  (30)  provides the interference pattern that appears far away  from the phase-space origin, where  Ω :=  �  tanh(2r)  sinh(r)  ,  (31)  and  ξ := − tanh(2r)  �  α2 − α2∗�  − 2|α|2 sech(2r),  (32)  with  α± := α∗ sinh(r) ± α cosh(r)  (33)  being the hyperbolic-rotated α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  For our purposes, we concentrate on the second term in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 29, which contributes to the chessboardlike pattern  that is visible at the phase-space origin for n ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This  9  (a)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (b)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  (c)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 9: Wigner distribution of the pure SPSSVS with (a) n = 10 (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Insets represent the central interference pattern of each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  101  102  n  10-2  "x"p  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 10: Variation of the area of the central  phase-space structure versus the photon number n of  the SPSSVS state with n chosen from 5 to 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  central interference pattern is equal to the sum of the  individual Wigner functions of PASVSs as  W⊞(ζ) := W|ψ+  PA⟩(ζ) + W|ψ−  PA⟩(ζ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (34)  The extension of a single tile in the chessboardlike pat-  tern is inversely proportional to n along any arbitrary  direction in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  This is demonstrated in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 6, where we see that as n increases, the support area  of a fundamental tile in the chessboardlike pattern de-  creases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The area of a fundamental tile can be roughly  estimated by calculating the zeros of the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' For  n ≫ 1, the support area of a fundamental tile may be  considerably lower than the area of the coherent state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  This is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 7, where we plot the area of the  center tile against n using a log-log plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Thus, the sub-  Planck structures that Zurek discovered for the compass  state [33] are also present in SPASVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The same sub-Planck structures are also contained by  following mixed state  ˆρPA := |ψ+  PA⟩⟨ψ−  PA| + |ψ−  PA⟩⟨ψ+  PA| ,  (35)  and its Wigner function, which is the same as the one  given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (34), is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Similarly, for the SPSSVS (28), the Wigner function is  also written into two terms (see Appendix A for detailed  derivations):  W|SPS⟩(ζ) = 2 Re [IΞ(ζ)] + W⊞(ζ),  (36)  which is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' With  ω :=  �  tanh(2r)  cosh(r)  ,  (37)  the term that contains  IΞ(ζ) :=  exp (ξ) [i tanh(2r)]n  π4n cosh(r)  �  1 + tanh2(r)  n  �  l=0  (n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' )2 [2i tanh(r)]l  [(n − l)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ]2  Hn−l [−ωα−] Hn−l  �  −iωα∗  +  �  (38)  causes the interference pattern that manifests as oscil-  lating peaks far from the phase-space origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Again, we  concentrate on the second term of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (36), which results  in the chessboardlike pattern at the phase-space origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  10  (a)  12  8  4  0  4  8  12  x  12  8  4  0  4  8  12  p  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
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+page_content='5  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 11: Wigner distribution of the mixed-state SPSSVS with (a) n = 10 (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases  r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Insets represent the central interference pattern of each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  This term is the sum of the Wigner functions (25) of  PSSVSs, that is,  W⊞(ζ) := W|ψ+  PS⟩(ζ) + W|ψ−  PS⟩(ζ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (39)  This pattern manifests sub-Planck oscillations around  the origin of the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' It is similar to the pattern  identified for the case of SPASVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Again, the extension of  a fundamental tile can be estimated by calculating zeros  of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 9, the extensions of these  alternating-sign tiles decrease isotropically as n increases,  and the support area of these tiles in the phase is signif-  icantly less than the coherent state for n ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This is  also shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 10, which is a log-log plot showing the  extension of the central tile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' It is interesting to note that  for a given r and n, the central tile in the chessboardlike  pattern is larger than that of the SPASVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Additionally, we demonstrate that the following mixed  state likewise has the same sub-Planck structures  ˆρPS := |ψ+  PS⟩⟨ψ−  PS| + |ψ−  PS⟩⟨ψ+  PS| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (40)  Similar to the case of the mixture of PASVSs (35), the  Wigner function of ˆρPS shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 11 is identical to  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Thus, the photon-addition or photon-subtraction op-  erations on the superpositions of the Gaussian SVS may  produce the sub-Planck structures in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The average photon number of the resulting states is ac-  tually increased by either adding or subtracting photons  from the superposition of the Gaussian SVS [82], with the  addition of photons producing a higher average photon  number than the subtraction of photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This difference  in holding the photons number in the states also effects  the size of the sub-Planck structures of such states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' As an  illustration, the photons addition case has demonstrated  to hold smaller sub-Planck structures in the phase space  than the photons subtraction for the same amount of  photons utilized in the Gaussian SVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Hence, the idea  of the sub-Planck structures connected to our states can  be understood in a manner similar to that of the com-  pass state [33], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=', a higher average photon number in  the states leads to the smaller tiles in the chessboardlike  pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  In summary, the sub-Planck structures of the compass  state are present in the Wigner functions of both SPASVS  and SPSSVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The mixtures associated to PASVSs or  PSSVSs likewise contain the same sub-Planck structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Additionally, for the available average photon number,  the SPASVS and its associated mixture show smaller sub-  Planck structures than their counterparts in the photon-  subtracted case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Sub-shot noise sensitivity of our states  In this subsection, we discuss the susceptibility of our  proposed states to phase-space displacement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Let us first  consider SPASVS (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The overlap (14) for this state un-  der the approximation |δα| ≪ 1 and n ≫ 1 leads to (see  Appendix A 2 for the detailed derivations)  OSPA(δα) =  �  ⟨ψ+  PA| ˆD(δα) |ψ+  PA⟩ + ⟨ψ−  PA| ˆD(δα) |ψ−  PA⟩  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (41)  11  (a)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
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+page_content='8  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 12: Overlap of the pure SPASVS state with its δα-displaced part with δα = (δx + iδp)/  √  2: (a) n = 10  (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
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+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  /p  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 13: Overlap of the mixed-state SPASVS with its δα-displaced part with δα = (δx + iδp)/  √  2: (a) n = 10  (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Each term of this overlap is calculated as  ⟨ψ±  PA| ˆD(δα) |ψ±  PA⟩ =[∓ sinh(2r)]n e−|η±|2/2  4n  n  �  l=0  (n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' )2  l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' [(n − l)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ]2  [∓2coth(r)]lHn−l [Θ±] Hn−l  �  Θ∗  ±  �  ,  (42)  where  Θ± = i  �  ±coth(r)  2  η±,  (43)  and  η± = δαcosh(r) ∓ δα∗sinh(r),  (44)  with  δα = δx + iδp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (45)  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 12, we plot this overlap for n=10, 15, and 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' For  the large n, a small displacement |δα| ≪ 1 can turn the  SPASVS into an state orthogonal to its original state,  and this orthogonality occurs in all phase-space direc-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' We have normalized overlaps to their maximum  amplitudes, Oˆρ(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Let us now consider the mixture of PASVSs (19), for  which the overlap (14) is calculated as  OˆρPA(δα) =  ���⟨ψ+  PA| ˆD(δα) |ψ+  PA⟩  ���  2  +  ���⟨ψ−  PA| ˆD(δα) |ψ−  PA⟩  ���  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (46)  We plot this overlap with n=10, 15, and 20 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Again, we see that the overlap OˆρPA(δα) disappears for  the displacement |δα| ≪ 1, but unlike the SPASVS, this  orthogonality now take place when δx = ±δp in the phase  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Similarly, overlap (14) for SPSSVS is obtained as  OSPS(δα) =  �  ⟨ψ+  PS| ˆD(δα) |ψ+  PS⟩ + ⟨ψ−  PS| ˆD(δα) |ψ−  PS⟩  �2  ,  (47)  where  ⟨ψ±  PS| ˆD(δα) |ψ±  PS⟩ =[∓ sinh(2r)]n e−|η±|2/2  4n  n  �  l=0  (n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' )2  l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' [(n − l)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ]2  [∓2tanh(r)]lHn−l [θ±] Hn−l  �  θ∗  ±  �  ,  (48)  with  θ± = i  �  ±tanh(r)  2  η±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (49)  12  (a)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
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+page_content='8  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  /p  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 14: Overlap of the pure SPSSVS state with its δα-displaced part with δα = (δx + iδp)/  √  2: (a) n = 10  (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (a)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
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+page_content='6  /x  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
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+page_content='6  /p  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='8  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 15: Overlap of the mixed-state SPSSVS with its δα-displaced part with δα = (δx + iδp)/  √  2: (a) n = 10  (b) n = 15 and (c) n = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In all cases r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 14, we plot this overlap with n equal to 10, 15, and  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The SPSSVS overlap plot exhibits the same behavior  as the SPASVS: the overlap disappears in any direction in  phase space when |δα| ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The only distinction is that,  for the same n and r, the central pattern of the overlap of  the SPSSVS is larger than that of the SPASVS, showing  that the SPSSVS is less sensitive than the SPASVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Finally, we consider mixtures of PSSVSs (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The  overlap (14) for this state leads to  OˆρPS(δα) =  ���⟨ψ+  PS| ˆD(δα) |ψ+  PS⟩  ���  2  +  ���⟨ψ−  PS| ˆD(δα) |ψ−  PS⟩  ���  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (50)  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 15, we plot the overlap OˆρPS(δα) using the same  parameter values as that of the SPSSVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' We observe that  the overlap of the mixture of the PSSVSs looks similar  to the mixture of the PASVSs, with the distinction being  that the mixture of PSSVSs appears to be less sensitive  for a given number of n and r, which is manifested as the  larger chessboardlike pattern in the center of the phase  space than that of the mixture of PASVSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  In summary, we have demonstrated that the sensitivity  associated to our proposed states depends on the quan-  tity of photons added (or subtracted), and it drops con-  siderably below the sensitivity of the coherent state when  there are excessive amount of photons added (or sub-  tracted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' For both SPASVS and SPSSVS, the enhanced  sensitivity is unaffected by the directions of phase-space  displacements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  However, for the mixtures related to  PASVSs or PSSVSs, this enhancement only takes place  in particular phase-space directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This implies that  compared to mixed states, our superposition states have  more potential for quantum sensing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' More-  over, it has been found that the quantum states associ-  ated with photon addition cases are more sensitive than  their counterparts of the photon subtraction cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  SUMMARY AND OUTLOOK  We have shown that the Wigner function of the  SPASVS (or SPSSVS) contains the chessboardlike pat-  tern around the origin of the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Similar chess-  boardlike pattern is also emerged by the mixtures related  to PASVSs and PSSVSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' The support area of the phase-  space structures contained by this chessboardlike pattern  varies inversely with the photon number added (or sub-  tracted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' When a sizable number of photons are added  (or subtracted), the support area of these structures is  noticeably smaller than that of the coherent state, and  these are the same sub-Planck structures, as shown by  compass states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The average photon numbers of our states, which  are increased either by photon-addition or photon-  13  subtraction actions on the Gaussian SVS, have an im-  pact on the size of the sub-Planck structures in the phase  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The sub-Planck structures associated with the  SPASVS are smaller than those of the SPSSVS for the  same number of photons added or subtracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This is be-  cause the photon-addition operation always leads to the  higher average photon number in the resultant states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  The association of the average photon number with the  sub-Planck structures in our states is much similar to  that of the compass states, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=', higher average photon  number in the compass state correspond to the smaller  sub-Planck structures in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  We have demonstrated that the sensitivity of our pro-  posed states is noticeably higher than that of the coherent  state when a significant number of photons are added (or  subtracted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Both the SPASVS and SPSSVS exhibit the  enhanced sensitivity, which is independent of the phase-  space directions, indicating that they hold more promise  for quantum metrology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' In addition, the difference in the  sensitivities between the photon addition and subtraction  cases is arose from the different average photon numbers  in the states;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' photon addition cases are demonstrated to  have greater sensitivity than the subtracted cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  It is incredibly exciting that sub-Planck structures can  possibly build from photons being added to or subtracted  from states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' As a result, it will be able to apply a va-  riety of ways to engineer compass-like states in associa-  tion with contemporary experiments [94–97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' For exam-  ple, the theoretical research in [94] shows that subtract-  ing a photon from the Gaussian SVS results in an odd  Schr¨odinger cat state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Another subsequent theoretical  approach introduces the idea of photon subtraction from  the Gaussian SVS to produce the compass-like states [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Additionally, theoretical research to construct the cat-  like states advocated in [94] is subsequently applied in  actual experiments [96, 97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' These illustrations unequiv-  ocally demonstrate that it is possible to add or subtract  photons from states in both theory and experiments to  produce compass-like states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' It may possible that some  of these techniques can be modified to produce SPASVS  and SPSSVS, which are entirely new research avenues  that can be adapted in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  NA acknowledges the support of postdoctoral fund  of  the  Zhejiang  Normal  University  under  Grant  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' ZC304021937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' GX acknowledges support by the Na-  tional Natural Science Foundation of China (Grants Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  11835011 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 12174346).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' WML acknowledges the  support from the National Key R&D Program of China  under grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 2021YFA1400900, 2021YFA0718300,  2021YFA1402100, NSFC under grants Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 61835013,  12174461, 12234012, and Space Application System of  China Manned Space Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Appendix A: Wigner functions of SPASVS and SPSSVS  This section provides the main steps to drive the Wigner functions of SPASVS and SPSSVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Derivations of the Wigner function of SPASVS  Let us first consider the Wigner function of SPASVS given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' First term of this Wigner function is given  by  IΞ(ζ) =  �  ψ+  PA  ��� ˆ∆(α)  ��� ψ−  PA  �  ,  (A1)  where the alternative form of the displaced parity operator ˆ∆(α) is [77]  ˆ∆(α) := 1  π2 e2|α|2 � ∞  −∞  d2βe−2α∗β+2αβ∗ |β⟩⟨−β| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A2)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (A1) can be rewritten as  IΞ(ζ) = (−1)ne2|α|2  π2 cosh(r)  � ∞  −∞  d2β|β|2n exp  �  − |β|2 − tanh(r)  2  �  β2 + β∗2�  − 2βα∗ + 2β∗α  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A3)  We incorporate the factor |β|2n into a differential equation as  IΞ(ζ) = (−1)ne2|α|2  π2 cosh(r)  ∂2n  ∂sn∂tn  � ∞  −∞  d2β exp  �  − |β|2 − tanh(r)  2  �  β2 − β∗2�  − 2βα∗ + 2β∗α + sβ + tβ∗  �����  s=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A4)  14  Consider the integral formula [107]  � ∞  −∞  d2β exp  �  a|β|2 + bβ + cβ∗ + dβ2 + kβ∗2  �  =  π  √  a2 − 4dk  exp  �−abc + b2k + c2d  a2 − 4dk  �  ,  (A5)  whose convergent conditions are Re [a ± d ± k] < 0 and Re  �  (a2−4dk)/a±d±k  �  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' By using this integral Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (A4) leads  to  IΞ(ζ) =  (−1)neξ  π cosh(r)  �  1 + tanh2(r)  ∂2n  ∂sn∂tn exp  �  tanh(2r)  4  s2 − tanh(2r)  4  t2 +  �  1 + tanh2(r)  �−1st − 2 cosh(r)sech(2r)α−s  − 2 cosh(r)sech(2r)α∗  +t  ������  s=t=0  ,  (A6)  with  ξ := −(α2 − α∗2) tanh(2r) − 2|α|2sech(2r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A7)  It is challenging to solve Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (A6) because it has eγst terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' We employ the following sum series [73] to get rid of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  exp(Cs + Dt + Est) =  ∞  �  l=0  El  l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  ∂2l  ∂Cl∂Dl [exp (Cs + Dt)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A8)  Using this formula Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (A6) modifies as  IΞ(ζ) =  (−1)neξ  π cosh(r)  �  1 + tanh2(r)  ∞  �  l=0  1  l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 22l  �  1 + tanh2(r)  �−l  cosh2l(r)sech2l(2r)  ∂2l  ∂α∗l  +αl  −  ∂2n  ∂sn∂tn exp  �tanh(2r)  4  s2 − tanh(2r)  4  t2  − 2 cosh(r)sech(2r)(α−s + α∗  +t)  �����  s=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A9)  Noticing the generating function of Hermite polynomial  Hn(x) = ∂n  ∂sn exp  �  2xs − s2� ��  s=0,  (A10)  and its recursive relation  dl  dxl Hn(x) =  2ln!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (n − l)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='Hn−l(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A11)  The preceding equation can then be simplified in the form of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (30) by applying the relationships (A10) and (A11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Let us now calculate second term of the Wigner function (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This term can be written as  W⊞(ζ) =  �  ψ+  PA  ��� ˆ∆(α)  ��� ψ+  PA  �  +  �  ψ−  PA  ��� ˆ∆(α)  ��� ψ−  PA  �  ,  (A12)  where  �  ψ±  PA  ��� ˆ∆(α)  ��� ψ±  PA  �  =(−1)n  π2  e2|α|2  cosh(r)  ∂2n  ∂sn∂tn  � ∞  −∞  d2β exp  �  − |β|2 ± 1  2 tanh(r)(β2 + β∗2) − 2βα∗ + 2β∗α + sβ + tβ∗���  s=t=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Using the integral (A5), we get  �  ψ±  PA  ��� ˆ∆(α)  ��� ψ±  PA  �  =(−1)n  π  exp  �  ± sinh(2r)(α∗2 + α2) − 4 cosh2(r)|α|2�  ∂2n  ∂sn∂tn exp  �  ± 1  4 sinh(2r)(s2 + t2)  + 2 cosh(r)(¯α±s − ¯α∗  ±t) + cosh2(r)st  �����  s=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A13)  Again, use of sum series (A8) eliminates the factors eγst, that is,  �  ψ±  PA  ��� ˆ∆(α)  ��� ψ±  PA  �  =  ∞  �  l=0  (−1)l  22ll!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  ∂2l  ∂ ¯αl  ±∂ ¯α∗l  ±  ∂2n  ∂sn∂tn exp  �  ±sinh(2r)  4  �  s2 + t2�  + 2 cosh r  �  ¯α±s − ¯α∗  ±t  ������  s=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A14)  Then, by using the relations (A10) and (A11), the expression (39) is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  15  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Derivations of the Wigner function of SPSSVS  This section presents the detailed derivation of the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (36), for which the first term gets form as below  IΞ(ζ) =  �  ψ+  PS  ��� ˆ∆(α)  ��� ψ−  PS  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A15)  This term is calculated as  IΞ(ζ) = 1  π2  e2|α|2  cosh(r)  ∂2n  ∂sn∂tn exp  �  − tanh(r)  2  �  t2 − s2�� � ∞  −∞  d2β exp  �  − |β|2 −  �  tanh(r)t + 2α∗�  β −  �  tanh(r)s  − 2α  �  β∗ − tanh(r)  2  (β2 − β∗2)  �����  s=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A16)  Using the integral (A5), we obtain  IΞ(ζ) =  eξ  π cosh(r)  �  1 + tanh2(r)  ∂2n  ∂sn∂tn exp  �tanh(2r)  4  s2 − tanh(2r)  4  t2 + 2sech(2r) sinh(r)(α∗  +s − α−t)  + sech(2r) sinh2(r)st  �����  s=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A17)  Now, we eliminate eγst terms by using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (A8)  IΞ(ζ) =  eξ  π cosh(r)  �  1 + tanh2(r)  ∞  �  l=0  1  l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='22lsechl(2r)  ∂2l  ∂α∗l  +∂αl  −  ∂2  ∂sn∂tn exp  �tanh(2r)  4  s2 − tanh(2r)  4  t2  + 2sech(2r) sinh(r)(α∗  +s + α−t)  �����  s=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A18)  Then, using the relations (A10) and (A11) we obtain expression (38).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Finally, we derive the second term of the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' This term can be written as  W⊞(ζ) =  �  ψ+  PS  ��� ˆ∆(α)  ��� ψ+  PS  �  +  �  ψ−  PS  ��� ˆ∆(α)  ��� ψ−  PS  �  ,  (A19)  where  �  ψ±  PS  ��� ˆ∆(α)  ��� ψ±  PS  �  = 1  π exp  �  ± sinh(2r)(α2 + α∗2) − 2 cosh(2r)|α|2� ∂2n  ∂sntn exp  �  ± 1  4 sinh(2r)(s2 + t2)  ± 2 sinh(r)(¯α±t + ¯α∗  ±s) − sinh2(r)st  �����  s,t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A20)  Again, we use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (A8) to get rid of all eγst factors, obtaining  �  ψ±  PS  ��� ˆ∆(α)  ��� ψ±  PS  �  = 1  π exp  �  ± sinh(2r)(α2 + α∗2) − 2 cosh(2r)|α|2� ∞  �  l=0  (−1)l  22ll!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  ∂2l  ∂ ¯αl  ±¯α∗l  ±  ∂2n  ∂sntn exp  �  ± sinh(2r)  4  �  s2 + t2�  ± 2 sinh(r)  �  ¯α±t + ¯α∗  ±s  ������  s=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A21)  Finally, this equation can be simplified to expression (39) by utilizing the relations (A10) and (A11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  OVERLAPS OF SPASV AND SPSSV  In this section, we calculate the overlap (14) of SPASVS and SPSSVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Note that, for n ≫ 1 and |δα| ≪ 1, the  contribution of the cross terms between the states to the overlap is negligible, that is,  ⟨ψ+  PA| ˆD(δα) |ψ−  PA⟩ = 0 and ⟨ψ+  PS| ˆD(δα) |ψ−  PS⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A22)  16  First, we drive each term of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (41).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' PASV (19) can be rewritten as [73]  |ψ±  PA⟩ = ˆS(±r)  �  ˆa† cosh(r) ± ˆa sinh(r)  �n |0⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A23)  Then, considering relation given by [73]  (fˆa + gˆa†) :=  �  − i  �  fg  2  �n  Hn  �  i  �  f  2g ˆa + i  � g  2f ˆa†  �  ,  (A24)  which leads to  [ˆa† cosh(r) + ˆa sinh(r)]n =  �  − i  �  sinh(2r)  4  �n  Hn  �  i  �  tanh(r)  2  ˆa + i  �  coth(r)  2  ˆa†  �  ,  (A25)  [ˆa cosh(r) + ˆa† sinh(r)]n =  �  − i  �  sinh(2r)  4  �n  Hn  �  i  �  tanh(r)  2  ˆa† + i  �  coth(r)  2  ˆa  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A26)  By using these relations, we obtain  ⟨ψ±  PA| ˆD(δα)|ψ±  PA⟩ =  �  ∓ sinh(2r)  4  �n �  0  ����� Hn  �  i  �  ±coth(r)  2  ˆa  �  ˆD(η±)Hn  �  i  �  ±coth(r)  2  ˆa†  � ����� 0  �  ,  =  �  ∓ sinh(2r)  4  �n � ∞  −∞  d2α  π  exp  �  − |α|2  2  − α  2 η∗  ± + α∗  2 η± − |α − η±|2  2  �  Hn  �  i  �  ±coth(r)  2  α  �  Hn  �  i  �  ±coth(r)  2  (α∗ − η∗  ±)  �  ,  (A27)  where  ˆD(η±) = ˆS†(±r) ˆD(δα) ˆS(±r) with η± = δα cosh(r) ∓ δα∗ sinh(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A28)  By using (A10), we get  ⟨ψ±  PA| ˆD(δα)|ψ±  PA⟩ =  �  ∓ sinh(2r)  4  �n  ∂2n  ∂τ n∂tn exp  �  − i  �  ±2 coth(r) η∗  ±τ  �  exp  �  − τ 2 − t2�  � ∞  −∞  d2α  π  exp  �  − |α|2  2  − α  2 η∗  ± + α∗  2 η± − |α − η±|2  2  + i  �  ±2 coth(r) αt + i  �  ±2 coth(r) α∗τ  �����  τ=t=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A29)  Using the integral (A5), the previous equation yields  ⟨ψ±  PA| ˆD(δα)|ψ±  PA⟩ =  �  ∓ sinh(2r)  4  �n  exp  �  − |η±|2  2  �  ∂2n  ∂τ n∂tn exp  �  − t2 + i  �  ±2 coth(r) η±t − τ 2 − i  �  ±2 coth(r) η∗  ±τ  (A30)  ∓ 2 coth(r) tτ  �����  t=τ=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A31)  First, we rid out the factors eγτt from above equation by using (A8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Then, by using (A10) and (A11), the preceding  equation is simplified to (42).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Similarly, PSSVS can be rewritten as [73]  |ψ±  PS⟩ = ˆS(±r)  �  ˆa cosh(r) ± ˆa† sinh(r)  �n |0⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (A32)  The overlap  ⟨ψ±  PS| ˆD(δα)|ψ±  PS⟩ =  �  ∓ sinh(2r)  4  �n �  0  ����� Hn  �  i  �  ±tanh(r)  2  ˆa  �  ˆD(η±)Hn  �  i  �  ±tanh(r)  2  ˆa†  � ����� 0  �  ,  =  �  ∓ sinh(2r)  4  �n � ∞  −∞  d2α  π  exp  �  − |α|2  2  − α  2 η∗  ± + α∗  2 η± − |α − η±|2  2  �  Hn  �  i  �  ±tanh(r)  2  α  �  Hn  �  i  �  ±tanh(r)  2  (α∗ − η∗  ±)  �  ,  (A33)  17  can be easily simplified to (48).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wigner, On the quantum correction for thermody-  namic equilibrium, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 40, 749 (1932).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Gerry and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Knight, Introductory Quantum Op-  tics (Cambridge University Press, England, Cambridge,  2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [3] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Schleich, Quantum Optics in Phase Space (Wiley-  VCH, Weinheim, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rundle and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Everitt, Overview of the phase  space formulation of quantum mechanics with applica-  tion to quantum technologies, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Quantum Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  4, 2100016 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [5] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Leonhardt, Measuring the quantum state of light,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 22 (Cambridge university press, United Kingdom,  1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [6] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Navarrete-Benlloch, An Introduction to the Formal-  ism of  Quantum Information with Continuous Variables (Mor-  gan & Claypool/IOP, Bristol, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [7] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Schumaker, Quantum mechanical pure states with  Gaussian wave functions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 135, 317 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [8] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Schr¨odinger, Der stetige ¨ubergang von der mikro- zur  makromechanik, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 14, 664 (1926).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [9] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Robertson, The uncertainty principle, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  34, 163 (1929).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wheeler and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zurek, Quantum Theory and  Measurement (Princeton University Press, Princeton,  NJ, 1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [11] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Buˇzek and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Knight, I: Quantum interference, su-  perposition states of light, and nonclassical effects (El-  sevier, 1995) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 1–158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Walschaers, Non-Gaussian quantum states and  where to find them, PRX Quantum 2, 030204 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' de Freitas and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dodonov, Non-Gaussianity  of four-photon superpositions of fock states, Quantum  Reports 3, 350 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [14] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dodonov, ‘Nonclassical’ states in quantum op-  tics: a ‘squeezed’ review of the first 75 years, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' B:  Quantum Semiclassical Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 4, R1 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Streltsov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Adesso, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Plenio, Colloquium:  Quantum coherence as a resource, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 89,  041003 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [16] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Drummond and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ficek, Quantum Squeezing  (Springer-Verlag, Berlin, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [17] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sanders, Entangled coherent states, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A  45, 6811 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [18] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sanders, Erratum:  Entangled coherent states  [Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 45, 6811 (1992)], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 46, 2966  (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sanders, Review of entangled coherent states, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 45, 244002 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mirrahimi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Leghtas, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Albert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Touzard,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Schoelkopf, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Jiang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Devoret, Dynami-  cally protected cat-qubits: a new paradigm for universal  quantum computation, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 16, 045014 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Bose, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Jacobs, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Knight, Scheme to probe  the decoherence of a macroscopic object, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A  59, 3204 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [22] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Marshall,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Simon,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Penrose,  and  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Bouwmeester,  Towards  quantum  superpositions  of a mirror, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 91, 130401 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [23] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Marshall,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Simon,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Penrose,  and  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Bouwmeester, Publisher’s note:  Towards quan-  tum superpositions of a mirror [Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 91,  130401 (2003)], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 91, 159903 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [24] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Walther, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Aspelmeyer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ursin,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Gasparoni, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zeilinger, De Broglie wavelength of  a non-local four-photon state, Nature 429, 158 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mitchell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lundeen, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Steinberg,  Super-resolving phase measurements with a multipho-  ton entangled state, Nature 429, 161 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [26] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Happ, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Efremov, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Nha, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Schle-  ich, Sufficient condition for a quantum state to be gen-  uinely quantum non-Gaussian, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 20, 023046  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [27] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sanders, Superposition of two squeezed vacuum  states and interference effects, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 39, 4284  (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [28] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Giovannetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lloyd, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Maccone, Quantum-  enhanced measurements: Beating the standard quan-  tum limit, Science 306, 1330 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [29] A gravitational wave observatory operating beyond the  quantum shot-noise limit, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Physics 7, 962 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [30] Enhancing the sensitivity of the ligo gravitational wave  detector by using squeezed states of light, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Physics  7, 962 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [31] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Milburn, Quantum and classical Liouville dynam-  ics of the anharmonic oscillator, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 33, 674  (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [32] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Yurke and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Stoler, Generating Quantum Mechan-  ical Superpositions of Macroscopically Distinguishable  States via Amplitude Dispersion, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 57,  13 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [33] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zurek, Sub-Planck structure in phase space and  its relevance for quantum decoherence, Nature 412, 712  (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [34] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zurek, Decoherence, einselection, and the quan-  tum origins of the classical, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 75, 715  (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [35] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pan and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Panigrahi, Cat state, sub-Planck  structure and weak measurement, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' D 67,  1 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [36] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dalvit, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' de Matos Filho, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Toscano,  Quantum metrology at the heisenberg limit with ion  trap motional compass states, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 8, 276  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [37] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Toscano, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dalvit, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Davidovich, and  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zurek, Sub-Planck phase-space structures and  Heisenberg-limited measurements, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 73,  023803 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ghosh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Bera, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Panigrahi, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Roy,  Sub-fourier quantum metrology through bright solitary  trains in Bose–Einstein condensate, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Quantum Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  17, 1950019 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [39] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Scott and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Caves, Teleportation fidelity as a  probe of sub-Planck phase-space structure, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  (NY) 323, 2685 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  18  [40] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Praxmeyer,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Wasylczyk,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Radzewicz,  and  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' W´odkiewicz, Time-Frequency Domain Analogues of  Phase Space Sub-Planck Structures, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  98, 063901 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [41] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Jacquod, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Adagideli, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Beenakker, Decay  of the Loschmidt Echo for Quantum States with Sub-  Planck-scale Structures, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 89, 154103  (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [42] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wisniacki, Short-time decay of the Loschmidt  echo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' E 67, 016205 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [43] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ghosh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Chiruvelli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Banerji, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pan-  igrahi, Mesoscopic superposition and sub-Planck-scale  structure in molecular wave packets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 73,  013411 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [44] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Bhatt,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Panigrahi,  and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Vyas,  Entanglement-induced sub-Planck phase-space struc-  tures, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 78, 034101 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [45] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Stobi´nska, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Milburn, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' W´odkiewicz,  Wigner function evolution of quantum states in the pres-  ence of self-Kerr interaction, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 78, 013810  (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [46] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ghosh, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Roy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Genes, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Vitali, Sub-Planck-  scale structures in a vibrating molecule in the presence  of decoherence, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 79, 052104 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [47] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Roy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ghosh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Panigrahi, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Vitali, Sub-  Planck-scale structures in the P¨oschl-teller potential  and their sensitivity to perturbations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 80,  052115 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [48] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ghosh, Coherent control of mesoscopic superpositions  in a diatomic molecule, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Quantum Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 10, 1250014  (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [49] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Kumari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pan, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Panigrahi, Sub-Planck  structure in a mixed state, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' D 69, 248 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [50] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dodonov, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Valverde, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Souza, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Baseia, De-  coherence of odd compass states in the phase-sensitive  amplifying/dissipating environment, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (NY)  371, 296 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [51] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Kumar and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lee, Sensitivity of sub-Planck  structures of mesoscopically superposed coherent states  to the thermal reservoirs induced decoherence, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 394, 23 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [52] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Howard,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Weinhold,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Shahandeh,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Combes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Vanner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' White, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ring-  bauer, Quantum Hypercube States, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  123, 020402 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [53] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Akhtar, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sanders, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Xianlong, Sub-Planck  phase-space structure and sensitivity for SU(1,1) com-  pass states, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 106, 043704 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [54] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Akhtar,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Sanders,  and  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Navarrete-  Benlloch, Sub-Planck structures: Analogies between the  Heisenberg-Weyl and SU(2) groups, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 103,  053711 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [55] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Shukla, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Akhtar, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sanders, Quantum  tetrachotomous states: Superposition of four coherent  states on a line in phase space, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 99, 063813  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [56] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Panigrahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=', Compass state: Effect of squeez-  ing and displacement on the Fock space, arXiv preprint  arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='10374 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [57] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Agarwal and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pathak, Mesoscopic superposi-  tion of states with sub-Planck structures in phase space,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 70, 053813 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [58] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pathak and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Agarwal, Generation of a super-  position of multiple mesoscopic states of radiation in a  resonant cavity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 71, 043823 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [59] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Stobi´nska, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Villar, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Leuchs, Generation  of Kerr non-Gaussian motional states of trapped ions,  Europhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 94, 54002 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [60] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Leghtas, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Kirchmair, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Vlastakis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Devoret,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Schoelkopf, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mirrahimi, Deterministic pro-  tocol for mapping a qubit to coherent state superposi-  tions in a cavity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 87, 042315 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [61] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Govia, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pritchett, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wilhelm,  Generating nonclassical states from classical radiation  by subtraction measurements, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 16, 045011  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [62] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Hastrup, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Neergaard-Nielsen, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ander-  sen, Deterministic generation of a four-component opti-  cal cat state, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 45, 640 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [63] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ofek, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Petrenko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Heeres, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Reinhold, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Legh-  tas, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Vlastakis, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Frunzio, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Girvin,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Jiang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mirrahimi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Devoret, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Schoelkopf, Extending the lifetime of a quantum bit  with error correction in superconducting circuits, Na-  ture 536, 441 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [64] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Vlastakis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Kirchmair, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Leghtas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Nigg,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Frunzio, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Girvin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mirrahimi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' De-  voret, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Schoelkopf, Deterministically encoding  quantum information using 100-photon Schr¨odinger cat  states, Science 342, 607 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [65] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lemos, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Gomes, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Walborn, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ribeiro, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Toscano, Experimental observation  of quantum chaos in a beam of light, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 3,  2041 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [66] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Austin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Witting, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wyatt, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Walmsley, Measuring sub-Planck structural analogues  in chronocyclic phase space, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 283, 855  (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [67] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Nha and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Carmichael, Proposed test of quantum  nonlocality for continuous variables, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  93, 020401 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [68] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Takahashi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Neergaard-Nielsen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Takeuchi,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Takeoka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Hayasaka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Furusawa, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sasaki,  Entanglement distillation from Gaussian input states,  Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Photonics 4, 178 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [69] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zhang and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Fan, Properties of states generated by  excitations on a squeezed vacuum state, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A  165, 14 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [70] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Hughes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Genoni, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Tufarelli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Paris,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Kim, Quantum non-Gaussianity witnesses in  phase space, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 90, 013810 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [71] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Quesne, Completeness of photon-added squeezed  vacuum and one-photon states and of photon-added co-  herent states on a circle, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 288, 241 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [72] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Si, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ji, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Jia, Nonclassicality of photon-  added squeezed vacuum states, Chin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' B 19,  064205 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [73] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Hu and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Fan, Nonclassicality of photon-  added squeezed vacuum and its decoherence in thermal  environment, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 57, 1344 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [74] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dey and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Nair, Generalized photon-subtracted  squeezed vacuum states, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 53,  385305 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [75] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Meng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Fan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wang,  Nonclassicality and decoherence of photon-subtracted  squeezed vacuum states, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' B 29, 3141  (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [76] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Biswas and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Agarwal, Nonclassicality and de-  19  coherence of photon-subtracted squeezed states, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 75, 032104 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [77] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ma and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Luo, Comparison of nonclassicality  between photon-added and photon-subtracted squeezed  vacuum states, Chin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' B 21, 024203 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [78] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' K¨uhn and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Vogel, Quantum non-Gaussianity  and quantification of nonclassicality, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 97,  053823 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [79] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Tang,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Gao,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Wang,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Wu,  and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Shuang, Non-Gaussian features from excited  squeezed vacuum state, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 345, 86 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [80] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Barnett, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ferenczi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Gilson, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Speirits, Statistics of photon-subtracted and photon-  added states, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 98, 013809 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [81] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lang and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Caves, Optimal quantum-  enhanced interferometry using a laser power source,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 111, 173601 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [82] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Xu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Xu, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zhang, Quantum in-  terferometry via a coherent state mixed with a photon-  added squeezed vacuum state, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 444, 102  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [83] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Birrittella and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Gerry, Quantum optical in-  terferometry via the mixing of coherent and photon-  subtracted squeezed vacuum states of light, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' B 31, 586 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [84] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Agarwal and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Tara, Nonclassical properties of  states generated by the excitations on a coherent state,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 43, 492 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [85] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zavatta, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Viciani, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Bellini, Quantum-to-  classical transition with single-photon-added coherent  states of light, Science 306, 660 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [86] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wenger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Tualle-Brouri, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Grangier, Non-  gaussian statistics from individual pulses of squeezed  light, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 92, 153601 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [87] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ourjoumtsev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dantan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Tualle-Brouri, and  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Grangier, Increasing entanglement between Gaussian  states by coherent photon subtraction, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  98, 030502 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [88] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Cochrane, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Milburn, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Munro,  Macroscopically distinct quantum-superposition states  as a bosonic code for amplitude damping, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A  59, 2631 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [89] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ralph, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Gilchrist, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Milburn, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Munro,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Glancy, Quantum computation with optical co-  herent states, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 68, 042319 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [90] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Le Jeannic, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ruaudel, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Verma,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Shaw, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Marsili, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Nam, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Zeng,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Jeong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Filip, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Morin, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Laurat, Opti-  cal synthesis of large-amplitude squeezed coherent-state  superpositions with minimal resources, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  115, 023602 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [91] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sychev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ulanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pushkina, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Richards, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Fedorov, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lvovsky, Enlargement  of optical Schr¨odinger’s cat states, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Photonics 11,  379 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [92] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ulanov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Fedorov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sychev, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Grang-  ier, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lvovsky, Loss-tolerant state engineering for  quantum-enhanced metrology via the reverse hong–ou–  mandel effect, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 7, 1 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [93] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Wakui, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Takahashi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Furusawa, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Sasaki,  Photon subtracted squeezed states generated with peri-  odically poled ktiopo4, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Express 15, 3568 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [94] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Dakna, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Anhut, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Opatrn´y, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Kn¨oll, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Welsch, Generating Schr¨odinger-cat-like states by  means of conditional measurements on a beam splitter,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A 55, 3184 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [95] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Takase, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Yoshikawa, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Asavanant, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Endo,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Furusawa, Generation of optical Schr¨odinger cat  states by generalized photon subtraction, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' A  103, 013710 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [96] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Neergaard-Nielsen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Nielsen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Hettich,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mølmer, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Polzik, Generation of a super-  position of odd photon number states for quantum in-  formation networks, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 97, 083604 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [97] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Ourjoumtsev,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Tualle-Brouri,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Laurat, and  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Grangier, Generating optical Schr¨odinger kittens  for quantum information processing, Science 312, 83  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [98] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Audenaert, Comparisons between quantum  state distinguishability measures, Quantum Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Com-  put.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 14, 31 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [99] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Braun, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Adesso, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Benatti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Floreanini, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mar-  zolino, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mitchell, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Pirandola, Quantum-  enhanced measurements without entanglement, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 90, 035006 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [100] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Luis, Quantum-limited metrology with nonlinear de-  tection schemes, SPIE Reviews 1, 018006 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [101] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Weyl, The Theory of Groups and Quantum Mechan-  ics (Dover, New York, 1950).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [102] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Perelomov, Generalized Coherent States and Their  Applications, Theoretical and Mathematical Physics  (Springer-Verlag, Berlin, 1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [103] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Gazeau, Coherent States in Quantum Physics  (Wiley-VCH, Berlin, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [104] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Moyal, Quantum mechanics as a statistical theory,  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Cambridge Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 45, 99 (1949).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [105] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Gilmore, Properties of coherent states, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Mex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  Fis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' 23, 143 (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [106] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Kok and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Lovett, Introduction to Optical Quan-  tum Information Processing, 1st ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' (Cambridge Univer-  sity Press, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content='  [107] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
+page_content=' Puri, Mathematical methods of quantum optics  (Springer-Verlag, Berlin, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdAyT4oBgHgl3EQfX_es/content/2301.00195v1.pdf'}
diff --git a/ktE1T4oBgHgl3EQf0gVV/content/tmp_files/2301.03456v1.pdf.txt b/ktE1T4oBgHgl3EQf0gVV/content/tmp_files/2301.03456v1.pdf.txt
new file mode 100644
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@@ -0,0 +1,1794 @@
+1
+UB3: Best Beam Identification in Millimeter Wave
+Systems via Pure Exploration Unimodal Bandits
+Debamita Ghosh1, Haseen Rahman2, Manjesh K. Hanawal3, and Nikola Zlatanov4
+1IITB-Monash Research Academy, IIT Bombay, India, email: debamita.ghosh@iitb.ac.in
+2MLiONS Lab, IEOR, IIT Bombay, India, email: haseenrahman@gmail.com
+3MLiONS Lab, IEOR IIT Bombay, India, email:mhanawal@iitb.ac.in
+4Innopolis University, Russia, email: n.zlatanov@innopolis.ru
+Abstract—Millimeter wave (mmWave) communications have
+a broad spectrum and can support data rates in the order
+of gigabits per second, as envisioned in 5G systems. However,
+they cannot be used for long distances due to their sensitivity
+to attenuation loss. To enable their use in the 5G network,
+it requires that the transmission energy be focused in sharp
+pencil beams. As any misalignment between the transmitter and
+receiver beam pair can reduce the data rate significantly, it is
+important that they are aligned as much as possible. To find
+the best transmit-receive beam pair, recent beam alignment (BA)
+techniques examine the entire beam space, which might result in
+a large amount of BA latency. Recent works propose to adaptively
+select the beams such that the cumulative reward measured in
+terms of received signal strength or throughput is maximized. In
+this paper, we develop an algorithm that exploits the unimodal
+structure of the received signal strengths of the beams to identify
+the best beam in a finite time using pure exploration strategies.
+Strategies that identify the best beam in a fixed time slot
+are more suitable for wireless network protocol design than
+cumulative reward maximization strategies that continuously
+perform exploration and exploitation. Our algorithm is named
+Unimodal Bandit for Best Beam (UB3) and identifies the best
+beam with a high probability in a few rounds. We prove that the
+error exponent in the probability does not depend on the number
+of beams and show that this is indeed the case by establishing a
+lower bound for the unimodal bandits. We demonstrate that UB3
+outperforms the state-of-the-art algorithms through extensive
+simulations. Moreover, our algorithm is simple to implement and
+has lower computational complexity.
+Index Terms—mmWave, Bandit learning, pure exploration
+I. INTRODUCTION
+There is a growing demand for higher data rates with the
+advent of emerging data-intensive applications like virtual
+reality, mobile gaming, and HD quality video streaming. The
+wireless networks have improved in terms of data rates but
+are still constrained by the available bandwidth in the sub-6
+GHz spectrum to meet the data rates required for emerging
+applications. The millimeter wave (mmWave) band, with a
+spectrum ranging from 30 GHz to 300 GHz, offers an abundant
+spectrum and can support data rates of gigabits per second
+that are envisioned in 5G networks. Significant efforts in the
+standardisation of mmWave systems, such as IEEE 802.11ad
+[1], [2] and ongoing IEEE 802.11ay [3], are underway, and
+the 5G networks with mmWave systems are on the path of
+commercialisation through extensive field trials.
+Though mmWave systems offer higher data rates, they
+come with a set of challenges—the small wavelengths
+of
+mmWaves
+make
+them
+suffer
+significant
+attenuation,
+resulting in a rapid deterioration of signal strength. Thus,
+unlike traditional terrestrial communication systems, mmWave
+communication requires highly directional communication
+with energy focused on narrow beams to achieve the required
+signal strengths at the receiver. Some challenges in using
+mmWave systems in mobile communications are highlighted
+in standards [1], [4]. However, on the brighter side, small
+wavelengths allow transmission antennas with small form
+factors to be packed closely and focus signal energy in specific
+directions, forming sharp beams.
+The other challenge in mmWave communication is that
+transmitter and receiver beams need to be aligned before data
+transfer; otherwise, any advantage of high data rates is not
+realised. A few degrees of misalignment in the beam directions
+between transmitter and receiver can reduce the data rates from
+gigabits per second to a few megabits per second, jeopardising
+the gain from the high spectrum of mmWave systems [5]–[7].
+This gives rise to the problem of beam alignment (BA), where
+one needs to find the best transmitter and receiver beam pair
+that provides the best rates. The BA problem is critical to
+building better 5G communication networks with mmWave
+systems. Our goal in this paper is to learn the best beam pair
+in a given number of slots with a high probability.
+One naive approach to performing BA is an exhaustive
+search of all available beams at the base station (BS) and user
+equipment (UE). This strategy does not scale well because it
+has the complexity of order O(K2), where K is the number
+of beams at BS and UE. The IEEE standard 802.11ad [1]
+decouples the BA by performing it in two stages. In the first
+stage, the BS uses a quasi-omnidirectional beam while the
+UE scans through its beams to identify the best one. In the
+next stage, the UE uses a quasi-omnidirectional beam while
+the BS scans through its beam to identify the best one. This
+search strategy has a complexity that is linear in K. However,
+as discussed in [8], [9], this method can still take time in
+seconds.
+The initial access (IA) phase in 5G mmWave provides a
+mechanism to identify beam directions between a BS and UE
+[10]–[13]. BSs periodically use the IA phase to discover new
+UEs and check if the best beam for already existing UEs has
+arXiv:2301.03456v1  [eess.SP]  26 Dec 2022
+
+2
+changed [14]. During the IA, BS transmits synchronization
+signals that UE can measure and report back the received
+signal strengths (RSS). IA can be used to explore and identify
+the best pair, as no data is transferred in this phase. Further,
+BS can adapt to the non-stationary environment by periodically
+rerunning the IA phase, where the periodicity can depend on
+the mobility rate and the atmospheric conditions.
+We address the BA and user tracking issues in mmWave
+using the fixed-budget pure exploration Multi-Armed Bandit
+(MAB) framework, where pure exploration is performed
+in
+the
+IA
+phase.
+The
+BA
+problem
+has
+already
+been
+addressed using the MAB framework, which uses cumulative
+regret minimization algorithms that balance exploration and
+exploitation to find the best beam pair [7], [15], [16]. However,
+the stopping time in these algorithms is random, leading to
+the following difficulties: 1) The learning phase may extend
+beyond the IA phase and reduce the number of time slots
+available for data transfer. 2) Due to continuous exploration,
+sub-optimal beams can be used for data transfer, resulting in
+outages. To overcome these issues, we complete the learning
+phase within a fixed number of time slots (budget) of the IA
+phase using adaptive exploration. Moreover, we exploit the
+structural properties of the RSS across the beams to accelerate
+the learning process.
+Several studies validate that the RSS of the beams in
+mmWave systems follows a multi-modal structure, with one
+peak corresponding to the line-of-sight path and others
+corresponding to the non-line-of-sight paths [7], [15]. Often,
+there is one dominant peak, and the multi-modal functions can
+be treated as unimodal. Bandits with a unimodal structure are
+well studied in the literature in the cumulative regret setting
+with optimal algorithms [17]–[19]. However, the fixed-budget
+pure exploration bandit with unimodal structure is not well
+studied, and optimal algorithms are not known. In this work,
+we develop a new fixed-budget pure exploration algorithm that
+exploits the unimodal structure. The new algorithm is named
+Unimodal Bandit for Best Beam (UB3) and is based on the idea
+of sequential elimination of sub-optimal beams. UB3 achieves
+an error probability of the order of O(log K exp(−T1D2
+L))
+after T1 time slots of IA phase, where DL is the minimum gap
+between two successive means of the arms. When no unimodal
+structure is assumed (unstructured), the best known achievable
+error probability is O(log K exp(−T1/H log K)) [20], where
+K is the number of beams and H is the problem-dependent
+constant. Thus, by exploiting unimodal structure, we achieve
+a better error probability where the error exponent does not
+depend on the number of beams, and demonstrate that this
+is anticipated by establishing a lower bound for unimodal
+bandits. Extensive simulation on realistic wireless networks
+demonstrates UB3 identifies the best arm with a probability
+more than 95% within 100 time slots for 16 beams, while
+the other state-of-the-art algorithms need 500 time slots. This
+translates into throughput gains of more than 15% compared
+to other algorithms. Moreover, UB3 does not require any
+prior knowledge of channel fluctuations. In summary, our
+contributions are as follows:
+• We set up the problem of beam alignment in mmWave
+systems as a fixed-budget pure exploration multi-armed
+bandit problem in Sec. II.
+• We exploit the unimodal structure of the RSS of the
+beams and develop an algorithm named Unimodal Bandit
+for Best Beam (UB3) to identify the best beam with a high
+probability in fixed time slots or within the IA phase of
+the BA in Sec. III.
+• We provide an upper bound on the error probability of
+UB3 in identifying the best beam and show that the error
+exponent does not depend on the number of beams. We
+demonstrate that is anticipated by establishing a lower
+bound for unimodal bandits in Sec. IV.
+• We perform extensive simulations to validate the superior
+performance of UB3 compared to other state-of-the-art
+algorithms like HOSUB, HBA, LSE and Sequential
+Halving in Sec. V. In agreement with the theoretical
+bounds, UB3 is not affected by the number of beams.
+A. Related Work
+As there is growing interest in mmWave systems in
+academia and industry, various aspects of mmWave are being
+studied. For the recent advances in the mmWave systems, we
+refer to surveys [21]–[23].
+Several approaches are proposed to solve the BA problem.
+The compressive sensing-based signal processing methods
+[24]–[26] utilize the sparse characterization of mmWave to
+learn the best beam. They work better when accurate channel
+state information is available. [27] proposes an Optimized
+Two-Stage Search (OTSS) where a suitable candidate set
+of beams is identified in the first stage based on the
+received signal profile, and in the second stage, the best
+beam from the surviving set is selected with additional
+measurements. Codebook-based hierarchical methods are
+proposed in [28]–[30] which also require channel state
+information for BA. [31], [32] utilizes the location information
+to perform fast BA, which is feasible only when the location
+information of the UE is available at the BS. [33], [34] use
+Kalman filters to detect the angles of arrivals and departures to
+track UE. Recently, machine learning [35], and deep learning
+[36], [37] methods have been used for BA, which requires
+offline training of the models.
+Our work is closer to [7], [15], [16], [38] which uses
+an online learning approach to optimize the BA problem.
+The authors in [7] develop an algorithm named Unimodal
+Beam Alignment (UBA) that exploits the unimodal structure
+of received power. The algorithm is built on the OSUB
+algorithm [17] by adding stopping criteria. The algorithm
+assumes that the mean powers are known, and the stopping
+criteria is based on these mean powers. The Hierarchical
+Beam Alignment (HBA) [15] algorithm also exploits the
+unimodal/multimodal structures of beam signal strengths to
+narrow down on the optimal beam. HBA has shown better
+performance for beam identification than UBA. However, for
+T time slots, the computational complexity of HBA is O(T 2),
+as in each time slot, the algorithm restarts the search, making
+the running time linear in each time slot. Moreover, HBA
+requires knowledge of channel fluctuations, which is not
+practical. The Hierarchical Optimal Sampling of Unimodal
+
+3
+Bandits (HOSUB) [38] exploits the benefits of hierarchical
+codebooks and the unimodality structure of the beam signal
+strengths to achieve fast beam steering. Simulations show
+better performance of HOSUB compared to HBA, as well
+as a large reduction in computational complexity. However,
+the authors in [38] did not provide any theoretical guarantees
+on their proposed algorithm. The authors in [16] develop
+an algorithm named MAMBA that aims to maximize the
+cumulative rate obtained over a period using the Thompson
+sampling algorithm named Adaptive Thompson Sampling
+(ATS). Unlike the UBA and HBA, the exploration never ends
+in ATS and may keep selecting the sub-optimal beams.
+Our work develops an online learning algorithm for BA
+using a fixed-budget pure exploration setup [20], [39]. We
+exploit the unimodal structure of beam RSS to eliminate the
+sub-optimal beams and narrow the beam search space quickly.
+Fixed-budget pure exploration strategies are more suitable for
+the BA problem, as the exploration can be completed in the IA
+phase, and no exploration is required during the data transfer,
+simplifying the design of protocols. To our knowledge, this
+has not been studied in 5G networks with mmWave systems.
+II. PROBLEM SETUP
+In this section, we discuss the system and channel model
+used in mmWave system. We follow the setup and notation
+similar to [15].
+A. System Model
+We consider a point-to-point mmWave wireless system
+between a transmitter, refer as mmWave BS, and a receiver,
+refer as mmWave UE, in a static environment as shown in
+Fig. 1. We focus on analog beamforming and consider one
+ADC with an RF chain that focuses on one direction at a
+time. The transmitter has K phased-array antennas, where
+each antenna has a phase shift to form a narrow directional
+beam. The antennas are evenly spaced by a distance D ≈
+λ/2 forming a uniform linear array, where λ is the carrier
+wavelength. As the IEEE 802.11ad can decouple the BA, we
+consider that the receiver keeps a quasi-omnidirectional beam
+and the transmitter scans over the beam space to identify the
+best beam. This is a reasonable assumption due to the small
+form factor and fewer antennas on UEs. In the following,
+we focus on beam alignment (BA) at the BS side, and the
+extension that involves both BS and UE is straightforward.
+B. Channel Model
+Due to the sparse characteristics of mmWave channel, we
+consider Saleh-Valenzuela channel model [40]. Suppose there
+are L paths where one is the dominant line-of-sight (LOS)
+path and L − 1 non-line-of-sight (NLOS) paths. Let C denote
+the set of complex numbers. The channel vector between the
+transmitter and the receiver is given by
+h = g0a(v0) +
+L−1
+�
+l=1
+gla(vl) ∈ CK×1
+(1)
+RF
+Chain
+RF
+Chain
+DAC
+ADC
+CHANNEL
+Beam Scan
+Omni-Directional
+mmWave  
+Base Station (BS)
+mmWave  
+User Equipment (UE)
+Fig. 1: A point-to-point mmWave Communication System.
+where a(v) =
+�
+ej 2πD
+λ
+kv : 0 ≤ k ≤ K − 1
+�
+∈ CK×1 denote
+the vector of sinusoids at spatial angle v, g0 is the channel
+gain of LOS path, and gl, 1 ≤ l ≤ L − 1 is the channel gains
+of lth NLOS path. v = cos θ denotes the spatial angle of the
+channel associated with physical angle θ. As assume that the
+channel remains static for a duration T time slots and the
+channel vector keeps invariant in the BA process.
+Let B
+∈
+CK×K denote the unitary discrete Fourier
+transform (DFT) of the transmit beam space, where the kth
+column corresponds to the kth beam, i.e.,
+B = [b1, b2, . . . , bK] =
+1
+√
+K
+[a(w1), a(w2), . . . , a(wK)]
+(2)
+where wk =
+2k−K
+K
+denotes the spatial angle of the kth
+beam. Then, the received signal of kth beam (with receiver
+omnidirectional) is given by
+yk =
+√
+PhHbk + n,
+(3)
+where n denotes the additive white Gaussian noise with mean
+noise power N0W, with noise power density N0 and channel
+bandwidth W. We denote the received signal strength (RSS)
+of the kth beam as rk = |yk|2 and denotes its mean value
+as µk = E [rk]. Let k∗ = arg maxk µk. Then the beam bk∗
+denotes the optimal beam with the best mean RSS.
+Definition
+1.
+(Unimodality):
+The
+unimodality
+structure
+indicates that, ∀bk ∈ B, there exist a path such that µ1 <
+µ2 < · · · < µk∗ and µk∗ > µK∗+1 > · · · > µK.
+For the case when only LOS path is present with channel
+gain g and spatial angle v, mean RSS is given as µk =
+P g2
+K δ(wk − v) + NoW for all bk ∈ B, where δ(x) =
+sin2(KπDx/λ)
+sin2(πDx/λ
+denotes the antenna directivity function for
+angular misalignment x. For bk ∈ B, µk is a function of
+angular misalignment wk − v and has unimodal property [15,
+Thm. 1]. In the following, we only consider the beams with
+the unimodal property as in [7] and later discuss how to extend
+our method to the multimodal case involving multiple NLOS
+of paths.
+Remark 1. We assumed that the Modulation and Coding
+Scheme (MCS) on each beam is fixed. However, we can easily
+accommodate different MCS on each beam by treating the RSS
+as a vector corresponding to MCS and considering the mean
+rate as done in [16].
+
+4
+Beams 
+t = T
+Exploration Phase (IA)
+Data Communication Phase
+t = 2T
+Exploration Phase (IA)
+t=1
+t=T+1
+t=T1
+t=T+T1
+...........
+...........
+Data Communication Phase
+Fig. 2: Beam exploration (IA) phase followed by data transfer phase.
+C. Problem Formulation
+We assume a slotted system where the length of the IA
+phase is T1 time slot. As specified in the 5G standards, we let
+the BS rerun IA phase periodically after every T time slot
+where T > T1. We assume that during the period T, the
+environment is stationary such that the best beam remains the
+same. We focus on one period between two successive reruns
+of the IA phase and index the time slots in that period as t = 1
+to t = T, refer to Fig. 2. In each time t, the BS can select
+one of the beams from set B and obtain as feedback the RSS
+at the receiver. The feedback is obtained through ACK/NACK
+sent back by the receiver – BS measures the signal strength of
+the received ACK/NACK, which gives the RSS at the receiver
+[16]. During the IA duration of T1 time slots, no information
+signals are transmitted and throughput or error probability is
+not a concern. However, during the period of T − T1 data is
+transmitted and it is desirable to obtain high throughput in this
+period using the best possible beam. We are thus interested in
+algorithms that output an optimal beam at the end of T1 time
+slots (IA phase).
+We model the problem as a fixed-budget pure exploration
+multi-armed bandit [20], [41] where the goal is to identify
+the optimal arm within a fixed budget with high confidence.
+Following the terminology of multi-armed bandits, we refer to
+beams as arms. A policy is any strategy that selects an arm in
+each time slot given the past observations. Let kt ∈ B denotes
+the arm selected by a policy at time t. By playing an arm kt,
+the policy observes the feedback rkt which is a noisy RSS.
+The choice of kt can depend on the beams selected in the past
+and their associated RSS values. We assume that RSS values
+observed in each time slot are independently and identically
+distributed across the arms and time. The distribution of RSS is
+governed by channel fluctuations, such as shadow fading and
+the disturbance effect, and follows unknown fixed distributions
+within a time period T. However, without loss of generality,
+we assume that values of RSS are bounded in some interval.
+For a given policy π, let ˆkπ
+T1 denote the index of the arm
+output by π at the end of T1 time slots. Let Π denote the set of
+all policies of pure-exploration that output algorithms within
+a fixed budget of T1. Then our goal is to find a policy in Π
+that minimizes the probability that the arm output at the end
+of T1 is not an optimal arm, i.e.,
+min
+π∈Π Pr
+�
+bπ
+ˆkT1 ̸= bk∗
+�
+,
+where for each policy, Pr(·) is calculated with respect to the
+samples induced by the policy. We note that our criteria is
+different from those set in UBA [7] and HBA [15] which
+aim to minimize cumulative regret. Though both UBA and
+HBA have stopping criteria beyond which they play a fixed
+arm, the stopping time can be random, making their practical
+implementation challenging. Whereas, the policy considered
+by us completes the exploration phase deterministically after
+time T1 which makes their implementation easier in a wireless
+setup. Fig. 2 depicts the structure of our policy.
+III. ALGORITHMS
+In
+this
+section,
+we
+propose
+an
+algorithm
+named
+UB3-Unimodal Bandit for Best Beam that finds the optimal
+beam after exploiting the unimodal structure of mean RSS
+within T1 time slots. The algorithm is based on the Line
+Search Elimination (LSE) algorithm developed in [18], where
+the algorithm samples and eliminate arms in multiple phases
+till one arm survives after L + 1 phases. The pseudo-code of
+UB3 is given in Unimodal Bandit for Best Beam (UB3). It is
+parameter free and only takes K and T1 as inputs.
+UB3 runs in L+1 phases. Arms are sampled and eliminated
+in each phase such that only one arm survives after the L + 1
+phase. We first explain the number of rounds in each phase.
+Let Nl, for l = 1, 2, . . . , L+1, denotes the number of samples
+in phase l. Then,
+Nl =
+�
+2L−2
+3L−1 T1
+for l = 1, 2
+2L−(l−1)
+3L−(l−2) T1
+for l = 3, 4, . . . , L + 1
+(4)
+which satisfies that
+2 × 2L−2T1
+3L−1
++
+L+1
+�
+l=3
+2L−(l−1)T1
+3L−(l−2)
+= T1.
+(5)
+After the first two phases, the number of samples increases by
+a factor of 3/2 in each subsequent phase. This increase in the
+number of samples helps to distinguish between the empirical
+means of the remaining arms, which are likely to be closer.
+UB3 works as follows. Let Bl = {b1, b2, . . . , bl} denote the
+set of arms available in phase l and jl := |Bl| is the number
+of arms in the set Bl. In phase l = 1, 2, . . . L, the algorithm
+selects four arms {kM, kA, kB, kN} ∈ Bl, which include the
+two extremes and two middle arms uniformly spaced from
+them (lines 4-7). Each of the arms is sampled for Nl
+4 number
+of times (line 8). At the end of the phase, their empirical means
+
+5
+𝒌𝑴
+𝒌𝑨
+𝒌𝑩
+𝒌𝑵
+𝒙𝒍
+∗ =
+𝑪𝒂𝒔𝒆 𝟏
+𝓑𝒍+𝟏
+𝓑𝒍
+𝒌𝑴
+𝒌𝑨
+𝒌𝑩
+𝒌𝑵
+𝒙𝒍
+∗ =
+𝑪𝒂𝒔𝒆 𝟐
+𝓑𝒍+𝟏
+𝓑𝒍
+Fig. 3: Different cases of elimination in phase l.
+denoted ˆµi (line 9) are obtained as follows:
+ˆµl
+i =
+1
+Nl/4
+Nl/4
+�
+s=1
+rl
+is,
+∀i ∈ {kM, kA, kB, kN}
+(6)
+where rl
+is denotes the sth noisy RSS sample from ith arm in
+phase l. Based on these empirical means, we eliminate at most
+1/3rd of the number of arms from the remaining set1. More
+specifically, if the arms kM or kA has the highest empirical
+means, then we eliminate all the arms succeeding kB in the
+set Bl (line 11 and 12). Similarly, if the arms kB or kN has
+the highest empirical means, then we eliminate all the arms
+preceding kA in the set Bl (line 13 and 14). Fig. 3 gives
+a pictorial representation of the elimination of arms in two
+possible cases. The remaining set of arms are then transferred
+to the next phase. In phase L + 1, we are left with three
+arms. Each one of them is sampled
+NL+1
+3
+number of times
+and the one with the highest empirical mean is the output of
+the algorithm as the optimal arm (lines 18-23).
+Remark 2. Arms between kM & kA or kB & kN are
+eliminated in phase, and the arms between kA & kB always
+survive.
+After phase l = 1, 2, . . . , L, ⌊ 2
+3jl⌋ of the arms survive. For
+ease of exposition, we will drop the ⌊⌋ function since this drop
+will influence only a few constants in the analysis. Thus, after
+the end of L phases there will be three arms as
+(2/3)L K = 3 =⇒ L = log2 K/3
+log2 3/2 .
+(7)
+Therefore, the UB3 outputs the best beam as ˆkL+1 which is
+equivalent to bˆkT1 after exploring for T1 time slots. In the next
+section, we upper bound the error probability of UB3.
+IV. ANALYSIS
+In this analysis, we find an upper bound and lower bound
+for the probability of best arm elimination for fixed-budget
+pure exploration bandit with unimodal structure. We first upper
+1If the number of arms in a phase is not a multiple of 4, then less than
+1/3rd will be eliminated in that phase.
+Unimodal Bandit for Best Beam (UB3)
+1: Input: T1 and K.
+2: Initialise: B1 = B, j1 ← |B1|. Calculate L from (7).
+3: for l = 1 to L do
+4:
+kM ← First arm of Bl;
+5:
+kN ← Last arm of Bl;
+6:
+kA ← ⌈jl/3⌉th arm of Bl;
+7:
+kB ← ⌊2jl/3⌋th arm of Bl;
+8:
+Sample each arm in {kM, kA, kB, kN} for Nl
+4 number
+of times from (4)
+9:
+Obtain ˆµl
+kM , ˆµl
+kA, ˆµl
+kB, ˆµl
+kN by (6).
+10:
+x∗
+l =
+arg max
+i∈{kM,kA,kB,kN}
+ˆµi.
+11:
+if x∗
+l == {kM, kA} then
+12:
+Bl+1 ← {k ∈ Bl : kM ≤ k ≤ kB} Shrink to left
+13:
+else if x∗
+l == {kB, kN} then
+14:
+Bl+1 ← {k ∈ Bl : kA ≤ k ≤ kN} Shrink to right
+15:
+end if
+16:
+jl+1 ← |Bl+1|;
+17: end for
+18: for l = L + 1 do
+19:
+BL+1 = {kM, kA, kN};
+20:
+Sample each arm in {kM, kA, kN} for T1
+9 no. of times.
+21:
+Obtain ˆkL+1 =
+arg max
+i∈{kM,kA,kN}
+ˆµL+1
+i
+.
+22: end for
+23: Output: bˆkT1 = ˆkL+1
+bound the error probability of Unimodal Bandit for Best Beam
+(UB3). For analysis, we use the following assumption:
+Assumption 1. There exists a constant DL > 0 such that
+|µk − µk−1| ≥ DL for 2 ≤ k ≤ K.
+We note that this assumption is the same as that used in
+from [18, Assumption 3.4] to analyze unimodal bandits in the
+regret minimization setting.
+A. Upper Bound for Algorithm UB3
+Theorem 1. Let UB3 is run for T1 time slots in L+1 number
+of phases, where L = log2 K/3
+log2 3/2 with output ˆkL+1. Then, the
+probability that ˆkL+1 output by UB3 is not the best arm after
+L + 1 phases is bounded as
+P(ˆkL+1 ̸= k∗) ≤ 2 exp
+�
+−T1
+18D2
+L
+�
++ 2 exp
+�
+−T1K
+32 D2
+L
+�
++ 2 exp
+�
+−T1K
+72 D2
+L
+�
++ 2(L − 2) exp
+�
+−T1
+16D2
+L
+�
+.
+(8)
+Proof. The proof is given in Appendix A.
+Observe that the dominant first and last terms in the
+upper bound do not depend on K. The error probability
+is thus of order O
+�
+log2 K exp
+�
+− T1D2
+L
+16
+��
+, where the
+error exponent term
+�
+exp
+�
+− T1D2
+L
+16
+��
+does not depend
+on K. The Sequential Halving (Seq. Halv.) algorithm is
+proposed in [42] for non-unimodal (unstructured) bandits
+and provided an upper bound for the probability of not
+
+6
+choosing the optimal arm. The error probability is shown to
+be O
+�
+log2(K) exp
+�
+−
+T1
+log(K)H2
+��
+. This bound matches with
+the lower bound derived in [43] for unstructured bandits up
+to multiplicative factor of log2(K), where H2 = max
+k̸=k∗
+k
+∆2
+k is
+the complexity parameter depended upon the sub-optimality
+gap. Note that the error exponent in this bound of Seq. Halv.
+has log2(K) factor. By exploiting the unimodal property,
+we shove off this factor. We next consider the lower
+bound for fixed-budget pure exploration with the unimodal
+structure which confirms that error exponent should be indeed
+independent of number of beams for any optimal algorithm.
+B. Lower bound for pure exploration unimodal bandit
+A lower bound on the probability of error for the fixed
+budget without assuming any structure is established in [43].
+We adapt the proof to include the unimodal structure to derive
+a lower bound. To this end, we first define a set of bandit
+instances as follows.
+Let us consider K arms that follow the unimodal structure.
+Let {pk}1≤k≤K be K real numbers in the interval [1/4, 1/2]
+with pk∗ = 1
+2 and p1 ≤ p2 ≤ · · · ≤ pk∗−1 ≤ pk∗ ≥ pk∗+1 ≥
+· · · ≥ pK. For any 1 ≤ k ≤ K we consider the distribution νk
+to be Bernoulli distribution with mean pk, i.e. νk := Ber(pk).
+We consider another distribution ν′
+k as Bernoulli distribution
+with mean 1 − pk, i.e., ν′
+k := Ber(1 − pk) with mean 1 − pk.
+We define K bandit problem as following. For i
+∈
+{1, . . . , K} define the product distributions Gi := νi
+1 ⊗ νi
+2 ⊗
+· · · ⊗ νi
+K where
+νi
+k :=
+�
+�
+�
+�
+�
+νk1{k ̸= i} + ν′
+k1{k = i}, if k ∈ {k∗ − 1,
+k∗, k∗ + 1}
+νk, otherwise
+where 1{A} denotes the indicator function. It is easy to note
+that only bandit instances Gi, where i ∈ {k∗ − 1, k∗, k∗ + 1}
+satisfy the unimodality structure and the not the others.
+Flipping of the reward for all other arms will result in a
+non-unimodal problem. Thus unlike [43] we have 3 bandit
+problems in the neighbourhood of k∗.
+We define dk := pk∗ − pk = 1
+2 − pk, for any 1 ≤ k ≤ K.
+Set ∆i
+k = di + dk, if k ̸= i and ∆i
+i = di, for any i ∈ {k∗ −
+1, k∗ + 1} and any k ∈ {1, . . . , K}. Note that {∆i
+k}k denotes
+the arm gaps of the bandit problem i. We also define for any
+i ∈ {k∗ − 1, k∗ + 1} the quantity
+¯H(i) :=
+�
+k∈{i−1,i+1}
+1
+(∆i
+k)2 and ¯h =
+�
+i∈{k∗−1,k∗+1}
+1
+d2
+i ¯H′(i).
+Theorem 2 from [43] can be rephrased in this setting as
+follows.
+Theorem 2. For any bandit strategy that returns the arm ˆkT1
+at time T1, it holds that
+max
+i∈{k∗−1,k∗+1}Pi(ˆkT1 ̸= i)
+≥ 1
+6 exp
+�
+−60
+T1
+¯H(k∗) − 2
+�
+T1 log(18T1)
+�
+,
+(9)
+and also
+max
+i∈{k∗−1,k∗+1}Pi(ˆkT1 ̸= i)
+≥ 1
+6 exp
+�
+−60
+T1
+¯h ¯H(i) − 2
+�
+T1 log(18T1)
+�
+.
+(10)
+The proof of this theorem follows the lines similar to [43,
+Thm. 2] after applying the change of measure rule to on the
+restricted set of arms. We skip the details.
+Corollary 1. Assume that
+T1 ≥ max
+�
+¯H(k∗), ¯H(i)¯h
+�2 4 log(6T1K)
+(60)2
+.
+For any bandit strategy that returns the arm ˆkT1 at time T1,
+it holds that
+max
+i∈{k∗−1,k∗+1} Pi(ˆkT1 ̸= i) ≥ 1
+6 exp
+�
+−120
+T1
+¯H(k∗)
+�
+,
+and also
+max
+i∈{k∗−1,k∗+1} Pi(ˆkT1 ̸= i) ≥ 1
+6 exp
+�
+−120
+T1
+¯H(i)¯h
+�
+.
+We can establish a lower bound using this corollary.
+Theorem 3. For any unimodal bandit strategy that returns
+arm ˆkT1 at time T1,
+max
+i∈{k∗−1,k∗+1} Pi(ˆkT1 ̸= i) ≥ 1
+6 exp
+�
+−75 T1
+¯H(i)
+�
+.
+(11)
+Proof. The proof is given in Appendix B.
+We see that unlike in the case of the lower bound found in
+[43], the lower bound of the error probability is not dependent
+on log2(K). In addition, the complexity factor depends only
+on the sub-optimality gap between the optimal arm and its
+neighbours. This observation is similar to the lowed bound on
+cumulative regret established in [17].
+V. NUMERICAL SIMULATIONS
+In this section, we corroborate our theoretical results using
+simulations. We first describe the simulation setup with
+parameters used and present the results in the following
+subsections.
+A. Simulation Parameters
+We use the IEEE 802.11ad system with parameters as
+described in [15] for numerical simulations. The carrier
+frequency (f) is set at 60 GHz and the bandwidth is set at
+2.16 GHz. The transmit power P = 50 dBm is shared between
+K antennas which vary from 16 to 128. For the line of sight
+(LOS) path, we have the path loss model as
+PL(dB) = −27.5 + 20 log10(f) + 10α log10(d) + χ, (12)
+where d is the transmission distance, the path loss exponent α
+is taken as 1.74, and χ is the shadow fading component which
+follows Normal distribution with zero mean and 2 dB variance.
+In (12) f is in MHz and d is in meters. Depending upon the
+
+7
+Parameter
+Value
+Carrier frequency (f)
+60 Ghz
+Bandwidth (W)
+2.16 GHz
+Noise spectrum density (N0)
+−174 dBm/Hz
+Shadow fading variance (log-normal σ)
+2 dB
+Number of beams (N)
+16-128
+HBA parameters (ρ1, γ, ζ)
+(3, 0.5, 0.1)
+Distance considered (d)
+(20, 40, 60, 80) m
+Path loss exponent
+1.74
+TABLE I: Parameters for simulation
+beam selected the signal strength varies in [−80, −20] dBm.
+The algorithm parameter are kept at ρ1 = 3, γ = 0.5 and
+ζ = 0.1. The channel parameters for the simulations are given
+in Table I. Simulation results are averaged over 1000 iterations
+and confidence intervals are shown (when significant).
+We compare the performance of Unimodal Bandit for Best
+Beam (UB3) with the following algorithms:
+• Sequential Halving (Seq. Halv.) [42]:
+This algorithm
+is used for pure exploration in non-unimodal bandits for
+a fixed T1 time slots. The algorithm was proved to be
+optimal [43], and hence a comparison would give the
+idea about, how the additional information of unimodality
+would improve the performance.
+• Linear Search Elimination (LSE) [18]: Although this
+algorithm was proposed for continuous arm unimodal
+bandit problems, we have considered the algorithm for
+fixed T1 time slots and for discrete arms. A comparison of
+UB3 with LSE is pertinent as it is a well-known algorithm
+for unimodal bandits.
+• Hierarchical
+Beam
+Alignment
+(HBA)
+[15]:
+This
+algorithm was shown to have good performance for regret
+minimization, when compared to existing algorithms,
+considering the prior knowledge of channel fluctuations.
+Our comparison with HBA will of throughput comparison
+for the period after the best beam has been identified.
+• Hierarchical Optimal Sampling of Unimodal Bandits
+(HOSUB) [38]: This algorithm exploits the benefits of
+hierarchical codebooks and the unimodality of RSS to
+achieve the best arm in the fixed T1 time slots. Our
+comparison with HOSUB will of throughput comparison
+for the period after the best beam has been identified.
+We did not include UBA algorithm [7] for comparison
+since HBA was shown to have better performance for beam
+identification. Also, the ATS algorithm is not compared against
+as it is designed to minimize the cumulative regret and does
+not stop the exploration process. We note the computational
+complexity of complexity HBA scales quadratically in T1
+whereas it is of O(T1) in UB3, where T1 is the duration of IA
+phase. In addition, HBA requires prior knowledge of channel
+fluctuations, i.e, the variance of the noise parameter, which is
+not required in UB3.
+B. Comparison with other pure exploration algorithms
+We define the probability of error as the probability of not
+identifying the best beam after sampling for T1 number of
+time slots. We consider T1 as the exploration (IA) phase. We
+first compare the probability of error for UB3 algorithm with
+LSE and Seq. Halv. which are used for pure exploration. We
+compare the probability of error performance of the algorithms
+for arm sizes of K = {16, 64, 128}. The probability of error
+against the exploration time slots (T1) is shown in Fig. 4.
+LSE, which has an equal number of sampling for the arms
+in all phases, has the worst probability of error performance
+than Seq. Halv.. The solid lines in the figure are for K = 16,
+the dashed lines are for K = 64 and the dot-dashed lines
+are for K = 128. The comparisons are done for distance of
+d = 20, 60 and 80 m. The probability of error increases as we
+increase the beam size. However, for a small number of arms,
+both Seq. Halv. and UB3 have comparable performance, but as
+the number of beams increases, UB3 has a lesser probability
+of error compared to Seq. Halv. as evident from the case of
+K = 64 and K = 128. However, UB3 can identify the best
+beam with a probability of more than 95% within 100 time
+slots for 16 number of beams, while the other state-of-the-art
+algorithms take need at least 200 time slots for executions.
+Note that for Seq. Halv. require at least 200, 400, 900 rounds
+for K = 16, 64, 128, respectively, to complete their execution
+hence their graph start after that many slots. Moreover, as
+distance increases the probability of error of all the algorithms
+increases for each beam size.
+It is to be noted that even though the minimum time slots
+requirement (as a function of K) for LSE is much smaller than
+both UB3 and Seq. Halv. for its feasible execution, the number
+of samples it runs for arms neighbouring to k∗ is much lesser
+resulting in more probability of error. Seq. Halv. needs at least
+K log2(K) number of time slots to complete one phase and
+has samples for all arms in every phase. Hence, it has much
+fewer time slots remaining when the algorithm is executed
+in the neighborhood of k∗ as compared to UB3. Thus, the
+minimum time slots requirement for UB3 as a function of K
+is much lesser than that of Seq. Halv., in addition to having a
+better probability of error performance. This demonstrates the
+advantage of exploiting the unimodality of the reward function.
+C. Comparison of throughput performance
+In this subsection we compare the throughput performance
+of UB3 with the HBA and HOSUB algorithms. We look at
+the mean cumulative throughput, which is defined as the
+product of the mean value of the selected beam at the end
+of exploration normalized with the mean power of the best
+beam and the remaining available time slots, i.e,
+Throughput = µnorm
+bL+1 × (T − T1),
+where T is the total available time slots and T1 is the number
+of time slots available for exploration of the best beam. Note
+that HBA will not have a fixed T1, and hence we will find
+the throughput after the expected exploration time E(T1),
+obtained as the average of many runs. Thus the throughput will
+be fixed for HBA for a fixed T, while it will vary for varying
+
+8
+0
+200
+400
+600
+800
+1000
+1200
+1400
+Exploration Phase (T1)
+0.00
+0.01
+0.02
+0.03
+0.04
+0.05
+Error
+UB3, K=16, d=20
+LSE, K=16, d=20
+Seq. Halving, K=16, d=20
+UB3, K=64, d=20
+LSE, K=64, d=20
+Seq. Halving, K=64, d=20
+UB3, K=128, d=20
+LSE, K=128, d=20
+Seq. Halving, K=128, d=20
+(a) Error Probability vs T1, d = 20.
+0
+200
+400
+600
+800
+1000
+1200
+1400
+Exploration Phase (T1)
+0.00
+0.02
+0.04
+0.06
+0.08
+0.10
+0.12
+Error
+UB3, K=16, d=60
+LSE, K=16, d=60
+Seq. Halving, K=16, d=60
+UB3, K=64, d=60
+LSE, K=64, d=60
+Seq. Halving, K=64, d=60
+UB3, K=128, d=60
+LSE, K=128, d=60
+Seq. Halving, K=128, d=60
+(b) Error Probability vs T1, d = 60.
+0
+200
+400
+600
+800
+1000
+1200
+1400
+Exploration Phase (T1)
+0.00
+0.02
+0.04
+0.06
+0.08
+0.10
+0.12
+Error
+UB3, K=16, d=80
+LSE, K=16, d=80
+Seq. Halving, K=16, d=80
+UB3, K=64, d=80
+LSE, K=64, d=80
+Seq. Halving, K=64, d=80
+UB3, K=128, d=80
+LSE, K=128, d=80
+Seq. Halving, K=128, d=80
+(c) Error Probability vs T1, d = 80.
+Fig. 4: Error performance of UB3 vs T1 for different no. of beams (K) and distance (d).
+400
+600
+800
+1000
+1200
+1400
+1600
+Exploration Phase (T1)
+10
+15
+20
+25
+30
+35
+Cumulative Throughput (in dB)
+UB3, K=16, d=20
+HOSUB, K=16, d=20
+HBA, K=16, d=20
+UB3, K=64, d=20
+HOSUB, K=64, d=20
+HBA, K=64, d=20
+UB3, K=128, d=20
+HOSUB, K=128, d=20
+HBA, K=128, d=20
+(a) Throughput vs T1, d = 20.
+400
+600
+800
+1000
+1200
+1400
+1600
+Exploration Phase (T1)
+5
+10
+15
+20
+25
+30
+35
+Cumulative Throughput (in dB)
+UB3, K=16, d=60
+HOSUB, K=16, d=60
+HBA, K=16, d=60
+UB3, K=64, d=60
+HOSUB, K=64, d=60
+HBA, K=64, d=60
+UB3, K=128, d=60
+HOSUB, K=128, d=60
+HBA, K=128, d=60
+(b) Throughput vs T1, d = 60.
+400
+600
+800
+1000
+1200
+1400
+1600
+Exploration Phase (T1)
+5
+10
+15
+20
+25
+30
+Cumulative Throughput (in dB)
+UB3, K=16, d=80
+HOSUB, K=16, d=80
+HBA, K=16, d=80
+UB3, K=64, d=80
+HOSUB, K=64, d=80
+HBA, K=64, d=80
+UB3, K=128, d=80
+HOSUB, K=128, d=80
+HBA, K=128, d=80
+(c) Throughput vs T1, d = 80.
+Fig. 5: Throughput performance of UB3 vs T1 for different no. of beams (K) and d.
+20
+40
+60
+80
+Distance (d)
+0
+5
+10
+15
+20
+25
+Cumulative Throughput (in dB)
+UB3,K=16,T1=500
+HOSUB,K=16,T1=500
+HBA,K=16,T1=500
+(a) Throughput vs d, K = 16, T1 = 500
+20
+40
+60
+80
+Distance (d)
+0
+5
+10
+15
+20
+25
+30
+35
+Cumulative Throughput (in dB)
+UB3,K=64,T1=500
+HOSUB,K=64,T1=500
+HBA,K=64,T1=500
+(b) Throughput vs d, K = 64, T1 = 500
+20
+40
+60
+80
+Distance (d)
+0
+5
+10
+15
+20
+25
+30
+35
+Cumulative Throughput (in dB)
+UB3,K=128,T1=500
+HOSUB,K=128,T1=500
+HBA,K=128,T1=500
+(c) Throughput vs d, K = 128, T1 = 500
+Fig. 6: Throughput performance of UB3 vs d for different no. of beams (K) for T1 = 500.
+T1 for UB3 and HOSUB. Fig. 5 compares the cumulative
+throughput of UB3, HBA and HOSUB for different K and
+distances of d = 20, 60 and 80 m for T = 3000 time slots.
+As the number of beams (arms) increases, the beam
+becomes narrower, and hence the reward for the best beam also
+increases. In that case, HOSUB requires more exploration time
+slots to learn the optimal beam, thereby exploiting sub-optimal
+beams in the data transmission phase for the given T1 time
+slots. On the other hand, for HBA, since the average time
+required to find the best arm increases, the average throughput
+will decrease as the number of arms increases. This increasing
+and decreasing of throughput for HBA is seen in Fig. 5 and
+Fig. 6. However, the UB3 algorithm is not much affected by
+the number of increases in arms for finding the best arm, and
+hence the throughput will only increase with increasing gain
+for the best arm. UB3 can improve the throughput by more
+than 45% compared to HBA and by more than 15% compared
+to HOSUB. This too is evident from both Fig. 5 and Fig.
+6. However, the throughput will decrease as we increase the
+transmission distance, refer Fig. 6.
+Finally, we compare the throughput performance for varying
+path loss exponent given as α ∈ {1.74, 1.94, 2.14}, as shown
+in Fig. 7. The path loss exponent increases when there are
+more barriers; for example when the receiver moves from
+outdoor to indoor. The throughput indeed decreases for all
+HBA, HOSUB and UB3, but UB3 still outperforms HBA and
+HOSUB.
+VI. CONCLUSION AND FUTURE WORK
+We investigated the problem of beam alignment in mmWave
+systems using the multi-armed bandits (MAB). While earlier
+works used the cumulative regret minimization setting to learn
+
+9
+400
+600
+800
+1000
+1200
+1400
+1600
+Exploration Phase (T1)
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+Cumulative Throughput (in dB)
+UB3,K=16,d=20,path-loss=1.74
+HOSUB,K=16,d=20,path-loss=1.74
+HBA,K=16,d=20,path-loss=1.74
+UB3,K=16,d=20,path-loss=1.94
+HOSUB,K=16,d=20,path-loss=1.94
+HBA,K=16,d=20,path-loss=1.94
+UB3,K=16,d=20,path-loss=2.14
+HOSUB,K=16,d=20,path-loss=2.14
+HBA,K=16,d=20,path-loss=2.14
+(a) Throughput vs T1, K = 16, d = 20.
+400
+600
+800
+1000
+1200
+1400
+1600
+Exploration Phase (T1)
+5
+10
+15
+20
+25
+30
+35
+Cumulative Throughput (in dB)
+UB3,K=64,d=20,path-loss=1.74
+HOSUB,K=64,d=20,path-loss=1.74
+HBA,K=64,d=20,path-loss=1.74
+UB3,K=64,d=20,path-loss=1.94
+HOSUB,K=64,d=20,path-loss=1.94
+HBA,K=64,d=20,path-loss=1.94
+UB3,K=64,d=20,path-loss=2.14
+HOSUB,K=64,d=20,path-loss=2.14
+HBA,K=64,d=20,path-loss=2.14
+(b) Throughput vs T1, K = 64, d = 20.
+400
+600
+800
+1000
+1200
+1400
+1600
+Exploration Phase (T1)
+5
+10
+15
+20
+25
+30
+35
+Cumulative Throughput (in dB)
+UB3,K=128,d=20,path-loss=1.74
+HOSUB,K=128,d=20,path-loss=1.74
+HBA,K=128,d=20,path-loss=1.74
+UB3,K=128,d=20,path-loss=1.94
+HOSUB,K=128,d=20,path-loss=1.94
+HBA,K=128,d=20,path-loss=1.94
+UB3,K=128,d=20,path-loss=2.14
+HOSUB,K=128,d=20,path-loss=2.14
+HBA,K=128,d=20,path-loss=2.14
+(c) Throughput vs T1, K = 128, d = 20.
+Fig. 7: Throughput performance of UB3 vs T1 for different path-loss exponent α and d = 20.
+the best arm, we used the fixed-budget pure-exploration setting
+framework exploiting the unimodal structure of the received
+signal strength of the beams. We developed an algorithm
+named Unimodal Bandit for Best Beam (UB3) that identified
+the best beam with high probability. We gave an upper bound
+on the error probability of UB3 and established that it is
+optimal. Simulations validated the efficiency of UB3 which can
+identify the best beam using a smaller number of explorations
+that can translate to improvement in throughput by more than
+15% compared to other state-of-art algorithms. Due to its
+simple structure, UB3 is easy to implement and comes with a
+lower computational complexity – UB3 has a computational
+complexity of O(T), whereas it is O(T 2) for HBA [15]. The
+UBA algorithm in [7] needs to solve a convex optimization
+problem in each time which is expensive.
+UB3 works well when only the LOS path is present and
+the RSS of beams satisfies the unimodal property. However,
+when NLOS paths are present, we are faced with multimodal
+functions. UB3 can be adapted to handle the multi-modal
+functions by using backtracking ideas proposed in [44]. In
+backtracking, eliminated arms are revisited to check if it is
+done by mistake and thus will not be stuck in a sub-optimal
+set of beams. It is interesting to evaluate the UB3 algorithms
+with backtracking on multimodal function and establish its
+performance guarantees.
+VII. APPENDIX
+In this section, we will provide proof of the main results.
+A. Proof of Theorem 1
+Proof. UB3 runs for T1 horizon in L + 1 number of phases
+that satisfies (5), where L =
+log2 K/3
+log2 3/2 and outputs the arm
+ˆkL+1. We will now upper bound the probability of error as,
+P(ˆkL+1 ̸= bk∗) =
+L+1
+�
+l=1
+P(bk∗ elim. in l|bk∗ not elim. in < l)
+≤
+L+1
+�
+l=1
+P(bk∗ elim. in l).
+(13)
+The best arm is eliminated in phase l in the following cases:
+1) bk∗ ∈ {kM, . . . , kA}, and ˆµl
+kB or ˆµl
+kN is greater than
+both ˆµl
+xM and ˆµl
+kA
+bk∗
+bk∗
+kM
+kA
+jl
+3 DL
+kB
+kN
+Case 1
+Case 2
+Fig. 8: Different cases of elimination in any phase l. bk∗ will
+not get eliminated if it is in between arms kA and kB.
+2) bk∗ ∈ {kB, . . . , kN}, and ˆµl
+kM or ˆµl
+kA is greater than
+both ˆµl
+kB and ˆµl
+kN
+The two cases are illustrated in Fig. 8. From Remark 2, bk∗
+will not get eliminated if bk∗ ∈ {kA, . . . , kB}. However we
+will upper bound the probability of error by assuming that
+bk∗ will always fall in the above two cases. Notice that Case
+1 and Case 2 are symmetrical. Hence we can consider that
+bk∗ will always fall in either one of the cases. Without loss of
+generality, we consider Case 1.
+P(bk∗ elim. in l) ≤ P(bk∗ elim. in l|bk∗ ∈ {kM, . . . , kA})
+P(bk∗ elim. in l)
+≤ P(ˆµl
+kB > ˆµl
+kM and ˆµl
+kA|bk∗ ∈ {kM, . . . , kA})
++ P(ˆµl
+kN > ˆµl
+kM and ˆµl
+kA|bk∗ ∈ {kM, . . . , kA})
+≤ 2P(ˆµl
+kB > ˆµl
+kM and ˆµl
+kA|bk∗ ∈ {kM, . . . , kA}),
+(14)
+where the last inequality is due to the fact that, for Case 1,
+µkB ≥ µkN by unimodality. Now for Case 1, µkA is always
+greater than µkB, but µkM may not be greater than µkB. Then,
+we can further upper bound (14) as
+P(bk∗ elim. in l) ≤ 2P(ˆµl
+kB > ˆµl
+kA|bk∗ ∈ {kM, .., kA}).
+(15)
+Applying Hoeffding’s inequality in (15), we have
+P(ˆµl
+kB > ˆµl
+kA) ≤ exp
+�
+−1
+2
+Nl
+4 (∆A,B)2
+�
+,
+(16)
+where ∆A,B = µkA −µkB which is greater than 0 for Case 1.
+From Assumption 1, and the fact that there are at least jl
+3 arms
+between kA and kB, for Case 1 we have, ∆A,B ≥ (jl/3)DL.
+
+10
+Thus from (14) and (16) we have,
+P(bk∗ elim. in l) ≤ 2 exp
+�
+−Nl
+72
+�
+jlDL
+�2�
+.
+(17)
+Using jl =
+� 2
+3
+�l K in (17) we can find the probability of best
+arm getting eliminated in phase 1 and 2, phase L + 1, and the
+rest of the phases separately. Using (7), we have
+P(bk∗ elim. in 1&2) ≤2 exp
+�
+−T1K
+32 D2
+L
+�
++ 2 exp
+�
+−T1K
+72 D2
+L
+�
+.
+(18)
+For phase L + 1, since the best arm is selected among 3 arms
+when each arm is sampled T1/9 times, we have
+P(bk∗ elim. in phase L + 1) ≤ 2 exp
+�
+−T1
+18D2
+L
+�
+.
+(19)
+From (17), the error probability for the remaining phases is
+P(best arm elim. in phase 3 to phase L)
+≤ 2
+L
+�
+l=3
+exp
+�
+−T1
+8
+K2
+9
+�2
+3
+�2(l−1) 2L−l+1
+3L−l+2 D2
+L
+�
+≤ 2
+L
+�
+l=3
+exp
+�
+−T1K
+48
+�2
+3
+�l
+D2
+L
+�
+≤ 2(L − 2) exp
+�
+−T1
+16D2
+L
+�
+.
+(20)
+By (13), (18), (19) and (20), we obtain the upper bound as
+P(ˆkL+1 ̸= bk∗)
+≤ 2 exp
+�
+−T1
+18D2
+L
+�
++ 2 exp
+�
+−T1K
+32 D2
+L
+�
++ 2 exp
+�
+−T1K
+72 D2
+L
+�
++ 2(L − 2) exp
+�
+−T1
+16D2
+L
+�
+.
+B. Proof of Theorem 3
+Proof. We have, pk = 1
+2 − dk such that pk ∈ [1/4, 1/2] and
+follows unimodality and pk∗ = 1
+2. Upper bounding ¯h, we have
+¯h =
+�
+i∈{k∗−1,k∗+1}
+1
+d2
+i ¯H(i)
+=
+1
+d2
+k∗−1 ¯H(k∗ − 1) +
+1
+d2
+k∗+1 ¯H(k∗ + 1)
+= (I) + (II).
+(21)
+We will upper bound (I) and (II),
+d2
+k∗−1 ¯H(k∗ − 1) = d2
+k∗−1
+�
+k∈{k∗−2,k∗}
+1
+(dk∗−1 + dk)2
+Since dk∗ = 0 and dk∗−2 ≥ dk∗−1, we get
+d2
+k∗−1 ¯H(k∗ − 1) ≤ 1 + 1
+4 = 5
+4
+(22)
+d2
+k∗+1 ¯H(k∗ + 1) = d2
+k∗+1
+�
+k∈{k∗,k∗+2}
+1
+(dk∗+1 + dk)2
+Since dk∗ = 0 and dk∗+2 ≥ dk∗+1, we get
+d2
+k∗+1 ¯H(k∗ + 1) ≤ 1 + 1
+4 = 5
+4.
+(23)
+By (22) and (23) we get
+¯h ≥ 4
+5 + 4
+5 = 8
+5.
+Putting the value of ¯h in Corollary we get
+=⇒
+max
+i∈{k∗−1,k∗+1} Pi(ˆkT ̸= i) ≥ exp
+�
+−75 T
+¯H(i)
+�
+.
+REFERENCES
+[1] “IEEE
+standard
+for
+information
+technology–
+amendment
+3:
+Enhancements for very high throughput in the 60 GHz band,”
+IEEE Std 802.11ad-2012 (Amendment to IEEE Std 802.11-2012, as
+amended by IEEE Std 802.11ae-2012 and IEEE Std 802.11aa-2012),
+pp. 1–628, 2012.
+[2] P. Zhou, X. Fang, Y. Fang, Y. Long, R. He, and X. Han, “Enhanced
+random access and beam training for millimeter wave wireless local
+networks with high user density,” IEEE Transactions on Wireless
+Communications, vol. 16, no. 12, pp. 7760–7773, 2017.
+[3] Y. Ghasempour, C. R. C. M. da Silva, C. Cordeiro, and E. W. Knightly,
+“Ieee 802.11ay: Next-generation 60 ghz communication for 100 gb/s
+wi-fi,” IEEE Communications Magazine, vol. 55, no. 12, pp. 186–192,
+2017.
+[4] T. Nitsche, C. Cordeiro, A. B. Flores, E. W. Knightly, E. Perahia, and
+J. C. Widmer, “Ieee 802.11ad: directional 60 ghz communication for
+multi-gigabit-per-second wi-fi [invited paper],” IEEE Communications
+Magazine, vol. 52, no. 12, pp. 132–141, 2014.
+[5] T. Nitsche, A. B. Flores, E. W. Knightly, and J. Widmer, “Steering with
+eyes closed: mm-wave beam steering without in-band measurement,”
+in 2015 IEEE Conference on Computer Communications (INFOCOM).
+IEEE, 2015, pp. 2416–2424.
+[6] I. . W. Group et al., “Ieee 802.11 ad, amendment 3: Enhancements for
+very high throughput in the 60 ghz band,” IEEE Stand, vol. 802, 2012.
+[7] M. Hashemi, A. Sabharwal, C. Emre Koksal, and N. B. Shroff, “Efficient
+beam alignment in millimeter wave systems using contextual bandits,”
+in IEEE Conference on Computer Communications (INFOCOM), 2018,
+pp. 2393–2401.
+[8] S. Sur, V. Venkateswaran, X. Zhang, and P. Ramanathan, “60 ghz
+indoor networking through flexible beams: A link-level profiling,” in
+Proceedings of the 2015 ACM SIGMETRICS International Conference
+on Measurement and Modeling of Computer Systems, 2015, pp. 71–84.
+[9] Y. Zhu, Z. Zhang, Z. Marzi, C. Nelson, U. Madhow, B. Y. Zhao, and
+H. Zheng, “Demystifying 60ghz outdoor picocells,” in Proceedings of
+the 20th annual international conference on Mobile computing and
+networking, 2014, pp. 5–16.
+[10] C. N. Barati, S. A. Hosseini, M. Mezzavilla, T. Korakis, S. S. Panwar,
+S. Rangan, and M. Zorzi, “Initial access in millimeter wave cellular
+systems,” IEEE Transactions on Wireless Communications, vol. 15,
+no. 12, pp. 7926–7940, 2016.
+[11] I. Aykin and M. Krunz, “Efficient beam sweeping algorithms and initial
+access protocols for millimeter-wave networks,” IEEE Transactions on
+Wireless Communications, vol. 19, no. 4, pp. 2504–2514, 2020.
+[12] I. Aykin, B. Akgun, and M. Krunz, “Smartlink: Exploiting channel
+clustering effects for reliable millimeter wave communications,” in
+IEEE Conference on Computer Communications (INFOCOM), 2019,
+pp. 1117–1125.
+[13] A. Zhou, T. Wei, X. Zhang, and H. Ma, “Fastnd: Accelerating directional
+neighbor discovery for 60-ghz millimeter-wave wireless networks,”
+IEEE/ACM Transactions on Networking, vol. 26, no. 5, pp. 2282–2295,
+2018.
+[14] 3GPP TR 38.802 (v14.2.0), “Study on new radio access technology
+physical layer aspects (release 14),” Sep 2017. [Online]. Available:
+https://www.3gpp.org/ftp/Specs/archive/38 series/38.802/38802-001.zip
+[15] W. Wu, N. Cheng, N. Zhang, P. Yang, W. Zhuang, and X. Shen,
+“Fast mmwave beam alignment via correlated bandit learning,” IEEE
+Transactions on Wireless Communications, vol. 18, no. 12, pp.
+5894–5908, 2019.
+
+11
+[16] I.
+Aykin,
+B.
+Akgun,
+M.
+Feng,
+and
+M.
+Krunz,
+“Mamba:
+A
+multi-armed bandit framework for beam tracking in millimeter-wave
+systems,” in IEEE INFOCOM 2020 - IEEE Conference on Computer
+Communications, 2020, pp. 1469–1478.
+[17] R. Combes and A. Proutiere, “Unimodal bandits: Regret lower bounds
+and optimal algorithms,” in Proceedings of the 31st International
+Conference on International Conference on Machine Learning - Volume
+32, ser. ICML’14, 2014, p. I–521–I–529.
+[18] J. Y. Yu and S. Mannor, “Unimodal bandits,” in Proceedings of the
+28th International Conference on International Conference on Machine
+Learning, 2011, p. 41–48.
+[19] H. Saber, P. M´enard, and O.-A. Maillard, “Forced-exploration free
+strategies for unimodal bandits,” arXiv preprint arXiv:2006.16569, 2020.
+[20] J.-Y. Audibert, S. Bubeck, and R. Munos, “Best arm identification in
+multi-armed bandits.” in COLT.
+Citeseer, 2010, pp. 41–53.
+[21] A. N. Uwaechia and N. M. Mahyuddin, “A comprehensive survey on
+millimeter wave communications for fifth-generation wireless networks:
+Feasibility and challenges,” IEEE Access, vol. 8, pp. 62 367–62 414,
+2020.
+[22] Y. Niu, Y. Li, D. Jin, L. Su, and A. V. Vasilakos, “A survey of millimeter
+wave communications (mmwave) for 5g: opportunities and challenges,”
+Wireless networks, vol. 21, no. 8, pp. 2657–2676, 2015.
+[23] X. Wang, L. Kong, F. Kong, F. Qiu, M. Xia, S. Arnon, and G. Chen,
+“Millimeter wave communication: A comprehensive survey,” IEEE
+Communications Surveys & Tutorials, vol. 20, no. 3, pp. 1616–1653,
+2018.
+[24] Z. Marzi, D. Ramasamy, and U. Madhow, “Compressive channel
+estimation and tracking for large arrays in mm-wave picocells,” IEEE
+Journal of Selected Topics in Signal Processing, vol. 10, no. 3, pp.
+514–527, 2016.
+[25] H. Hassanieh, O. Abari, M. Rodriguez, M. Abdelghany, D. Katabi,
+and P. Indyk, “Fast millimeter wave beam alignment,” in Proceedings
+of the 2018 Conference of the ACM Special Interest Group on Data
+Communication.
+Association for Computing Machinery, 2018, p.
+432–445.
+[26] X. Li, J. Fang, H. Duan, Z. Chen, and H. Li, “Fast beam alignment
+for millimeter wave communications: A sparse encoding and phaseless
+decoding approach,” IEEE Transactions on Signal Processing, vol. 67,
+no. 17, pp. 4402–4417, 2019.
+[27] M. Li, C. Liu, S. V. Hanly, I. B. Collings, and P. Whiting, “Explore
+and eliminate: Optimized two-stage search for millimeter-wave beam
+alignment,” IEEE Transactions on Wireless Communications, vol. 18,
+no. 9, pp. 4379–4393, 2019.
+[28] J. Wang, Z. Lan, C. woo Pyo, T. Baykas, C. sean Sum, M. Rahman,
+J. Gao, R. Funada, F. Kojima, H. Harada, and S. Kato, “Beam
+codebook based beamforming protocol for multi-gbps millimeter-wave
+wpan systems,” IEEE Journal on Selected Areas in Communications,
+vol. 27, no. 8, pp. 1390–1399, 2009.
+[29] Z. Xiao, T. He, P. Xia, and X.-G. Xia, “Hierarchical codebook
+design for beamforming training in millimeter-wave communication,”
+IEEE Transactions on Wireless Communications, vol. 15, no. 5, pp.
+3380–3392, 2016.
+[30] Y. Shabara, C. E. Koksal, and E. Ekici, “Linear block coding for
+efficient beam discovery in millimeter wave communication networks,”
+in IEEE Conference on Computer Communications (INFOCOM), 2018,
+pp. 2285–2293.
+[31] V. Va, T. Shimizu, G. Bansal, and R. W. Heath, “Online learning for
+position-aided millimeter wave beam training,” IEEE Access, vol. 7, pp.
+30 507–30 526, 2019.
+[32] A. Asadi, S. M¨uller, G. H. Sim, A. Klein, and M. Hollick, “Fml:
+Fast machine learning for 5g mmwave vehicular communications,” in
+IEEE Conference on Computer Communications (INFOCOM), 2018, pp.
+1961–1969.
+[33] V. Va, H. Vikalo, and R. W. Heath, “Beam tracking for mobile millimeter
+wave communication systems,” in IEEE Global Conference on Signal
+and Information Processing (GlobalSIP), 2016, pp. 743–747.
+[34] C. Zhang, D. Guo, and P. Fan, “Tracking angles of departure and
+arrival in a mobile millimeter wave channel,” in 2016 IEEE International
+Conference on Communications (ICC), 2016, pp. 1–6.
+[35] Y. Heng and J. G. Andrews, “Machine learning-assisted beam alignment
+for mmwave systems,” IEEE Transactions on Cognitive Communications
+and Networking, vol. 7, no. 4, pp. 1142–1155, 2021.
+[36] N. J. Myers, Y. Wang, N. Gonz´alez-Prelcic, and R. W. Heath, “Deep
+learning-based beam alignment in mmwave vehicular networks,” in
+ICASSP 2020 - 2020 IEEE International Conference on Acoustics,
+Speech and Signal Processing (ICASSP), 2020, pp. 8569–8573.
+[37] V. Raj, N. Nayak, and S. Kalyani, “Deep reinforcement learning based
+blind mmwave mimo beam alignment,” IEEE Transactions on Wireless
+Communications, pp. 1–1, 2022.
+[38] N. Blinn, J. Boerger, and M. Bloch, “mmwave beam steering with
+hierarchical optimal sampling for unimodal bandits,” in ICC 2021-IEEE
+International Conference on Communications.
+IEEE, 2021, pp. 1–6.
+[39] E. Kaufmann, O. Capp´e, and A. Garivier, “On the complexity of
+best-arm identification in multi-armed bandit models,” Joural of Machine
+Learning Research, vol. 17, no. 1, p. 1–42, January 2016.
+[40] M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S.
+Rappaport, and E. Erkip, “Millimeter wave channel modeling and
+cellular capacity evaluation,” IEEE journal on selected areas in
+communications, vol. 32, no. 6, pp. 1164–1179, 2014.
+[41] S. Kalyanakrishnan, A. Tewari, P. Auer, and P. Stone, “Pac subset
+selection in stochastic multi-armed bandits,” in Proceedings of the
+29th International Coference on International Conference on Machine
+Learning (ICML).
+Madison, WI, USA: Omnipress, 2012, p. 227–234.
+[42] Z. Karnin, T. Koren, and O. Somekh, “Almost optimal exploration in
+multi-armed bandits,” in International Conference on Machine Learning.
+PMLR, 2013, pp. 1238–1246.
+[43] A. Carpentier and A. Locatelli, “Tight (lower) bounds for the fixed
+budget best arm identification bandit problem,” in Conference on
+Learning Theory.
+PMLR, 2016, pp. 590–604.
+[44] S. Kunne, L. Maggi, J. Cohen, and X. Xu, “Anytime backtrack unimodal
+bandits and applications to cloud computing,” in 2020 IFIP Networking
+Conference (Networking).
+IEEE, 2020, pp. 82–90.
+
diff --git a/ktE1T4oBgHgl3EQf0gVV/content/tmp_files/load_file.txt b/ktE1T4oBgHgl3EQf0gVV/content/tmp_files/load_file.txt
new file mode 100644
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--- /dev/null
+++ b/ktE1T4oBgHgl3EQf0gVV/content/tmp_files/load_file.txt
@@ -0,0 +1,969 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf,len=968
+page_content='1  UB3: Best Beam Identification in Millimeter Wave  Systems via Pure Exploration Unimodal Bandits  Debamita Ghosh1, Haseen Rahman2, Manjesh K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Hanawal3, and Nikola Zlatanov4  1IITB-Monash Research Academy, IIT Bombay, India, email: debamita.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='ghosh@iitb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='in  2MLiONS Lab, IEOR, IIT Bombay, India, email: haseenrahman@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='com  3MLiONS Lab, IEOR IIT Bombay, India, email:mhanawal@iitb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='in  4Innopolis University, Russia, email: n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='zlatanov@innopolis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='ru  Abstract—Millimeter wave (mmWave) communications have  a broad spectrum and can support data rates in the order  of gigabits per second, as envisioned in 5G systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However,  they cannot be used for long distances due to their sensitivity  to attenuation loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' To enable their use in the 5G network,  it requires that the transmission energy be focused in sharp  pencil beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' As any misalignment between the transmitter and  receiver beam pair can reduce the data rate significantly, it is  important that they are aligned as much as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' To find  the best transmit-receive beam pair, recent beam alignment (BA)  techniques examine the entire beam space, which might result in  a large amount of BA latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Recent works propose to adaptively  select the beams such that the cumulative reward measured in  terms of received signal strength or throughput is maximized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In  this paper, we develop an algorithm that exploits the unimodal  structure of the received signal strengths of the beams to identify  the best beam in a finite time using pure exploration strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Strategies that identify the best beam in a fixed time slot  are more suitable for wireless network protocol design than  cumulative reward maximization strategies that continuously  perform exploration and exploitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Our algorithm is named  Unimodal Bandit for Best Beam (UB3) and identifies the best  beam with a high probability in a few rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We prove that the  error exponent in the probability does not depend on the number  of beams and show that this is indeed the case by establishing a  lower bound for the unimodal bandits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We demonstrate that UB3  outperforms the state-of-the-art algorithms through extensive  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Moreover, our algorithm is simple to implement and  has lower computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Index Terms—mmWave, Bandit learning, pure exploration  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' INTRODUCTION  There is a growing demand for higher data rates with the  advent of emerging data-intensive applications like virtual  reality, mobile gaming, and HD quality video streaming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The  wireless networks have improved in terms of data rates but  are still constrained by the available bandwidth in the sub-6  GHz spectrum to meet the data rates required for emerging  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The millimeter wave (mmWave) band, with a  spectrum ranging from 30 GHz to 300 GHz, offers an abundant  spectrum and can support data rates of gigabits per second  that are envisioned in 5G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Significant efforts in the  standardisation of mmWave systems, such as IEEE 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ad  [1], [2] and ongoing IEEE 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ay [3], are underway, and  the 5G networks with mmWave systems are on the path of  commercialisation through extensive field trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Though mmWave systems offer higher data rates, they  come with a set of challenges—the small wavelengths  of  mmWaves  make  them  suffer  significant  attenuation,  resulting in a rapid deterioration of signal strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Thus,  unlike traditional terrestrial communication systems, mmWave  communication requires highly directional communication  with energy focused on narrow beams to achieve the required  signal strengths at the receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Some challenges in using  mmWave systems in mobile communications are highlighted  in standards [1], [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, on the brighter side, small  wavelengths allow transmission antennas with small form  factors to be packed closely and focus signal energy in specific  directions, forming sharp beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  The other challenge in mmWave communication is that  transmitter and receiver beams need to be aligned before data  transfer;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' otherwise, any advantage of high data rates is not  realised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' A few degrees of misalignment in the beam directions  between transmitter and receiver can reduce the data rates from  gigabits per second to a few megabits per second, jeopardising  the gain from the high spectrum of mmWave systems [5]–[7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  This gives rise to the problem of beam alignment (BA), where  one needs to find the best transmitter and receiver beam pair  that provides the best rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The BA problem is critical to  building better 5G communication networks with mmWave  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Our goal in this paper is to learn the best beam pair  in a given number of slots with a high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  One naive approach to performing BA is an exhaustive  search of all available beams at the base station (BS) and user  equipment (UE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This strategy does not scale well because it  has the complexity of order O(K2), where K is the number  of beams at BS and UE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The IEEE standard 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ad [1]  decouples the BA by performing it in two stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In the first  stage, the BS uses a quasi-omnidirectional beam while the  UE scans through its beams to identify the best one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In the  next stage, the UE uses a quasi-omnidirectional beam while  the BS scans through its beam to identify the best one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This  search strategy has a complexity that is linear in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However,  as discussed in [8], [9], this method can still take time in  seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  The initial access (IA) phase in 5G mmWave provides a  mechanism to identify beam directions between a BS and UE  [10]–[13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' BSs periodically use the IA phase to discover new  UEs and check if the best beam for already existing UEs has  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='03456v1  [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='SP]  26 Dec 2022  2  changed [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' During the IA, BS transmits synchronization  signals that UE can measure and report back the received  signal strengths (RSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' IA can be used to explore and identify  the best pair, as no data is transferred in this phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Further,  BS can adapt to the non-stationary environment by periodically  rerunning the IA phase, where the periodicity can depend on  the mobility rate and the atmospheric conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We address the BA and user tracking issues in mmWave  using the fixed-budget pure exploration Multi-Armed Bandit  (MAB) framework, where pure exploration is performed  in  the  IA  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  The  BA  problem  has  already  been  addressed using the MAB framework, which uses cumulative  regret minimization algorithms that balance exploration and  exploitation to find the best beam pair [7], [15], [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However,  the stopping time in these algorithms is random, leading to  the following difficulties: 1) The learning phase may extend  beyond the IA phase and reduce the number of time slots  available for data transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2) Due to continuous exploration,  sub-optimal beams can be used for data transfer, resulting in  outages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' To overcome these issues, we complete the learning  phase within a fixed number of time slots (budget) of the IA  phase using adaptive exploration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Moreover, we exploit the  structural properties of the RSS across the beams to accelerate  the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Several studies validate that the RSS of the beams in  mmWave systems follows a multi-modal structure, with one  peak corresponding to the line-of-sight path and others  corresponding to the non-line-of-sight paths [7], [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Often,  there is one dominant peak, and the multi-modal functions can  be treated as unimodal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Bandits with a unimodal structure are  well studied in the literature in the cumulative regret setting  with optimal algorithms [17]–[19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, the fixed-budget  pure exploration bandit with unimodal structure is not well  studied, and optimal algorithms are not known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In this work,  we develop a new fixed-budget pure exploration algorithm that  exploits the unimodal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The new algorithm is named  Unimodal Bandit for Best Beam (UB3) and is based on the idea  of sequential elimination of sub-optimal beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' UB3 achieves  an error probability of the order of O(log K exp(−T1D2  L))  after T1 time slots of IA phase, where DL is the minimum gap  between two successive means of the arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' When no unimodal  structure is assumed (unstructured), the best known achievable  error probability is O(log K exp(−T1/H log K)) [20], where  K is the number of beams and H is the problem-dependent  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Thus, by exploiting unimodal structure, we achieve  a better error probability where the error exponent does not  depend on the number of beams, and demonstrate that this  is anticipated by establishing a lower bound for unimodal  bandits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Extensive simulation on realistic wireless networks  demonstrates UB3 identifies the best arm with a probability  more than 95% within 100 time slots for 16 beams, while  the other state-of-the-art algorithms need 500 time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This  translates into throughput gains of more than 15% compared  to other algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Moreover, UB3 does not require any  prior knowledge of channel fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In summary, our  contributions are as follows:  We set up the problem of beam alignment in mmWave  systems as a fixed-budget pure exploration multi-armed  bandit problem in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We exploit the unimodal structure of the RSS of the  beams and develop an algorithm named Unimodal Bandit  for Best Beam (UB3) to identify the best beam with a high  probability in fixed time slots or within the IA phase of  the BA in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We provide an upper bound on the error probability of  UB3 in identifying the best beam and show that the error  exponent does not depend on the number of beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We  demonstrate that is anticipated by establishing a lower  bound for unimodal bandits in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We perform extensive simulations to validate the superior  performance of UB3 compared to other state-of-the-art  algorithms like HOSUB, HBA, LSE and Sequential  Halving in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In agreement with the theoretical  bounds, UB3 is not affected by the number of beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Related Work  As there is growing interest in mmWave systems in  academia and industry, various aspects of mmWave are being  studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For the recent advances in the mmWave systems, we  refer to surveys [21]–[23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Several approaches are proposed to solve the BA problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  The compressive sensing-based signal processing methods  [24]–[26] utilize the sparse characterization of mmWave to  learn the best beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' They work better when accurate channel  state information is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' [27] proposes an Optimized  Two-Stage Search (OTSS) where a suitable candidate set  of beams is identified in the first stage based on the  received signal profile, and in the second stage, the best  beam from the surviving set is selected with additional  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Codebook-based hierarchical methods are  proposed in [28]–[30] which also require channel state  information for BA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' [31], [32] utilizes the location information  to perform fast BA, which is feasible only when the location  information of the UE is available at the BS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' [33], [34] use  Kalman filters to detect the angles of arrivals and departures to  track UE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Recently, machine learning [35], and deep learning  [36], [37] methods have been used for BA, which requires  offline training of the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Our work is closer to [7], [15], [16], [38] which uses  an online learning approach to optimize the BA problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  The authors in [7] develop an algorithm named Unimodal  Beam Alignment (UBA) that exploits the unimodal structure  of received power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The algorithm is built on the OSUB  algorithm [17] by adding stopping criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The algorithm  assumes that the mean powers are known, and the stopping  criteria is based on these mean powers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The Hierarchical  Beam Alignment (HBA) [15] algorithm also exploits the  unimodal/multimodal structures of beam signal strengths to  narrow down on the optimal beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' HBA has shown better  performance for beam identification than UBA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, for  T time slots, the computational complexity of HBA is O(T 2),  as in each time slot, the algorithm restarts the search, making  the running time linear in each time slot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Moreover, HBA  requires knowledge of channel fluctuations, which is not  practical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The Hierarchical Optimal Sampling of Unimodal  3  Bandits (HOSUB) [38] exploits the benefits of hierarchical  codebooks and the unimodality structure of the beam signal  strengths to achieve fast beam steering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Simulations show  better performance of HOSUB compared to HBA, as well  as a large reduction in computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However,  the authors in [38] did not provide any theoretical guarantees  on their proposed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The authors in [16] develop  an algorithm named MAMBA that aims to maximize the  cumulative rate obtained over a period using the Thompson  sampling algorithm named Adaptive Thompson Sampling  (ATS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Unlike the UBA and HBA, the exploration never ends  in ATS and may keep selecting the sub-optimal beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Our work develops an online learning algorithm for BA  using a fixed-budget pure exploration setup [20], [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We  exploit the unimodal structure of beam RSS to eliminate the  sub-optimal beams and narrow the beam search space quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Fixed-budget pure exploration strategies are more suitable for  the BA problem, as the exploration can be completed in the IA  phase, and no exploration is required during the data transfer,  simplifying the design of protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' To our knowledge, this  has not been studied in 5G networks with mmWave systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' PROBLEM SETUP  In this section, we discuss the system and channel model  used in mmWave system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We follow the setup and notation  similar to [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' System Model  We consider a point-to-point mmWave wireless system  between a transmitter, refer as mmWave BS, and a receiver,  refer as mmWave UE, in a static environment as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We focus on analog beamforming and consider one  ADC with an RF chain that focuses on one direction at a  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The transmitter has K phased-array antennas, where  each antenna has a phase shift to form a narrow directional  beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The antennas are evenly spaced by a distance D ≈  λ/2 forming a uniform linear array, where λ is the carrier  wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' As the IEEE 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ad can decouple the BA, we  consider that the receiver keeps a quasi-omnidirectional beam  and the transmitter scans over the beam space to identify the  best beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This is a reasonable assumption due to the small  form factor and fewer antennas on UEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In the following,  we focus on beam alignment (BA) at the BS side, and the  extension that involves both BS and UE is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Channel Model  Due to the sparse characteristics of mmWave channel, we  consider Saleh-Valenzuela channel model [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Suppose there  are L paths where one is the dominant line-of-sight (LOS)  path and L − 1 non-line-of-sight (NLOS) paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Let C denote  the set of complex numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The channel vector between the  transmitter and the receiver is given by  h = g0a(v0) +  L−1  �  l=1  gla(vl) ∈ CK×1  (1)  RF  Chain  RF  Chain  DAC  ADC  CHANNEL  Beam Scan  Omni-Directional  mmWave  Base Station (BS)  mmWave  User Equipment (UE)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1: A point-to-point mmWave Communication System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  where a(v) =  �  ej 2πD  λ  kv : 0 ≤ k ≤ K − 1  �  ∈ CK×1 denote  the vector of sinusoids at spatial angle v, g0 is the channel  gain of LOS path, and gl, 1 ≤ l ≤ L − 1 is the channel gains  of lth NLOS path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' v = cos θ denotes the spatial angle of the  channel associated with physical angle θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' As assume that the  channel remains static for a duration T time slots and the  channel vector keeps invariant in the BA process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Let B  ∈  CK×K denote the unitary discrete Fourier  transform (DFT) of the transmit beam space, where the kth  column corresponds to the kth beam, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=',  B = [b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , bK] =  1  √  K  [a(w1), a(w2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , a(wK)]  (2)  where wk =  2k−K  K  denotes the spatial angle of the kth  beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Then, the received signal of kth beam (with receiver  omnidirectional) is given by  yk =  √  PhHbk + n,  (3)  where n denotes the additive white Gaussian noise with mean  noise power N0W, with noise power density N0 and channel  bandwidth W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We denote the received signal strength (RSS)  of the kth beam as rk = |yk|2 and denotes its mean value  as µk = E [rk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Let k∗ = arg maxk µk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Then the beam bk∗  denotes the optimal beam with the best mean RSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Definition  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (Unimodality):  The  unimodality  structure  indicates that, ∀bk ∈ B, there exist a path such that µ1 <  µ2 < · · · < µk∗ and µk∗ > µK∗+1 > · · · > µK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  For the case when only LOS path is present with channel  gain g and spatial angle v, mean RSS is given as µk =  P g2  K δ(wk − v) + NoW for all bk ∈ B, where δ(x) =  sin2(KπDx/λ)  sin2(πDx/λ  denotes the antenna directivity function for  angular misalignment x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For bk ∈ B, µk is a function of  angular misalignment wk − v and has unimodal property [15,  Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In the following, we only consider the beams with  the unimodal property as in [7] and later discuss how to extend  our method to the multimodal case involving multiple NLOS  of paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We assumed that the Modulation and Coding  Scheme (MCS) on each beam is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, we can easily  accommodate different MCS on each beam by treating the RSS  as a vector corresponding to MCS and considering the mean  rate as done in [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  4  Beams  t = T  Exploration Phase (IA)  Data Communication Phase  t = 2T  Exploration Phase (IA)  t=1  t=T+1  t=T1  t=T+T1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Data Communication Phase  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2: Beam exploration (IA) phase followed by data transfer phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Problem Formulation  We assume a slotted system where the length of the IA  phase is T1 time slot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' As specified in the 5G standards, we let  the BS rerun IA phase periodically after every T time slot  where T > T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We assume that during the period T, the  environment is stationary such that the best beam remains the  same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We focus on one period between two successive reruns  of the IA phase and index the time slots in that period as t = 1  to t = T, refer to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In each time t, the BS can select  one of the beams from set B and obtain as feedback the RSS  at the receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The feedback is obtained through ACK/NACK  sent back by the receiver – BS measures the signal strength of  the received ACK/NACK, which gives the RSS at the receiver  [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' During the IA duration of T1 time slots, no information  signals are transmitted and throughput or error probability is  not a concern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, during the period of T − T1 data is  transmitted and it is desirable to obtain high throughput in this  period using the best possible beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We are thus interested in  algorithms that output an optimal beam at the end of T1 time  slots (IA phase).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We model the problem as a fixed-budget pure exploration  multi-armed bandit [20], [41] where the goal is to identify  the optimal arm within a fixed budget with high confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Following the terminology of multi-armed bandits, we refer to  beams as arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' A policy is any strategy that selects an arm in  each time slot given the past observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Let kt ∈ B denotes  the arm selected by a policy at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' By playing an arm kt,  the policy observes the feedback rkt which is a noisy RSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  The choice of kt can depend on the beams selected in the past  and their associated RSS values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We assume that RSS values  observed in each time slot are independently and identically  distributed across the arms and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The distribution of RSS is  governed by channel fluctuations, such as shadow fading and  the disturbance effect, and follows unknown fixed distributions  within a time period T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, without loss of generality,  we assume that values of RSS are bounded in some interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  For a given policy π, let ˆkπ  T1 denote the index of the arm  output by π at the end of T1 time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Let Π denote the set of  all policies of pure-exploration that output algorithms within  a fixed budget of T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Then our goal is to find a policy in Π  that minimizes the probability that the arm output at the end  of T1 is not an optimal arm, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=',  min  π∈Π Pr  �  bπ  ˆkT1 ̸= bk∗  �  ,  where for each policy, Pr(·) is calculated with respect to the  samples induced by the policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We note that our criteria is  different from those set in UBA [7] and HBA [15] which  aim to minimize cumulative regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Though both UBA and  HBA have stopping criteria beyond which they play a fixed  arm, the stopping time can be random, making their practical  implementation challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Whereas, the policy considered  by us completes the exploration phase deterministically after  time T1 which makes their implementation easier in a wireless  setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2 depicts the structure of our policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' ALGORITHMS  In  this  section,  we  propose  an  algorithm  named  UB3-Unimodal Bandit for Best Beam that finds the optimal  beam after exploiting the unimodal structure of mean RSS  within T1 time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The algorithm is based on the Line  Search Elimination (LSE) algorithm developed in [18], where  the algorithm samples and eliminate arms in multiple phases  till one arm survives after L + 1 phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The pseudo-code of  UB3 is given in Unimodal Bandit for Best Beam (UB3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' It is  parameter free and only takes K and T1 as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  UB3 runs in L+1 phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Arms are sampled and eliminated  in each phase such that only one arm survives after the L + 1  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We first explain the number of rounds in each phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Let Nl, for l = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , L+1, denotes the number of samples  in phase l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Then,  Nl =  �  2L−2  3L−1 T1  for l = 1, 2  2L−(l−1)  3L−(l−2) T1  for l = 3, 4, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , L + 1  (4)  which satisfies that  2 × 2L−2T1  3L−1  +  L+1  �  l=3  2L−(l−1)T1  3L−(l−2)  = T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (5)  After the first two phases, the number of samples increases by  a factor of 3/2 in each subsequent phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This increase in the  number of samples helps to distinguish between the empirical  means of the remaining arms, which are likely to be closer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  UB3 works as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Let Bl = {b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , bl} denote the  set of arms available in phase l and jl := |Bl| is the number  of arms in the set Bl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In phase l = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' L, the algorithm  selects four arms {kM, kA, kB, kN} ∈ Bl, which include the  two extremes and two middle arms uniformly spaced from  them (lines 4-7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Each of the arms is sampled for Nl  4 number  of times (line 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' At the end of the phase, their empirical means  5  𝒌𝑴  𝒌𝑨  𝒌𝑩  𝒌𝑵  𝒙𝒍  ∗ =  𝑪𝒂𝒔𝒆 𝟏  𝓑𝒍+𝟏  𝓑𝒍  𝒌𝑴  𝒌𝑨  𝒌𝑩  𝒌𝑵  𝒙𝒍  ∗ =  𝑪𝒂𝒔𝒆 𝟐  𝓑𝒍+𝟏  𝓑𝒍  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 3: Different cases of elimination in phase l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  denoted ˆµi (line 9) are obtained as follows:  ˆµl  i =  1  Nl/4  Nl/4  �  s=1  rl  is,  ∀i ∈ {kM, kA, kB, kN}  (6)  where rl  is denotes the sth noisy RSS sample from ith arm in  phase l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Based on these empirical means, we eliminate at most  1/3rd of the number of arms from the remaining set1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' More  specifically, if the arms kM or kA has the highest empirical  means, then we eliminate all the arms succeeding kB in the  set Bl (line 11 and 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Similarly, if the arms kB or kN has  the highest empirical means, then we eliminate all the arms  preceding kA in the set Bl (line 13 and 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 3 gives  a pictorial representation of the elimination of arms in two  possible cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The remaining set of arms are then transferred  to the next phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In phase L + 1, we are left with three  arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Each one of them is sampled  NL+1  3  number of times  and the one with the highest empirical mean is the output of  the algorithm as the optimal arm (lines 18-23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Arms between kM & kA or kB & kN are  eliminated in phase, and the arms between kA & kB always  survive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  After phase l = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , L, ⌊ 2  3jl⌋ of the arms survive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For  ease of exposition, we will drop the ⌊⌋ function since this drop  will influence only a few constants in the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Thus, after  the end of L phases there will be three arms as  (2/3)L K = 3 =⇒ L = log2 K/3  log2 3/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (7)  Therefore, the UB3 outputs the best beam as ˆkL+1 which is  equivalent to bˆkT1 after exploring for T1 time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In the next  section, we upper bound the error probability of UB3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' ANALYSIS  In this analysis, we find an upper bound and lower bound  for the probability of best arm elimination for fixed-budget  pure exploration bandit with unimodal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We first upper  1If the number of arms in a phase is not a multiple of 4, then less than  1/3rd will be eliminated in that phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Unimodal Bandit for Best Beam (UB3)  1: Input: T1 and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  2: Initialise: B1 = B, j1 ← |B1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Calculate L from (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  3: for l = 1 to L do  4:  kM ← First arm of Bl;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  5:  kN ← Last arm of Bl;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  6:  kA ← ⌈jl/3⌉th arm of Bl;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  7:  kB ← ⌊2jl/3⌋th arm of Bl;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  8:  Sample each arm in {kM, kA, kB, kN} for Nl  4 number  of times from (4)  9:  Obtain ˆµl  kM , ˆµl  kA, ˆµl  kB, ˆµl  kN by (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  10:  x∗  l =  arg max  i∈{kM,kA,kB,kN}  ˆµi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  11:  if x∗  l == {kM, kA} then  12:  Bl+1 ← {k ∈ Bl : kM ≤ k ≤ kB} Shrink to left  13:  else if x∗  l == {kB, kN} then  14:  Bl+1 ← {k ∈ Bl : kA ≤ k ≤ kN} Shrink to right  15:  end if  16:  jl+1 ← |Bl+1|;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  17: end for  18: for l = L + 1 do  19:  BL+1 = {kM, kA, kN};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  20:  Sample each arm in {kM, kA, kN} for T1  9 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' of times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  21:  Obtain ˆkL+1 =  arg max  i∈{kM,kA,kN}  ˆµL+1  i  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  22: end for  23: Output: bˆkT1 = ˆkL+1  bound the error probability of Unimodal Bandit for Best Beam  (UB3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For analysis, we use the following assumption:  Assumption 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' There exists a constant DL > 0 such that  |µk − µk−1| ≥ DL for 2 ≤ k ≤ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We note that this assumption is the same as that used in  from [18, Assumption 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='4] to analyze unimodal bandits in the  regret minimization setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Upper Bound for Algorithm UB3  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Let UB3 is run for T1 time slots in L+1 number  of phases, where L = log2 K/3  log2 3/2 with output ˆkL+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Then, the  probability that ˆkL+1 output by UB3 is not the best arm after  L + 1 phases is bounded as  P(ˆkL+1 ̸= k∗) ≤ 2 exp  �  −T1  18D2  L  �  + 2 exp  �  −T1K  32 D2  L  �  + 2 exp  �  −T1K  72 D2  L  �  + 2(L − 2) exp  �  −T1  16D2  L  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (8)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The proof is given in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Observe that the dominant first and last terms in the  upper bound do not depend on K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The error probability  is thus of order O  �  log2 K exp  �  − T1D2  L  16  ��  , where the  error exponent term  �  exp  �  − T1D2  L  16  ��  does not depend  on K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The Sequential Halving (Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=') algorithm is  proposed in [42] for non-unimodal (unstructured) bandits  and provided an upper bound for the probability of not  6  choosing the optimal arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The error probability is shown to  be O  �  log2(K) exp  �  −  T1  log(K)H2  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This bound matches with  the lower bound derived in [43] for unstructured bandits up  to multiplicative factor of log2(K), where H2 = max  k̸=k∗  k  ∆2  k is  the complexity parameter depended upon the sub-optimality  gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Note that the error exponent in this bound of Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  has log2(K) factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' By exploiting the unimodal property,  we shove off this factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We next consider the lower  bound for fixed-budget pure exploration with the unimodal  structure which confirms that error exponent should be indeed  independent of number of beams for any optimal algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Lower bound for pure exploration unimodal bandit  A lower bound on the probability of error for the fixed  budget without assuming any structure is established in [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We adapt the proof to include the unimodal structure to derive  a lower bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' To this end, we first define a set of bandit  instances as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Let us consider K arms that follow the unimodal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Let {pk}1≤k≤K be K real numbers in the interval [1/4, 1/2]  with pk∗ = 1  2 and p1 ≤ p2 ≤ · · · ≤ pk∗−1 ≤ pk∗ ≥ pk∗+1 ≥  · · ≥ pK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For any 1 ≤ k ≤ K we consider the distribution νk  to be Bernoulli distribution with mean pk, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' νk := Ber(pk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We consider another distribution ν′  k as Bernoulli distribution  with mean 1 − pk, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=', ν′  k := Ber(1 − pk) with mean 1 − pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We define K bandit problem as following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For i  ∈  {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , K} define the product distributions Gi := νi  1 ⊗ νi  2 ⊗  · · ⊗ νi  K where  νi  k :=  �  �  �  �  �  νk1{k ̸= i} + ν′  k1{k = i}, if k ∈ {k∗ − 1,  k∗, k∗ + 1}  νk, otherwise  where 1{A} denotes the indicator function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' It is easy to note  that only bandit instances Gi, where i ∈ {k∗ − 1, k∗, k∗ + 1}  satisfy the unimodality structure and the not the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Flipping of the reward for all other arms will result in a  non-unimodal problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Thus unlike [43] we have 3 bandit  problems in the neighbourhood of k∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We define dk := pk∗ − pk = 1  2 − pk, for any 1 ≤ k ≤ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Set ∆i  k = di + dk, if k ̸= i and ∆i  i = di, for any i ∈ {k∗ −  1, k∗ + 1} and any k ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , K}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Note that {∆i  k}k denotes  the arm gaps of the bandit problem i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We also define for any  i ∈ {k∗ − 1, k∗ + 1} the quantity  ¯H(i) :=  �  k∈{i−1,i+1}  1  (∆i  k)2 and ¯h =  �  i∈{k∗−1,k∗+1}  1  d2  i ¯H′(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Theorem 2 from [43] can be rephrased in this setting as  follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For any bandit strategy that returns the arm ˆkT1  at time T1, it holds that  max  i∈{k∗−1,k∗+1}Pi(ˆkT1 ̸= i)  ≥ 1  6 exp  �  −60  T1  ¯H(k∗) − 2  �  T1 log(18T1)  �  ,  (9)  and also  max  i∈{k∗−1,k∗+1}Pi(ˆkT1 ̸= i)  ≥ 1  6 exp  �  −60  T1  ¯h ¯H(i) − 2  �  T1 log(18T1)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (10)  The proof of this theorem follows the lines similar to [43,  Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2] after applying the change of measure rule to on the  restricted set of arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We skip the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Assume that  T1 ≥ max  �  ¯H(k∗), ¯H(i)¯h  �2 4 log(6T1K)  (60)2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  For any bandit strategy that returns the arm ˆkT1 at time T1,  it holds that  max  i∈{k∗−1,k∗+1} Pi(ˆkT1 ̸= i) ≥ 1  6 exp  �  −120  T1  ¯H(k∗)  �  ,  and also  max  i∈{k∗−1,k∗+1} Pi(ˆkT1 ̸= i) ≥ 1  6 exp  �  −120  T1  ¯H(i)¯h  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We can establish a lower bound using this corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For any unimodal bandit strategy that returns  arm ˆkT1 at time T1,  max  i∈{k∗−1,k∗+1} Pi(ˆkT1 ̸= i) ≥ 1  6 exp  �  −75 T1  ¯H(i)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (11)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The proof is given in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We see that unlike in the case of the lower bound found in  [43], the lower bound of the error probability is not dependent  on log2(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In addition, the complexity factor depends only  on the sub-optimality gap between the optimal arm and its  neighbours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This observation is similar to the lowed bound on  cumulative regret established in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' NUMERICAL SIMULATIONS  In this section, we corroborate our theoretical results using  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We first describe the simulation setup with  parameters used and present the results in the following  subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Simulation Parameters  We use the IEEE 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ad system with parameters as  described in [15] for numerical simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The carrier  frequency (f) is set at 60 GHz and the bandwidth is set at  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='16 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The transmit power P = 50 dBm is shared between  K antennas which vary from 16 to 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' For the line of sight  (LOS) path, we have the path loss model as  PL(dB) = −27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='5 + 20 log10(f) + 10α log10(d) + χ, (12)  where d is the transmission distance, the path loss exponent α  is taken as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74, and χ is the shadow fading component which  follows Normal distribution with zero mean and 2 dB variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  In (12) f is in MHz and d is in meters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Depending upon the  7  Parameter  Value  Carrier frequency (f)  60 Ghz  Bandwidth (W)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='16 GHz  Noise spectrum density (N0)  −174 dBm/Hz  Shadow fading variance (log-normal σ)  2 dB  Number of beams (N)  16-128  HBA parameters (ρ1, γ, ζ)  (3, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='1)  Distance considered (d)  (20, 40, 60, 80) m  Path loss exponent  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  TABLE I: Parameters for simulation  beam selected the signal strength varies in [−80, −20] dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  The algorithm parameter are kept at ρ1 = 3, γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='5 and  ζ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The channel parameters for the simulations are given  in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Simulation results are averaged over 1000 iterations  and confidence intervals are shown (when significant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We compare the performance of Unimodal Bandit for Best  Beam (UB3) with the following algorithms:  Sequential Halving (Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=') [42]:  This algorithm  is used for pure exploration in non-unimodal bandits for  a fixed T1 time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The algorithm was proved to be  optimal [43], and hence a comparison would give the  idea about, how the additional information of unimodality  would improve the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Linear Search Elimination (LSE) [18]: Although this  algorithm was proposed for continuous arm unimodal  bandit problems, we have considered the algorithm for  fixed T1 time slots and for discrete arms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' A comparison of  UB3 with LSE is pertinent as it is a well-known algorithm  for unimodal bandits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Hierarchical  Beam  Alignment  (HBA)  [15]:  This  algorithm was shown to have good performance for regret  minimization, when compared to existing algorithms,  considering the prior knowledge of channel fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Our comparison with HBA will of throughput comparison  for the period after the best beam has been identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Hierarchical Optimal Sampling of Unimodal Bandits  (HOSUB) [38]: This algorithm exploits the benefits of  hierarchical codebooks and the unimodality of RSS to  achieve the best arm in the fixed T1 time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Our  comparison with HOSUB will of throughput comparison  for the period after the best beam has been identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  We did not include UBA algorithm [7] for comparison  since HBA was shown to have better performance for beam  identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Also, the ATS algorithm is not compared against  as it is designed to minimize the cumulative regret and does  not stop the exploration process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We note the computational  complexity of complexity HBA scales quadratically in T1  whereas it is of O(T1) in UB3, where T1 is the duration of IA  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In addition, HBA requires prior knowledge of channel  fluctuations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='e, the variance of the noise parameter, which is  not required in UB3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Comparison with other pure exploration algorithms  We define the probability of error as the probability of not  identifying the best beam after sampling for T1 number of  time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We consider T1 as the exploration (IA) phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We  first compare the probability of error for UB3 algorithm with  LSE and Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' which are used for pure exploration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We  compare the probability of error performance of the algorithms  for arm sizes of K = {16, 64, 128}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The probability of error  against the exploration time slots (T1) is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  LSE, which has an equal number of sampling for the arms  in all phases, has the worst probability of error performance  than Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='. The solid lines in the figure are for K = 16,  the dashed lines are for K = 64 and the dot-dashed lines  are for K = 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The comparisons are done for distance of  d = 20, 60 and 80 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The probability of error increases as we  increase the beam size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, for a small number of arms,  both Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' and UB3 have comparable performance, but as  the number of beams increases, UB3 has a lesser probability  of error compared to Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' as evident from the case of  K = 64 and K = 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, UB3 can identify the best  beam with a probability of more than 95% within 100 time  slots for 16 number of beams, while the other state-of-the-art  algorithms take need at least 200 time slots for executions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Note that for Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' require at least 200, 400, 900 rounds  for K = 16, 64, 128, respectively, to complete their execution  hence their graph start after that many slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Moreover, as  distance increases the probability of error of all the algorithms  increases for each beam size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  It is to be noted that even though the minimum time slots  requirement (as a function of K) for LSE is much smaller than  both UB3 and Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' for its feasible execution, the number  of samples it runs for arms neighbouring to k∗ is much lesser  resulting in more probability of error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' needs at least  K log2(K) number of time slots to complete one phase and  has samples for all arms in every phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Hence, it has much  fewer time slots remaining when the algorithm is executed  in the neighborhood of k∗ as compared to UB3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Thus, the  minimum time slots requirement for UB3 as a function of K  is much lesser than that of Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=', in addition to having a  better probability of error performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This demonstrates the  advantage of exploiting the unimodality of the reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Comparison of throughput performance  In this subsection we compare the throughput performance  of UB3 with the HBA and HOSUB algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We look at  the mean cumulative throughput, which is defined as the  product of the mean value of the selected beam at the end  of exploration normalized with the mean power of the best  beam and the remaining available time slots, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='e,  Throughput = µnorm  bL+1 × (T − T1),  where T is the total available time slots and T1 is the number  of time slots available for exploration of the best beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Note  that HBA will not have a fixed T1, and hence we will find  the throughput after the expected exploration time E(T1),  obtained as the average of many runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Thus the throughput will  be fixed for HBA for a fixed T, while it will vary for varying  8  0  200  400  600  800  1000  1200  1400  Exploration Phase (T1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='05  Error  UB3, K=16, d=20  LSE, K=16, d=20  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=16, d=20  UB3, K=64, d=20  LSE, K=64, d=20  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=64, d=20  UB3, K=128, d=20  LSE, K=128, d=20  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=128, d=20  (a) Error Probability vs T1, d = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  0  200  400  600  800  1000  1200  1400  Exploration Phase (T1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='12  Error  UB3, K=16, d=60  LSE, K=16, d=60  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=16, d=60  UB3, K=64, d=60  LSE, K=64, d=60  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=64, d=60  UB3, K=128, d=60  LSE, K=128, d=60  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=128, d=60  (b) Error Probability vs T1, d = 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  0  200  400  600  800  1000  1200  1400  Exploration Phase (T1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='12  Error  UB3, K=16, d=80  LSE, K=16, d=80  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=16, d=80  UB3, K=64, d=80  LSE, K=64, d=80  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=64, d=80  UB3, K=128, d=80  LSE, K=128, d=80  Seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Halving, K=128, d=80  (c) Error Probability vs T1, d = 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 4: Error performance of UB3 vs T1 for different no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' of beams (K) and distance (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  400  600  800  1000  1200  1400  1600  Exploration Phase (T1)  10  15  20  25  30  35  Cumulative Throughput (in dB)  UB3, K=16, d=20  HOSUB, K=16, d=20  HBA, K=16, d=20  UB3, K=64, d=20  HOSUB, K=64, d=20  HBA, K=64, d=20  UB3, K=128, d=20  HOSUB, K=128, d=20  HBA, K=128, d=20  (a) Throughput vs T1, d = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  400  600  800  1000  1200  1400  1600  Exploration Phase (T1)  5  10  15  20  25  30  35  Cumulative Throughput (in dB)  UB3, K=16, d=60  HOSUB, K=16, d=60  HBA, K=16, d=60  UB3, K=64, d=60  HOSUB, K=64, d=60  HBA, K=64, d=60  UB3, K=128, d=60  HOSUB, K=128, d=60  HBA, K=128, d=60  (b) Throughput vs T1, d = 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  400  600  800  1000  1200  1400  1600  Exploration Phase (T1)  5  10  15  20  25  30  Cumulative Throughput (in dB)  UB3, K=16, d=80  HOSUB, K=16, d=80  HBA, K=16, d=80  UB3, K=64, d=80  HOSUB, K=64, d=80  HBA, K=64, d=80  UB3, K=128, d=80  HOSUB, K=128, d=80  HBA, K=128, d=80  (c) Throughput vs T1, d = 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 5: Throughput performance of UB3 vs T1 for different no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' of beams (K) and d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  20  40  60  80  Distance (d)  0  5  10  15  20  25  Cumulative Throughput (in dB)  UB3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  HOSUB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  HBA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  (a) Throughput vs d,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' K = 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' T1 = 500  20  40  60  80  Distance (d)  0  5  10  15  20  25  30  35  Cumulative Throughput (in dB)  UB3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  HOSUB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  HBA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  (b) Throughput vs d,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' K = 64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' T1 = 500  20  40  60  80  Distance (d)  0  5  10  15  20  25  30  35  Cumulative Throughput (in dB)  UB3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=128,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  HOSUB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=128,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  HBA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='K=128,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='T1=500  (c) Throughput vs d,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' K = 128,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' T1 = 500  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 6: Throughput performance of UB3 vs d for different no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' of beams (K) for T1 = 500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  T1 for UB3 and HOSUB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 5 compares the cumulative  throughput of UB3, HBA and HOSUB for different K and  distances of d = 20, 60 and 80 m for T = 3000 time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  As the number of beams (arms) increases, the beam  becomes narrower, and hence the reward for the best beam also  increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In that case, HOSUB requires more exploration time  slots to learn the optimal beam, thereby exploiting sub-optimal  beams in the data transmission phase for the given T1 time  slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' On the other hand, for HBA, since the average time  required to find the best arm increases, the average throughput  will decrease as the number of arms increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This increasing  and decreasing of throughput for HBA is seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 5 and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, the UB3 algorithm is not much affected by  the number of increases in arms for finding the best arm, and  hence the throughput will only increase with increasing gain  for the best arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' UB3 can improve the throughput by more  than 45% compared to HBA and by more than 15% compared  to HOSUB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' This too is evident from both Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 5 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However, the throughput will decrease as we increase the  transmission distance, refer Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Finally, we compare the throughput performance for varying  path loss exponent given as α ∈ {1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14}, as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The path loss exponent increases when there are  more barriers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' for example when the receiver moves from  outdoor to indoor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The throughput indeed decreases for all  HBA, HOSUB and UB3, but UB3 still outperforms HBA and  HOSUB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' CONCLUSION AND FUTURE WORK  We investigated the problem of beam alignment in mmWave  systems using the multi-armed bandits (MAB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' While earlier  works used the cumulative regret minimization setting to learn  9  400  600  800  1000  1200  1400  1600  Exploration Phase (T1)  11  12  13  14  15  16  17  18  19  20  21  Cumulative Throughput (in dB)  UB3,K=16,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  HOSUB,K=16,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  HBA,K=16,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  UB3,K=16,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  HOSUB,K=16,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  HBA,K=16,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  UB3,K=16,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  HOSUB,K=16,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  HBA,K=16,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  (a) Throughput vs T1, K = 16, d = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  400  600  800  1000  1200  1400  1600  Exploration Phase (T1)  5  10  15  20  25  30  35  Cumulative Throughput (in dB)  UB3,K=64,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  HOSUB,K=64,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  HBA,K=64,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  UB3,K=64,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  HOSUB,K=64,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  HBA,K=64,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  UB3,K=64,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  HOSUB,K=64,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  HBA,K=64,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  (b) Throughput vs T1, K = 64, d = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  400  600  800  1000  1200  1400  1600  Exploration Phase (T1)  5  10  15  20  25  30  35  Cumulative Throughput (in dB)  UB3,K=128,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  HOSUB,K=128,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  HBA,K=128,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='74  UB3,K=128,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  HOSUB,K=128,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  HBA,K=128,d=20,path-loss=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='94  UB3,K=128,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  HOSUB,K=128,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  HBA,K=128,d=20,path-loss=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='14  (c) Throughput vs T1, K = 128, d = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 7: Throughput performance of UB3 vs T1 for different path-loss exponent α and d = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  the best arm, we used the fixed-budget pure-exploration setting  framework exploiting the unimodal structure of the received  signal strength of the beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We developed an algorithm  named Unimodal Bandit for Best Beam (UB3) that identified  the best beam with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We gave an upper bound  on the error probability of UB3 and established that it is  optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Simulations validated the efficiency of UB3 which can  identify the best beam using a smaller number of explorations  that can translate to improvement in throughput by more than  15% compared to other state-of-art algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Due to its  simple structure, UB3 is easy to implement and comes with a  lower computational complexity – UB3 has a computational  complexity of O(T), whereas it is O(T 2) for HBA [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' The  UBA algorithm in [7] needs to solve a convex optimization  problem in each time which is expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  UB3 works well when only the LOS path is present and  the RSS of beams satisfies the unimodal property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However,  when NLOS paths are present, we are faced with multimodal  functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' UB3 can be adapted to handle the multi-modal  functions by using backtracking ideas proposed in [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' In  backtracking, eliminated arms are revisited to check if it is  done by mistake and thus will not be stuck in a sub-optimal  set of beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' It is interesting to evaluate the UB3 algorithms  with backtracking on multimodal function and establish its  performance guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' APPENDIX  In this section, we will provide proof of the main results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Proof of Theorem 1  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' UB3 runs for T1 horizon in L + 1 number of phases  that satisfies (5), where L =  log2 K/3  log2 3/2 and outputs the arm  ˆkL+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We will now upper bound the probability of error as,  P(ˆkL+1 ̸= bk∗) =  L+1  �  l=1  P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in l|bk∗ not elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in < l)  ≤  L+1  �  l=1  P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (13)  The best arm is eliminated in phase l in the following cases:  1) bk∗ ∈ {kM, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , kA}, and ˆµl  kB or ˆµl  kN is greater than  both ˆµl  xM and ˆµl  kA  bk∗  bk∗  kM  kA  jl  3 DL  kB  kN  Case 1  Case 2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 8: Different cases of elimination in any phase l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' bk∗ will  not get eliminated if it is in between arms kA and kB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  2) bk∗ ∈ {kB, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , kN}, and ˆµl  kM or ˆµl  kA is greater than  both ˆµl  kB and ˆµl  kN  The two cases are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' From Remark 2, bk∗  will not get eliminated if bk∗ ∈ {kA, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , kB}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' However we  will upper bound the probability of error by assuming that  bk∗ will always fall in the above two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Notice that Case  1 and Case 2 are symmetrical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Hence we can consider that  bk∗ will always fall in either one of the cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Without loss of  generality, we consider Case 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in l) ≤ P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in l|bk∗ ∈ {kM, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , kA})  P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in l)  ≤ P(ˆµl  kB > ˆµl  kM and ˆµl  kA|bk∗ ∈ {kM, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , kA})  + P(ˆµl  kN > ˆµl  kM and ˆµl  kA|bk∗ ∈ {kM, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , kA})  ≤ 2P(ˆµl  kB > ˆµl  kM and ˆµl  kA|bk∗ ∈ {kM, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' , kA}),  (14)  where the last inequality is due to the fact that, for Case 1,  µkB ≥ µkN by unimodality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Now for Case 1, µkA is always  greater than µkB, but µkM may not be greater than µkB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Then,  we can further upper bound (14) as  P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in l) ≤ 2P(ˆµl  kB > ˆµl  kA|bk∗ ∈ {kM, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='., kA}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (15)  Applying Hoeffding’s inequality in (15), we have  P(ˆµl  kB > ˆµl  kA) ≤ exp  �  −1  2  Nl  4 (∆A,B)2  �  ,  (16)  where ∆A,B = µkA −µkB which is greater than 0 for Case 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  From Assumption 1, and the fact that there are at least jl  3 arms  between kA and kB, for Case 1 we have, ∆A,B ≥ (jl/3)DL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  10  Thus from (14) and (16) we have,  P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in l) ≤ 2 exp  �  −Nl  72  �  jlDL  �2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (17)  Using jl =  � 2  3  �l K in (17) we can find the probability of best  arm getting eliminated in phase 1 and 2, phase L + 1, and the  rest of the phases separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Using (7), we have  P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in 1&2) ≤2 exp  �  −T1K  32 D2  L  �  + 2 exp  �  −T1K  72 D2  L  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (18)  For phase L + 1, since the best arm is selected among 3 arms  when each arm is sampled T1/9 times, we have  P(bk∗ elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in phase L + 1) ≤ 2 exp  �  −T1  18D2  L  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (19)  From (17), the error probability for the remaining phases is  P(best arm elim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' in phase 3 to phase L)  ≤ 2  L  �  l=3  exp  �  −T1  8  K2  9  �2  3  �2(l−1) 2L−l+1  3L−l+2 D2  L  �  ≤ 2  L  �  l=3  exp  �  −T1K  48  �2  3  �l  D2  L  �  ≤ 2(L − 2) exp  �  −T1  16D2  L  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (20)  By (13), (18), (19) and (20), we obtain the upper bound as  P(ˆkL+1 ̸= bk∗)  ≤ 2 exp  �  −T1  18D2  L  �  + 2 exp  �  −T1K  32 D2  L  �  + 2 exp  �  −T1K  72 D2  L  �  + 2(L − 2) exp  �  −T1  16D2  L  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Proof of Theorem 3  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' We have, pk = 1  2 − dk such that pk ∈ [1/4, 1/2] and  follows unimodality and pk∗ = 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Upper bounding ¯h, we have  ¯h =  �  i∈{k∗−1,k∗+1}  1  d2  i ¯H(i)  =  1  d2  k∗−1 ¯H(k∗ − 1) +  1  d2  k∗+1 ¯H(k∗ + 1)  = (I) + (II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (21)  We will upper bound (I) and (II),  d2  k∗−1 ¯H(k∗ − 1) = d2  k∗−1  �  k∈{k∗−2,k∗}  1  (dk∗−1 + dk)2  Since dk∗ = 0 and dk∗−2 ≥ dk∗−1, we get  d2  k∗−1 ¯H(k∗ − 1) ≤ 1 + 1  4 = 5  4  (22)  d2  k∗+1 ¯H(k∗ + 1) = d2  k∗+1  �  k∈{k∗,k∗+2}  1  (dk∗+1 + dk)2  Since dk∗ = 0 and dk∗+2 ≥ dk∗+1, we get  d2  k∗+1 ¯H(k∗ + 1) ≤ 1 + 1  4 = 5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  (23)  By (22) and (23) we get  ¯h ≥ 4  5 + 4  5 = 8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Putting the value of ¯h in Corollary we get  =⇒  max  i∈{k∗−1,k∗+1} Pi(ˆkT ̸= i) ≥ exp  �  −75 T  ¯H(i)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  REFERENCES  [1] “IEEE  standard  for  information  technology–  amendment  3:  Enhancements for very high throughput in the 60 GHz band,”  IEEE Std 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ad-2012 (Amendment to IEEE Std 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11-2012, as  amended by IEEE Std 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ae-2012 and IEEE Std 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11aa-2012),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1–628, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Fang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Fang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Long, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' He, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Han, “Enhanced  random access and beam training for millimeter wave wireless local  networks with high user density,” IEEE Transactions on Wireless  Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 7760–7773, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [3] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Ghasempour, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' da Silva, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Cordeiro, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Knightly,  “Ieee 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ay: Next-generation 60 ghz communication for 100 gb/s  wi-fi,” IEEE Communications Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 55, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 186–192,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Nitsche, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Cordeiro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Flores, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Knightly, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Perahia, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Widmer, “Ieee 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11ad: directional 60 ghz communication for  multi-gigabit-per-second wi-fi [invited paper],” IEEE Communications  Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 52, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 132–141, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Nitsche, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Flores, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Knightly, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Widmer, “Steering with  eyes closed: mm-wave beam steering without in-band measurement,”  in 2015 IEEE Conference on Computer Communications (INFOCOM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  IEEE, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2416–2424.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [6] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Group et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=', “Ieee 802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='11 ad, amendment 3: Enhancements for  very high throughput in the 60 ghz band,” IEEE Stand, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 802, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Hashemi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Sabharwal, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Emre Koksal, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Shroff, “Efficient  beam alignment in millimeter wave systems using contextual bandits,”  in IEEE Conference on Computer Communications (INFOCOM), 2018,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2393–2401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Sur, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Venkateswaran, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhang, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Ramanathan, “60 ghz  indoor networking through flexible beams: A link-level profiling,” in  Proceedings of the 2015 ACM SIGMETRICS International Conference  on Measurement and Modeling of Computer Systems, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 71–84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Marzi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Nelson, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Madhow, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhao, and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zheng, “Demystifying 60ghz outdoor picocells,” in Proceedings of  the 20th annual international conference on Mobile computing and  networking, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 5–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [10] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Barati, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Hosseini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Mezzavilla, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Korakis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Panwar,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Rangan, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zorzi, “Initial access in millimeter wave cellular  systems,” IEEE Transactions on Wireless Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 15,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 7926–7940, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [11] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Aykin and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Krunz, “Efficient beam sweeping algorithms and initial  access protocols for millimeter-wave networks,” IEEE Transactions on  Wireless Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2504–2514, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [12] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Aykin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Akgun, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Krunz, “Smartlink: Exploiting channel  clustering effects for reliable millimeter wave communications,” in  IEEE Conference on Computer Communications (INFOCOM), 2019,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1117–1125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhou, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Wei, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhang, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Ma, “Fastnd: Accelerating directional  neighbor discovery for 60-ghz millimeter-wave wireless networks,”  IEEE/ACM Transactions on Networking, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2282–2295,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [14] 3GPP TR 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='802 (v14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='0), “Study on new radio access technology  physical layer aspects (release 14),” Sep 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='3gpp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='org/ftp/Specs/archive/38 series/38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='802/38802-001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='zip  [15] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Wu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Cheng, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Yang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhuang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Shen,  “Fast mmwave beam alignment via correlated bandit learning,” IEEE  Transactions on Wireless Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  5894–5908, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  11  [16] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Aykin,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Akgun,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Feng,  and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Krunz,  “Mamba:  A  multi-armed bandit framework for beam tracking in millimeter-wave  systems,” in IEEE INFOCOM 2020 - IEEE Conference on Computer  Communications, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1469–1478.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Combes and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Proutiere, “Unimodal bandits: Regret lower bounds  and optimal algorithms,” in Proceedings of the 31st International  Conference on International Conference on Machine Learning - Volume  32, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' ICML’14, 2014, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' I–521–I–529.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Yu and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Mannor, “Unimodal bandits,” in Proceedings of the  28th International Conference on International Conference on Machine  Learning, 2011, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 41–48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Saber, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' M´enard, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Maillard, “Forced-exploration free  strategies for unimodal bandits,” arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='16569, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Audibert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Bubeck, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Munos, “Best arm identification in  multi-armed bandits.” in COLT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Citeseer, 2010, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 41–53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Uwaechia and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Mahyuddin, “A comprehensive survey on  millimeter wave communications for fifth-generation wireless networks:  Feasibility and challenges,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 62 367–62 414,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [22] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Niu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Jin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Su, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Vasilakos, “A survey of millimeter  wave communications (mmwave) for 5g: opportunities and challenges,”  Wireless networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2657–2676, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [23] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Kong, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Kong, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Qiu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Xia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Arnon, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Chen,  “Millimeter wave communication: A comprehensive survey,” IEEE  Communications Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1616–1653,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [24] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Marzi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Ramasamy, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Madhow, “Compressive channel  estimation and tracking for large arrays in mm-wave picocells,” IEEE  Journal of Selected Topics in Signal Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  514–527, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [25] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Hassanieh, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Abari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Rodriguez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Abdelghany, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Katabi,  and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Indyk, “Fast millimeter wave beam alignment,” in Proceedings  of the 2018 Conference of the ACM Special Interest Group on Data  Communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Association for Computing Machinery, 2018, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  432–445.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [26] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Fang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Duan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Chen, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Li, “Fast beam alignment  for millimeter wave communications: A sparse encoding and phaseless  decoding approach,” IEEE Transactions on Signal Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 67,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 17, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 4402–4417, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Hanly, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Collings, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Whiting, “Explore  and eliminate: Optimized two-stage search for millimeter-wave beam  alignment,” IEEE Transactions on Wireless Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 18,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 4379–4393, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Lan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' woo Pyo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Baykas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' sean Sum, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Rahman,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Gao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Funada, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Kojima, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Harada, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Kato, “Beam  codebook based beamforming protocol for multi-gbps millimeter-wave  wpan systems,” IEEE Journal on Selected Areas in Communications,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1390–1399, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [29] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Xiao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' He, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Xia, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Xia, “Hierarchical codebook  design for beamforming training in millimeter-wave communication,”  IEEE Transactions on Wireless Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  3380–3392, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [30] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Shabara, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Koksal, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Ekici, “Linear block coding for  efficient beam discovery in millimeter wave communication networks,”  in IEEE Conference on Computer Communications (INFOCOM), 2018,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 2285–2293.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [31] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Va, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Shimizu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Bansal, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Heath, “Online learning for  position-aided millimeter wave beam training,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  30 507–30 526, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Asadi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' M¨uller, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Sim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Klein, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Hollick, “Fml:  Fast machine learning for 5g mmwave vehicular communications,” in  IEEE Conference on Computer Communications (INFOCOM), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  1961–1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [33] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Va, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Vikalo, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Heath, “Beam tracking for mobile millimeter  wave communication systems,” in IEEE Global Conference on Signal  and Information Processing (GlobalSIP), 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 743–747.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [34] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Guo, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Fan, “Tracking angles of departure and  arrival in a mobile millimeter wave channel,” in 2016 IEEE International  Conference on Communications (ICC), 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [35] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Heng and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Andrews, “Machine learning-assisted beam alignment  for mmwave systems,” IEEE Transactions on Cognitive Communications  and Networking, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1142–1155, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [36] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Myers, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Wang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Gonz´alez-Prelcic, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Heath, “Deep  learning-based beam alignment in mmwave vehicular networks,” in  ICASSP 2020 - 2020 IEEE International Conference on Acoustics,  Speech and Signal Processing (ICASSP), 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 8569–8573.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [37] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Raj, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Nayak, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Kalyani, “Deep reinforcement learning based  blind mmwave mimo beam alignment,” IEEE Transactions on Wireless  Communications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1–1, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [38] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Blinn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Boerger, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Bloch, “mmwave beam steering with  hierarchical optimal sampling for unimodal bandits,” in ICC 2021-IEEE  International Conference on Communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [39] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Kaufmann, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Capp´e, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Garivier, “On the complexity of  best-arm identification in multi-armed bandit models,” Joural of Machine  Learning Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1–42, January 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Akdeniz, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Samimi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Sun, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Rangan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Rappaport, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Erkip, “Millimeter wave channel modeling and  cellular capacity evaluation,” IEEE journal on selected areas in  communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1164–1179, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [41] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Kalyanakrishnan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Tewari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Auer, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Stone, “Pac subset  selection in stochastic multi-armed bandits,” in Proceedings of the  29th International Coference on International Conference on Machine  Learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  Madison, WI, USA: Omnipress, 2012, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 227–234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [42] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Karnin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Koren, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Somekh, “Almost optimal exploration in  multi-armed bandits,” in International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  PMLR, 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 1238–1246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Carpentier and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Locatelli, “Tight (lower) bounds for the fixed  budget best arm identification bandit problem,” in Conference on  Learning Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  PMLR, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 590–604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  [44] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Kunne, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Maggi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Cohen, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' Xu, “Anytime backtrack unimodal  bandits and applications to cloud computing,” in 2020 IFIP Networking  Conference (Networking).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content='  IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
+page_content=' 82–90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE1T4oBgHgl3EQf0gVV/content/2301.03456v1.pdf'}
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+MODELING AND ANALYSIS OF ENSEMBLE AVERAGE SOLVATION ENERGY AND
+SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+YUANZHEN SHAO∗†, ZHAN CHEN∗∗, AND SHAN ZHAO∗∗∗
+Abstract. Variational implicit solvation models (VISM), because of their relatively low computational
+cost and satisfactory accuracy, have been widely used in the solvation analysis of biological systems at
+molecular level. Central in the construction of VISM is an interface separating the solute and the solvent.
+Compared with sharp-interface models, diffuse-interface VISMs have shown some initial success in improving
+the efficiency and accuracy of the solvation energy estimation of biomolecules. However, on a theoretical level,
+several questions concerning the diffuse-interface VISMs remain open: (1) What is the physical meaning of a
+diffuse interface? (2) What energy does a diffuse-interface VISM predict? This work aims at addressing the
+above questions. Our research reveals the relationship between a diffuse interface definition and the random
+movement of the solute-solvent interface due to thermal fluctuations. Then, we use this diffuse interface
+setting to construct a VISM that is capable of capturing ensemble average solvation energy, which is an
+experimentally observable quantity in solvation processes. The well-posedness and variational analysis of
+the model are further investigated. Our work is the first step towards estimating ensemble average solvation
+energy by using diffuse-interface VISMs.
+1. Introduction
+In the quantitative analysis of biological processes, the complex interactions between the solute and solvent
+are typically described by solvation energies (or closely related quantities): the free energy of transferring the
+solute (e.g. biomolecules, such as proteins, DNA, RNA) from the vacuum to a solvent environment of interest
+(e.g. water at a certain ionic strength). There are two major approaches for solvation energy calculations:
+explicit solvent models and implicit solvent models [39]. Explicit models, treating both the solute and the
+solvent as individual molecules, are too computationally expensive for large solute-solvent systems, such as
+the solvation of macromolecules in ionic environments. In contrast, implicit models, by averaging the effect
+of solvent phase as continuum media [1,2,5,6,9,25,38], are much more efficient and thus are able to handle
+much larger systems [2,16,27,30,31,33,43,51].
+An inevitable prerequisite for describing the solvation energy in implicit solvent models is an interface
+separating the discrete solute and the continuum solvent domains. All of the physical properties related
+to solvation processes, including biomolecular surface area, biomolecular cavitation volume, pKa value and
+electrostatic free energy, are very sensitive to the interface definition [20, 50, 52]. There are a number of
+different surface definitions, which include the van der Waals surface, the solvent excluded surface and the
+solvent accessible surface. These surface definitions have found many successful applications in biomolecular
+modeling [18,21,32,49]. However, these predetermined interfaces are ad hoc partitions and thus either non-
+negligibly overestimate or underestimate the solvation free energies [52]. Moreover, none of them takes into
+account the minimization of interfacial free energies during the equilibrium solvation.
+Variational implicit solvation models (VISM) stand out as a successful approach to compute the disposition
+of an interface separating the solute and the solvent [4,10,12,17,19,56,61]. In a VISM, the desired interface
+profile is obtained by optimizing a solvation energy functional coupling the discrete description of the solute
+and the continuum description of the solvent in addition to polar and non-polar interactions. However, a
+sharp-interface VISM is incapable to describe the randomness of a solute-solvent boundary, which is due
+to atom vibrations or thermodynamic fluctuations. Indeed, ions, solute and solvent molecules are not rigid
+2020 Mathematics Subject Classification. Primary: 49Q10; Secondary: 35J20; 92C40.
+Key words and phrases. Biomolecule solvation, Poisson-Boltzmann, Variational implicit solvation model, Ensemble average
+solvation energy.
+†Corresponding author.
+∗Department of Mathematics, The University of Alabama, Tuscaloosa, AL, USA. yshao8@ua.edu.
+∗∗Department of Mathematical Sciences, Georgia Southern University, GA, USA. zchen@georgiasouthern.edu.
+∗∗∗Department of Mathematics, The University of Alabama, Tuscaloosa, AL, USA. szhao@ua.edu.
+1
+arXiv:2301.08560v1  [physics.bio-ph]  6 Jan 2023
+
+2
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+objects and they undergo small or large conformational changes in real applications. Disregarding this can
+cause severe errors in predictions of solvation free energies [42]. This calls for the need of a new notion of
+solvent-solute interface, which is known as the diffuse interface.
+Arguably, the most extensively used diffuse interface models are: (1) the phase-field based models (PF-
+BVISM), cf. [19, 37, 59]; and (2) the geometric flow based models (GFBVISM), cf. [12, 22, 53–55, 58]. For
+a solute-solvent system contained in a region Ω ⊂ R3, a typical PFBVISM is a functional defined by a
+phase-field variable u : Ω → R, which plays the role of a solute-solvent interface. The Allen-Cahn functional
+�
+Ω
+�
+ξ
+2|∇u|2 + 1
+ξW(u)
+�
+dx, where W(x) = 18x2(1 − x)2, is used because it Γ-converges to the area of a sharp
+interface as ξ → 0. The diffuse interface in GFBVISM is defined in terms of a transition parameter u : Ω → R,
+which takes value 1 in the solute and 0 in the solvent region. The solute-solvent surface area is replaced
+by
+�
+Ω |∇u| dx. By the coarea formula, this integral approximates the mean surface area of the level sets of
+a Lipschitz continuous function u, cf. [54]. Numerical simulations show that these diffuse-interface models
+can improve the efficiency and accuracy of solvation energy computation [15,37,53,55,57,58]. However, on
+a theoretical level, the diffuse interfaces in use were created in an ad hoc way and lack rigorous justifications
+of their physical meanings. Hence, a persuasive physical interpretation of the solvation energies predicted
+by those diffuse-interface models is still absent.
+The key to an effective diffuse interface definition is to understand the source of inaccuracy in sharp-
+interface VISMs. A solute-solvent interface is determined by both the solute molecular structure and the
+surrounding solvent configuration. Due to thermodynamic fluctuations, when a fixed solute molecular struc-
+ture being considered, solvent molecules and ions can still adopt different configurations [3], or equivalently,
+from statistical mechanics standpoint, can form various microstates. This implies that the disposition of the
+interface is not unique. On the other hand, experimentally observable quantities are ensemble averaged. Us-
+ing the energy computed from one microstate (even if the one with minimum energy) to predict the averaged
+energy from all microstates is doomed to be inaccurate. Therefore, it is of imminent practical importance
+to develop a solvation model capable of calculating ensemble average solvation energy with thermodynamic
+fluctuations being taken into account.
+It is the first goal of this study to develop a VISM for ensemble average solvation energy. In Section 2,
+we show that the ensemble average of various solvation energy components (e.g. the biomolecular surface
+areas, cavity volumes and electrostatic free energies) can be rigorously derived if the diffuse-interface profile
+u : Ω → [0, 1] is constructed so that u(x) represents the probability of a point x ∈ Ω found in the solute phase
+among all microstates in the grand canonical ensemble under consideration. For the first time in literature,
+the physical meaning of a diffuse interface will be illuminated and in turn the energy predicted by the
+corresponding diffuse-interface model will be justified in this work. It is worthwhile to point out that one of
+the grand challenges of calculating the ensemble average solvation energy is how to determine the Boltzmann
+weight of each microstate, without which an effective sampling of different solvation states is impossible.
+Our new ensemble average VISM (2.19) bypasses the above difficulty by encoding the Boltzmann weight
+information to the argument u and thus is capable of directly capturing the ensemble averaged information.
+The second goal of this work is to discuss the computational models for capturing the global minimum of
+(2.19). Unlike most energy variational models, what plays a central role in many applications of VISMs [13,60]
+is the minimum value of the solvation energy functional (i.e. the solvation energy) but not the dynamical
+processes generated by the functional (e.g. the gradient flow). For example, the calculation of the binding
+affinity for computational drug design [7, 40], which measures how strong a ligand (e.g. drug) binds to a
+biomolecule (e.g. protein), consists of the computation of solvation energies of the protein and ligand separ-
+ately and then as a complex. Unfortunately, the VISMs in use, no matter sharp or diffuse interface, except
+for GFBVISM, all have non-convex structures. Consequently, the corresponding computational models only
+calculate their local minima [19, 37, 45, 59].
+Further challenges arise in our new VISM, which is a total
+variation based model with a two-sided obstacle 0 ≤ u ≤ 1 and a computational domain of complex shape.
+The conventional Euler-Lagrange approach to similar but simpler problems, e.g. Rudin-Osher-Fatemi mod-
+els [46], faces several challenges. First, with the presence of the obstacle, on a heuristic level with sufficiently
+smooth minimizer u and functional, one expects the first variations of (2.19) with respect to u to take the
+form of a variational inequality, or equivalently, of a 1−Laplacian type equation involving a measure sup-
+ported on the coincidence sets {u = 0} and {u = 1}. Unfortunately, both the functional and the minimizer
+fail to enjoy the required smoothness. Second, the computational models of total variation problems are
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+3
+usually studied by certain regularization, e.g. non-parametric minimal surface equations. However, it is
+well known that the solutions of non-parametric minimal surface equations may admit jump discontinuities
+along the boundary unless the boundary satisfies certain geometric conditions [29,41]. Such conditions are
+unrealistic for most biomolecules due to their complex shapes. The possible presence of jump discontinuities
+may become a source of inaccuracy in numerical simulations. In Section 3, we will develop a novel approach
+to regularize (2.19), which enables us to relax the two-sided obstacle and avoid boundary jump discontinuity.
+Most importantly, the first variations of the regularized problems can be rigorously derived, which generates
+a system of elliptic differential equations that has a unique solution – the global minimizer of the regularized
+problem. This paves the way for the numerical implementations of our new ensemble average VISM, which
+will be investigated in several subsequent papers.
+The rest of this paper is organized as follows. In Section 2, we develop a new VISM for the ensemble average
+solvation energy. In Section 3, we study regularizations of our new ensemble average energy functional and
+conduct variational analysis of the regularized problems. In Section 4, we compare our new model with some
+existing diffuse-interface VISMs. Some technical lemmas are collected in Appendix A. In Appendix B, we
+provide some justifications for the robustness of our new models. Finally, in Section 5, we draw conclusions.
+2. Ensemble Averaged Solvation Energy
+List of Notations: Given any open sets U and Ω, U ⋐ Ω means that U ⊂ Ω and U stands for the closure
+of U. We denote by LN and HN−1 the N−dimensional Lebesgue measure and the (N − 1)−dimensional
+Hausdorff measure, respectively. For any 1 ≤ p ≤ ∞, p′ is the H¨older conjugate of p. The phrase l.s.c is the
+abbreviation of lower semi-continuous.
+2.1. A Sharp Interface VISM. We consider a solute-solvent system with a fixed biomolecular structure
+contained in a bounded Lipschitz domain Ω ⊆ R3 using the grand canonical ensemble. Hence, the chemical
+potential, temperature and volume of the system are kept constant. Suppose that the solute atoms are
+centered at x1, · · · , xNm and there are Nc ion species in Ω. Assume that the system undergoes K microstates,
+labelled by k = 1, 2, · · · , K.
+Microstate k occurs with a probability pk, in which the solute occupies a
+Caccioppoli subset Dk ⋐ Ω, or equivalently, Uk = Ω \ Dk is the solvent region. See Figure 1(A) for an
+illustration. By our assumption, �
+k∈K pk = 1. For notational brevity, we put K = {1, 2, · · · , K}.
+(a)
+(b)
+Figure 1. (A) Illustration of the microstate k: Dk is the solute region; Uk is the solvent region; (B)
+Domain decomposition for a grand canonical ensemble:
+Ωi is the region occupied by the solute in all
+microstates; Ωs denotes the region occupied by the solvent in all microstates; Ωt denotes the transition
+region where 0 ≤ u ≤ 1.
+We define the sample space S to be the set of all distributions (of ions and solvent molecules) in the grand
+canonical ensemble. Then S = �
+k∈K
+Sk, where Sk is the sample space of all distributions in microstate k. The
+following random variables will be used throughout.
+• Z : S → K indicates the microstate that a distribution belongs to.
+• Cj(x) : S → R+ is the (number) concentration of the j-th ion species at x ∈ Ω in a given distribution.
+
+Solvent
+Z
+Soluteu=0
+>n>0
+Solvent
+2
+Solute
+o4
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+In microstate k, for every fixed x ∈ Ω, the (number) concentration of the j-th ion species at x can be
+represented by
+ck
+j (x) = E(Cj(x)|Z = k).
+Here E(Cj(x)|Z = k) represents the conditional expectation of the random variable Cj(x) (with fixed x)
+given Z = k. In this article, we treat the solute atoms as hard spheres. More precisely, we consider the atom
+centered at xi, i = 1, · · · , Nm, as a sphere of radius σi > 0, i.e., B(xi, σi), for which the solvent molecules
+and the ions cannot enter. On the other hand, the solvent and ion concentrations are the same as their bulk
+concentrations in regions sufficiently far away from the solute. As a consequence, such regions cannot be
+contained in the solute phase in any microstate. Based on these observations, we may assume that there are
+two open Lipschitz subsets, Ωi and Ωe, of Ω with �Nm
+i=1 B(xi, σi) ⊂ Ωi ⋐ Ω \ Ωe and ∂Ω ⊂ ∂Ωe such that
+Ωi ⊂ Dk ⊂ Ω \ Ωe.
+(2.1)
+By Assumption (2.1), all ion species are located outside Ωi. Let Ωt := Ω \
+�
+Ωi ∪ Ωe
+�
+be the transition region
+in microstate k. In addition, we define Σ1 = ∂Ωi and Σ0 = ∂Ωe \ ∂Ω. See Figure 1(B) for an illustration.
+The hydrophobicity of the amino acids in the biomolecule varies from position to position. To account
+for this phenomenon, we introduce a positive variable surface tension function θ ∈ C1(Ωt). Without loss of
+generality, we may extend θ to be a function in C1(Ω), still denoted by θ, such that
+θ0 ≤ θ(x) ≤ θ1,
+x ∈ Ω
+for some constants 0 < θ0 < θ1. By [8, Lemma 1]
+�
+Ω
+θ(x)d|Df(x)| = sup
+��
+Ω
+f(x)∇ · (θ(x)φ(x)) dx : φ ∈ C1
+c (Ω; R3), ∥φ∥∞ ≤ 1
+�
+.
+It is clear that, for any f ∈ BV (Ω) with f ≡ 0 in Ωe and f ≡ 1 in Ωi, the value of
+�
+Ω θ(x)d|Df(x)| is
+independent of how θ is extended outside Ωt.
+As proposed in [22,23], the solvation free energy in microstate k predicted by a sharp-interface VISM is
+the minimum value of the following energy functional
+E(χDk) = Inp(χDk) + Ip(χDk, ψ),
+where ψ : Ω → R is the electrostatic potential. The two components Inp and Ip are termed the nonpolar and
+polar portion of the solvation energy, respectively. Σ = ∂Dk is considered as the solute-solvent interface. For
+every fixed Dk, ψ = ψχDk is chosen to maximize Ip(χDk, ψ) among all ψ taking a predetermined Dirichlet
+boundary value ψD on ∂Ω. It seems to be a little counterintuitive that ψ maximizes the polar energy instead
+of minimizing it. An explanation of this fact can be found in [9] for the case ψD = 0.
+The nonpolar solvation energy consists of three parts:
+Inp(χDk) =
+�
+Ω
+θd|DχDk| + PhVol(Dk) +
+�
+Uk
+ρsU vdW(x) dx.
+When θ ≡ γ for some constant γ > 0, the first term reduces to γPer(Dk; Ω) with Per(Dk; Ω) being the
+perimeter (in Ω) of the biomolecule region Dk. This term measures the disruption of intermolecular and/or
+intramolecular bonds that occurs when a surface is created. In addition, Vol(Dk) represents the volume of
+Dk; Ph is the (constant) hydrodynamic pressure. Therefore, PhVol(Dk) is the mechanical work of creating
+the biomolecular size vacuum in the solvent. In the last integral, ρs is the (constant) solvent bulk density;
+and U vdW represents the Lennard-Jones potential [52]; as such U vdW ∈ C∞(Ω \ {x1, · · · , xNm}).
+Currently, one of the most widely-used polar solvation models is the Poisson-Boltzmann (PB) theory
+[1,26,27,31,33]. In the framework of classical PB theory, the polar energy is expressed as
+Ip(χDk, ψ) =
+�
+Dk
+�
+ρ(x)ψ(x) − ϵp
+2 |∇ψ(x)|2�
+dx −
+�
+Uk
+�
+�ϵs
+2 |∇ψ(x)|2 + β−1
+Nc
+�
+j=1
+c∞
+j (e−βqjψ(x) − 1)
+�
+� dx, (2.2)
+where ρ is an L∞-approximation of the solute partial charges supported in �Nm
+i=1 B(xi, σi). ϵp and ϵs are the
+dielectric constants of the solute and the solvent, respectively. Usually, ϵp ≈ 1 for the protein and ϵs ≈ 80
+for the water. qj is the charge of ion species j, j = 1, 2, · · · , Nc, and β = 1/kBT, where kB is the Boltzmann
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+5
+constant, T is the (constant) absolute temperature. c∞
+j
+is the (constant) bulk concentration of the j−th
+ionic species. For notational brevity, we put
+B(s) = β−1
+�
+�
+Nc
+�
+j=1
+c∞
+j
+�
+e−βsqj − 1
+�
+�
+� .
+In addition, we assume the charge neutrality condition
+Nc
+�
+j=1
+c∞
+j qj = 0.
+(2.3)
+It is important to observe that B(0) = 0 and, by (2.3), B′(0) = 0 and B′(±∞) = ±∞. Further, B′′(s) > 0.
+We thus conclude that B(0) = min
+s∈RB(s) and B is strictly convex.
+Remark 2.1. A closer look into the derivation of (2.2) will help us to understand the physical meanings of ψ
+and Ip. In the PB theory, in every microstate k, the mean electrostatic potential ψ (among all distributions
+in microstate k) satisfies the fundamental equation of electrostatics, the Poisson equation:
+−∇ · [(ϵχDk + ϵsχUk)∇ψ] = ρ +
+Nc
+�
+j=1
+qjck
+j
+in A.
+(2.4)
+The average (number) concentration, ck
+j , of the j-th ion speices in microstate k, can be derived by minimizing
+the Helmholtz free energy for the fixed solute-solvent interface ∂Dk.
+The Helmholtz free energy H in
+microstate k is expressed as Hk = Ek − TSk, cf. [26, 36], where E is the internal energy, S is the entropy.
+The subscript k is to indicate that the corresponding quantity is defined in microstate k. Here
+Ek =
+�
+Dk
+�
+ρψ − ϵp
+2 |∇ψ|2�
+dx +
+�
+Uk
+�
+�
+Nc
+�
+j=1
+qjck
+j ψ − ϵs
+2 |∇ψ|2 −
+Nc
+�
+j=1
+µjck
+j
+�
+� dx,
+(2.5)
+where µj is the chemical potential of the j-th ion species so that c∞
+j = eβµj, and
+−TSk = β−1
+�
+Uk
+Nc
+�
+j=1
+ck
+j
+�
+ln(ck
+j ) − 1
+�
+dx.
+Hk is an “averaged” quantity because Ek is obtained by averaging the internal energy over all distributions in
+microstate k. Setting the first variation of Hk with respect to ck
+j to be zero gives the Boltzmann distribution
+ck
+j (x) = χUk(x)c∞
+j e−βqjψ(x).
+(2.6)
+Plugging (2.6) back into the expression of Hk yields
+Hk =
+�
+Dk
+�
+ρ(x)ψ(x) − ϵp
+2 |∇ψ(x)|2�
+dx −
+�
+Uk
+�
+�ϵs
+2 |∇ψ(x)|2 + β−1
+Nc
+�
+j=1
+c∞
+j e−βqjψ(x)
+�
+� dx.
+(2.7)
+Since the polar energy equals zero when ψ vanishes everywhere, following [48], a constant term
+β−1
+�
+Uk
+Nc
+�
+j=1
+c∞
+j dx
+(2.8)
+should be added to (2.7), which yields the polar energy (2.2) in microstate k.
+Note that
+Nc
+�
+j=1
+qjck
+j =
+−χUkB′(ψ). Plugging this expression into (2.4) shows that ψ solves the PB equation:
+∇ · ((ϵpχDk + ϵsχUk)∇ψ) − χUkB′(ψ) + ρ = 0
+in Ω
+in microstate k, in the admissible set
+A = {ψ ∈ H1(Ω) : ψ|∂Ω = ψD}
+for some ψD ∈ W 1,∞(Ω).
+(2.9)
+Consequently, ψ maximizes Ip(χDk, ·) in A.
+
+6
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+To sum up, in the framework of the PB theory, when deriving ensemble average polar solvation energy,
+one should use the mean electrostatic potential ψ among all microstates. Consequently, instead of directly
+ensemble averaging Ip, one should optimize the Helmholtz free energy, which is obtained by averaging the
+internal energy among all micrstates.
+2.2. Modeling of Ensemble Average Solvation Energy.
+2.2.1. Ensemble Average Bulk Energies. The argument we use to define the ensemble average solvation
+energy functional is
+u =
+�
+k∈K
+pkχDk.
+As such, u(x) represents the probability of x ∈ Ω found in the solute phase among all microstates. Figure 1(B)
+shows the range of u in different regions. The definition of u enforces the following physical constraints
+u(x) ∈ [0, 1]
+for a.a. x ∈ Ω
+(2.10)
+and
+u = 1
+a.e. in Ωi
+and
+u = 0
+a.e. in Ωe.
+(2.11)
+Then the admissible set for u is defined as
+X = {u ∈ BV (Ω) : u satisfies Constraints (2.10) and (2.11)}.
+The first step of constructing the ensemble average solvation energy functional is to derive formulas for
+ensemble average bulk energy contributions. Assume f ∈ L1(Ω) is the energy density function of some bulk
+energy F, that is, the energy F stored in a region E ⊂ Ω equals
+�
+E f(x) dx.
+Proposition 2.2. The ensemble average bulk energies can be computed as follows
+⟨Fi⟩ :=
+�
+k∈K
+pk
+�
+Dk
+f dx =
+�
+Ω
+uf dx
+and
+⟨Fe⟩ :=
+�
+k∈K
+pk
+�
+Uk
+f dx =
+�
+Ω
+(1 − u)f dx.
+Proof. The proof is straightforward. Indeed, we will only check the equality for ⟨Fi⟩.
+⟨Fi⟩ =
+�
+k∈K
+pk
+�
+Dk
+f dx =
+�
+Ω
+�
+k∈K
+pkχDkf dx =
+�
+Ω
+uf dx.
+□
+2.2.2. Ensemble Average Polar Energy. Following the discussion in Remark 2.1, in the classic PB theory,
+we will use the mean electrostatic potential ψ among all possible distributions (in all microstates) to derive
+the “average” polar energy. Let cj be the mean ion concentration of the j-th ion species among all possible
+distributions (in all microstates), i.e. cj(x) = E(Cj(x)). Then
+cj(x) = E[E(Cj(x)|Z = k)] =
+�
+k∈K
+pkck
+j (x).
+(2.12)
+Because
+E[ϵpχDk(x) + ϵsχUk(x)] = u(x)ϵp + (1 − u(x))ϵs =: ϵ(u)(x),
+ϵ(u) can be regarded as the “mean” dielectric coefficient. Now the PB theory suggests that ψ ∈ A solves
+−∇ · [ϵ(u)∇ψ] = ρ +
+Nc
+�
+j=1
+qjcj
+in Ω.
+To derive the Boltzmann distribution that gives cj, we first compute the ensemble average of E, cf. (2.5),
+by using Proposition 2.2 and (2.12)
+⟨E⟩ =
+�
+k∈K
+pkEk =
+�
+Ω
+�
+�ρψ +
+Nc
+�
+j=1
+qjcjψ − ϵ(u)
+2 |∇ψ|2 −
+Nc
+�
+j=1
+µjcj
+�
+� dx.
+However, the entropy cannot be ensemble averaged by using Sk. Instead, by the definition of entropy
+−TS = β−1
+�
+{u<1}
+Nc
+�
+j=1
+cj [ln(cj) − 1] dx.
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+7
+The domain of integration {u < 1} is due to the fact that cj vanishes identically in {u = 1}. Setting the
+first variation of the Helmholtz free energy H = ⟨E⟩ − ST with respect to cj to be zero yields
+cj = χ{u<1}c∞
+j e−βqjψ.
+(2.13)
+After plugging (2.13) into the expression of H, as in (2.8), the constant term
+β−1
+�
+Ω
+χ{u<1}
+Nc
+�
+j=1
+c∞
+j dx
+(2.14)
+needs to be added to H to adjust the reference state of the zero energy in the grand canonical ensemble
+under consideration. Finally, we arrive at ensemble average polar energy
+Ip(u, ψ) = H + β−1
+�
+Ω
+χ{u<1}
+Nc
+�
+j=1
+c∞
+j dx =
+�
+Ω
+�
+ρψ − ϵ(u)
+2 |∇ψ|2 − χ{u<1}B(ψ)
+�
+dx.
+(2.15)
+On the other hand, replacing cj in (2.4) by (2.13) shows that ψ ∈ A solves
+∇ · [ϵ(u)∇ψ] − χ{u<1}B′(ψ) + ρ = 0
+in Ω.
+(2.16)
+Hence, ψ maximizes Ip(u, ·) in A for any fixed u ∈ X.
+Remark 2.3. Although, for every fixed j, there can be multiple choices of ck
+j that minimize H, any such
+choice gives rise to (2.13) by means of (2.12). To see this, we set the first variation of H with respect to ck
+j
+to be zero and infer that cj = c∞
+j e−βqjψ in Uk. Going through all k, one readily get (2.13).
+2.2.3. Ensemble Average Interfacial Energies. Based on Formulation (2.15), one can define
+L(u, ψu) = ⟨Inp(χDk)⟩ + Ip(u, ψu),
+where ψu maximizes Ip(u, ·) in A. It only remains to calculate the ensemble average of interfacial energy
+contributions. Before doing that, we will first state a technical lemma.
+Lemma 2.4. Let {Dk}k∈K be a family of Caccioppoli sets with Dk ⋐ Ω and pk ∈ [0, 1] with �
+k∈K pk = 1.
+Then for each ε > 0, there exists another family { �Dk}k∈K of Caccioppoli sets satisfying �Dk ⋐ Ω and
+H2(∂∗ �Dk ∩ ∂∗ �Dj) = 0,
+∀k, j ∈ K, k ̸= j,
+(2.17)
+with ∂∗D being the reduced boundary of a Caccioppoli set D, such that
+|L(u, ψu) − L(�u, ψ�u)| < ε,
+u =
+�
+k∈K
+pkχDk and �u =
+�
+k∈K
+pkχ �
+Dk.
+Here, for every v ∈ X, ψv maximizes Ip(v, ·) in A.
+Proof. In view of Lemma A.2, it suffices to construct a family of Caccioppoli sets {Dk,j}∞
+j=1 satisfying
+Assumption (2.17) such that
+lim
+n→∞ ∥χDk − χDk,n∥1 = 0,
+lim
+n→∞
+�
+Ω
+θd|DχDk,n| =
+�
+Ω
+θd|DχDk|.
+(2.18)
+Following the proof of Lemma A.3, we can show that there exists a family of smooth functions {fk,n}∞
+n=1
+such that 0 ≤ fk,j ≤ 1 a.e. in Ω and
+lim
+j→∞ ∥χDk − fk,j∥1 = 0,
+lim
+j→∞
+�
+Ω
+θd|Dfk,j| =
+�
+Ω
+θd|DχDk|.
+By the Sard’s Theorem, there exists some S ⊂ (0, 1) with L1((0, 1) \ S) = 0 such that, for all t ∈ S, the
+super-level set Et
+k,j = {fk,j > t} has a smooth boundary. The coarea formula implies that
+�
+Ω
+θd|DχDk| = lim
+j→∞
+�
+Ω
+θd|Dfk,j| = lim
+j→∞
+� 1
+0
+�
+Ω
+θd|DχEt
+k,j| dt ≥
+� 1
+0
+lim inf
+j→∞
+�
+Ω
+θd|DχEt
+k,j| dt.
+Therefore, for some t ∈ S,
+lim inf
+j→∞
+�
+Ω
+θd|DχEt
+k,j| ≤
+�
+Ω
+θd|DχDk|.
+
+8
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+Pick the subsequence {jn}∞
+n=1 such that
+lim inf
+j→∞
+�
+Ω
+θd|DχEt
+k,j| = lim
+n→∞
+�
+Ω
+θd|DχEt
+k,jn |.
+On the other hand, we can infer from the Chebyshev’s Theorem that
+L3(Et
+k,jn \ Dk) ≤ 1
+t ∥fk,jn − χDk∥1,
+L3(Dk \ Et
+k,jn) ≤
+1
+1 − t∥fk,jn − χDk∥1.
+This implies that
+lim
+n→∞ ∥χEt
+k,jn − χDk∥1 = 0.
+Therefore, it follows from [8, Corollary 1] that �Dk,n = Et
+k,jn satisfies (2.18) with Dk,n replaced by �Dk,n.
+Assume that H2(∂χ �
+Dk,n ∩ ∂χ �
+Dj,n) > 0 for some k, j ∈ K and k ̸= j. Since ∂ �Dk,n is C2, there exists
+some a > 0 such that ∂ �Dk,n has a tubular neighborhood Ba(∂ �Dk,n) of width a > 0, cf. [28, Exercise 2.11]
+and [34, Remark 3.1]. Denote by ν the outward unit normal of �Dk,n pointing into Ω \ �Dk,n. Then the map
+defined by
+Λ : ∂ �Dk,n × (−a, a) → R3 : (x, r) �→ x + rν(x),
+is a C1-diffeomorphism. Let Γr := Λ(∂ �Dk,n, r). Then, for every i ∈ K, there are at most countably many
+r ∈ (−a, a) such that H2(Γr ∩ ∂χ �
+Di,n) > 0. Hence we can find r ∈ (−a, a) sufficiently close to 0 such that
+H2(Γr ∩ ∂χ �
+Di,n) = 0,
+∀i ∈ K
+and Γr ⊂ Ωt and
+���χDk,n − χ �
+Dk,n
+���
+1 +
+����
+�
+Ω
+θd|DχDk,n| −
+�
+Ω
+θd|Dχ �
+Dk,n|
+���� < 1/n,
+where Dk,n is the region enclosed by Γr. Modifying all �Dk,n, k ∈ K, in such a way yields a family of smooth
+sets {Dk,n}k∈K satisfying Assumption (2.17) and (2.18).
+□
+The above lemma tells us that, for any grand canonical ensemble, we can slightly modify the solute regions
+{Dk}k∈K to fulfil (2.17) so that the changes in the corresponding solvation energy is “infinitesimally” small.
+Hence, we can always assume that {Dk}k∈K satisfies (2.17).
+Proposition 2.5. Assume that {Dk}k∈K satisfies (2.17). Then
+�
+Ω
+θ d|Du| =
+�
+k∈K
+pk
+�
+Ω
+θ d|DχEk|.
+Proof. By the De Giorgi’s structure theorem, cf. [24, Theorem 5.7.2], χDk are 2-rectifiable, i.e. there exist
+Borel sets Fk and C1-functions gk,n : Uk,n → R3, Uk,n ⊂ R2 compact, such that ∥∂Dk∥(Fk) = 0 and
+∂∗Dk = Fk ∪
+∞
+�
+n=1
+gk,n(Uk,n).
+Pick arbitrary ε > 0. For every k ∈ K, we can find Nk = Nk(ε) such that
+∥∂Dk∥(Ω ∩
+∞
+�
+n=Nk+1
+gk,n(Uk,n)) ≤
+ε
+Kθ1pk
+.
+Recall K = |K|. Therefore, we obtain compact sets
+Gk,ε :=
+Nk(ε)
+�
+n=1
+gk,n(Uk,n),
+k ∈ K,
+and
+Gε :=
+�
+k∈K
+Gk,ε.
+By the definition of the reduced boundary, the unit normal ν exists everywhere on Gε. By the Urysohn’s
+Lemma, there exists a continuous function φ : R3 → R3 such that φ|Gε = ν. Restricting φ on Ω and applying
+Stone-Weierstrass, we can find a smooth function φε : Ω :→ R3 such that
+∥φε − φ∥L∞(Gε) < ε.
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+9
+Then, in a neighborhood H ⋐ Ω of Gε, we have |φε| > 1/2. Pick h ∈ C∞
+0 (Ω; [0, 1]) in such that h ≡ 1 in H.
+Setting ψε(x) = h(x) φε(x)
+|φε(x)|, it is an easy task to check that
+1 ≥ ψε(x) · ν(x) ≥ 1 − ε
+1 + ε,
+x ∈ Gε.
+By [8, Lemma 1], we can estimate
+�
+Ω
+θ d|Du| ≥
+�
+Ω
+(θψε) · dDu =
+�
+k∈K
+pk
+�
+Ω
+θψε · DχDk dx =
+�
+k∈K
+pk
+�
+Gk,ε
+θψε · DχDk dx − ε
+≥
+�
+k∈K
+pk(1 − ε)
+1 + ε
+�
+Gk,ε
+θ d|DχDk| − ε
+≥
+�
+k∈K
+pk(1 − ε)
+1 + ε
+��
+Ω
+θ d|DχDk| −
+�
+Ω\Gk,ε
+θ d|DχDk|
+�
+− ε
+=
+�
+k∈K
+pk(1 − ε)
+1 + ε
+�
+Ω
+θ d|DχDk| − 2ε − ε2
+1 + ε .
+Since ε is arbitrary, we have
+�
+Ω
+θ d|Du| ≥
+�
+k∈K
+pk
+�
+Ω
+θ d|DχDk|.
+The inverse inequality is obvious. We have thus proved the assertion.
+□
+2.2.4. Total Energy Functional. Based on Propositions 2.2 and 2.5, the ensemble average nonpolar energy
+is given by
+Inp(u) := ⟨Inp(χDk)⟩ =
+�
+Ω
+θd|Du| +
+�
+Ω
+�
+Phu + ρs(1 − u)U vdW�
+dx.
+Using Formulation (2.15) for the polar energy, we can define the ensemble average total solvation energy as
+the minimum value of
+E(u) =
+�
+Ω
+θd|Du| +
+�
+Ω
+�
+Phu + ρs(1 − u)U vdW�
+dx +
+�
+Ω
+�
+ρψ − ϵ(u)
+2 |∇ψ|2 − χ{u<1}B(ψ)
+�
+dx
+(2.19)
+in X and ψ = ψu is determined via the generalized PB equation (2.16); or equivalently, we seek the value of
+L(u, ψ) = Inp(u) + Ip(u, ψ)
+evaluated at its saddle points in X × A.
+Note that Constraint (2.11) is defined in terms of Ωi and Ωe. In Appendix B, we will justify the robustness
+of (2.19) by showing that its minimum value depends continuously on Ωi and Ωe in a proper topology.
+2.3. Analysis of Ensemble Average Solvation Energy.
+Theorem 2.6. E has a global minimizer in X.
+Proof. We infer from Lemma A.1 that
+Ip(u, ψu) ≥ −ϵs∥ψu∥2
+H1 − (∥B(ψu)∥∞ + ∥ρ∥∞∥ψu∥∞) Vol(Ω) ≥ C
+(2.20)
+for some C independent of u ∈ X. Here and in the sequel, for any u ∈ X, ψu always denotes the solution of
+(2.16). Therefore, E is bounded from below and we can pick up a minimizing sequence {˜un}∞
+n=1 ⊂ X of E.
+However, E is not l.s.c. in X. To prove the existence of a minimizer, we will use a relaxation technique. For
+m ∈ N, we define
+Lm(u, ψ) = Inp(u) +
+�
+Ω
+�
+ρψ − ϵ(u)
+2 |∇ψ|2 − (1 − u)1/(2m+1)B(ψ)
+�
+dx
+and
+Em(u) = Lm(u, ψu,m),
+where ψu,m ∈ A solves
+∇ · [ϵ(u)∇ψ] − (1 − u)1/(2m+1)B′(ψ) + ρ = 0
+in Ω.
+
+10
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+Note that ψu,m is the unique maximizer of Lm(u, ·) in A. Easy computations show that Em is strictly convex
+and l.s.c. in X with respect to convergence in L1(Ω) in view of [8, Corollary 1]. By the direct method of
+calculus of variation, Em has a unique minimizer um in X. Set
+M = inf
+u∈X E(u),
+Mm = Em(um).
+Claim 1:
+lim
+m→∞ Mm = M.
+Proof of Claim 1. We first show that Mm is monotonically decreasing and Mm ≥ M. Indeed,
+Mm ≥ Lm(um, ψum) ≥ L(um, ψum) ≥ M,
+where ψum is the solution of (3.1) with u = um, and similarly
+Mm ≥ Lm(um, ψum+1,m+1) ≥ Lm+1(um, ψum+1,m+1) ≥ Mm+1.
+Given any ε > 0, for sufficiently large n
+M ≤ E(˜un) ≤ M + ε.
+On the other hand, since, for any fixed u ∈ X,
+lim
+m→∞ ∥(1 − u)1/(2m+1) − χ{u<1}∥1 = 0, Lemma A.2 implies
+that
+M ≤ Em(˜un) ≤ M + 2ε
+(2.21)
+for sufficiently large n and m. The arbitrariness of ε shows that lim
+m→∞ Mm = M.
+■
+(2.21) and Lemma A.1 imply that ∥um∥BV is uniformly bounded and, by [24, Theorem 5.2.3.4], there
+exists a subsequence of {um}∞
+m=1, not relabelled, such that as m → ∞
+um → u0
+in L1(Ω)
+for some u0 ∈ X. Then for any m ∈ N, by [8, Lemma 2]
+Mm ≥ Lm(um, ψu0) ≥ L(um, ψu0) ≥ L(u0, ψu0) ≥ M.
+In view of Claim 1, pushing m → ∞ shows that u0 is a minimizer of E.
+□
+Remark 2.7. Note that the convexity of E implies that any local minimizer of E must be global.
+3. A regularization approach to solvation energy calculatiion
+3.1. Regularization by p-energy. Regularization is a popular approach in the derivation of computational
+models of non-differentiable functionals like E. Here we will develop a p-energy regularization approach based
+on our previous work [14, 47]. In particular, this approach enables us to relax the two-sided obstacle, i.e.
+Constraint (2.10), in the variational analysis.
+In the rest of this section, we will assume U vdW ∈ C∞(Ω \ �Nm
+i=1 B(xi, σi), R−). This can be realized by
+taking U vdW as the attractive part of Lennard-Jones potential [52]. Note that this assumption is reasonable
+in the solvation analysis of real-world macromolecules since u ≡ 1 in Ωi. The L-J potential can be divided
+into attractive and repulsive parts in different ways. For instance, we can take a Weeks-Chandler-Andersen
+(WCA) decomposition based on the original WCA theory [35].
+Define pn =
+2n
+2n−1 for n ∈ N. We are interested in sufficiently large n so that pn ∈ (1, ϵs/(ϵs − ϵp)). Denote
+the set of all such n by N. Let
+Inp;n(u) = γ
+�
+Ω
+|∇u|pn dx +
+�
+Ω
+�
+Phupn + ρs(1 − upn)U vdW�
+dx.
+For the polar portion, due to the extra non-differentiable term χ{u<1}, we will consider the regularization of
+Em in view of Claim 1 in the proof of Theorem 2.6. More precisely, define
+Ip;m,n(u, ψ) =
+�
+Ω
+�
+ρψ − 1
+2ϵn(u)|∇ψ|2 − (pn − upn)1/(2m+1)B(ψ)
+�
+dx,
+where ϵn(u) = ϵpupn + ϵs(1 − upn). We seek to minimize
+Em,n(u) = Inp;n(u) + Ip;m,n(u, ψu;m,n),
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+11
+in the admissible sets
+Xn = {u ∈ W 1,pn(Ω) : |u|pn ≤ pn a.e. in Ω
+and u satisfies Constraint (2.11)},
+where ψu;m,n ∈ A solves
+∇ · (ϵn(u)∇ψ) − (pn − upn)1/(2m+1)B′(ψ) + ρ = 0
+in Ω.
+(3.1)
+Define
+Lm,n(u, ψ) = Inp;n(u) + Ip;m,n(u, ψ).
+Then by Lemma A.1, it is not hard to check that u is a global minimizer of Em,n in Xn iff (u, ψu;m,n) is a
+saddle point of Lm,n in Xn × A, where ψu;m,n solves (3.1). See [14, Theorem 6.3] for a related problem.
+Theorem 3.1. For every n ∈ N and m ∈ N, Em,n has a unique minimizer in Xn, which actually belongs to
+X.
+Proof. To show the lower semi-continuity of Em,n in Xn, we first observe that
+Qn(w) =
+�
+Ω
+(θ|∇w|pn + Phupn) dx,
+w ∈ Wn := {w ∈ W 1,pn(Ω) : w satisfies Constraint (2.11)},
+is an equivalent norm of Wn. Therefore, Qn is weakly l.s.c. in Wn, which further implies that Em,n is weakly
+l.s.c. in Xn in view of Lemma A.2. The existence and uniqueness of a minimizer of Em,n can be proved by
+the direct method of calculus of variation and the strict convexity of Em,n.
+It remains to show that the minimizer umin;m,n of Em,n in Xn indeed belongs to X. Let ψmin;m,n be the
+solution to (3.1) with u = umin;m,n. If L3({umin;m,n > 1} ∪ {umin;m,n < 0}) > 0, define
+¯umin;m,n(x) =
+�
+�
+�
+�
+�
+1,
+if umin;m,n(x) > 1,
+0,
+if umin;m,n(x) < 0,
+umin;m,n(x),
+elsewhere.
+Then ¯umin;m,n ∈ X ∩ Xn; and direct computations show that
+Lm,n(¯umin;m,n, ψmin;m,n) < Lm,n(umin;m,n, ψmin;m,n).
+A contradiction. Hence, umin;m,n ∈ X.
+□
+3.2. Asymptotic behaviour of the regularized energy. When n ∈ N, let umin;m,n be the unique
+minimizer of Em,n in Xn. The following theorem establishes the asymptotic behavior of Em,n(umin;m,n).
+Theorem 3.2. Assume that Σi ∈ C2, i = 0, 1. As n → ∞, umin;m,n converges to a minimizer of E in Lp(Ω)
+for any 1 ≤ p < ∞ and weak∗ in BV (Ω). Moreover, lim
+n→∞ Em,n(umin;m,n) = min
+u∈X Em(u).
+Proof. The constants Ci in this proof are independent of n. First, fix arbitrary v ∈ Xn, we have
+Em,n(umin;m,n) ≤ Em,n(v) ≤
+�
+Ω
+θ|∇v|pn dx + 2PhVol(Ω \ Ωi) −
+�
+Ωt
+ρsU vdW dx + ∥ψv∥∞∥ρ∥∞Vol(Ωi) ≤ C1,
+where ψv ∈ A solves (3.1) with u = v. A similar computation as in (2.20) shows that
+C1 ≥ Em,n(umin;m,n) ≥
+�
+Ω
+θ|∇umin;m,n|pn dx + Ph∥umin;m,n∥pn
+pn +
+�
+Ω\Ωi
+ρsU vdW dx + Ip;m,n(umin;m,n, ψmin;m,n)
+≥
+��
+Ω
+θd|Dumin;m,n|
+�pn ��
+Ω
+θ dx
+�1−pn
++ Ph∥umin;m,n∥pn
+1 (Vol(Ω))1−pn + C2,
+(3.2)
+where ψmin;m,n ∈ A solves (3.1) with u = umin;m,n. We thus infer from (3.2) that
+∥umin;m,n∥W 1,1 = ∥umin;m,n∥BV ≤ C3.
+Then [24, Theorem 5.2.3.4] implies that for any subsequence of {umin;m,n}∞
+k=1, there exists a further sub-
+sequence, not relabelled, converging to some u0 ∈ X in L1(Ω) and weak∗ in BV (Ω). The Riesz-Thorin
+interpolation theorem then implies that umin;m,n → u0 in Lp(Ω) for all p ∈ [1, ∞) as n → ∞. Further, it
+follows from [8, Corollary 1], (3.2) and Lemma A.2 that
+Em(u0) ≤ lim inf
+n→∞ Em,n(umin;m,n).
+
+12
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+On the other hand, for sufficiently large j ∈ N, we define
+wj(x) =
+�
+�
+�
+�
+�
+1,
+x ∈ Ωi;j
+0,
+x ∈ Ωe;j
+u0(x),
+elsewhere,
+where Ωl;j := {x ∈ Ω : dist(x, Ωl) < 1/j} with l ∈ {i, e}. We will show that
+lim sup
+n→∞ Em,n(umin;m,n) ≤ Em(wj).
+(3.3)
+Lemma A.3 implies that we can find a sequence {wj,h}∞
+h=1 such that wj,h ∈ C∞(Ω) ∩ Xn for all n and
+wj,i → wj in L1(Ω)
+and
+�
+Ω
+θd|Dwj,h| →
+�
+Ω
+θd|Dwj|
+as h → ∞.
+Since umin;m,n minimizes Em,n in Xn ⊃ C∞(Ω) ∩ Xn, we have
+Em,n(umin;m,n) ≤ Em,n(wj,h).
+Pushing n → ∞, the dominated convergence theorem implies that
+lim sup
+n→∞ Em,n(umin;m,n) ≤ Em(wj,h).
+Then Lemmas A.2 and A.3 immediately yield (3.3). Now Lemmas A.2 and A.4 imply that
+lim sup
+n→∞ Em,n(umin;m,n) ≤ Em(u0).
+(3.4)
+Let umin be a global minimizer of Em. It is important to notice that the proof of (3.4) actually holds for any
+element of X, in particular umin. Hence
+Em(umin) ≥ lim
+n→∞ Em,n(umin;m,n) = Em(u0) ≥ Em(umin).
+Therefore, u0 is indeed a global minimizer of Em.
+□
+The following conclusion of Theorem 3.2 can be easily obtained in view of Claim 1 in the proof of
+Theorem 2.6.
+Corollary 3.3. Under the conditions of Theorem 3.2,
+lim
+m→∞ lim
+n→∞ Em,n(umin;m,n) = min
+u∈X E(u).
+Remark 3.4. It seems to be more natural to use non-parametric minimal surface type functionals to regularize
+Em. For example, when θ ≡ γ, one may consider the following regularization of (2.19)
+Eε(u) = γ
+�
+Ω
+�
+ε + |∇u|2 dx +
+�
+Ω
+�
+Phupn + ρs(1 − upn)U vdW�
+dx + Ip;m,n(u, ψu)
+with ε > 0, where ψu ∈ A solves (3.1). However, the minimizer of Eε may admit jump discontinuous along
+Σi unless Ωt satisfies certain geometric conditions, e.g. the mean curvature of Σi is large enough. See [29,41]
+for instance. Such geometric conditions are unrealistic for most biomolecules due to their complex shapes.
+The possible presence of jump discontinuities may become a source of inaccuracy in numerical simulations.
+3.3. Critical Points of the regularized energy. Let umin;m,n be the minimizer of Em,n in Xn and
+ψmin;m,n ∈ A be the solution of (3.1) with u = umin;m,n. Since umin;m,n ∈ X, given any φ ∈ C∞
+0 (Ωt), for
+sufficiently small ε > 0, whenever t ∈ (−ε, ε), umin;m,n + tφ ∈ Xn. We thus have
+lim
+t→0
+Lm,n(umin;m,n + tφ, ψmin;m,n) − Lm,n(umin;m,n, ψmin;m,n)
+t
+= 0.
+This implies that umin;m,n solves
+∇ ·
+�
+θ|∇u|pn−2∇u
+�
+− upn−1Vm,n(u, ψ) = 0
+in Ωt
+in the weak sense. Here
+Vm,n(u, ψ) = Ph − ρsU vdW +
+B(ψ)
+(2m + 1)(upn − pn)2m/(2m+1) + ϵs − ϵp
+2
+|∇ψ|2.
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+13
+Combining with (3.1), (umin;m,n, ψmin;m,n) is a weak solution to the following system
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+∇ · (ϵn(u)∇ψ) + (pn − upn)1/(2m+1)
+Nc
+�
+j=1
+c∞
+j qje−βψqj + ρ = 0
+in
+Ω;
+ψ = ψD
+on
+∂Ω;
+∇ ·
+�
+θ|∇u|pn−2∇u
+�
+− upn−1Vm,n(u, ψ) = 0
+in
+Ωt;
+u = 1
+in
+Ωi ∪ Σ1;
+u = 0
+in
+Ωe ∪ Σ0
+(3.5)
+in ˚
+Xn × A, where
+˚
+Xn = {u ∈ W 1,pn(Ω) : |u|pn < pn a.e. in Ω
+and
+u satisfies Constraint (2.11)}.
+We are interested in the case of sufficiently large n and m.
+Theorem 3.5. (3.5) has a unique solution (u, ψ) in ˚
+Xn × A, which actually belongs to X × A.
+Proof. (i) Let Cm,n be the set of all solutions of (3.5) in ˚
+Xn × A. Assume that (u, ψ) ∈ Cm,n. Then
+−∇ ·
+�
+θ|∇u|pn−2∇u
+�
+= −upn−1Vm,n(u, ψ)
+in Ωt
+(3.6)
+in the distributional sense.
+Since ∇ ·
+�
+θ|∇u|pn−2∇u
+�
+∈ W −1,p′
+n(Ωt), it follows that upn−1Vm,n(u, ψ) ∈
+W −1,p′
+n(Ωt). Note that u− := min{u, 0} ∈ W 1,pn
+0
+(Ωt). Multiplying both sides of (3.6) by u− and integrating
+over Ωt yield
+0 ≤
+�
+Ωt
+θ|∇u−|pn dx = −
+�
+Ωt
+|u−|pnVm,n(u, ψ) dx ≤ 0
+because Vm,n(u, ψ) ≥ 0. This shows that u− = 0 a.e. in Ωt and thus 0 ≤ u a.e. in Ωt. For the essential
+upper bound of u, we consider w = 1 − u, which weakly solves
+−∇ ·
+�
+θ|∇w|pn−2∇w
+�
+= (1 − w)pn−1Vm,n(u, ψ)
+in Ωt.
+Following the argument above, one has for w− ∈ W 1,pn
+0
+(Ωt) that
+0 ≤
+�
+Ωt
+θ|∇w−|pn dx =
+�
+Ωt
+(1 − w)pn−1w−Vm,n(u, ψ) dx ≤ 0.
+This implies that w− = 0 a.e. in Ωt and thus u ≤ 1 a.e. in Ωt. Therefore, (u, ψ) ∈ X × A.
+(ii) Suppose that (v, ψv), (u, ψu) ∈ Cm,n satisfy
+Lm,n(v, ψv) < Lm,n(u, ψu).
+Since v − u ∈ W 1,pn
+0
+(Ωt) ∩ L∞(Ωt), we have
+�
+Ωt
+�
+θ|∇u|pn−2∇u · ∇(v − u) + upn−1V (ψu)(v − u)
+�
+dx = 0.
+(3.7)
+By Lemma A.1, it holds that
+Lm,n(v, ψu) ≤ Lm,n(v, ψv) < Lm,n(u, ψu).
+Put h = Lm,n(v, ψu) − Lm,n(u, ψu) < 0. Note that ˚
+Xn is convex in W 1,pn(Ω). Put
+J(t) = (1 − t)u + tv ∈ ˚
+Xn,
+t ∈ [0, 1].
+Then by the convexity of Lm,n(·, ·) in its first argument,
+Lm,n(J(t), ψu) − Lm,n(u, ψu) ≤ (1 − t)Lm,n(u, ψu) + tLm,n(v, ψu) − Lm,n(u, ψu) ≤ th < 0
+for all t ∈ (0, 1). Dividing both sides by t and pushing t → 0+ in the above inequality yield
+pn
+�
+Ωt
+�
+θ|∇u|pn−2∇u · ∇(v − u) + upn−1Vm,n(u, ψu)(v − u)
+�
+dx ≤ h < 0.
+A contradiction to (3.7).
+We thus infer that Lm,n(·, ·) is constant on Cm,n.
+From the uniqueness of a
+minimizer of Em,n in Xn, we infer that (u, ψu) = (v, ψv).
+□
+
+14
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+4. A comparison with GFBVISM
+It is of both theoretical and practical importance to understand the difference between the proposed
+model (2.19) and the existing VISMs. In this section, we will compare (2.19) with a closely related solvation
+model, geometric-flow based VISM (GFBVISM), whose original formulation [11] reads as
+E(2)(u) = Inp(u) + I(2)
+p (u, ψ),
+(4.1)
+where
+I(2)
+p (u, ψ) =
+�
+Ω
+�
+ρψ − ϵ(u)
+2 |∇ψ|2 − (1 − u)B(ψ)
+�
+dx,
+(4.2)
+and ψ ∈ A solves
+∇ · [ϵ(u)∇ψ] − (1 − u)B′(ψ) + ρ = 0
+in Ω.
+(4.3)
+Although (2.19) shares some common feature with GFBVISM, they differ in several fundamental aspects.
+First, (4.1) was introduced in an ad hoc way to create a transition region between the solute and solvent
+without an explanation of the physical meanings of the transition parameter u and the predicted energy.
+Second, Constraints (2.10) and (2.11) are absent in the original formulation of GFBVISM [11]. Without
+these two conditions, GFBVISM may admit non-physical minimizers, e.g. u is trivial or u < 0.
+Third and most importantly, the proposed model corrects the derivation of the ensemble average polar
+energy. Due to Proposition 2.2, one may guess that I(2)
+p
+approximates the ensemble average polar energy.
+However, Formulation (4.2) is questionable in the sense that it is derived from an erroneous “entropy”
+formulation. To see this, on a heuristic level, one can ensemble average the entropy and obtain
+−T⟨S⟩ = −T
+�
+k∈K
+pkSk = β−1 �
+k∈K
+pk
+�
+Ω
+Nc
+�
+j=1
+ck
+j
+�
+ln(ck
+j ) − 1
+�
+dx
+and
+⟨H⟩ := ⟨E⟩ − T⟨S⟩.
+In view of Remark 2.3, we put the first variations of ⟨H⟩ with respect to all ck
+j to be zero. This gives (2.6).
+It follows from (2.12) that
+cj(x) =
+�
+k∈K
+pkck
+j (x) =
+�
+k∈K
+pkχUk(x)ck
+j (x) = (1 − u(x))c∞
+j e−βqjψ(x).
+(4.4)
+Plugging (4.4) into (2.4) yields (4.3). Using the expression (4.4) of cj in ⟨H⟩ and adding a constant term
+β−1 �Nc
+j=1 c∞
+j
+�
+Ω(1 − u)dx to adjust the state of zero energy as in (2.14) give the polar energy formulation
+(4.2). However, from a statistical mechanics point of view, the choice of the “entropy” ⟨S⟩ and “Helmholtz
+free energy” ⟨H⟩ in the above derivation are incorrect. Therefore, the polar energy formulation (2.15) is
+more physical than (4.2).
+5. Conclusion
+Diffuse-interface variational implicit solvation models (VISM) have achieved great success in solvation
+energy calculations. In contrast, on a theoretical level, several questions concerning the diffuse-interface
+VISMs remain open: (1) What is the physical meaning of a diffuse interface?
+(2) What energy does a
+diffuse-interface VISM predict? In this paper, a novel diffuse-interface VISM is introduced and analyzed.
+Based on statistical mechanics and geometric measure theory, we show that the diffuse interface profile u(x)
+represents the probability of a point x ∈ Ω found in the solute phase among all microstates in the grand
+canonical ensemble under consideration and the new VISM is capable of capturing the ensemble average
+solvation energy, the experimentally observable energy in solvation processes.
+The significance of the work is multi-fold. First, it illuminates the physical meaning of a diffuse interface
+in VISM and unveils the relationship between VISM and ensemble average solvation energy. Second, in the
+routine calculation of the ensemble average solvation energy, one needs to carry out molecular dynamics (MD)
+simulations to obtain thousands of solute-solvent configures (snapshots) and perform energy calculations for
+each snapshot.
+By rigorously modeling the impact of conformational changes in the solvent media, the
+proposed model will reproduce the ensemble average solvation energy by means of one diffuse-interface
+configuration, which is expected to be significantly faster than ensemble averaging the energies computed
+from thousands of snapshots. Last but not least, the modeling paradigm in this work seems to be applicable
+to a large variety of multi-scale problems with both interfacial and bulky energy components.
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+15
+A new computational model is proposed to capture the global minimum of the ensemble average VISM.
+The robustness of the model is justified by verifying the continuous dependence of the predicted energy on
+the model constraints. Numerical implementations based on the proposed computational model and further
+theoretical analysis of the new VISM will be conducted in a series of future works.
+Appendix A. Some Technical Lemma
+The following two lemmas can be obtained by following the proofs of [14, Propositions 3.1 and 3.2].
+Lemma A.1. Assume that a, b, c ∈ L∞(Ω) satisfy
+0 < L0 ≤ a ≤ L1,
+0 ≤ b ≤ L2,
+∥c∥∞ ≤ L3
+(A.1)
+for some constants Li. Then the functional
+G(ψ) =
+�
+Ω
+�a
+2|∇ψ|2 + bB(ψ) − cψ
+�
+dx
+has a unique minimizer ψ ∈ A for every ψD ∈ W 1,∞(Ω), c.f. (2.9), or equivalently, ψ weakly solves
+�
+∇ · (a∇ψ) − bB′(ψ) + c = 0
+in
+Ω;
+ψ = ψD
+on
+∂Ω.
+Moreover, for some constant C∞ depending only on Li and ψD
+∥ψ∥H1 + ∥ψ∥∞ ≤ C∞.
+Lemma A.2. Let an, bn, c ∈ L∞(Ω) satisfy (A.1), n = 0, 1, · · · . Assume that ψn is the unique minimizer of
+Gn(ψ) =
+�
+Ω
+�an
+2 |∇ψ|2 + bnB(ψ) − cψ
+�
+dx
+in A for some ψD ∈ W 1,∞(Ω). If an → a0 and bn → b0 in L1(Ω) as n → ∞, then
+ψn → ψ0
+in H1(Ω),
+and
+lim
+n→∞ Gn(ψn) = G0(ψ0).
+Assuming that Σi ∈ C2, i = 0, 1. For sufficiently large j ∈ N, we define
+Ωl;j := {x ∈ Ω : dis(x, Ωl) < 1/j},
+l ∈ {i, e},
+and
+Yj := {u ∈ X : u ≡ 1 in Ωi;j
+and
+u ≡ 0 in Ωe;j}.
+Lemma A.3. For every f ∈ Yj, there exists a sequence {fn}∞
+n=1 ⊂ C∞(Ω) satisfying Constraints (2.10)
+and (2.11) such that as n → ∞
+fn → f in L1(Ω)
+and
+�
+Ω
+θd|Dfn(x)| →
+�
+Ω
+θd|Df(x)|.
+Proof. For any δ > 0, let ηδ be a positive Friedrichs mollifying kernel. For any n ∈ N, we choose εn > 0
+so small that fn := ηεn ∗ f satisfies Constrain (2.11) and ∥fn − f∥1 ≤ 1/n. Constraint (2.10) is obviously
+fulfilled by fn. Thus, lim
+n→∞ ∥fn − f∥1 = 0.
+[8, Corollary 1] implies that
+�
+Ω θd|Df(x)| ≤ lim inf
+n→∞
+�
+Ω θd|Dfn(x)|. Extending f to be identically zero outside
+Ω, we can consider f as an element in BV (R3). For any φ ∈ C1
+0(Ω) with ∥φ∥∞ ≤ 1, we have
+�
+Ω
+fn∇ · (θφ) dx =
+�
+Ω
+(ηεn ∗ f) ∇ · (θφ) dx =
+�
+Ω
+f∇ · [ηεn ∗ (θφ)] dx =
+�
+Ω
+f∇ ·
+�
+θ
+�ηεn ∗ (θφ)
+θ
+��
+dx
+≤ ∥(ηεn ∗ θ)/θ∥L∞(Ω)
+�
+Ω
+θd|Df(x)|.
+Here (ηεn ∗ θ)(x) =
+�
+Ω ηεn(x − y)θ(y) dy for x ∈ Ω. Taking supremum over all such φ, we derive that
+�
+Ω
+θd|Dfn(x)| ≤ ∥(ηεn ∗ θ)/θ∥L∞(Ω)
+�
+Ω
+θd|Df(x)|.
+By the uniform continuity of θ, it is not a hard task to verify that lim
+n→∞ ∥(ηεn ∗ θ)/θ∥L∞(Ω) = 1. Therefore,
+the above inequality implies that lim sup
+n→∞
+�
+Ω θd|Dfn(x)| ≤
+�
+Ω θd|Df(x)|.
+□
+
+16
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+Lemma A.4. For every f ∈ X, we define {fj}∞
+j=1 ⊂ BV (Ω) by
+fj(x) =
+�
+�
+�
+�
+�
+1,
+x ∈ Ωi;j
+0,
+x ∈ Ωe;j
+f(x),
+elsewhere.
+Then fj → f in L1(Ω) and
+�
+Ω θd|Dfj(x)| →
+�
+Ω θd|Df(x)| as j → ∞.
+Proof. The proof for fj → f in L1(Ω) is straightforward. So we will only show the second part. In the rest
+of the proof, it is assumed that i ∈ {0, 1}. Denote by νΣi the outward pointing (into Ωt) unit normal of Σi.
+Following the proof of Lemma 2.4, the map
+Λi : Σi × (−a, a) → R3 : (x, r) �→ x + rνΣi(x)
+is a C1-diffeomorphism for sufficiently small a > 0; and Σi,r := Λi(Σi, r) is a C1-hypersurface, whose outward
+unit normal is denoted by νi,r. In particular, νi,0 = νΣi. We define the orientation of Σi,r in such a way that
+νi,r are continuous vector fields. By the inverse function theorem, there exist two maps Pi ∈ C1(Ba(Σi), Σi)
+and di ∈ C1(Ba(Σi), (−a, a)), where Pi is the nearest point projection onto Σi and di is the signed distance
+to Σi with di(x) > 0 for x ∈ Ba(Σi) ∩ Ωt. Note that di is indeed C2, see [44] for example. We can define
+two C1-vector fields Vi : Ba(Σi) → R3 by
+Vi(x) = νi,di(x)(x).
+For any r ∈ (0, a), put Ui,r := Br(Σi)∩Ωt. Due to the trace theorem of BV -functions, cf. [24, Theorem 5.3.1],
+we have for all f ∈ X that
+�
+Ui,r
+f∇ · (θVi) dx +
+�
+Ui,r
+(θVi) · d[Df] =
+�
+Σi,r
+θTrf dH2 −
+�
+Σi
+θTrf dH2.
+Here Trf is the trace of f|Ui,r on ∂Ui,r; and [Df] is the vector-valued measure for the gradient of f.
+Pushing r → 0+ above yields that
+lim
+r→0+
+�
+Σi,r
+θTrf dH2 =
+�
+Σi
+θTrf dH2.
+(A.2)
+[8, Lemma 1] implies that
+�
+Ω θd|Df(x)| ≤ lim inf
+j→∞
+�
+Ω θd|Dfj(x)|. Observe that ∂Ωi;j = Σ1,1/j and ∂Ωe;j\∂Ω =
+Σ0,1/j for sufficiently large j. Denote by �Trf the trace of f|Ωt\(U0,r∪U1,r) on ∂ [Ωt \ (U0,r ∪ U1,r)]. For any
+u ∈ X, we will show
+�
+Ω
+θd|Du(x)| =
+�
+Ωt\(U0,r∪U1,r)
+θd|Du(x)| +
+�
+i=0,1
+�
+Ui,r
+θd|Du(x)|
++
+�
+i=0,1
+�
+Σi
+θ|i − Tru| dH2 +
+�
+i=0,1
+�
+Σi,r
+θ
+���Tru − �Tru
+��� dH2.
+(A.3)
+Indeed, for any φ ∈ C1
+c (Ω) with ∥φ∥∞ ≤ 1,
+�
+Ω
+u∇ · (θφ) = −
+�
+Ωt\(U0,r∪U1,r)
+(θφ) · d[Du] −
+�
+i=0,1
+�
+Ui,r
+(θφ) · d[Du] − (−1)i �
+i=0,1
+�
+Σi
+θ(i − Tru)φ · νΣi dH2
+− (−1)i �
+i=0,1
+�
+Σi,r
+θ(Tru − �Tru)φ · νi,r dH2
+≤
+�
+Ωt\(U0,r∪U1,r)
+θd|Du(x)| +
+�
+i=0,1
+�
+Ui,r
+θd|Du(x)| +
+�
+i=0,1
+�
+Σi
+θ|i − Tru| dH2
++
+�
+i=0,1
+�
+Σi,r
+θ
+���Tru − �Tru
+��� dH2.
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+17
+Taking supremum over all φ ∈ C1
+c (Ω) with ∥φ∥∞ ≤ 1 shows that the LHS of (A.3) is less than or equal to
+the RHS. To show the equality in (A.3), note that
+�
+i=0,1
+�
+Σi
+(θφ) · d[Du] +
+�
+i=0,1
+�
+Σi,r
+(θφ) · d[Du] =(−1)i �
+i=0,1
+�
+Σi
+θ(i − Tru)φ · νΣi dH2
++ (−1)i �
+i=0,1
+�
+Σi,r
+θ(Tru − �Tru)φ · νi,r dH2.
+Taking φ ∈ C1
+c (Ω) with ∥φ∥∞ ≤ 1 such that φ = (−1)i+1Vi in U i,r, we can infer from the above equality
+that
+�
+i=0,1
+�
+Σi
+θd|Du| +
+�
+i=0,1
+�
+Σi,r
+θd|Du| ≥
+�
+i=0,1
+�
+Σi
+θ|i − Tru| dH2 +
+�
+i=0,1
+�
+Σi,r
+θ
+���Tru − �Tru
+��� dH2.
+Therefore, the other direction of the inequality in (A.3) holds and (A.3) is valid. This implies that
+�
+Ω
+θd|Dfj(x)| −
+�
+Ω
+θd|Df(x)| =
+�
+i=0,1
+��
+Σi,1/j
+θ|i − �T1/jf| dH2 −
+�
+Σi
+θ|i − T1/jf| dH2 −
+�
+Ui,1/j
+θd|Df(x)|
+�
+−
+�
+i=0,1
+��
+Σi,1/j
+θ
+���T1/jf − �T1/jf
+��� dH2
+�
+≤
+�
+i=0,1
+��
+Σi,1/j
+θ|i − T1/jf| dH2 −
+�
+Σi
+θ|i − T1/jf| dH2 −
+�
+Ui,1/j
+θd|Df(x)|
+�
+.
+From (A.2), we infer that
+lim
+j→∞
+��
+Σi,1/j
+θ|i − T1/jf| dH2 −
+�
+Σi
+θ|i − T1/jf| dH2 −
+�
+Ui,1/j
+θd|Df(x)|
+�
+= 0.
+This implies that lim sup
+j→∞
+�
+Ω θd|Dfj(x)| ≤
+�
+Ω θd|Df(x)|.
+□
+Appendix B. Continuous dependence on Ωi and Ωe
+Assume that {�Ωi;n}∞
+n=1 and {�Ωe;n}∞
+n=1 are two sequences of Lipschitz subdomains in Ω with
+Nm
+�
+j=1
+B(xj, σj) ⊂ �Ωi;n ⋐ Ω \ �Ωe;n
+and
+∂Ω ⊂ ∂�Ωe;n.
+We consider the family of energy functionals �En defined by replacing Ωi and Ωe by �Ωi;n and �Ωe;n in E,
+respectively. The corresponding admissible sets are
+�
+Xn = {u ∈ BV (Ω) : 0 ≤ u ≤ 1 a.e. in Ω
+and
+u = 1 a.e. in �Ωi;n and u = 0 a.e. in �Ωe;n}.
+Then for each n, there is a unique minimizer �umin,n of �En in �
+Xn.
+The lemma below can be proved by following the proof of [14, Theorem 4.2] line by line.
+Lemma B.1. Assume that {�Ωi;n}∞
+n=1 and {�Ωe;n}∞
+n=1 satisfy �Ωi;n ⊆ Ωi and �Ωe;n ⊆ Ωe. Suppose further that
+χ�Ωi;n → χΩi
+and
+χ�Ωe;n → χΩe
+in L1(Ω)
+as n → ∞.
+Then, lim
+n→∞
+�En(�umin,n) = E(umin), where umin is a minimizer of E.
+Recall that the Hausdorff metric on compact subsets K ⊂ R3 is defined by
+dH(K1, K2) = max{ sup
+x∈K1
+d(x, K2), sup
+x∈K2
+d(x, K1)}.
+Given a closed surface Σ in R3, its normal bundle is given by
+NΣ = {(q, νΣ(q)) : q ∈ Σ} ⊂ R3 × R3,
+
+18
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+where νΣ(q) is the outward unit normal of Σ at q ∈ Σ. When {�Ωi;n}∞
+n=1 and {�Ωe;n}∞
+n=1 approximate Ωi and
+Ωe from the exterior, the following counterpart of Lemma B.1 holds.
+Lemma B.2. Suppose that Σj ∈ C2, j = 0, 1. Assume that {�Ωi;n}∞
+n=1 and {�Ωe;n}∞
+n=1 are C1 and
+Ωi ⊆ �Ωi;n
+and
+Ωe ⊆ �Ωe;n.
+Let Σ1;n = ∂�Ωi;n and Σ0;n = ∂�Ωe;n \ ∂Ω. Suppose further that
+lim
+n→∞ dH(NΣ1;n, NΣ1) = lim
+n→∞ dH(NΣ0;n, NΣ0) = 0.
+Then, lim
+n→∞
+�En(�umin,n) = E(umin), where umin is a minimizer of E.
+Proof. It suffices to consider the case Ωe = �Ωe;n. The proof for the general situation is similar. Following
+the proof of Proposition 2.5 and Lemma A.4, the map
+Λ : Σ1 × (−a, a) → R3 : (q, r) �→ q + rνΣ1(q)
+is a C1-diffeomorphism for some a > 0, where the outward unit normal νΣ1 points into Ωt. Σr := Λ(Σ1, r) is
+a C1-hypersurface, whose outward unit normal is denoted by νr. By [44, Section 4.3], for sufficiently large
+n, there exist ρn ∈ C1(Σ1) with 0 ≤ ρn ≤ a such that Σ1;n is the image of the following C1-diffeomorphism
+Ψρn : Σ1 → R3 : q �→ q + ρn(q)νΣ1(q).
+Let rn := ∥ρn∥∞. Then lim
+n→∞ rn = 0. For sufficiently large n ∈ N, we define
+un(x) =
+�
+1,
+x ∈ Ωn,
+umin(x),
+elsewhere,
+where Ωn is the region enclosed by Σrn. Since un ∈ �
+Xn and �umin,n ∈ X, we have
+E(umin) ≤ �En(�umin,n) ≤ E(un).
+(B.1)
+From a slight variant of Lemma A.4, we learn that as n → ∞
+un → umin
+in L1(Ω)
+and
+�
+Ω
+θd|Dun| →
+�
+Ω
+θd|Dumin|.
+The dominated convergence theorem and Lemma A.2 give lim
+n→∞ E(un) = E(umin). Then the asserted state-
+ment follows by pushing n → ∞ in (B.1).
+□
+Theorem B.3. Suppose that Σj ∈ C2, j = 0, 1.
+Assume that {�Ωi;n}∞
+n=1 and {�Ωe;n}∞
+n=1 are C1.
+Let
+Σ1;n = ∂�Ωi;n and Σ0;n = ∂�Ωe;n \ ∂Ω. Suppose further that
+lim
+n→∞ dH(NΣ1;n, NΣ1) = lim
+n→∞ dH(NΣ0;n, NΣ0) = 0.
+Then, lim
+n→∞
+�En(�umin,n) = E(umin), where umin is a minimizer of E.
+Proof. As in the above proof, we only consider the case that Ωe = �Ωe;n. It again follows from [44, Section 4.3]
+that, for sufficiently large n, Σ1;n can be expressed as a C1−normal graph over Σ1 with height function
+ρn ∈ C1(Σ1, (−a, a)). Let rn = ∥ρn∥∞. Following the notations in the proof of Lemma B.2, we define
+Σ±rn := Λ(Σ1, ±rn) and Ω±
+n to be the region enclosed by Σ±rn, respectively. We introduce �E±
+n as defined
+by replacing Ωi by Ω±
+n , respectively. Their corresponding minimizers are denoted by u±
+min,n. Then
+�E−
+n (u−
+min,n) ≤ �En(�umin,n) ≤ �E+
+n (u+
+min,n).
+From Lemmas B.1 and B.2, we learn that lim
+n→∞
+�E−
+n (u−
+min,n) = lim
+n→∞
+�E+
+n (u+
+min,n) = E(umin).
+□
+Acknowledgements
+The research of Zhao was supported in part by the National Science Foundation (NSF) grant DMS-
+2110914. The research of Chen was supported in part by the National Science Foundation (NSF) grant
+DMS-1818748.
+
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+19
+References
+[1] N. A. Baker. Improving implicit solvent simulations:
+a Poisson-centric view. Current Opinion in Structural Biology,
+15(2):137–43, 2005.
+[2] N. A. Baker, D. Sept, S. Joseph, M. J. Holst, and J. A. McCammon. Electrostatics of nanosystems: Application to
+microtubules and the ribosome. Proceedings of the National Academy of Sciences, 98(18):10037–10041, 2001.
+[3] P. Ball. How to keep dry in water. Nature, 423(6935):25–26, May 2003.
+[4] P. W. Bates, G. W. Wei, and S. Zhao. Minimal molecular surfaces and their applications. Journal of Computational
+Chemistry, 29(3):380–91, 2008.
+[5] A. H. Boschitsch and M. O. Fenley. Hybrid boundary element and finite difference method for solving the nonlinear
+Poisson-Boltzmann equation. Journal of Computational Chemistry, 25(7):935–955, 2004.
+[6] W. M. Botello-Smith, X. Liu, Q. Cai, Z. Li, H. Zhao, and R. Luo. Numerical poisson–boltzmann model for continuum
+membrane systems. Chemical Physics Letters, 555:274–281, 2013.
+[7] R. C. Braga, V. M. Alves, A. C. Silva, M. N. Nascimento, F. C. Silva, L. M. Liao, and C. H. Andrade. Virtual screening
+strategies in medicinal chemistry: the state of the art and current challenges. Curr Top Med Chem, 14(16):1899–1912,
+2014.
+[8] G. Carlier and M. Comte. On a weighted total variation minimization problem. J. Funct. Anal., 250(1):214–226, 2007.
+[9] J. Che, J. Dzubiella, B. Li, and J. A. McCammon. Electrostatic free energy and its variations in implicit solvent models.
+The Journal of Physical Chemistry B, 112(10):3058–3069, 2008. PMID: 18275182.
+[10] C. J. Chen, R. Saxena, and G. W. Wei. Differential geometry based multiscale models for virus formation and evolution.
+Int. J. Biomed. Imaging, 2010(308627), 2010.
+[11] Z. Chen, N. A. Baker, and G. W. Wei. Differential geometry based solvation model I: Eulerian formulation. J. Comput.
+Phys., 229(22):8231–8258, 2010.
+[12] Z. Chen, N. A. Baker, and G. W. Wei. Differential geometry based solvation models I: Eulerian formulation. J. Comput.
+Phys., 229:8231–8258, 2010.
+[13] Z. Chen, N. A. Baker, and G. W. Wei. Differential geometry based solvation models II: Lagrangian formulation. J. Math.
+Biol., 63:1139–1200, 2010.
+[14] Z. Chen and Y. Shao. A new approach to constrained total variation solvation models and the study of solute-solvent
+interface profiles. Comput. Math. Appl., 130:119–136, 2023.
+[15] Z. Chen and G. W. Wei. Differential geometry based solvation models III: Quantum formulation. J. Chem. Phys.,
+135:1941108, 2011.
+[16] Z. Chen, S. Zhao, J. Chun, D. G. Thomas, N. A. Baker, P. W. Bates, and G. W. Wei. Variational approach for nonpolar
+solvation analysis. The Journal of Chemical Physics, 137(8):084101, 2012.
+[17] L. T. Cheng, J. Dzubiella, A. J. McCammon, and B. Li. Application of the level-set method to the implicit solvation of
+nonpolar molecules. Journal of Chemical Physics, 127(8), 2007.
+[18] P. B. Crowley and A. Golovin. Cation-pi interactions in protein-protein interfaces. Proteins: Structure, Function, and
+Bioinformatics, 59(2):231–239, 2005.
+[19] S. Dai, B. Li, and J. Lu. Convergence of phase-field free energy and boundary force for molecular solvation. Arch. Ration.
+Mech. Anal., 227(1):105–147, 2018.
+[20] F. Dong and H. X. Zhou. Electrostatic contribution to the binding stability of protein-protein complexes. Proteins, 65(1):87–
+102, 2006.
+[21] A. I. Dragan, C. M. Read, E. N. Makeyeva, E. I. Milgotina, M. E. Churchill, C. Crane-Robinson, and P. L. Privalov. DNA
+binding and bending by HMG boxes: Energetic determinants of specificity. Journal of Molecular Biology, 343(2):371–393,
+2004.
+[22] J. Dzubiella, J. M. J. Swanson, and J. A. McCammon. Coupling hydrophobicity, dispersion, and electrostatics in continuum
+solvent models. Phys. Rev. Lett., 96:087802, Mar 2006.
+[23] J. Dzubiella, J. M. J. Swanson, and J. A. McCammon. Coupling nonpolar and polar solvation free energies in implicit
+solvent models. The Journal of Chemical Physics, 124(8):084905, 2006.
+[24] L. C. Evans and R. F. Gariepy. Measure theory and fine properties of functions. Studies in Advanced Mathematics. CRC
+Press, Boca Raton, FL, 1992.
+[25] M. Feig and C. L. Brooks III. Recent advances in the development and application of implicit solvent models in biomolecule
+simulations. Curr Opin Struct Biol., 14:217 – 224, 2004.
+[26] F. Fogolari and J. M. Briggs. On the variational approach to poisson–boltzmann free energies. Chemical Physics Letters,
+281(1):135–139, 1997.
+[27] F. Fogolari, A. Brigo, and H. Molinari. The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural
+biology. Journal of Molecular Recognition, 15(6):377–92, 2002.
+[28] D. Gilbarg and N. S. Trudinger. Elliptic partial differential equations of second order, volume 224 of Grundlehren der Math-
+ematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, second edition,
+1983.
+[29] E. Giusti. Minimal surfaces and functions of bounded variation, volume 80 of Monographs in Mathematics. Birkh¨auser
+Verlag, Basel, 1984.
+[30] J. A. Grant, B. T. Pickup, M. T. Sykes, C. A. Kitchen, and A. Nicholls. The Gaussian Generalized Born model: application
+to small molecules. Physical Chemistry Chemical Physics, 9:4913–22, 2007.
+[31] P. Grochowski and J. Trylska. Continuum molecular electrostatics, salt effects and counterion binding. a review of the
+Poisson-Boltzmann theory and its modifications. Biopolymers, 89(2):93–113, 2007.
+
+20
+ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS
+[32] L. A. Kuhn, M. A. Siani, M. E. Pique, C. L. Fisher, E. D. Getzoff, and J. A. Tainer. The interdependence of protein
+surface topography and bound water molecules revealed by surface accessibility and fractal density measures. Journal of
+Molecular Biology, 228(1):13–22, 1992.
+[33] G. Lamm. The Poisson-Boltzmann equation. In K. B. Lipkowitz, R. Larter, and T. R. Cundari, editors, Reviews in
+Computational Chemistry, pages 147–366. John Wiley and Sons, Inc., Hoboken, N.J., 2003.
+[34] J. LeCrone, Y. Shao, and G. Simonett. The surface diffusion and the Willmore flow for uniformly regular hypersurfaces.
+Discrete Contin. Dyn. Syst. Ser. S, 13(12):3503–3524, 2020.
+[35] R. M. Levy, L. Y. Zhang, E. Gallicchio, and A. K. Felts. On the nonpolar hydration free energy of proteins: surface
+area and continuum solvent models for the solute-solvent interaction energy. Journal of the American Chemical Society,
+125(31):9523–9530, 2003.
+[36] B. Li. Minimization of electrostatic free energy and the poisson–boltzmann equation for molecular solvation with implicit
+solvent. SIAM Journal on Mathematical Analysis, 40(6):2536–2566, 2009.
+[37] B. Li and Y. Liu. Diffused solute-solvent interface with Poisson-Boltzmann electrostatics: free-energy variation and sharp-
+interface limit. SIAM J. Appl. Math., 75(5):2072–2092, 2015.
+[38] C. Li, L. Li, J. Zhang, and E. Alexov. Highly efficient and exact method for parallelization of grid-based algorithms and
+its implementation in delphi. Journal of Computational Chemistry, 33(24):1960–1966, 2012.
+[39] L. Li, C. Li, Z. Zhang, and E. Alexov. On the dielectric “constant” of proteins: Smooth dielectric function for macromolec-
+ular modeling and its implementation in delphi. Journal of Chemical Theory and Computation, 9(4):2126–2136, 2013.
+PMID: 23585741.
+[40] E. Lionta, G. Spyrou, D. K. Vassilatis, and Z. Cournia. Structure-based virtual screening for drug discovery: principles,
+applications and recent advances. Curr Top Med Chem, 14(16):1923–1938, 2014.
+[41] M. Miranda. Un principio di massimo forte per le frontiere minimali e una sua applicazione alla risoluzione del problema
+al contorno per l’equazione delle superfici di area minima. Rend. Sem. Mat. Univ. Padova, 45:355–366, 1971.
+[42] D. L. Mobley, K. A. Dill, and J. D. Chodera. Treating entropy and conformational changes in implicit solvent simulations
+of small molecules. The Journal of Physical Chemistry B, 112(3):938–946, 2008. PMID: 18171044.
+[43] J. Mongan, C. Simmerling, J. A. McCammon, D. A. Case, and A. Onufriev. Generalized Born model with a simple, robust
+molecular volume correction. Journal of Chemical Theory and Computation, 3(1):159–69, 2007.
+[44] J. Pr¨uss and G. Simonett. On the manifold of closed hypersurfaces in Rn. Discrete Contin. Dyn. Syst., 33(11-12):5407–5428,
+2013.
+[45] C. G. Ricci, B. Li, L. Cheng, J. Dzubiella, and J. A. McCammon. Tailoring the variational implicit solvent method for
+new challenges: Biomolecular recognition and assembly. Frontiers in Molecular Biosciences, 5:13, 2018.
+[46] L. I. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. volume 60, pages 259–268.
+1992. Experimental mathematics: computational issues in nonlinear science (Los Alamos, NM, 1991).
+[47] Y. Shao, E. Hawkins, K. Wang, and Z. Chen. A constrained variational model of biomolecular solvation and its numerical
+implementation. Comput. Math. Appl., 107:17–28, 2022.
+[48] K. A. Sharp and B. Honig. Calculating total electrostatic energies with the nonlinear poisson-boltzmann equation. The
+Journal of Physical Chemistry, 94(19):7684–7692, Sep 1990.
+[49] R. S. Spolar, J. H. Ha, and M. T. Record Jr. Hydrophobic effect in protein folding and other noncovalent processes involving
+proteins. Proceedings of the National Academy of Sciences of the United States of America, 86(21):8382–8385, 1989.
+[50] J. M. J. Swanson, J. Mongan, and J. A. McCammon. Limitations of atom-centered dielectric functions in implicit solvent
+models. Journal of Physical Chemistry B, 109(31):14769–72, 2005.
+[51] H. Tjong and H. X. Zhou. GBr6NL: A generalized Born method for accurately reproducing solvation energy of the nonlinear
+Poisson-Boltzmann equation. Journal of Chemical Physics, 126:195102, 2007.
+[52] J. A. Wagoner and N. A. Baker. Assessing implicit models for nonpolar mean solvation forces: the importance of dispersion
+and volume terms. Proceedings of the National Academy of Sciences of the United States of America, 103(22):8331–6, 2006.
+[53] B. Wang and G. W. Wei. Parameter optimization in differential geometry based solvation models. The Journal of chemical
+physics, 143(13):134119, 2015.
+[54] G. W. Wei. Differential geometry based multiscale models. Bulletin of Mathematical Biology, 72(6):1562–1622, Aug 2010.
+[55] G. W. Wei and N. A Baker. Differential geometry-based solvation and electrolyte transport models for biomolecular
+modeling: a review. In Many-Body Effects and Electrostatics in Biomolecules, pages 435–480. Jenny Stanford Publishing,
+2016.
+[56] G. W. Wei, Y. H. Sun, Y. C. Zhou, and M. Feig. Molecular multiresolution surfaces. arXiv:math-ph/0511001v1, pages 1 –
+11, 2005.
+[57] G. W. Wei, Q. Zheng, Z. Chen, and K.n Xia. Variational multiscale models for charge transport. siam REVIEW, 54(4):699–
+754, 2012.
+[58] S. Zhao. Pseudo-time-coupled nonlinear models for biomolecular surface representation and solvation analysis. International
+Journal for Numerical Methods in Biomedical Engineering, 27(12):1964–1981, 2011.
+[59] Y. Zhao, Y. Kwan, J. Che, B. Li, and J. A. McCammon. Phase-field approach to implicit solvation of biomolecules with
+coulomb-field approximation. The Journal of chemical physics, 139(2):024111, 2013.
+[60] S. Zhou, K. E. Rogers, C. A. F. de Oliveira, R. Baron, L. Cheng, J. Dzubiella, B. Li, and J. A. McCammon. Variational
+implicit-solvent modeling of host–guest binding:
+A case study on cucurbit[7]uril—. Journal of Chemical Theory and
+Computation, 9(9):4195–4204, Sep 2013.
+[61] Y. Zhou. On curvature driven rotational diffusion of proteins on membrane surfaces. SIAM Journal on Applied Mathem-
+atics, 80(1):359–381, 2020.
+
diff --git a/ltFAT4oBgHgl3EQfbx2O/content/tmp_files/load_file.txt b/ltFAT4oBgHgl3EQfbx2O/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1d5ef733fbc46e5ac5f134a336945ee01c784c58
--- /dev/null
+++ b/ltFAT4oBgHgl3EQfbx2O/content/tmp_files/load_file.txt
@@ -0,0 +1,1479 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf,len=1478
+page_content='MODELING AND ANALYSIS OF ENSEMBLE AVERAGE SOLVATION ENERGY AND  SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  YUANZHEN SHAO∗†, ZHAN CHEN∗∗, AND SHAN ZHAO∗∗∗  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Variational implicit solvation models (VISM), because of their relatively low computational  cost and satisfactory accuracy, have been widely used in the solvation analysis of biological systems at  molecular level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Central in the construction of VISM is an interface separating the solute and the solvent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Compared with sharp-interface models, diffuse-interface VISMs have shown some initial success in improving  the efficiency and accuracy of the solvation energy estimation of biomolecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' However, on a theoretical level,  several questions concerning the diffuse-interface VISMs remain open: (1) What is the physical meaning of a  diffuse interface?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' (2) What energy does a diffuse-interface VISM predict?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This work aims at addressing the  above questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Our research reveals the relationship between a diffuse interface definition and the random  movement of the solute-solvent interface due to thermal fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then, we use this diffuse interface  setting to construct a VISM that is capable of capturing ensemble average solvation energy, which is an  experimentally observable quantity in solvation processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The well-posedness and variational analysis of  the model are further investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Our work is the first step towards estimating ensemble average solvation  energy by using diffuse-interface VISMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Introduction  In the quantitative analysis of biological processes, the complex interactions between the solute and solvent  are typically described by solvation energies (or closely related quantities): the free energy of transferring the  solute (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' biomolecules, such as proteins, DNA, RNA) from the vacuum to a solvent environment of interest  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' water at a certain ionic strength).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' There are two major approaches for solvation energy calculations:  explicit solvent models and implicit solvent models [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Explicit models, treating both the solute and the  solvent as individual molecules, are too computationally expensive for large solute-solvent systems, such as  the solvation of macromolecules in ionic environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In contrast, implicit models, by averaging the effect  of solvent phase as continuum media [1,2,5,6,9,25,38], are much more efficient and thus are able to handle  much larger systems [2,16,27,30,31,33,43,51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  An inevitable prerequisite for describing the solvation energy in implicit solvent models is an interface  separating the discrete solute and the continuum solvent domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' All of the physical properties related  to solvation processes, including biomolecular surface area, biomolecular cavitation volume, pKa value and  electrostatic free energy, are very sensitive to the interface definition [20, 50, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' There are a number of  different surface definitions, which include the van der Waals surface, the solvent excluded surface and the  solvent accessible surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' These surface definitions have found many successful applications in biomolecular  modeling [18,21,32,49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' However, these predetermined interfaces are ad hoc partitions and thus either non-  negligibly overestimate or underestimate the solvation free energies [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Moreover, none of them takes into  account the minimization of interfacial free energies during the equilibrium solvation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Variational implicit solvation models (VISM) stand out as a successful approach to compute the disposition  of an interface separating the solute and the solvent [4,10,12,17,19,56,61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In a VISM, the desired interface  profile is obtained by optimizing a solvation energy functional coupling the discrete description of the solute  and the continuum description of the solvent in addition to polar and non-polar interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' However, a  sharp-interface VISM is incapable to describe the randomness of a solute-solvent boundary, which is due  to atom vibrations or thermodynamic fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Indeed, ions, solute and solvent molecules are not rigid  2020 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Primary: 49Q10;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Secondary: 35J20;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' 92C40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Biomolecule solvation, Poisson-Boltzmann, Variational implicit solvation model, Ensemble average  solvation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  †Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ∗Department of Mathematics, The University of Alabama, Tuscaloosa, AL, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' yshao8@ua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ∗∗Department of Mathematical Sciences, Georgia Southern University, GA, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' zchen@georgiasouthern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ∗∗∗Department of Mathematics, The University of Alabama, Tuscaloosa, AL, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' szhao@ua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='08560v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='bio-ph]  6 Jan 2023  2  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  objects and they undergo small or large conformational changes in real applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Disregarding this can  cause severe errors in predictions of solvation free energies [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This calls for the need of a new notion of  solvent-solute interface, which is known as the diffuse interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Arguably, the most extensively used diffuse interface models are: (1) the phase-field based models (PF-  BVISM), cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' [19, 37, 59];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' and (2) the geometric flow based models (GFBVISM), cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' [12, 22, 53–55, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For  a solute-solvent system contained in a region Ω ⊂ R3, a typical PFBVISM is a functional defined by a  phase-field variable u : Ω → R, which plays the role of a solute-solvent interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Allen-Cahn functional  �  Ω  �  ξ  2|∇u|2 + 1  ξW(u)  �  dx, where W(x) = 18x2(1 − x)2, is used because it Γ-converges to the area of a sharp  interface as ξ → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The diffuse interface in GFBVISM is defined in terms of a transition parameter u : Ω → R,  which takes value 1 in the solute and 0 in the solvent region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The solute-solvent surface area is replaced  by  �  Ω |∇u| dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' By the coarea formula, this integral approximates the mean surface area of the level sets of  a Lipschitz continuous function u, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Numerical simulations show that these diffuse-interface models  can improve the efficiency and accuracy of solvation energy computation [15,37,53,55,57,58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' However, on  a theoretical level, the diffuse interfaces in use were created in an ad hoc way and lack rigorous justifications  of their physical meanings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Hence, a persuasive physical interpretation of the solvation energies predicted  by those diffuse-interface models is still absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The key to an effective diffuse interface definition is to understand the source of inaccuracy in sharp-  interface VISMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A solute-solvent interface is determined by both the solute molecular structure and the  surrounding solvent configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Due to thermodynamic fluctuations, when a fixed solute molecular struc-  ture being considered, solvent molecules and ions can still adopt different configurations [3], or equivalently,  from statistical mechanics standpoint, can form various microstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This implies that the disposition of the  interface is not unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' On the other hand, experimentally observable quantities are ensemble averaged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Us-  ing the energy computed from one microstate (even if the one with minimum energy) to predict the averaged  energy from all microstates is doomed to be inaccurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Therefore, it is of imminent practical importance  to develop a solvation model capable of calculating ensemble average solvation energy with thermodynamic  fluctuations being taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  It is the first goal of this study to develop a VISM for ensemble average solvation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In Section 2,  we show that the ensemble average of various solvation energy components (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' the biomolecular surface  areas, cavity volumes and electrostatic free energies) can be rigorously derived if the diffuse-interface profile  u : Ω → [0, 1] is constructed so that u(x) represents the probability of a point x ∈ Ω found in the solute phase  among all microstates in the grand canonical ensemble under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For the first time in literature,  the physical meaning of a diffuse interface will be illuminated and in turn the energy predicted by the  corresponding diffuse-interface model will be justified in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' It is worthwhile to point out that one of  the grand challenges of calculating the ensemble average solvation energy is how to determine the Boltzmann  weight of each microstate, without which an effective sampling of different solvation states is impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Our new ensemble average VISM (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19) bypasses the above difficulty by encoding the Boltzmann weight  information to the argument u and thus is capable of directly capturing the ensemble averaged information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The second goal of this work is to discuss the computational models for capturing the global minimum of  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Unlike most energy variational models, what plays a central role in many applications of VISMs [13,60]  is the minimum value of the solvation energy functional (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' the solvation energy) but not the dynamical  processes generated by the functional (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' the gradient flow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For example, the calculation of the binding  affinity for computational drug design [7, 40], which measures how strong a ligand (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' drug) binds to a  biomolecule (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' protein), consists of the computation of solvation energies of the protein and ligand separ-  ately and then as a complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Unfortunately, the VISMs in use, no matter sharp or diffuse interface, except  for GFBVISM, all have non-convex structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Consequently, the corresponding computational models only  calculate their local minima [19, 37, 45, 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Further challenges arise in our new VISM, which is a total  variation based model with a two-sided obstacle 0 ≤ u ≤ 1 and a computational domain of complex shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The conventional Euler-Lagrange approach to similar but simpler problems, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Rudin-Osher-Fatemi mod-  els [46], faces several challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' First, with the presence of the obstacle, on a heuristic level with sufficiently  smooth minimizer u and functional, one expects the first variations of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19) with respect to u to take the  form of a variational inequality, or equivalently, of a 1−Laplacian type equation involving a measure sup-  ported on the coincidence sets {u = 0} and {u = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Unfortunately, both the functional and the minimizer  fail to enjoy the required smoothness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Second, the computational models of total variation problems are  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  3  usually studied by certain regularization, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' non-parametric minimal surface equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' However, it is  well known that the solutions of non-parametric minimal surface equations may admit jump discontinuities  along the boundary unless the boundary satisfies certain geometric conditions [29,41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Such conditions are  unrealistic for most biomolecules due to their complex shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The possible presence of jump discontinuities  may become a source of inaccuracy in numerical simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In Section 3, we will develop a novel approach  to regularize (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19), which enables us to relax the two-sided obstacle and avoid boundary jump discontinuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Most importantly, the first variations of the regularized problems can be rigorously derived, which generates  a system of elliptic differential equations that has a unique solution – the global minimizer of the regularized  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This paves the way for the numerical implementations of our new ensemble average VISM, which  will be investigated in several subsequent papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In Section 2, we develop a new VISM for the ensemble average  solvation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In Section 3, we study regularizations of our new ensemble average energy functional and  conduct variational analysis of the regularized problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In Section 4, we compare our new model with some  existing diffuse-interface VISMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Some technical lemmas are collected in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In Appendix B, we  provide some justifications for the robustness of our new models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Finally, in Section 5, we draw conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ensemble Averaged Solvation Energy  List of Notations: Given any open sets U and Ω, U ⋐ Ω means that U ⊂ Ω and U stands for the closure  of U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We denote by LN and HN−1 the N−dimensional Lebesgue measure and the (N − 1)−dimensional  Hausdorff measure, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For any 1 ≤ p ≤ ∞, p′ is the H¨older conjugate of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The phrase l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='c is the  abbreviation of lower semi-continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A Sharp Interface VISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We consider a solute-solvent system with a fixed biomolecular structure  contained in a bounded Lipschitz domain Ω ⊆ R3 using the grand canonical ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Hence, the chemical  potential, temperature and volume of the system are kept constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Suppose that the solute atoms are  centered at x1, · · · , xNm and there are Nc ion species in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume that the system undergoes K microstates,  labelled by k = 1, 2, · · · , K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Microstate k occurs with a probability pk, in which the solute occupies a  Caccioppoli subset Dk ⋐ Ω, or equivalently, Uk = Ω \\ Dk is the solvent region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' See Figure 1(A) for an  illustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' By our assumption, �  k∈K pk = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For notational brevity, we put K = {1, 2, · · · , K}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (a)  (b)  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' (A) Illustration of the microstate k: Dk is the solute region;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Uk is the solvent region;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' (B)  Domain decomposition for a grand canonical ensemble:  Ωi is the region occupied by the solute in all  microstates;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ωs denotes the region occupied by the solvent in all microstates;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ωt denotes the transition  region where 0 ≤ u ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  We define the sample space S to be the set of all distributions (of ions and solvent molecules) in the grand  canonical ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then S = �  k∈K  Sk, where Sk is the sample space of all distributions in microstate k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The  following random variables will be used throughout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Z : S → K indicates the microstate that a distribution belongs to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Cj(x) : S → R+ is the (number) concentration of the j-th ion species at x ∈ Ω in a given distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Solvent  Z  Soluteu=0  >n>0  Solvent  2  Solute  o4  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  In microstate k, for every fixed x ∈ Ω, the (number) concentration of the j-th ion species at x can be  represented by  ck  j (x) = E(Cj(x)|Z = k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Here E(Cj(x)|Z = k) represents the conditional expectation of the random variable Cj(x) (with fixed x)  given Z = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In this article, we treat the solute atoms as hard spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' More precisely, we consider the atom  centered at xi, i = 1, · · · , Nm, as a sphere of radius σi > 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', B(xi, σi), for which the solvent molecules  and the ions cannot enter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' On the other hand, the solvent and ion concentrations are the same as their bulk  concentrations in regions sufficiently far away from the solute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' As a consequence, such regions cannot be  contained in the solute phase in any microstate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Based on these observations, we may assume that there are  two open Lipschitz subsets, Ωi and Ωe, of Ω with �Nm  i=1 B(xi, σi) ⊂ Ωi ⋐ Ω \\ Ωe and ∂Ω ⊂ ∂Ωe such that  Ωi ⊂ Dk ⊂ Ω \\ Ωe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1)  By Assumption (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1), all ion species are located outside Ωi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let Ωt := Ω \\  �  Ωi ∪ Ωe  �  be the transition region  in microstate k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In addition, we define Σ1 = ∂Ωi and Σ0 = ∂Ωe \\ ∂Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' See Figure 1(B) for an illustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The hydrophobicity of the amino acids in the biomolecule varies from position to position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' To account  for this phenomenon, we introduce a positive variable surface tension function θ ∈ C1(Ωt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Without loss of  generality, we may extend θ to be a function in C1(Ω), still denoted by θ, such that  θ0 ≤ θ(x) ≤ θ1,  x ∈ Ω  for some constants 0 < θ0 < θ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' By [8, Lemma 1]  �  Ω  θ(x)d|Df(x)| = sup  ��  Ω  f(x)∇ · (θ(x)φ(x)) dx : φ ∈ C1  c (Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' R3), ∥φ∥∞ ≤ 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  It is clear that, for any f ∈ BV (Ω) with f ≡ 0 in Ωe and f ≡ 1 in Ωi, the value of  �  Ω θ(x)d|Df(x)| is  independent of how θ is extended outside Ωt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  As proposed in [22,23], the solvation free energy in microstate k predicted by a sharp-interface VISM is  the minimum value of the following energy functional  E(χDk) = Inp(χDk) + Ip(χDk, ψ),  where ψ : Ω → R is the electrostatic potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The two components Inp and Ip are termed the nonpolar and  polar portion of the solvation energy, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Σ = ∂Dk is considered as the solute-solvent interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For  every fixed Dk, ψ = ψχDk is chosen to maximize Ip(χDk, ψ) among all ψ taking a predetermined Dirichlet  boundary value ψD on ∂Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' It seems to be a little counterintuitive that ψ maximizes the polar energy instead  of minimizing it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' An explanation of this fact can be found in [9] for the case ψD = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The nonpolar solvation energy consists of three parts:  Inp(χDk) =  �  Ω  θd|DχDk| + PhVol(Dk) +  �  Uk  ρsU vdW(x) dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  When θ ≡ γ for some constant γ > 0, the first term reduces to γPer(Dk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ω) with Per(Dk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ω) being the  perimeter (in Ω) of the biomolecule region Dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This term measures the disruption of intermolecular and/or  intramolecular bonds that occurs when a surface is created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In addition, Vol(Dk) represents the volume of  Dk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ph is the (constant) hydrodynamic pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Therefore, PhVol(Dk) is the mechanical work of creating  the biomolecular size vacuum in the solvent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In the last integral, ρs is the (constant) solvent bulk density;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  and U vdW represents the Lennard-Jones potential [52];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' as such U vdW ∈ C∞(Ω \\ {x1, · · · , xNm}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Currently, one of the most widely-used polar solvation models is the Poisson-Boltzmann (PB) theory  [1,26,27,31,33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In the framework of classical PB theory, the polar energy is expressed as  Ip(χDk, ψ) =  �  Dk  �  ρ(x)ψ(x) − ϵp  2 |∇ψ(x)|2�  dx −  �  Uk  �  �ϵs  2 |∇ψ(x)|2 + β−1  Nc  �  j=1  c∞  j (e−βqjψ(x) − 1)  �  � dx, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2)  where ρ is an L∞-approximation of the solute partial charges supported in �Nm  i=1 B(xi, σi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' ϵp and ϵs are the  dielectric constants of the solute and the solvent, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Usually, ϵp ≈ 1 for the protein and ϵs ≈ 80  for the water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' qj is the charge of ion species j, j = 1, 2, · · · , Nc, and β = 1/kBT, where kB is the Boltzmann  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  5  constant, T is the (constant) absolute temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' c∞  j  is the (constant) bulk concentration of the j−th  ionic species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For notational brevity, we put  B(s) = β−1  �  �  Nc  �  j=1  c∞  j  �  e−βsqj − 1  �  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  In addition, we assume the charge neutrality condition  Nc  �  j=1  c∞  j qj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3)  It is important to observe that B(0) = 0 and, by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3), B′(0) = 0 and B′(±∞) = ±∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Further, B′′(s) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  We thus conclude that B(0) = min  s∈RB(s) and B is strictly convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A closer look into the derivation of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2) will help us to understand the physical meanings of ψ  and Ip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In the PB theory, in every microstate k, the mean electrostatic potential ψ (among all distributions  in microstate k) satisfies the fundamental equation of electrostatics, the Poisson equation:  −∇ · [(ϵχDk + ϵsχUk)∇ψ] = ρ +  Nc  �  j=1  qjck  j  in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4)  The average (number) concentration, ck  j , of the j-th ion speices in microstate k, can be derived by minimizing  the Helmholtz free energy for the fixed solute-solvent interface ∂Dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The Helmholtz free energy H in  microstate k is expressed as Hk = Ek − TSk, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' [26, 36], where E is the internal energy, S is the entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The subscript k is to indicate that the corresponding quantity is defined in microstate k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Here  Ek =  �  Dk  �  ρψ − ϵp  2 |∇ψ|2�  dx +  �  Uk  �  �  Nc  �  j=1  qjck  j ψ − ϵs  2 |∇ψ|2 −  Nc  �  j=1  µjck  j  �  � dx,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5)  where µj is the chemical potential of the j-th ion species so that c∞  j = eβµj, and  −TSk = β−1  �  Uk  Nc  �  j=1  ck  j  �  ln(ck  j ) − 1  �  dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Hk is an “averaged” quantity because Ek is obtained by averaging the internal energy over all distributions in  microstate k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Setting the first variation of Hk with respect to ck  j to be zero gives the Boltzmann distribution  ck  j (x) = χUk(x)c∞  j e−βqjψ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='6)  Plugging (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='6) back into the expression of Hk yields  Hk =  �  Dk  �  ρ(x)ψ(x) − ϵp  2 |∇ψ(x)|2�  dx −  �  Uk  �  �ϵs  2 |∇ψ(x)|2 + β−1  Nc  �  j=1  c∞  j e−βqjψ(x)  �  � dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='7)  Since the polar energy equals zero when ψ vanishes everywhere, following [48], a constant term  β−1  �  Uk  Nc  �  j=1  c∞  j dx  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='8)  should be added to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='7), which yields the polar energy (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2) in microstate k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Note that  Nc  �  j=1  qjck  j =  −χUkB′(ψ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Plugging this expression into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4) shows that ψ solves the PB equation:  ∇ · ((ϵpχDk + ϵsχUk)∇ψ) − χUkB′(ψ) + ρ = 0  in Ω  in microstate k, in the admissible set  A = {ψ ∈ H1(Ω) : ψ|∂Ω = ψD}  for some ψD ∈ W 1,∞(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='9)  Consequently, ψ maximizes Ip(χDk, ·) in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  6  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  To sum up, in the framework of the PB theory, when deriving ensemble average polar solvation energy,  one should use the mean electrostatic potential ψ among all microstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Consequently, instead of directly  ensemble averaging Ip, one should optimize the Helmholtz free energy, which is obtained by averaging the  internal energy among all micrstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Modeling of Ensemble Average Solvation Energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ensemble Average Bulk Energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The argument we use to define the ensemble average solvation  energy functional is  u =  �  k∈K  pkχDk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  As such, u(x) represents the probability of x ∈ Ω found in the solute phase among all microstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Figure 1(B)  shows the range of u in different regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The definition of u enforces the following physical constraints  u(x) ∈ [0, 1]  for a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' x ∈ Ω  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='10)  and  u = 1  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ωi  and  u = 0  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ωe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11)  Then the admissible set for u is defined as  X = {u ∈ BV (Ω) : u satisfies Constraints (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='10) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The first step of constructing the ensemble average solvation energy functional is to derive formulas for  ensemble average bulk energy contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume f ∈ L1(Ω) is the energy density function of some bulk  energy F, that is, the energy F stored in a region E ⊂ Ω equals  �  E f(x) dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The ensemble average bulk energies can be computed as follows  ⟨Fi⟩ :=  �  k∈K  pk  �  Dk  f dx =  �  Ω  uf dx  and  ⟨Fe⟩ :=  �  k∈K  pk  �  Uk  f dx =  �  Ω  (1 − u)f dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The proof is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Indeed, we will only check the equality for ⟨Fi⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ⟨Fi⟩ =  �  k∈K  pk  �  Dk  f dx =  �  Ω  �  k∈K  pkχDkf dx =  �  Ω  uf dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ensemble Average Polar Energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Following the discussion in Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1, in the classic PB theory,  we will use the mean electrostatic potential ψ among all possible distributions (in all microstates) to derive  the “average” polar energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let cj be the mean ion concentration of the j-th ion species among all possible  distributions (in all microstates), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' cj(x) = E(Cj(x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then  cj(x) = E[E(Cj(x)|Z = k)] =  �  k∈K  pkck  j (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='12)  Because  E[ϵpχDk(x) + ϵsχUk(x)] = u(x)ϵp + (1 − u(x))ϵs =: ϵ(u)(x),  ϵ(u) can be regarded as the “mean” dielectric coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Now the PB theory suggests that ψ ∈ A solves  −∇ · [ϵ(u)∇ψ] = ρ +  Nc  �  j=1  qjcj  in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  To derive the Boltzmann distribution that gives cj, we first compute the ensemble average of E, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5),  by using Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2 and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='12)  ⟨E⟩ =  �  k∈K  pkEk =  �  Ω  �  �ρψ +  Nc  �  j=1  qjcjψ − ϵ(u)  2 |∇ψ|2 −  Nc  �  j=1  µjcj  �  � dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  However, the entropy cannot be ensemble averaged by using Sk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Instead, by the definition of entropy  −TS = β−1  �  {u<1}  Nc  �  j=1  cj [ln(cj) − 1] dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  7  The domain of integration {u < 1} is due to the fact that cj vanishes identically in {u = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Setting the  first variation of the Helmholtz free energy H = ⟨E⟩ − ST with respect to cj to be zero yields  cj = χ{u<1}c∞  j e−βqjψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='13)  After plugging (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='13) into the expression of H, as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='8), the constant term  β−1  �  Ω  χ{u<1}  Nc  �  j=1  c∞  j dx  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='14)  needs to be added to H to adjust the reference state of the zero energy in the grand canonical ensemble  under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Finally, we arrive at ensemble average polar energy  Ip(u, ψ) = H + β−1  �  Ω  χ{u<1}  Nc  �  j=1  c∞  j dx =  �  Ω  �  ρψ − ϵ(u)  2 |∇ψ|2 − χ{u<1}B(ψ)  �  dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='15)  On the other hand, replacing cj in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4) by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='13) shows that ψ ∈ A solves  ∇ · [ϵ(u)∇ψ] − χ{u<1}B′(ψ) + ρ = 0  in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='16)  Hence, ψ maximizes Ip(u, ·) in A for any fixed u ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Although, for every fixed j, there can be multiple choices of ck  j that minimize H, any such  choice gives rise to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='13) by means of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' To see this, we set the first variation of H with respect to ck  j  to be zero and infer that cj = c∞  j e−βqjψ in Uk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Going through all k, one readily get (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ensemble Average Interfacial Energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Based on Formulation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='15), one can define  L(u, ψu) = ⟨Inp(χDk)⟩ + Ip(u, ψu),  where ψu maximizes Ip(u, ·) in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' It only remains to calculate the ensemble average of interfacial energy  contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Before doing that, we will first state a technical lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let {Dk}k∈K be a family of Caccioppoli sets with Dk ⋐ Ω and pk ∈ [0, 1] with �  k∈K pk = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then for each ε > 0, there exists another family { �Dk}k∈K of Caccioppoli sets satisfying �Dk ⋐ Ω and  H2(∂∗ �Dk ∩ ∂∗ �Dj) = 0,  ∀k, j ∈ K, k ̸= j,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='17)  with ∂∗D being the reduced boundary of a Caccioppoli set D, such that  |L(u, ψu) − L(�u, ψ�u)| < ε,  u =  �  k∈K  pkχDk and �u =  �  k∈K  pkχ �  Dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Here, for every v ∈ X, ψv maximizes Ip(v, ·) in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In view of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2, it suffices to construct a family of Caccioppoli sets {Dk,j}∞  j=1 satisfying  Assumption (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='17) such that  lim  n→∞ ∥χDk − χDk,n∥1 = 0,  lim  n→∞  �  Ω  θd|DχDk,n| =  �  Ω  θd|DχDk|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='18)  Following the proof of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3, we can show that there exists a family of smooth functions {fk,n}∞  n=1  such that 0 ≤ fk,j ≤ 1 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ω and  lim  j→∞ ∥χDk − fk,j∥1 = 0,  lim  j→∞  �  Ω  θd|Dfk,j| =  �  Ω  θd|DχDk|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  By the Sard’s Theorem, there exists some S ⊂ (0, 1) with L1((0, 1) \\ S) = 0 such that, for all t ∈ S, the  super-level set Et  k,j = {fk,j > t} has a smooth boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The coarea formula implies that  �  Ω  θd|DχDk| = lim  j→∞  �  Ω  θd|Dfk,j| = lim  j→∞  � 1  0  �  Ω  θd|DχEt  k,j| dt ≥  � 1  0  lim inf  j→∞  �  Ω  θd|DχEt  k,j| dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Therefore, for some t ∈ S,  lim inf  j→∞  �  Ω  θd|DχEt  k,j| ≤  �  Ω  θd|DχDk|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  8  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  Pick the subsequence {jn}∞  n=1 such that  lim inf  j→∞  �  Ω  θd|DχEt  k,j| = lim  n→∞  �  Ω  θd|DχEt  k,jn |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  On the other hand, we can infer from the Chebyshev’s Theorem that  L3(Et  k,jn \\ Dk) ≤ 1  t ∥fk,jn − χDk∥1,  L3(Dk \\ Et  k,jn) ≤  1  1 − t∥fk,jn − χDk∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  This implies that  lim  n→∞ ∥χEt  k,jn − χDk∥1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Therefore, it follows from [8, Corollary 1] that �Dk,n = Et  k,jn satisfies (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='18) with Dk,n replaced by �Dk,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Assume that H2(∂χ �  Dk,n ∩ ∂χ �  Dj,n) > 0 for some k, j ∈ K and k ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Since ∂ �Dk,n is C2, there exists  some a > 0 such that ∂ �Dk,n has a tubular neighborhood Ba(∂ �Dk,n) of width a > 0, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' [28, Exercise 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11]  and [34, Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Denote by ν the outward unit normal of �Dk,n pointing into Ω \\ �Dk,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then the map  defined by  Λ : ∂ �Dk,n × (−a, a) → R3 : (x, r) �→ x + rν(x),  is a C1-diffeomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let Γr := Λ(∂ �Dk,n, r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then, for every i ∈ K, there are at most countably many  r ∈ (−a, a) such that H2(Γr ∩ ∂χ �  Di,n) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Hence we can find r ∈ (−a, a) sufficiently close to 0 such that  H2(Γr ∩ ∂χ �  Di,n) = 0,  ∀i ∈ K  and Γr ⊂ Ωt and  ���χDk,n − χ �  Dk,n  ���  1 +  ����  �  Ω  θd|DχDk,n| −  �  Ω  θd|Dχ �  Dk,n|  ���� < 1/n,  where Dk,n is the region enclosed by Γr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Modifying all �Dk,n, k ∈ K, in such a way yields a family of smooth  sets {Dk,n}k∈K satisfying Assumption (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='17) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  The above lemma tells us that, for any grand canonical ensemble, we can slightly modify the solute regions  {Dk}k∈K to fulfil (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='17) so that the changes in the corresponding solvation energy is “infinitesimally” small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Hence, we can always assume that {Dk}k∈K satisfies (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume that {Dk}k∈K satisfies (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then  �  Ω  θ d|Du| =  �  k∈K  pk  �  Ω  θ d|DχEk|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' By the De Giorgi’s structure theorem, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' [24, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2], χDk are 2-rectifiable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' there exist  Borel sets Fk and C1-functions gk,n : Uk,n → R3, Uk,n ⊂ R2 compact, such that ∥∂Dk∥(Fk) = 0 and  ∂∗Dk = Fk ∪  ∞  �  n=1  gk,n(Uk,n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Pick arbitrary ε > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For every k ∈ K, we can find Nk = Nk(ε) such that  ∥∂Dk∥(Ω ∩  ∞  �  n=Nk+1  gk,n(Uk,n)) ≤  ε  Kθ1pk  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Recall K = |K|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Therefore, we obtain compact sets  Gk,ε :=  Nk(ε)  �  n=1  gk,n(Uk,n),  k ∈ K,  and  Gε :=  �  k∈K  Gk,ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  By the definition of the reduced boundary, the unit normal ν exists everywhere on Gε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' By the Urysohn’s  Lemma, there exists a continuous function φ : R3 → R3 such that φ|Gε = ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Restricting φ on Ω and applying  Stone-Weierstrass, we can find a smooth function φε : Ω :→ R3 such that  ∥φε − φ∥L∞(Gε) < ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  9  Then, in a neighborhood H ⋐ Ω of Gε, we have |φε| > 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Pick h ∈ C∞  0 (Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' [0, 1]) in such that h ≡ 1 in H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Setting ψε(x) = h(x) φε(x)  |φε(x)|, it is an easy task to check that  1 ≥ ψε(x) · ν(x) ≥ 1 − ε  1 + ε,  x ∈ Gε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  By [8, Lemma 1], we can estimate  �  Ω  θ d|Du| ≥  �  Ω  (θψε) · dDu =  �  k∈K  pk  �  Ω  θψε · DχDk dx =  �  k∈K  pk  �  Gk,ε  θψε · DχDk dx − ε  ≥  �  k∈K  pk(1 − ε)  1 + ε  �  Gk,ε  θ d|DχDk| − ε  ≥  �  k∈K  pk(1 − ε)  1 + ε  ��  Ω  θ d|DχDk| −  �  Ω\\Gk,ε  θ d|DχDk|  �  − ε  =  �  k∈K  pk(1 − ε)  1 + ε  �  Ω  θ d|DχDk| − 2ε − ε2  1 + ε .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Since ε is arbitrary, we have  �  Ω  θ d|Du| ≥  �  k∈K  pk  �  Ω  θ d|DχDk|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The inverse inequality is obvious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We have thus proved the assertion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Total Energy Functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Based on Propositions 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5, the ensemble average nonpolar energy  is given by  Inp(u) := ⟨Inp(χDk)⟩ =  �  Ω  θd|Du| +  �  Ω  �  Phu + ρs(1 − u)U vdW�  dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Using Formulation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='15) for the polar energy, we can define the ensemble average total solvation energy as  the minimum value of  E(u) =  �  Ω  θd|Du| +  �  Ω  �  Phu + ρs(1 − u)U vdW�  dx +  �  Ω  �  ρψ − ϵ(u)  2 |∇ψ|2 − χ{u<1}B(ψ)  �  dx  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19)  in X and ψ = ψu is determined via the generalized PB equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='16);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' or equivalently, we seek the value of  L(u, ψ) = Inp(u) + Ip(u, ψ)  evaluated at its saddle points in X × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Note that Constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11) is defined in terms of Ωi and Ωe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In Appendix B, we will justify the robustness  of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19) by showing that its minimum value depends continuously on Ωi and Ωe in a proper topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Analysis of Ensemble Average Solvation Energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' E has a global minimizer in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We infer from Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1 that  Ip(u, ψu) ≥ −ϵs∥ψu∥2  H1 − (∥B(ψu)∥∞ + ∥ρ∥∞∥ψu∥∞) Vol(Ω) ≥ C  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='20)  for some C independent of u ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Here and in the sequel, for any u ∈ X, ψu always denotes the solution of  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Therefore, E is bounded from below and we can pick up a minimizing sequence {˜un}∞  n=1 ⊂ X of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  However, E is not l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' To prove the existence of a minimizer, we will use a relaxation technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For  m ∈ N, we define  Lm(u, ψ) = Inp(u) +  �  Ω  �  ρψ − ϵ(u)  2 |∇ψ|2 − (1 − u)1/(2m+1)B(ψ)  �  dx  and  Em(u) = Lm(u, ψu,m),  where ψu,m ∈ A solves  ∇ · [ϵ(u)∇ψ] − (1 − u)1/(2m+1)B′(ψ) + ρ = 0  in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  10  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  Note that ψu,m is the unique maximizer of Lm(u, ·) in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Easy computations show that Em is strictly convex  and l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in X with respect to convergence in L1(Ω) in view of [8, Corollary 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' By the direct method of  calculus of variation, Em has a unique minimizer um in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Set  M = inf  u∈X E(u),  Mm = Em(um).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Claim 1:  lim  m→∞ Mm = M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof of Claim 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We first show that Mm is monotonically decreasing and Mm ≥ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Indeed,  Mm ≥ Lm(um, ψum) ≥ L(um, ψum) ≥ M,  where ψum is the solution of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1) with u = um, and similarly  Mm ≥ Lm(um, ψum+1,m+1) ≥ Lm+1(um, ψum+1,m+1) ≥ Mm+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Given any ε > 0, for sufficiently large n  M ≤ E(˜un) ≤ M + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  On the other hand, since, for any fixed u ∈ X,  lim  m→∞ ∥(1 − u)1/(2m+1) − χ{u<1}∥1 = 0, Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2 implies  that  M ≤ Em(˜un) ≤ M + 2ε  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='21)  for sufficiently large n and m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The arbitrariness of ε shows that lim  m→∞ Mm = M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ■  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='21) and Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1 imply that ∥um∥BV is uniformly bounded and, by [24, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4], there  exists a subsequence of {um}∞  m=1, not relabelled, such that as m → ∞  um → u0  in L1(Ω)  for some u0 ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then for any m ∈ N, by [8, Lemma 2]  Mm ≥ Lm(um, ψu0) ≥ L(um, ψu0) ≥ L(u0, ψu0) ≥ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  In view of Claim 1, pushing m → ∞ shows that u0 is a minimizer of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Note that the convexity of E implies that any local minimizer of E must be global.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A regularization approach to solvation energy calculatiion  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Regularization by p-energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Regularization is a popular approach in the derivation of computational  models of non-differentiable functionals like E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Here we will develop a p-energy regularization approach based  on our previous work [14, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In particular, this approach enables us to relax the two-sided obstacle, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='10), in the variational analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  In the rest of this section, we will assume U vdW ∈ C∞(Ω \\ �Nm  i=1 B(xi, σi), R−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This can be realized by  taking U vdW as the attractive part of Lennard-Jones potential [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Note that this assumption is reasonable  in the solvation analysis of real-world macromolecules since u ≡ 1 in Ωi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The L-J potential can be divided  into attractive and repulsive parts in different ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For instance, we can take a Weeks-Chandler-Andersen  (WCA) decomposition based on the original WCA theory [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Define pn =  2n  2n−1 for n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We are interested in sufficiently large n so that pn ∈ (1, ϵs/(ϵs − ϵp)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Denote  the set of all such n by N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let  Inp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n(u) = γ  �  Ω  |∇u|pn dx +  �  Ω  �  Phupn + ρs(1 − upn)U vdW�  dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  For the polar portion, due to the extra non-differentiable term χ{u<1}, we will consider the regularization of  Em in view of Claim 1 in the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' More precisely, define  Ip;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(u, ψ) =  �  Ω  �  ρψ − 1  2ϵn(u)|∇ψ|2 − (pn − upn)1/(2m+1)B(ψ)  �  dx,  where ϵn(u) = ϵpupn + ϵs(1 − upn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We seek to minimize  Em,n(u) = Inp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n(u) + Ip;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(u, ψu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n),  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  11  in the admissible sets  Xn = {u ∈ W 1,pn(Ω) : |u|pn ≤ pn a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ω  and u satisfies Constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11)},  where ψu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n ∈ A solves  ∇ · (ϵn(u)∇ψ) − (pn − upn)1/(2m+1)B′(ψ) + ρ = 0  in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1)  Define  Lm,n(u, ψ) = Inp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n(u) + Ip;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(u, ψ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then by Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1, it is not hard to check that u is a global minimizer of Em,n in Xn iff (u, ψu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) is a  saddle point of Lm,n in Xn × A, where ψu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n solves (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' See [14, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3] for a related problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For every n ∈ N and m ∈ N, Em,n has a unique minimizer in Xn, which actually belongs to  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' To show the lower semi-continuity of Em,n in Xn, we first observe that  Qn(w) =  �  Ω  (θ|∇w|pn + Phupn) dx,  w ∈ Wn := {w ∈ W 1,pn(Ω) : w satisfies Constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11)},  is an equivalent norm of Wn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Therefore, Qn is weakly l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Wn, which further implies that Em,n is weakly  l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Xn in view of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The existence and uniqueness of a minimizer of Em,n can be proved by  the direct method of calculus of variation and the strict convexity of Em,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  It remains to show that the minimizer umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n of Em,n in Xn indeed belongs to X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n be the  solution to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1) with u = umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' If L3({umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n > 1} ∪ {umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n < 0}) > 0, define  ¯umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(x) =  �  �  �  �  �  1,  if umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(x) > 1,  0,  if umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(x) < 0,  umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(x),  elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then ¯umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n ∈ X ∩ Xn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' and direct computations show that  Lm,n(¯umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n, ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) < Lm,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n, ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  A contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Hence, umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Asymptotic behaviour of the regularized energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' When n ∈ N, let umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n be the unique  minimizer of Em,n in Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The following theorem establishes the asymptotic behavior of Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume that Σi ∈ C2, i = 0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' As n → ∞, umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n converges to a minimizer of E in Lp(Ω)  for any 1 ≤ p < ∞ and weak∗ in BV (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Moreover, lim  n→∞ Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) = min  u∈X Em(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The constants Ci in this proof are independent of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' First, fix arbitrary v ∈ Xn, we have  Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) ≤ Em,n(v) ≤  �  Ω  θ|∇v|pn dx + 2PhVol(Ω \\ Ωi) −  �  Ωt  ρsU vdW dx + ∥ψv∥∞∥ρ∥∞Vol(Ωi) ≤ C1,  where ψv ∈ A solves (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1) with u = v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A similar computation as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='20) shows that  C1 ≥ Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) ≥  �  Ω  θ|∇umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n|pn dx + Ph∥umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n∥pn  pn +  �  Ω\\Ωi  ρsU vdW dx + Ip;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n, ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n)  ≥  ��  Ω  θd|Dumin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n|  �pn ��  Ω  θ dx  �1−pn  + Ph∥umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n∥pn  1 (Vol(Ω))1−pn + C2,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2)  where ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n ∈ A solves (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1) with u = umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We thus infer from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2) that  ∥umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n∥W 1,1 = ∥umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n∥BV ≤ C3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then [24, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4] implies that for any subsequence of {umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n}∞  k=1, there exists a further sub-  sequence, not relabelled, converging to some u0 ∈ X in L1(Ω) and weak∗ in BV (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Riesz-Thorin  interpolation theorem then implies that umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n → u0 in Lp(Ω) for all p ∈ [1, ∞) as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Further, it  follows from [8, Corollary 1], (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2) and Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2 that  Em(u0) ≤ lim inf  n→∞ Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  12  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  On the other hand, for sufficiently large j ∈ N, we define  wj(x) =  �  �  �  �  �  1,  x ∈ Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j  0,  x ∈ Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j  u0(x),  elsewhere,  where Ωl;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j := {x ∈ Ω : dist(x, Ωl) < 1/j} with l ∈ {i, e}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We will show that  lim sup  n→∞ Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) ≤ Em(wj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3)  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3 implies that we can find a sequence {wj,h}∞  h=1 such that wj,h ∈ C∞(Ω) ∩ Xn for all n and  wj,i → wj in L1(Ω)  and  �  Ω  θd|Dwj,h| →  �  Ω  θd|Dwj|  as h → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Since umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n minimizes Em,n in Xn ⊃ C∞(Ω) ∩ Xn, we have  Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) ≤ Em,n(wj,h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Pushing n → ∞, the dominated convergence theorem implies that  lim sup  n→∞ Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) ≤ Em(wj,h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then Lemmas A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2 and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3 immediately yield (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Now Lemmas A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2 and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4 imply that  lim sup  n→∞ Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) ≤ Em(u0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4)  Let umin be a global minimizer of Em.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' It is important to notice that the proof of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4) actually holds for any  element of X, in particular umin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Hence  Em(umin) ≥ lim  n→∞ Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) = Em(u0) ≥ Em(umin).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Therefore, u0 is indeed a global minimizer of Em.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  The following conclusion of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2 can be easily obtained in view of Claim 1 in the proof of  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Under the conditions of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2,  lim  m→∞ lim  n→∞ Em,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) = min  u∈X E(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' It seems to be more natural to use non-parametric minimal surface type functionals to regularize  Em.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For example, when θ ≡ γ, one may consider the following regularization of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19)  Eε(u) = γ  �  Ω  �  ε + |∇u|2 dx +  �  Ω  �  Phupn + ρs(1 − upn)U vdW�  dx + Ip;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n(u, ψu)  with ε > 0, where ψu ∈ A solves (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' However, the minimizer of Eε may admit jump discontinuous along  Σi unless Ωt satisfies certain geometric conditions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' the mean curvature of Σi is large enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' See [29,41]  for instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Such geometric conditions are unrealistic for most biomolecules due to their complex shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The possible presence of jump discontinuities may become a source of inaccuracy in numerical simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Critical Points of the regularized energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n be the minimizer of Em,n in Xn and  ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n ∈ A be the solution of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1) with u = umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Since umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n ∈ X, given any φ ∈ C∞  0 (Ωt), for  sufficiently small ε > 0, whenever t ∈ (−ε, ε), umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n + tφ ∈ Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We thus have  lim  t→0  Lm,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n + tφ, ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) − Lm,n(umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n, ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n)  t  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  This implies that umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n solves  ∇ ·  �  θ|∇u|pn−2∇u  �  − upn−1Vm,n(u, ψ) = 0  in Ωt  in the weak sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Here  Vm,n(u, ψ) = Ph − ρsU vdW +  B(ψ)  (2m + 1)(upn − pn)2m/(2m+1) + ϵs − ϵp  2  |∇ψ|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  13  Combining with (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1), (umin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n, ψmin;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='m,n) is a weak solution to the following system  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  ∇ · (ϵn(u)∇ψ) + (pn − upn)1/(2m+1)  Nc  �  j=1  c∞  j qje−βψqj + ρ = 0  in  Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ψ = ψD  on  ∂Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ∇ ·  �  θ|∇u|pn−2∇u  �  − upn−1Vm,n(u, ψ) = 0  in  Ωt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  u = 1  in  Ωi ∪ Σ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  u = 0  in  Ωe ∪ Σ0  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5)  in ˚  Xn × A, where  ˚  Xn = {u ∈ W 1,pn(Ω) : |u|pn < pn a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ω  and  u satisfies Constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  We are interested in the case of sufficiently large n and m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5) has a unique solution (u, ψ) in ˚  Xn × A, which actually belongs to X × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' (i) Let Cm,n be the set of all solutions of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5) in ˚  Xn × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume that (u, ψ) ∈ Cm,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then  −∇ ·  �  θ|∇u|pn−2∇u  �  = −upn−1Vm,n(u, ψ)  in Ωt  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='6)  in the distributional sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Since ∇ ·  �  θ|∇u|pn−2∇u  �  ∈ W −1,p′  n(Ωt), it follows that upn−1Vm,n(u, ψ) ∈  W −1,p′  n(Ωt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Note that u− := min{u, 0} ∈ W 1,pn  0  (Ωt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Multiplying both sides of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='6) by u− and integrating  over Ωt yield  0 ≤  �  Ωt  θ|∇u−|pn dx = −  �  Ωt  |u−|pnVm,n(u, ψ) dx ≤ 0  because Vm,n(u, ψ) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This shows that u− = 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ωt and thus 0 ≤ u a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ωt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For the essential  upper bound of u, we consider w = 1 − u, which weakly solves  −∇ ·  �  θ|∇w|pn−2∇w  �  = (1 − w)pn−1Vm,n(u, ψ)  in Ωt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Following the argument above, one has for w− ∈ W 1,pn  0  (Ωt) that  0 ≤  �  Ωt  θ|∇w−|pn dx =  �  Ωt  (1 − w)pn−1w−Vm,n(u, ψ) dx ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  This implies that w− = 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ωt and thus u ≤ 1 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ωt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Therefore, (u, ψ) ∈ X × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (ii) Suppose that (v, ψv), (u, ψu) ∈ Cm,n satisfy  Lm,n(v, ψv) < Lm,n(u, ψu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Since v − u ∈ W 1,pn  0  (Ωt) ∩ L∞(Ωt), we have  �  Ωt  �  θ|∇u|pn−2∇u · ∇(v − u) + upn−1V (ψu)(v − u)  �  dx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='7)  By Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1, it holds that  Lm,n(v, ψu) ≤ Lm,n(v, ψv) < Lm,n(u, ψu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Put h = Lm,n(v, ψu) − Lm,n(u, ψu) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Note that ˚  Xn is convex in W 1,pn(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Put  J(t) = (1 − t)u + tv ∈ ˚  Xn,  t ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then by the convexity of Lm,n(·, ·) in its first argument,  Lm,n(J(t), ψu) − Lm,n(u, ψu) ≤ (1 − t)Lm,n(u, ψu) + tLm,n(v, ψu) − Lm,n(u, ψu) ≤ th < 0  for all t ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dividing both sides by t and pushing t → 0+ in the above inequality yield  pn  �  Ωt  �  θ|∇u|pn−2∇u · ∇(v − u) + upn−1Vm,n(u, ψu)(v − u)  �  dx ≤ h < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  A contradiction to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  We thus infer that Lm,n(·, ·) is constant on Cm,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  From the uniqueness of a  minimizer of Em,n in Xn, we infer that (u, ψu) = (v, ψv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  14  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A comparison with GFBVISM  It is of both theoretical and practical importance to understand the difference between the proposed  model (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19) and the existing VISMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In this section, we will compare (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19) with a closely related solvation  model, geometric-flow based VISM (GFBVISM), whose original formulation [11] reads as  E(2)(u) = Inp(u) + I(2)  p (u, ψ),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1)  where  I(2)  p (u, ψ) =  �  Ω  �  ρψ − ϵ(u)  2 |∇ψ|2 − (1 − u)B(ψ)  �  dx,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2)  and ψ ∈ A solves  ∇ · [ϵ(u)∇ψ] − (1 − u)B′(ψ) + ρ = 0  in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3)  Although (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='19) shares some common feature with GFBVISM, they differ in several fundamental aspects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  First, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1) was introduced in an ad hoc way to create a transition region between the solute and solvent  without an explanation of the physical meanings of the transition parameter u and the predicted energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Second, Constraints (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='10) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11) are absent in the original formulation of GFBVISM [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Without  these two conditions, GFBVISM may admit non-physical minimizers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' u is trivial or u < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Third and most importantly, the proposed model corrects the derivation of the ensemble average polar  energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Due to Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2, one may guess that I(2)  p  approximates the ensemble average polar energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  However, Formulation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2) is questionable in the sense that it is derived from an erroneous “entropy”  formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' To see this, on a heuristic level, one can ensemble average the entropy and obtain  −T⟨S⟩ = −T  �  k∈K  pkSk = β−1 �  k∈K  pk  �  Ω  Nc  �  j=1  ck  j  �  ln(ck  j ) − 1  �  dx  and  ⟨H⟩ := ⟨E⟩ − T⟨S⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  In view of Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3, we put the first variations of ⟨H⟩ with respect to all ck  j to be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This gives (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  It follows from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='12) that  cj(x) =  �  k∈K  pkck  j (x) =  �  k∈K  pkχUk(x)ck  j (x) = (1 − u(x))c∞  j e−βqjψ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4)  Plugging (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4) into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4) yields (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Using the expression (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4) of cj in ⟨H⟩ and adding a constant term  β−1 �Nc  j=1 c∞  j  �  Ω(1 − u)dx to adjust the state of zero energy as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='14) give the polar energy formulation  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' However, from a statistical mechanics point of view, the choice of the “entropy” ⟨S⟩ and “Helmholtz  free energy” ⟨H⟩ in the above derivation are incorrect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Therefore, the polar energy formulation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='15) is  more physical than (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Conclusion  Diffuse-interface variational implicit solvation models (VISM) have achieved great success in solvation  energy calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In contrast, on a theoretical level, several questions concerning the diffuse-interface  VISMs remain open: (1) What is the physical meaning of a diffuse interface?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (2) What energy does a  diffuse-interface VISM predict?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In this paper, a novel diffuse-interface VISM is introduced and analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Based on statistical mechanics and geometric measure theory, we show that the diffuse interface profile u(x)  represents the probability of a point x ∈ Ω found in the solute phase among all microstates in the grand  canonical ensemble under consideration and the new VISM is capable of capturing the ensemble average  solvation energy, the experimentally observable energy in solvation processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The significance of the work is multi-fold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' First, it illuminates the physical meaning of a diffuse interface  in VISM and unveils the relationship between VISM and ensemble average solvation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Second, in the  routine calculation of the ensemble average solvation energy, one needs to carry out molecular dynamics (MD)  simulations to obtain thousands of solute-solvent configures (snapshots) and perform energy calculations for  each snapshot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  By rigorously modeling the impact of conformational changes in the solvent media, the  proposed model will reproduce the ensemble average solvation energy by means of one diffuse-interface  configuration, which is expected to be significantly faster than ensemble averaging the energies computed  from thousands of snapshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Last but not least, the modeling paradigm in this work seems to be applicable  to a large variety of multi-scale problems with both interfacial and bulky energy components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  15  A new computational model is proposed to capture the global minimum of the ensemble average VISM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The robustness of the model is justified by verifying the continuous dependence of the predicted energy on  the model constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Numerical implementations based on the proposed computational model and further  theoretical analysis of the new VISM will be conducted in a series of future works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Some Technical Lemma  The following two lemmas can be obtained by following the proofs of [14, Propositions 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume that a, b, c ∈ L∞(Ω) satisfy  0 < L0 ≤ a ≤ L1,  0 ≤ b ≤ L2,  ∥c∥∞ ≤ L3  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1)  for some constants Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then the functional  G(ψ) =  �  Ω  �a  2|∇ψ|2 + bB(ψ) − cψ  �  dx  has a unique minimizer ψ ∈ A for every ψD ∈ W 1,∞(Ω), c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='9), or equivalently, ψ weakly solves  �  ∇ · (a∇ψ) − bB′(ψ) + c = 0  in  Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ψ = ψD  on  ∂Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Moreover, for some constant C∞ depending only on Li and ψD  ∥ψ∥H1 + ∥ψ∥∞ ≤ C∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let an, bn, c ∈ L∞(Ω) satisfy (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1), n = 0, 1, · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume that ψn is the unique minimizer of  Gn(ψ) =  �  Ω  �an  2 |∇ψ|2 + bnB(ψ) − cψ  �  dx  in A for some ψD ∈ W 1,∞(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' If an → a0 and bn → b0 in L1(Ω) as n → ∞, then  ψn → ψ0  in H1(Ω),  and  lim  n→∞ Gn(ψn) = G0(ψ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Assuming that Σi ∈ C2, i = 0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For sufficiently large j ∈ N, we define  Ωl;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j := {x ∈ Ω : dis(x, Ωl) < 1/j},  l ∈ {i, e},  and  Yj := {u ∈ X : u ≡ 1 in Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j  and  u ≡ 0 in Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For every f ∈ Yj, there exists a sequence {fn}∞  n=1 ⊂ C∞(Ω) satisfying Constraints (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='10)  and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11) such that as n → ∞  fn → f in L1(Ω)  and  �  Ω  θd|Dfn(x)| →  �  Ω  θd|Df(x)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For any δ > 0, let ηδ be a positive Friedrichs mollifying kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For any n ∈ N, we choose εn > 0  so small that fn := ηεn ∗ f satisfies Constrain (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='11) and ∥fn − f∥1 ≤ 1/n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Constraint (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='10) is obviously  fulfilled by fn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Thus, lim  n→∞ ∥fn − f∥1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [8, Corollary 1] implies that  �  Ω θd|Df(x)| ≤ lim inf  n→∞  �  Ω θd|Dfn(x)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Extending f to be identically zero outside  Ω, we can consider f as an element in BV (R3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For any φ ∈ C1  0(Ω) with ∥φ∥∞ ≤ 1, we have  �  Ω  fn∇ · (θφ) dx =  �  Ω  (ηεn ∗ f) ∇ · (θφ) dx =  �  Ω  f∇ · [ηεn ∗ (θφ)] dx =  �  Ω  f∇ ·  �  θ  �ηεn ∗ (θφ)  θ  ��  dx  ≤ ∥(ηεn ∗ θ)/θ∥L∞(Ω)  �  Ω  θd|Df(x)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Here (ηεn ∗ θ)(x) =  �  Ω ηεn(x − y)θ(y) dy for x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Taking supremum over all such φ, we derive that  �  Ω  θd|Dfn(x)| ≤ ∥(ηεn ∗ θ)/θ∥L∞(Ω)  �  Ω  θd|Df(x)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  By the uniform continuity of θ, it is not a hard task to verify that lim  n→∞ ∥(ηεn ∗ θ)/θ∥L∞(Ω) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Therefore,  the above inequality implies that lim sup  n→∞  �  Ω θd|Dfn(x)| ≤  �  Ω θd|Df(x)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  16  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For every f ∈ X, we define {fj}∞  j=1 ⊂ BV (Ω) by  fj(x) =  �  �  �  �  �  1,  x ∈ Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j  0,  x ∈ Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j  f(x),  elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then fj → f in L1(Ω) and  �  Ω θd|Dfj(x)| →  �  Ω θd|Df(x)| as j → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The proof for fj → f in L1(Ω) is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' So we will only show the second part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In the rest  of the proof, it is assumed that i ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Denote by νΣi the outward pointing (into Ωt) unit normal of Σi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Following the proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4, the map  Λi : Σi × (−a, a) → R3 : (x, r) �→ x + rνΣi(x)  is a C1-diffeomorphism for sufficiently small a > 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' and Σi,r := Λi(Σi, r) is a C1-hypersurface, whose outward  unit normal is denoted by νi,r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In particular, νi,0 = νΣi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We define the orientation of Σi,r in such a way that  νi,r are continuous vector fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' By the inverse function theorem, there exist two maps Pi ∈ C1(Ba(Σi), Σi)  and di ∈ C1(Ba(Σi), (−a, a)), where Pi is the nearest point projection onto Σi and di is the signed distance  to Σi with di(x) > 0 for x ∈ Ba(Σi) ∩ Ωt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Note that di is indeed C2, see [44] for example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We can define  two C1-vector fields Vi : Ba(Σi) → R3 by  Vi(x) = νi,di(x)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  For any r ∈ (0, a), put Ui,r := Br(Σi)∩Ωt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Due to the trace theorem of BV -functions, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' [24, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1],  we have for all f ∈ X that  �  Ui,r  f∇ · (θVi) dx +  �  Ui,r  (θVi) · d[Df] =  �  Σi,r  θTrf dH2 −  �  Σi  θTrf dH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Here Trf is the trace of f|Ui,r on ∂Ui,r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' and [Df] is the vector-valued measure for the gradient of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Pushing r → 0+ above yields that  lim  r→0+  �  Σi,r  θTrf dH2 =  �  Σi  θTrf dH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2)  [8, Lemma 1] implies that  �  Ω θd|Df(x)| ≤ lim inf  j→∞  �  Ω θd|Dfj(x)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Observe that ∂Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j = Σ1,1/j and ∂Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='j\\∂Ω =  Σ0,1/j for sufficiently large j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Denote by �Trf the trace of f|Ωt\\(U0,r∪U1,r) on ∂ [Ωt \\ (U0,r ∪ U1,r)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For any  u ∈ X, we will show  �  Ω  θd|Du(x)| =  �  Ωt\\(U0,r∪U1,r)  θd|Du(x)| +  �  i=0,1  �  Ui,r  θd|Du(x)|  +  �  i=0,1  �  Σi  θ|i − Tru| dH2 +  �  i=0,1  �  Σi,r  θ  ���Tru − �Tru  ��� dH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3)  Indeed, for any φ ∈ C1  c (Ω) with ∥φ∥∞ ≤ 1,  �  Ω  u∇ · (θφ) = −  �  Ωt\\(U0,r∪U1,r)  (θφ) · d[Du] −  �  i=0,1  �  Ui,r  (θφ) · d[Du] − (−1)i �  i=0,1  �  Σi  θ(i − Tru)φ · νΣi dH2  − (−1)i �  i=0,1  �  Σi,r  θ(Tru − �Tru)φ · νi,r dH2  ≤  �  Ωt\\(U0,r∪U1,r)  θd|Du(x)| +  �  i=0,1  �  Ui,r  θd|Du(x)| +  �  i=0,1  �  Σi  θ|i − Tru| dH2  +  �  i=0,1  �  Σi,r  θ  ���Tru − �Tru  ��� dH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  17  Taking supremum over all φ ∈ C1  c (Ω) with ∥φ∥∞ ≤ 1 shows that the LHS of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3) is less than or equal to  the RHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' To show the equality in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3), note that  �  i=0,1  �  Σi  (θφ) · d[Du] +  �  i=0,1  �  Σi,r  (θφ) · d[Du] =(−1)i �  i=0,1  �  Σi  θ(i − Tru)φ · νΣi dH2  + (−1)i �  i=0,1  �  Σi,r  θ(Tru − �Tru)φ · νi,r dH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Taking φ ∈ C1  c (Ω) with ∥φ∥∞ ≤ 1 such that φ = (−1)i+1Vi in U i,r, we can infer from the above equality  that  �  i=0,1  �  Σi  θd|Du| +  �  i=0,1  �  Σi,r  θd|Du| ≥  �  i=0,1  �  Σi  θ|i − Tru| dH2 +  �  i=0,1  �  Σi,r  θ  ���Tru − �Tru  ��� dH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Therefore, the other direction of the inequality in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3) holds and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3) is valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' This implies that  �  Ω  θd|Dfj(x)| −  �  Ω  θd|Df(x)| =  �  i=0,1  ��  Σi,1/j  θ|i − �T1/jf| dH2 −  �  Σi  θ|i − T1/jf| dH2 −  �  Ui,1/j  θd|Df(x)|  �  −  �  i=0,1  ��  Σi,1/j  θ  ���T1/jf − �T1/jf  ��� dH2  �  ≤  �  i=0,1  ��  Σi,1/j  θ|i − T1/jf| dH2 −  �  Σi  θ|i − T1/jf| dH2 −  �  Ui,1/j  θd|Df(x)|  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  From (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2), we infer that  lim  j→∞  ��  Σi,1/j  θ|i − T1/jf| dH2 −  �  Σi  θ|i − T1/jf| dH2 −  �  Ui,1/j  θd|Df(x)|  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  This implies that lim sup  j→∞  �  Ω θd|Dfj(x)| ≤  �  Ω θd|Df(x)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Continuous dependence on Ωi and Ωe  Assume that {�Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 and {�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 are two sequences of Lipschitz subdomains in Ω with  Nm  �  j=1  B(xj, σj) ⊂ �Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n ⋐ Ω \\ �Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n  and  ∂Ω ⊂ ∂�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  We consider the family of energy functionals �En defined by replacing Ωi and Ωe by �Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n and �Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n in E,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The corresponding admissible sets are  �  Xn = {u ∈ BV (Ω) : 0 ≤ u ≤ 1 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in Ω  and  u = 1 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in �Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n and u = 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' in �Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then for each n, there is a unique minimizer �umin,n of �En in �  Xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The lemma below can be proved by following the proof of [14, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2] line by line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume that {�Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 and {�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 satisfy �Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n ⊆ Ωi and �Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n ⊆ Ωe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Suppose further that  χ�Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n → χΩi  and  χ�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n → χΩe  in L1(Ω)  as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then, lim  n→∞  �En(�umin,n) = E(umin), where umin is a minimizer of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Recall that the Hausdorff metric on compact subsets K ⊂ R3 is defined by  dH(K1, K2) = max{ sup  x∈K1  d(x, K2), sup  x∈K2  d(x, K1)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Given a closed surface Σ in R3, its normal bundle is given by  NΣ = {(q, νΣ(q)) : q ∈ Σ} ⊂ R3 × R3,  18  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  where νΣ(q) is the outward unit normal of Σ at q ∈ Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' When {�Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 and {�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 approximate Ωi and  Ωe from the exterior, the following counterpart of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Suppose that Σj ∈ C2, j = 0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assume that {�Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 and {�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 are C1 and  Ωi ⊆ �Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n  and  Ωe ⊆ �Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Let Σ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n = ∂�Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n and Σ0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n = ∂�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n \\ ∂Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Suppose further that  lim  n→∞ dH(NΣ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n, NΣ1) = lim  n→∞ dH(NΣ0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n, NΣ0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then, lim  n→∞  �En(�umin,n) = E(umin), where umin is a minimizer of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' It suffices to consider the case Ωe = �Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The proof for the general situation is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Following  the proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='5 and Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4, the map  Λ : Σ1 × (−a, a) → R3 : (q, r) �→ q + rνΣ1(q)  is a C1-diffeomorphism for some a > 0, where the outward unit normal νΣ1 points into Ωt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Σr := Λ(Σ1, r) is  a C1-hypersurface, whose outward unit normal is denoted by νr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' By [44, Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3], for sufficiently large  n, there exist ρn ∈ C1(Σ1) with 0 ≤ ρn ≤ a such that Σ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n is the image of the following C1-diffeomorphism  Ψρn : Σ1 → R3 : q �→ q + ρn(q)νΣ1(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Let rn := ∥ρn∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then lim  n→∞ rn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' For sufficiently large n ∈ N, we define  un(x) =  �  1,  x ∈ Ωn,  umin(x),  elsewhere,  where Ωn is the region enclosed by Σrn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Since un ∈ �  Xn and �umin,n ∈ X, we have  E(umin) ≤ �En(�umin,n) ≤ E(un).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1)  From a slight variant of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='4, we learn that as n → ∞  un → umin  in L1(Ω)  and  �  Ω  θd|Dun| →  �  Ω  θd|Dumin|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  The dominated convergence theorem and Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2 give lim  n→∞ E(un) = E(umin).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then the asserted state-  ment follows by pushing n → ∞ in (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Suppose that Σj ∈ C2, j = 0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Assume that {�Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 and {�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n}∞  n=1 are C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Let  Σ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n = ∂�Ωi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n and Σ0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n = ∂�Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n \\ ∂Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Suppose further that  lim  n→∞ dH(NΣ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n, NΣ1) = lim  n→∞ dH(NΣ0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n, NΣ0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Then, lim  n→∞  �En(�umin,n) = E(umin), where umin is a minimizer of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' As in the above proof, we only consider the case that Ωe = �Ωe;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' It again follows from [44, Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='3]  that, for sufficiently large n, Σ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n can be expressed as a C1−normal graph over Σ1 with height function  ρn ∈ C1(Σ1, (−a, a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Let rn = ∥ρn∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Following the notations in the proof of Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2, we define  Σ±rn := Λ(Σ1, ±rn) and Ω±  n to be the region enclosed by Σ±rn, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' We introduce �E±  n as defined  by replacing Ωi by Ω±  n , respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Their corresponding minimizers are denoted by u±  min,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Then  �E−  n (u−  min,n) ≤ �En(�umin,n) ≤ �E+  n (u+  min,n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  From Lemmas B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='1 and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='2, we learn that lim  n→∞  �E−  n (u−  min,n) = lim  n→∞  �E+  n (u+  min,n) = E(umin).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  □  Acknowledgements  The research of Zhao was supported in part by the National Science Foundation (NSF) grant DMS-  2110914.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The research of Chen was supported in part by the National Science Foundation (NSF) grant  DMS-1818748.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  19  References  [1] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Baker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Improving implicit solvent simulations:  a Poisson-centric view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Current Opinion in Structural Biology,  15(2):137–43, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [2] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Baker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Sept, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Joseph, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Holst, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Electrostatics of nanosystems: Application to  microtubules and the ribosome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences, 98(18):10037–10041, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' How to keep dry in water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Nature, 423(6935):25–26, May 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [4] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Bates, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wei, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Minimal molecular surfaces and their applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Computational  Chemistry, 29(3):380–91, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Boschitsch and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Fenley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Hybrid boundary element and finite difference method for solving the nonlinear  Poisson-Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Computational Chemistry, 25(7):935–955, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [6] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Botello-Smith, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Liu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Cai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhao, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Luo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Numerical poisson–boltzmann model for continuum  membrane systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chemical Physics Letters, 555:274–281, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [7] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Braga, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Alves, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Silva, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Nascimento, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Silva, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Andrade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' Curr Top Med Chem, 14(16):1899–1912,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [8] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Carlier and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Comte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' On a weighted total variation minimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=', 250(1):214–226, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Che, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dzubiella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content='  [10] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Imaging, 2010(308627), 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [11] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Differential geometry based solvation model I: Eulerian formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=', 229(22):8231–8258, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [12] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' Differential geometry based solvation models I: Eulerian formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=', 229:8231–8258, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [13] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' Differential geometry based solvation models II: Lagrangian formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 63:1139–1200, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [14] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Shao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A new approach to constrained total variation solvation models and the study of solute-solvent  interface profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
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+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 130:119–136, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [15] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Differential geometry based solvation models III: Quantum formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=',  135:1941108, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [16] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chun, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Thomas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Baker, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Bates, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Variational approach for nonpolar  solvation analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Journal of Chemical Physics, 137(8):084101, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [17] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Cheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dzubiella, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Application of the level-set method to the implicit solvation of  nonpolar molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Chemical Physics, 127(8), 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Crowley and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Golovin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Cation-pi interactions in protein-protein interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Proteins: Structure, Function, and  Bioinformatics, 59(2):231–239, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [19] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dai, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Lu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Convergence of phase-field free energy and boundary force for molecular solvation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 227(1):105–147, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [20] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Electrostatic contribution to the binding stability of protein-protein complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Proteins, 65(1):87–  102, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dragan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Read, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Makeyeva, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Milgotina, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Churchill, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Crane-Robinson, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Privalov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' DNA  binding and bending by HMG boxes: Energetic determinants of specificity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Molecular Biology, 343(2):371–393,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dzubiella, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Swanson, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Coupling hydrophobicity, dispersion, and electrostatics in continuum  solvent models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 96:087802, Mar 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dzubiella, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Swanson, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Coupling nonpolar and polar solvation free energies in implicit  solvent models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Journal of Chemical Physics, 124(8):084905, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [24] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Evans and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Gariepy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Measure theory and fine properties of functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Studies in Advanced Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' CRC  Press, Boca Raton, FL, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Feig and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Brooks III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Recent advances in the development and application of implicit solvent models in biomolecule  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Curr Opin Struct Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 14:217 – 224, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [26] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Fogolari and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Briggs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' On the variational approach to poisson–boltzmann free energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chemical Physics Letters,  281(1):135–139, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [27] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Fogolari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Brigo, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Molinari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural  biology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Molecular Recognition, 15(6):377–92, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [28] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Gilbarg and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Trudinger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Elliptic partial differential equations of second order, volume 224 of Grundlehren der Math-  ematischen Wissenschaften [Fundamental Principles of Mathematical Sciences].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Springer-Verlag, Berlin, second edition,  1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [29] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Giusti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Minimal surfaces and functions of bounded variation, volume 80 of Monographs in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Birkh¨auser  Verlag, Basel, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Grant, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Pickup, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Sykes, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Kitchen, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Nicholls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Gaussian Generalized Born model: application  to small molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Physical Chemistry Chemical Physics, 9:4913–22, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [31] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Grochowski and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Trylska.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Continuum molecular electrostatics, salt effects and counterion binding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' a review of the  Poisson-Boltzmann theory and its modifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Biopolymers, 89(2):93–113, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  20  ENSEMBLE AVERAGE ENERGY AND SOLUTE-SOLVENT INTERFACIAL FLUCTUATIONS  [32] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Kuhn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Siani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Pique, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Fisher, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Getzoff, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Tainer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The interdependence of protein  surface topography and bound water molecules revealed by surface accessibility and fractal density measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of  Molecular Biology, 228(1):13–22, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [33] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Lamm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Poisson-Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Lipkowitz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Larter, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Cundari, editors, Reviews in  Computational Chemistry, pages 147–366.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' John Wiley and Sons, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', Hoboken, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' LeCrone, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Shao, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Simonett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The surface diffusion and the Willmore flow for uniformly regular hypersurfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  Discrete Contin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' S, 13(12):3503–3524, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [35] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Levy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Gallicchio, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Felts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' On the nonpolar hydration free energy of proteins: surface  area and continuum solvent models for the solute-solvent interaction energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of the American Chemical Society,  125(31):9523–9530, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [36] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Minimization of electrostatic free energy and the poisson–boltzmann equation for molecular solvation with implicit  solvent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' SIAM Journal on Mathematical Analysis, 40(6):2536–2566, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [37] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Diffused solute-solvent interface with Poisson-Boltzmann electrostatics: free-energy variation and sharp-  interface limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 75(5):2072–2092, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [38] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhang, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Alexov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Highly efficient and exact method for parallelization of grid-based algorithms and  its implementation in delphi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Computational Chemistry, 33(24):1960–1966, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [39] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhang, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Alexov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' On the dielectric “constant” of proteins: Smooth dielectric function for macromolec-  ular modeling and its implementation in delphi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Chemical Theory and Computation, 9(4):2126–2136, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  PMID: 23585741.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [40] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Lionta, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Spyrou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Vassilatis, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Cournia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Structure-based virtual screening for drug discovery: principles,  applications and recent advances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Curr Top Med Chem, 14(16):1923–1938, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [41] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Miranda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Un principio di massimo forte per le frontiere minimali e una sua applicazione alla risoluzione del problema  al contorno per l’equazione delle superfici di area minima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Rend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Sem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Padova, 45:355–366, 1971.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [42] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Mobley, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dill, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chodera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Treating entropy and conformational changes in implicit solvent simulations  of small molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Journal of Physical Chemistry B, 112(3):938–946, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' PMID: 18171044.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [43] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Mongan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Simmerling, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Case, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Onufriev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Generalized Born model with a simple, robust  molecular volume correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Chemical Theory and Computation, 3(1):159–69, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [44] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Pr¨uss and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Simonett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' On the manifold of closed hypersurfaces in Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Discrete Contin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 33(11-12):5407–5428,  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [45] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ricci, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Cheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dzubiella, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Tailoring the variational implicit solvent method for  new challenges: Biomolecular recognition and assembly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Frontiers in Molecular Biosciences, 5:13, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [46] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Rudin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Osher, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Fatemi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Nonlinear total variation based noise removal algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' volume 60, pages 259–268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Experimental mathematics: computational issues in nonlinear science (Los Alamos, NM, 1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [47] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Shao, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Hawkins, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wang, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A constrained variational model of biomolecular solvation and its numerical  implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=', 107:17–28, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [48] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Sharp and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Honig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Calculating total electrostatic energies with the nonlinear poisson-boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The  Journal of Physical Chemistry, 94(19):7684–7692, Sep 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [49] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Spolar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Ha, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Record Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Hydrophobic effect in protein folding and other noncovalent processes involving  proteins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences of the United States of America, 86(21):8382–8385, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [50] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Swanson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Mongan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Limitations of atom-centered dielectric functions in implicit solvent  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Physical Chemistry B, 109(31):14769–72, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [51] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Tjong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' GBr6NL: A generalized Born method for accurately reproducing solvation energy of the nonlinear  Poisson-Boltzmann equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Chemical Physics, 126:195102, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [52] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wagoner and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Baker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Assessing implicit models for nonpolar mean solvation forces: the importance of dispersion  and volume terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences of the United States of America, 103(22):8331–6, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [53] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wang and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Parameter optimization in differential geometry based solvation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Journal of chemical  physics, 143(13):134119, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [54] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Differential geometry based multiscale models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Bulletin of Mathematical Biology, 72(6):1562–1622, Aug 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [55] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wei and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A Baker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Differential geometry-based solvation and electrolyte transport models for biomolecular  modeling: a review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' In Many-Body Effects and Electrostatics in Biomolecules, pages 435–480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Jenny Stanford Publishing,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [56] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wei, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Sun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhou, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Feig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Molecular multiresolution surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' arXiv:math-ph/0511001v1, pages 1 –  11, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [57] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Wei, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Chen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='n Xia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Variational multiscale models for charge transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' siam REVIEW, 54(4):699–  754, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [58] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Pseudo-time-coupled nonlinear models for biomolecular surface representation and solvation analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' International  Journal for Numerical Methods in Biomedical Engineering, 27(12):1964–1981, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [59] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Kwan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Che, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Phase-field approach to implicit solvation of biomolecules with  coulomb-field approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' The Journal of chemical physics, 139(2):024111, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [60] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhou, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Rogers, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' de Oliveira, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Baron, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Cheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Dzubiella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Li, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' McCammon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Variational  implicit-solvent modeling of host–guest binding:  A case study on cucurbit[7]uril—.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Journal of Chemical Theory and  Computation, 9(9):4195–4204, Sep 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content='  [61] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' On curvature driven rotational diffusion of proteins on membrane surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
+page_content=' SIAM Journal on Applied Mathem-  atics, 80(1):359–381, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFAT4oBgHgl3EQfbx2O/content/2301.08560v1.pdf'}
diff --git a/mNAyT4oBgHgl3EQf_vq9/content/tmp_files/2301.00915v1.pdf.txt b/mNAyT4oBgHgl3EQf_vq9/content/tmp_files/2301.00915v1.pdf.txt
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+Entanglement and work statistics in the driven open system
+He Wang1, 2 and Jin Wang3, ∗
+1College of Physics, Jilin University,
+Changchun 130021, China
+2State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry,
+Changchun 130021, China.
+3Department of Chemistry and of Physics and Astronomy, Stony Brook University, Stony Brook,
+NY 11794-3400, USA
+We study the entanglement and work statistics in a driven two-qubit system. The regulation
+of periodic driving has much more versatility and universality in contrast to reservoir engineering
+in static systems. We found the quasi-steady state entanglement can be amplified effectively by
+the external drive in certain parameter regimes. The drive extends the range of temperatures or
+temperature differences at which entanglement can emerge. From the view of the effective Hamil-
+tonian, the addition of the driving alters the inter-qubit coupling and system-bath coupling, which
+are crucial in determining the quasi-steady state. The work statistics are also investigated. The
+driven system, as a continuous quantum thermal machine, output work continuously and steadily
+at the quasi-steady state. There is a distinct operation of modes and corresponding performance
+by changing driving. It can also be understood that the drive changes the effective Hamiltonian,
+and further the modes of energy exchanges between the system and the baths as well as the work
+reservoir.
+∗ jin.wang.1@stonybrook.edu
+arXiv:2301.00915v1  [quant-ph]  3 Jan 2023
+
+2
+I.
+INTRODUCTION
+For the past few years, the periodically driven quantum system has drawn much attention. This has been a result
+of experimental advances in state-of-the-art laser technology, which makes it implementable in the lab. In accordance
+with the Floquet theorem [1] and the follow-up theoretical developments [2, 3], physical characteristics of the driven
+system are primarily understood by the so-called effective Hamiltonian, which reflects the periodic driving. Periodic
+driving largely extends the controllability of the systems since time as a new control dimension is introduced. It gets
+rid of the down-to-earth difficulty of reservoir engineering in static systems that the parameter is hard to change once
+the material is prepared. By designing a suitable driving protocol, one can engineer the effective Hamiltonian, which
+empowers us to have desirable properties and functionalities of the physical systems. Coherent control through periodic
+driving (often known as Floquet engineering) has become a commonly used tool in quantum control, which has been
+used to realize topologically nontrivial systems [4–7], nonequilibrium phase transitions [8, 9], artificial gauge fields
+[10–12], and discrete time crystals [13, 14]. Additionally, it comes into play in the coherent destruction of tunneling
+[15, 16] and the manipulation of spin-orbit coupling [17, 18], etc. Meanwhile, significant progress has been made
+toward the experimental realization of small-scale thermal machines where fluctuations play a significant role. The
+thermal machines in the quantum regime have been realized on several platforms [19–26]. Specific examples include a
+quantum absorption refrigerator with trapped ions [27], quantum heat engines using an ensemble of nitrogen-vacancy
+centers [28]. Continuous thermal machines [29] do not require intermittent couplings and decouplings between the
+working fluid and the baths, which are particularly challenging to implement at microscopic scales, in contrast to their
+reciprocating counterparts. As a result, they have greater experimental relevance. Continuous thermal machines are
+typically implemented by a periodic modulation of the system Hamiltonian, which drives the system to a periodic
+quasi-steady state in general. The temporal driving methods may drive small systems in nonequilibrium quasi-steady
+states with far greater versatility and universality than the static manipulation methods, which hinge on steady
+nonequilibrium sources such as temperature bias, chemical potential difference, etc.[30].
+A real system is always inevitably influenced by its surroundings and this can lead to the system’s decoherence
+eventually.
+The environmental effect plays a crucial role in the evolution of the system [31].
+How to confront
+dissipation and decoherence is a fundamental challenge in quantum technology. It has been shown that the dissipation
+can be effectively suppressed by the formation of the Floquet bound state under temporal driving [32–34].
+The
+scheme to generate a maximally entangled state and then protect it based on Floquet engineering is also proposed
+[33, 35]. However, the entanglement of the nonequilibrium quasi-steady state still lacks of investigations based on
+our knowledge. Indeed, the balance of the periodic driving and dissipation can yield a variety of nonequilibrium
+steady states and phase transitions in various systems including cavity-QED systems [36, 37], cold atoms [38, 39],
+ideal Bose gases [40–42], and so on. A natural question is raised: Is entanglement in the quasi-steady state? Can we
+enhance it with Floquet engineering? The answer is positive. The entanglement can be magnified significantly by
+the befitting driving. The system can become entangled in a wider range of temperatures or temperature differences
+as a result of the drive. From the standpoint of effective Hamiltonian, the existing driving gives rise to the change
+of inter-qubit coupling and system-bath coupling, as well as further, modifies steady state entanglement. The work
+statistics of the open system are also of interest. The net flow from the baths to the system disappears when the static
+system approaches the steady state. When certain external driving is applied, the system can operate continually and
+steadily as a continuous quantum thermal machine. The different drivings contribute to the various modes of energy
+exchanges between the system and the baths as well as the work reservoir (energy source of the external agent which
+modulates the system) in the quasi-steady state, which bring about the thermal machine with numerous operation of
+modes. We quantify the performance efficiency of different operation modes, which is bounded by the Carnot limit
+in general.
+The rest of the paper is organized as follows. In Section II, we introduce our model. We then derive a generalized
+master equation by means of double-projective measurement protocol and Floquet theory. In Section III, the quasi-
+steady state entanglement is studied. In Section IV, we investigate the work statistics at a quasi-steady state. Finally,
+we draw our conclusions in Section V.
+II.
+THEORETICAL FRAMEWORK
+To start, we first introduce the model we studied. The system is composed of a pair of interacting qubits, and each
+qubit couples to its own bosonic bath with a certain temperature. Meanwhile, the system is driven by external field
+
+3
+control. The sketch of the model is shown in Fig.1. The Hamiltonian of the whole system is
+H
+H
+H = H
+H
+HS(t) + H
+H
+HB + H
+H
+HSB
+=
+�
+i=A,B
+ωi + Di(t)
+2
+σσσi
+z + λ(σσσA
++σσσB
+− + σσσA
+−σσσB
++) +
+�
+i=A,B
+�
+k
+ω2
+ikaaa†
+ikaaaik +
+�
+i=A,B
+σσσi
+x
+�
+k
+cccikxxxik,
+(1)
+where σσσi
+z are Pauli matrices for the i-th qubit, it reads σσσA
+z = σσσz
+�III for the A qubit or σσσB
+z = III �σσσz for the B qubit.
+ωi is the energy spacing of the i-th qubit. Di(t) is the external field control. λ measures the coupling interaction
+between two qubits. aaa†
+ik(aaaik) is the creation (annihilation) operator of k-th bosonic mode in i-th bath and satisfies the
+commute relation [aaaik,aaa†
+i′k′] = δii′δkk′I. The cik are coupling constants that describe the coupling of the i-th qubit
+to its own reservoir modes aaaik. To fully characterize the interaction between the system and baths, we need to define
+the spectral density of the baths, which follows
+Ji(ω) = π
+2
+�
+k
+c2
+ik
+ωik
+δ(ω − ωik)
+(2)
+A structure-less spectral density (e.g. linear form
+di
+ω0 ω) typically empowers a Markovian treatment of the reservoirs
+due to the fast decay of its associated correlation functions, while a more structured spectral density (e.g. strongly
+peaked around a frequency
+diγω
+(ω2−ω2res)2+γ2ω2 ) requires a more involved treatment [43]. In this paper, we simply take a
+structure-less spectral density Ji(ω) = di
+ω0 ω into consideration.
+FIG. 1.
+A sketch of the model. There are two interacting qubits, which are coupled with individual baths as well. The qubit
+A is driven by the external field.
+The drives Di(t) may be any time-dependent function, but we only take into account an easily implementable drive
+scheme: a monochromatic drive with frequency ωL and amplitude K only acts on the qubit A, i.e., DA(t) = K cos ωLt
+and DB(t) = 0.
+Note that the total Hamiltonian is periodic in time. One can take advantage of the Floquet theorem to solve a
+time-periodic Schr¨odinger equation i∂t|ψr(t)⟩ = H
+H
+HS(t)|ψr(t)⟩, where H
+H
+HS(t) = H
+H
+HS(t+T) = �
+k eik ωLtH
+H
+Hk, with period
+T =
+2π
+ωL . A solution to this Schr¨odinger equation is given by Floquet states |ψr(t)⟩ = e−iεrt|r(t)⟩, where εr are
+called quasienergies and |r(t)⟩ = |r(t + T)⟩ are Floquet modes. The existence of Floquet states in time-periodically
+driven systems follows from the Floquet theorem in a similar way to the existence of Bloch states in spatially periodic
+systems [1, 2]. We also mention that there is a similar Floquet theorem for open systems in [44, 45]. In Appendix.A,
+we review more details on the Floquet theory.
+To study the heat statistics of the driven system, we follow the full counting statistics formalism in [43, 46, 47]. The
+heat moments are expediently described in terms of the characteristic function G(χ) =
+�
+d∆E e−iχ∆Ep(∆E), which
+is based on double-projective measurement of the environment. With the help of conditional probability p(E1; E0),
+which one measured the energy of environment E = E0 at time t0, and a follow-up measurement gave E1 at time t1,
+and the probability p(E0) to measure E0 at time t0, the probability distribution function for the heat energy exchange
+∆E to be transported to the reservoir between times t = t0 and t = t1 can be expressed as
+p(∆E, t) =
+�
+E1,E0
+δ(E1 − E0 − ∆E)p(E1; E0)p(E0).
+(3)
+Taking account into the projective operator PPP Em and its property PPP EmPPP En = δmnPPP Em, we have
+p(E1, E0) = Tr[PPP E1UUU(t)PPP E0ρρρtot(0)PPP E0UUU †(t)PPP E1]
+= Tr[UUU †(t)PPP E1UUU(t)PPP E0ρρρtot(0)PPP E0].
+(4)
+
+4
+The generating function is given by
+G(χ, t) =
+�
+d∆E e−iχ∆Ep(∆E)
+=
+�
+d∆E e−iχ∆E �
+E1,E0
+δ(E1 − E0 − ∆E)p(E1; E0)p(E0)
+=
+�
+E1,E0
+p(E1; E0)p(E0)e−iχ∆E
+(5)
+Assume the initial total density matrix ρρρtot(0) = ρρρS(0) ⊗ ρρρB(0) to be factorized into the system density matrix
+ρρρS(0) and the thermalized environment density matrix ρρρB(0) = e−βH
+H
+HB/Z, where Z is the partition function of the
+environment. Particularly, this assumption indicates that all projectors PPP Em commute with ρρρ(0), ensuring that the
+dynamics of the reservoir are unaffected by the initial measurement of the observable.
+By the use of e−iχH
+H
+HB =
+�
+Em PPP Eme−iχEm, we have
+G(χ, t) =
+�
+E1,E0
+Tr[UUU †(t)PPP E1UUU(t)PPP E0ρρρtot(0)PPP E0]e−iχ∆E
+= Tr[UUU †(t)
+�
+E1
+PPP E1e−iχE1UUU(t)
+�
+E0
+PPP E0eiχE0ρρρtot(0)]
+= Tr[UUU †(t)e−iχH
+H
+HBUUU(t)eiχH
+H
+HBρρρtot(0)]
+= Tr[UUU(χ, t)ρρρtot(0)UUU †(−χ, t)]
+= Tr[ρρρtot(χ, t)],
+(6)
+where UUU(χ, t) = e−iχH
+H
+HB/2UUU(t)eiχH
+H
+HB/2 and ρρρtot(χ, t) = UUU(χ, t)ρρρtot(0)UUU †(−χ, t). It enables us to compute the statistics
+of the energy transferred between the system and reservoir by straightforward differentiation
+⟨∆En⟩ = −
+∂n
+∂(iχ)n G(χ)|χ=0.
+(7)
+Utilize the modified time evolution operator UUU(χ, t) and modified density matrix ρρρtot(χ, t), and assume that the
+coupling between the system and baths are weak enough such that the Born–Markov approximation is valid. We
+derive a generalized Markov master equation without secular approximation
+∂tρρρ(χ, t) = LLL(χ, t)ρρρ(χ, t)
+= −i [H
+H
+HS(t),ρρρ(χ, t)]
+−
+�
+{i=1,2;ω;n}
+ei∆ω,nt{Ji(∆ω,n)Ni(∆ω,n)SSSi,ω,n(t)SSSiρρρ(χ, t)
+− Ji(∆ω,n) [1 + Ni(∆ω,n)]SSSiρρρ(χ, t)SSSi,ω,n(t)ei∆i,ω,nχ
+− Ji(∆ω,n)Ni(∆ω,n)SSSi,ω,n(t)ρρρ(χ, t)SSSie−i∆i,ω,nχ
++ Ji(∆ω,n) [1 + Ni(∆ω,n)]ρρρ(χ, t)SSSi,ω,n(t)SSSi},
+(8)
+where SSS1 = σσσA
+x and SSS2 = σσσB
+x , ∆ω,n = ω + nωL and SSSi,ω,n(t) =
+�� T
+0
+dt
+T ⟨r(t)|SSSi e−inωlt|r′(t)⟩
+�
+|r(t)⟩⟨r′(t)| such that
+ω = εr − εr′. εr is quasi-energy in the first Brillouin zone and |r(t)⟩ corresponds to Floquet modes. Ji(ω) and Ni(ω)
+are the spectral density and Bose distribution for the i-th baths respectively. The details are in Appendix.B. Similar
+master equations have been derived in different research backgrounds [43, 47, 51, 52].
+III.
+ENTANGLEMENT IN THE DRIVEN OPEN SYSTEM
+In this section, we will study the entanglement in the quasi-steady state of the driven open system. Note that due
+to the periodicity of the Floquet modes |r(t)⟩, the superoperator LLL(χ, t) also has the same periodicity. The evolution
+
+5
+of the system can be computed just by setting χ = 0 in Eqn. (8),
+∂tρρρ(t) = − i [H
+H
+H(t),ρρρ(t)] −
+�
+{i=1,2;ω;n}
+einωLtJi(∆ω,n){Ni(∆ω,n) [SSSiSSSi,ω,n(t)ρρρ(t) − SSSi,ω,n(t)ρρρ(t)SSSi]
++ [1 + Ni(∆i,ω,n)] [ρρρ(t)SSSi,ω,n(t)SSSi − SSSiρρρ(t)SSSi,ω,n(t)]}.
+(9)
+Assuming that in the long-time limit the density matrix ρρρ(t) is time-periodic with the same period as the Floquet
+modes, in the extended space this equation has the form
+��
+k
+TTT k ⊗ LLLk − iωLFFF z
+�
+⃗ρρρ = 0 ,
+(10)
+with ⃗ρρρ a vector containing all Fourier components of ρρρ(t). The definition of TTT k and FFF z can be found in Appendix.A.
+Therefore, one can numerically obtain a quasi-steady state by truncating the basis of the temporal space. The number
+of basis should be as large enough as possible to ensure that the result converges. For general two qubits state ρρρ,
+the entanglement can be quantified using the concurrence, which is defined as C = max {0, λ1 − λ2 − λ3 − λ4} in
+bare basis, where {λ1, λ2, λ3, λ4} are the square roots of the eigenvalues of √ρρρ(σσσy ⊗ σσσy)ρρρ∗(σσσy ⊗ σσσy)√ρρρ sorted in a
+descending order [53].
+FIG. 2.
+Entanglement varies w.r.t. (a) the temperatures of baths, (b) the driving amplitude K in one period, and (c) the
+driving frequency ωL in one period. The reservoir temperatures are T1 = 0.5 and T2 = 0.1 in (a) and (b). And the driving
+frequency ωL = 0.5 for (b) and the driving amplitude K = 0.5 for (c). Other parameters are d1 = d2 = 0.001, ω01 = ω02 = 1.
+The coupling strength between two qubits is λ = 0.25, and the energy gaps of the qubits are ω1 = ω2 = 0.5.
+We first consider what happened provided that K = 0, i.e., there is no external driving. This is the case shown in
+Fig.2(a), which comprises both equilibrium and nonequilibrium scenarios. The steady-state entanglement only survives
+in a limited temperature range. The steady-state entanglement varies non-monotonically with both temperatures
+or temperature differences.
+With rising temperatures or temperature differences, the entanglement grows, then
+diminishes, and finally vanishes. A similar phenomenon has been found in [54], which can be phenomenologically
+explained by the competition between coherence and populations. The system has the same period as the external field
+when it is driven by an external field. The equilibrium/nonequilibrium steady state is replaced with a nonequilibrium
+quasi-steady state. The entanglement of the nonequilibrium quasi-steady state changes non-monotonically with the
+driving amplitude. If the driving amplitude is low, entanglement does not exist. If the amplitude is tuned higher, one
+may be able to harvest more entanglement at certain time slices. Particularly, the entanglement covers the most time
+in one period when K ∼ 0.5 as shown in Fig.2(b). The entanglement of the nonequilibrium quasi-steady state also
+varies non-monotonically with the driving frequency in Fig.2(c). The entanglement disappears if the driving frequency
+is less. One may harvest larger entanglement at some time slices if one tunes the driving frequency properly. The
+entanglement lasts longest in one period when ωL ∼ 0.5, which is resonant with the qubit.
+Indeed, the nonequilibrium quasi-steady state is a result of the competition between periodic driving and dissipa-
+tion. Provided that the drive is weak, the dissipation dominates the quasi-steady state. But the quasi-steady state
+has periodicity as well. This case is depicted in Fig.3(a,d). Despite being weak, driving still changes the system
+significantly. Entanglement even survives at high temperatures or high-temperature differences. Entanglement is
+visibly enhanced and lasts for the majority of one period if the driving amplitude is comparative with the energy
+gap of the qubit in Fig.3(b,e). Too dramatic driving can also be damaging to the entanglement of the quasi-steady
+state, as seen in Fig.3(c,f), where the driving dominates the quasi-steady state. The behavior of the entanglement is
+sensitive to temperature changes or variances, therefore the influence of the baths is still considerable.
+
+(b)
+(c)
+(a)
+0.8
+0.8
+0.08
+0.8
+0.8
+0.8
+0.6
+0.6
+0.06
+0.6
+0.6
+0.6
+K
+0.4
+0.4
+0.04
+0.4
+0.4
+0.4
+0.2
+0.02
+0.2
+0.2
+0.2
+0.2
+0.01
+0.01
+0.01
+0
+0
+0.010.20.40.60.8
+0.2
+0.4
+0.6
+0.8
+0.2
+0.4
+0.6
+0.8
+1
+1
+0
+0
+t/S6
+FIG. 3.
+Variation of entanglement w.r.t temperatures in (a ∼ c) and temperature differences in (d∼f) with the driving
+frequency ωL = 0.5, where K = 0.05, 0.5, 5 for (a, d), (b, e), (c, f) respectively. ∆T = T1 − T2 and T1 increases from 0.01. Other
+parameters are the same as Fig.2.
+Similar behaviors also happen when we choose different driving frequencies. A driving frequency that is too strong or
+too weak will be not helpful to harvest more entanglement. When the frequency is low, the harvesting entanglement is
+considerable only at relatively low temperatures or temperature differences depicted in Fig.4(a,d). Under the Floquet-
+Magnus expansion approximation [49, 50], the effective system Hamiltonian is H
+H
+Heff ≈ H
+H
+H0 + �
+n>0
+[H
+H
+Hn,H
+H
+H−n]
+nωL
++ O(ω2
+L)
+in high frequency regime, where H
+H
+Hn is the n-th Fourier component of the system Hamiltonian. One can verify that
+H
+H
+Heff ≈ H
+H
+H0 in our setting. As a result, when the driving frequency is so high that the system has no time to respond
+to the external driving, the quasi-steady state entanglement behavior is very similar to that of steady state without
+driving, as shown in Fig.4(c,f). When the frequency is in the middle value, the drive is quite effective at improving
+the entanglement shown in Fig.4(b,e).
+The behavior in the low and medium frequency regime can also be somewhat understood by the effective Hamilto-
+nian. Using the flow equation approach [3], we obtain the effective system plus system-reservoirs interaction Hamil-
+tonian (rather than the sole system Hamiltonian)
+H
+H
+HS
+eff + H
+H
+HSB
+eff = ωA
+2 σσσA
+z + ωB
+2 σσσB
+z + λJ0(K/ωL)(σσσ1
++σσσ2
+− + σσσ1
+−σσσ2
++) + J0(K/ωL)σσσA
+x BBBA + σσσB
+x BBBB,
+(11)
+where J0(x) is the first kind Bessel function and BBBi = �
+K cikxxxik are the reservoir coupling operators. The derivation
+details of Eqn. 11 is in Appendix.C. The drive affects both the system-reservoirs coupling and the inter-qubit coupling.
+Note that J0(0) = 1, we may conclude that the effective Hamiltonian is equal to the original Hamiltonian when the
+frequency ωL is set to a very high value and the amplitude K is fixed at a certain finite value, which conforms with
+the conclusion we got above. Similar to this, when the frequency ωL is set to a finite value and K is made to be
+extremely small, the effective Hamiltonian is identical to the original Hamiltonian as well. Therefore, the effect of the
+drive is not remarkable in the two kinds of limits. This, however, is not the story for K/ωL being finite. First, the
+change of the inter-qubit coupling modifies the eigenenergy of the bare system, resulting in an effect on the population
+distribution at the steady state. Second, the change of system-reservoirs coupling alters the dissipative effect of the
+environment and further changes the steady coherence. |J0(s)| ≤ 1 indicates that the dissipative effect of one of the
+
+(a)
+(b)
+(c)
+0.7
+0.07
+0.3
+0.6
+0.8
+0.8
+0.8
+0.06
+0.25
+0.5
+0.05
+0.6
+0.6
+0.6
+0.2
+0.4
+0.04
+T
+0.15
+0.3
+0.4
+0.03
+0.4
+0.4
+0.1
+0.2
+0.02
+0.2
+0.2
+0.2
+0.05
+0.1
+0.01
+0.01
+0.01
+0.01
+0
+0
+0
+0
+0.2
+0.2
+0.4
+0.6
+0.8
+¥0.4
+0.6
+0.8
+0.2
+0.4
+0.6
+0.8
+1
+0
+1
+7
+0
+1/
+1/4
++ / 2元
+(f)
+(d)
+(e)
+0.7
+0.08
+0.3
+0.6
+0.8
+0.8
+0.8
+0.25
+0.5
+0.06
+0.6
+0.6
+0.6
+0.2
+△T
+0.4
+0.04
+0.15
+0.3
+0.4
+0.4
+0.4
+0.1
+0.2
+0.02
+0.2
+0.2
+0.2
+0.05
+0.1
+0.01
+0
+0.01
+0.01
+0
+0
+0.2
+0.40.60.8
+0.2
+0.4
+0.6
+0.8
+0.2
+0.4
+1
+0
+0.6
+0.8
+1
+0
+0
+t/2
+t/ 2
+T37
+FIG. 4.
+Variation of entanglement w.r.t temperatures in (a ∼ c) and temperature differences in (d∼f) with the driving
+amplitude K = 0.5, where ωL = 0.05, 0.5, 5 for (a, d), (b, e), (c, f) respectively. ∆T = T1 − T2 and T1 increases from 0.01. Other
+parameters are the same as Fig.2.
+baths is weakened and the inter-qubit interaction that induces entanglement within the system diminishes as well. The
+end result is generated by the combination of these two effects. However, we point out that the effective Hamiltonian
+is unable to provide a master equation to propagate the system. The reason is also clear: the effective Hamiltonian
+can only describe the stroboscopic time evolution, it can not support a continuous time master equation. However,
+as we have seen, the effective Hamiltonian still offers certain perspectives for comprehending evolution.
+IV.
+WORK STATISTICS IN THE DRIVEN OPEN SYSTEM
+We investigate work statistics of the driven open system in this section. Using the counting field and its responding
+generalized master equation, the heat flow from the ith bath to the system is obtained by
+˙Qi(t) = −∂t ⟨H
+H
+HBi⟩ = Tr {(∂iχLLLi(χ, t)) · ρρρ(χ, t)} |χ=0
+=
+�
+{ω;n}
+einωLt
+Tr{−Ji(∆ω,n) [1 + Ni(∆ω,n)] ∆ω,nSSSiρρρ(t)SSSi,ω,n(t)
++ Ji(∆ω,n)Ni(∆ω,n)∆ω,nSSSi,ω,n(t)ρρρ(t)SSSi}.
+(12)
+The heat flow, we define, is positive if it flows from the bath to the system. The system must abide by the energy
+balance at the quasi-steady state, which means ˙QA + ˙QB + ˙W=0. In Fig.5, we plot the variations of the heat flow and
+workflow with respect to the amplitude K in (a) and to the frequency in (b). If there is no drive, the system relaxes
+to the nonequilibrium steady state, and the net flow from the reservoirs to the system vanishes, which also hints that
+extracted work ˙Wnd = 0. By varying the driving amplitude, the heat flow from bath B is always negative while the
+heat flow from bath-A drops from a specific positive value to a certain negative value. The combination of the change
+of ˙QA and ˙QB determines the ˙W. As a result, one may classify thermal operation regimes into three modes in K
+parameter space in Fig.5(a). When K ∈ (0.01, 0.18) roughly, ˙QA > 0, ˙QB < 0, and ˙W < 0, the system operates as a
+
+(a)
+(c)
+(b)
+1
+10.7
+0.7
+0.08
+0.6
+0.6
+0.8
+0.8
+0.8
+0.06
+0.5
+0.5
+0.6
+0.6
+0.6
+0.4
+0.4
+T
+0.04
+0.3
+0.3
+0.4
+0.4
+0.4
+0.2
+0.2
+0.02
+0.2
+0.2
+0.2
+0.1
+0.1
+0.01
+0.01
+0.01
+0
+0
+0
+0.4
+0.2
+0.4
+0.6
+0.8
+0.6
+0.8
+0.2
+0.6
+0.8
+0
+0
+1
+7
+1
+0
+1/4
+t/
+(d)
+(f)
+(e)
+1
+0.7
+0.08
+0.7
+0.6
+0.8
+0.8
+0.6
+0.8
+0.06
+0.5
+0.5
+0.6
+0.6
+0.6
+0.4
+△T
+0.4
+0.04
+0.3
+0.3
+0.4
+0.4
+0.4
+0.2
+0.2
+0.02
+0.2
+0.2
+0.2
+0.1
+0.1
+0.01
+0.01
+0.01
+0
+0
+0
+0.2
+0.40.60.8
+0.2
+0.4
+0.6
+0.8
+0.2
+0.4
+0
+0.6
+0.8
+0
+1
+1
+0
+t/
+t/
+t/ 2元8
+FIG. 5.
+Variation of mean heat flow and work flow w.r.t the driving amplitude K in (a) and w.r.t. the driving frequency ωL
+in (b). Variation of performance of operation modes w.r.t the driving amplitude K in (c) and w.r.t. the driving frequency ωL
+in (d). ωL = 0.5 in (a,c), and K = 0.05 in (b,d). TA = 1 and TB = 0.01. Other parameters are the same as Fig.2.
+heat engine. Additionally, there is a transition region, K ∈ (0.18, 0.35) approximately, ˙QA > 0, ˙QB < 0, and ˙W > 0,
+this operation mode of the system serves no useful purpose. When K > 0.35, the system functions as a heat pump.
+Similarly, there are three regimes of thermal operations in ωL parameter space in Fig.5(b). There is a small region
+around ωL = 0.5, ˙QA > 0, ˙QB < 0, and
+˙W < 0, the system functions as a heat engine. After going through the
+narrow transition regime, the system operates as a heat pump when deviates ωL = 0.5 significantly. We also quantify
+the performance of different operation modes. The efficiency of the heat engine is measured by | ˙W/ ˙QA| ≤ η and that
+of heat pump as | ˙QA/ ˙W| ≤ η−1, where η = 1 − TB
+TA = 0.99 is Carnot bound in this case. We can verify that both the
+engine and heat pump are bounded by the Carnot limit in Fig.5(c,d). As the amplitude grows, the engine’s efficiency
+increases before declining. and the heat pump becomes more efficient. The efficiency of both the heat pump and the
+engine fluctuates non-monotonically as a function of frequency.
+FIG. 6.
+Variation of mean heat flow and work flow w.r.t the temperature in (a) and Variation of performance of operation
+modes in (b). ωL = 0.5 and K = 0.05 in (a,b). TA = TB + ∆T and TB = 0.01. Other parameters are the same as Fig.2.
+
+(b)
+(a)
+X10-4
+6 ,×10-4
+10
+4
+M-
+QA
+5
+QB
+Wnd
+0
+0
+-2 
+-5 
+-4 
+0.2
+0.3
+0.44
+0.52
+0.56
+0.1
+0.4
+0.5
+0.6
+0.01
+0.4
+0.48
+K
+(d)
+(c)
+0.8
+0.6
+-- engine
+- heat pump
+0.5
+0.6
+0.4E
+0.3
+0.4
+0.2
+0.2
+0.1
+0
+0.01
+0.1
+0.4
+0.44
+0.52
+0.56
+0.2
+0.3
+0.4
+0.5
+0.48
+0.6
+K(b)
+(a)
+X10-4
+6 ,×10-4
+10
+4
+M-
+QA
+5
+QB
+Wnd
+0
+0
+-2 
+-5 
+-4 
+0.2
+0.3
+0.44
+0.52
+0.56
+0.1
+0.4
+0.5
+0.6
+0.01
+0.4
+0.48
+K
+(d)
+(c)
+0.8
+0.6
+-- engine
+- heat pump
+0.5
+0.6
+0.4E
+0.3
+0.4
+0.2
+0.2
+0.1
+0
+0.01
+0.1
+0.4
+0.44
+0.52
+0.56
+0.2
+0.3
+0.4
+0.5
+0.48
+0.6
+K(a)
+(b)
+0.5
+M-
+QA
+0.4
+2
+QB
+Wn
+0.3
+0.2
+0.1
+-1
+engine
+ heat pump
+-2 
+0
+0.2
+0.4
+0.6
+0.2
+0.4
+0.6
+0.8
+0
+0
+0.8
+1
+△T
+△T(a)
+(b)
+0.5
+M-
+QA
+0.4
+2
+QB
+Wn
+0.3
+0.2
+0.1
+-1
+engine
+ heat pump
+-2 
+0
+0.2
+0.4
+0.6
+0.2
+0.4
+0.6
+0.8
+0
+0
+0.8
+1
+△T
+△T9
+We can also gain some insights into the reason why the system exhibits distinct operation modes and various
+performances when we regulate the driving from the perspective of the effective Hamiltonian. The change of inter-
+qubits coupling and the system-reservoirs coupling re-determines the heat flow and furthermore leads to output work
+being modified. The heat flow is also changed directly by controlling temperature difference. If the drive is fixed, the
+system displays various operation modes as the temperature difference changes. When the temperature difference is
+less, the system performs as a heat pump; after passing through a transition region, the system behaves as a heat
+engine at higher temperature differences. This is depicted in Fig.6(a). The performance efficiency of the heat pump is
+lowered as the temperature difference increases, on the contrary, that of the engine increases as illustrated in Fig.6(b).
+V.
+CONCLUSION
+In conclusion, we computed the nonequilibrium quasi-steady state entanglement within the two-qubit system by
+deriving a generalized master equation. We have better control over the system with external field regulation. The
+system may harvest more entanglement from the reservoirs compared with the static system. The driven system
+can be entangled even at high temperatures or temperature differences in contrast to the system without driving.
+We try to get to the bottom of why the driven system behaves differently from the static system from the effective
+Hamiltonian. The introduced driving modifies the inter-qubit coupling and system-reservoirs coupling. The total
+effect influences the quasi-steady state. We also investigate the work statistics in the driven open system. Changing
+the drive frequency or amplitude, the system will have different modes of operation, e.g., heat pump and engine or
+others. Their performances related to the heat flow from the reservoirs to the system can be changed by modifying
+driving and temperature differences.
+As it stands, our model is likely to be realizable with state-of-the-art laser
+technology and quantum simulation platforms. Further optimization of the model parameters may relax experimental
+requirements.
+Appendix A: Floquet Theory and the Extended Space
+We give a more detailed introduction to Floquet theory in this section [2, 43]. Consider a time-periodic Hamiltonian
+H
+H
+HS(t) = H
+H
+HS(t + T) = �
+k eik ωLtH
+H
+Hk, with period T =
+2π
+ωL , according to Floquet theory, a solution to Schr¨odinger
+equation i∂t|ψr(t)⟩ = H
+H
+HS(t)|ψr(t)⟩ is given by Floquet states |ψr(t)⟩ = e−iεrt|r(t)⟩, where εr are dubbed as quasiener-
+gies and |r(t)⟩ = |r(t + T)⟩ are Floquet modes (states). Similar to the way Bloch states exist in spatially periodic
+systems, the existence of Floquet states in time-periodically driven systems comes from the Floquet theorem. [1, 2].
+We also mention that there is a similar Floquet theorem for open systems in [44, 45].
+One can ignore the micromotion and focus on the time evolution in a stroboscopic fashion in steps of the driving
+period T as long as the dynamics we studied over a time span that is long compared to a single driving period. Such
+a stroboscopic time evolution is governed by the time-independent Floquet Hamiltonian H
+H
+HF
+t0, which is defined in a
+way that it generates the time evolution over one period,
+exp
+�
+− iTH
+H
+HF
+t0
+�
+= UUU(t0 + T, t0).
+(A1)
+and can be expressed like
+H
+H
+HF
+t0 =
+�
+r
+εr|r(t0)⟩⟨r(t0)|.
+(A2)
+The parametric dependence on the initial time t0 is periodic, H
+H
+HF
+t0+T = H
+H
+HF
+t0, and related to the micromotion. One
+can construct a Floquet Hamiltonian for a different initial time t′
+0 by applying a unitary transformation, H
+H
+HF
+t′
+0 =
+UUU †(t0, t′
+0)H
+H
+HF
+t0UUU(t0, t′
+0), on a Floquet Hamiltonian H
+H
+HF
+t0 obtained for the initial time t0. It is difficult to obtain the
+Floquet Hamiltonian in general, however, various methods are developed based on high-frequency expansion [2, 49, 50]
+or others [3].
+We can introduce a unitary operator that describes the periodic time dependence of the Floquet modes, i.e., the
+micromotion. The corresponding two-point micromotion operator can be defined by
+PPP(t2, t1) =
+�
+r
+|r(t2)⟩⟨r(t1)|
+(A3)
+
+10
+as a result of its construction, it is periodic in both arguments, PPP(t2 + T, t1) = PPP(t2, t1 + T) = PPP(t2, t1), and evolves
+the Floquet modes in time,
+|r(t2)⟩ = PPP(t2, t1)|r(t1)⟩.
+(A4)
+The Floquet Hamiltonian and the micromotion operator can be written down immediately using Eqn.A2 and
+Eqn.A3 if the Floquet states and their quasienergies are known by diagonalizing the time evolution operator over
+one period. One can then write out the time evolution operator using the Floquet Hamiltonian and the micromotion
+operator as
+UUU(t2, t1) = e−i(t2−t1)H
+H
+HF
+t2PPP(t2, t1) = PPP(t2, t1)e−i(t2−t1)H
+H
+HF
+t1 .
+(A5)
+From the above analysis, we can see that quasienergies and Floquet modes are extremely crucial for the evolution
+of the driven system. We show how to solve them numerically in the following. The Floquet modes are time-periodic
+and form a complete basis. To find them one solves the eigenvalue problem
+(H
+H
+HS(t) − i∂t) |r(t)⟩ = εr|r(t)⟩.
+(A6)
+The periodicity of the Floquet modes enables us to map the eigenvalue problem to a time-independent one in
+an extended Hilbert space, also known as Sambe space [48]. To do this, an infinite-dimensional space with integer
+quantum numbers is introduced. Its basis is given by
+HT = {. . . , | − 3⟩, | − 2⟩, | − 1⟩, |0⟩, |1⟩, |2⟩, |3⟩ . . .} .
+(A7)
+There are two operators TTT k and FFF z in Sambe space, which are defined as
+TTT k|m⟩ = |m + k⟩,
+FFF z|m⟩ = m|m⟩.
+(A8)
+Combining the basis denoted by HS = {|φ1⟩, |φ2⟩, |φ3⟩ . . . |φK⟩} for the quantum system living in original Hilbert
+space HS, one can construt the basis of the extended Hilbert space,
+H = HT ⊗ HS =
+�
+|n, φ⟩⟩ |n ∈ Z, i ∈ {1, . . . , K}
+�
+,
+(A9)
+with the scalar product ⟨⟨u|v⟩⟩ = 1
+T
+� T
+0 dt⟨u(t)|v(t)⟩ = ⟨u(t)|v(t)⟩ in the extended space. We have denoted vectors in
+the Sambe space by a double ket notation |r⟩⟩, which corresponds to |r(t)⟩ in HS. Moreover, a periodic time-dependent
+operator OOO(t) = �
+k OOOkeiωLt in extended space is expressed as
+OOOext =
+�
+k
+TTT k ⊗ OOOk.
+(A10)
+With the above definitions, we rewrite the operator QQQ = H
+H
+H(t) − i∂t and solve eigenvalue problem in extended space
+as
+QQQext =
+�
+k
+TTT k ⊗ H
+H
+Hk + ωLFFF z ⊗ 111
+−→
+QQQext|rm⟩⟩ = εrm|rm⟩⟩,
+(A11)
+where H
+H
+Hk are the Fourier components of the Hamiltonian H
+H
+H(t). Note that εr is periodic with period ωL because
+|r(t)⟩eimωLt is also the eigenstate of Eqn.A6 with eigenvalue εrm = εr + mωl. This is the reason why the eigenstates
+and quasienergies have been denoted with an additional index m in the extended space. The complete set of solutions
+of the quasienergies eigenvalue problem Eqn.A6 contains a lot of redundant information. All Floquet states of the
+system can, thus, be constructed, for example, from those Floquet modes whose quasienergies lie in a single Brillouin
+zone of the ωL periodic quasienergy spectrum. From now on we will denote Floquet modes in the extended space just
+by |r⟩⟩, assuming that all lie in the same Brillouin zone.
+One can re-formulate the evolution of any operator with the help of The Floquet modes. Take into account an
+
+11
+arbitrary operator SSS.
+SSS(t) = UUU †(t)SSSUUU(t)
+= (PPP(t, 0)e−itH
+H
+HF
+0 )†SSSPPP(t, 0)e−itH
+H
+HF
+0
+= eitH
+H
+HF
+0 PPP †(t, 0)SSSPPP(t, 0)e−itH
+H
+HF
+0
+=
+�
+r
+eitεr|r(0)⟩⟨r(0)|
+�
+m
+|m(0)⟩⟨m(t)|SSS
+�
+r′
+|r′(t)⟩⟨r′(0)|
+�
+m′
+e−itεm′ |m′(0)⟩⟨m′(0)|
+=
+�
+r,r′
+eit(εr−εr′)⟨r(t)|SSS|r′(t)⟩|r(0)⟩⟨r′(0)|
+=
+�
+ω,n
+eit(ω+nωL)SSSω,n.
+(A12)
+where SSSω,n =
+�� T
+0
+dt
+T ⟨r(t)|S e−inωlt|r′(t)⟩
+�
+|r(0)⟩⟨r′(0)| and εr − εr′ = ω.
+Due to the periodicity of the Floquet
+modes |r(t)⟩(|r′(t)⟩), we can perform the Fourier transform, i.e. ⟨r(t)|SSS|r′(t)⟩|r(0)⟩⟨r′(0)| = �
+k einωLtSSSω,n, where
+SSSω,n =
+�� T
+0
+dt
+T ⟨r(t)|S e−inωlt|r′(t)⟩
+�
+|r(0)⟩⟨r′(0)|. In extended space, using Eqn.A8 this is easily computed by
+� T
+0
+dt
+T ⟨r(t)|SSS e−inωLt|r′(t)⟩ = ⟨⟨r|TTT −n ⊗ SSS|r⟩⟩.
+(A13)
+It is now straightforward to obtain a master equation for a driven open quantum system thanks to decomposition
+Eqn.A12.
+Appendix B: The derivation of the Generalized Master Equation
+The total Hamiltonian, including system and reservoir is H
+H
+Htot = H
+H
+HS(t) + H
+H
+HB + H
+H
+HSB and we assume an initial
+factorizing state of the form ρρρtot(0) = ρρρ(0) ⊗ ρρρB, with ρρρB ∼ e−βH
+H
+HB. Define the modified density matrix
+ρρρtot(χ, t) = UUU(χ, t)ρρρtot(0)UUU †(−χ, t),
+(B1)
+with total (system plus reservoirs) initial density matrix ρρρtot(0) and modified evolution operator UUU(χ, t) =
+e−iχH
+H
+HB/2UUU(t)eiχH
+H
+HB/2, where UUU(t) is the evolution operator corresponding to Hamiltonian H
+H
+H.
+The variable χ is
+usually referred to as the counting field. The evolution of operator ρρρtot(χ, t) is given by
+∂tρρρtot(χ, t) = −i [H
+H
+H(χ, t)ρρρtot(χ, t) − ρρρtot(χ, t)H
+H
+H(−χ, t)] .
+(B2)
+Taking the trace over the reservoir degrees of freedom we define
+ρρρ(χ, t) = TrB {ρρρtot(χ, t)} .
+(B3)
+Note that the total density matrix and the reduced density matrix of our system are both recovered by setting χ = 0.
+Transform Eqn. B2 into the interaction picture by ˜AAA(t) = UUU †
+0(t)AAAUUU 0(t), with UUU 0(t) the evolution operator associated
+to Hamiltonian H
+H
+H0(t) = H
+H
+HS(t) + H
+H
+HB. And considering the standard Born–Markov approximations [31], we obtain
+∂t˜ρρρ(χ, t) = −
+� ∞
+0
+dsTrB{ ˜H
+H
+HI(χ, t) ˜H
+H
+HI(χ, t − s)˜ρρρ(χ, t)ρρρB − ˜H
+H
+HI(χ, t)˜ρρρ(χ, t)ρρρB ˜H
+H
+HI(−χ, t − s)
+− ˜H
+H
+HI(χ, t − s)˜ρρρ(χ, t)ρρρB ˜H
+H
+HI(−χ, t) + ˜ρρρ(χ, t)ρρρB ˜H
+H
+HI(−χ, t − s) ˜H
+H
+HI(−χ, t)}.
+(B4)
+We take the interaction Hamiltonian with the form H
+H
+HSB = SSS ⊗BBB = SSS ⊗�
+k ckxxxk and define the correlation function
+C(χ, t) ≡ ⟨ ˜BBB(χ, t)BBB⟩ = TrB
+�
+˜BBB(χ, t)BBBρρρB
+�
+. Using the fact that
+�
+˜BBB(χ, t) ˜BBB(ξ, s)
+�
+=
+�
+˜BBB(χ − ξ, t − s)BBB
+�
+, we have
+∂t˜ρρρ(χ, t) = −
+� ∞
+0
+ds{C(0, s)˜SSS(t)˜SSS(t − s)˜ρρρ(χ, t) − C(−2χ, −s)˜SSS(t)˜ρρρ(χ, t)˜SSS(t − s)
+− C(−2χ, s)˜SSS(t − s)˜ρρρ(χ, t)˜SSS(t) + C(0, −s)˜ρρρ(χ, t)˜SSS(t − s)˜SSS(t)}.
+(B5)
+
+12
+The correlation functions can actually be written as
+C(−2χ, t) =TrB(eiχH
+H
+HBeitH
+H
+HBBBBe−itH
+H
+HBe−iχH
+H
+HBBBBρρρB)
+=TrB(eiχH
+H
+HBeitH
+H
+HB �
+k
+ckxxxke−itH
+H
+HBe−iχH
+H
+HB �
+k′
+c′
+kxxx′
+kρρρB)
+=TrB(eiχH
+H
+HBeitH
+H
+HB �
+k
+ck
+�
+ℏ
+2mω (ˆaaak + ˆaaa†
+k)e−itH
+H
+HBe−iχH
+H
+HB �
+k′
+c′
+k
+�
+ℏ
+2mω (ˆaaak′ + ˆaaa†
+k′)ρρρB)
+(B6)
+Set ℏ = m = 1 and use ˆaaa†
+k(t) = eitH
+H
+HBˆaaa†
+ke−itH
+H
+HB = ˆaaa†
+keiwkt and ˆaaak(t) = eitH
+H
+HBˆaaake−itH
+H
+HB = ˆaaake−iwkt.
+We derive
+⟨ˆaaak(t)ˆaaak′(t′)⟩ = ⟨ˆaaa†
+k(t)ˆaaa†
+k′(t′)⟩ = 0, ⟨ˆaaa†
+k(t)ˆaaak′(t′)⟩ = δk,k′eiωk(t−t′)N(ωk), and ⟨ˆaaak(t)ˆaaa†
+k′(t′)⟩ = δk,k′e−iωk(t−t′)(N(ωk) +
+1). Going on the derivation,
+C(−2χ, t) =TrB(eiχH
+H
+HBeitH
+H
+HB �
+k
+ck
+�
+ℏ
+2mωk
+(ˆaaak + ˆaaa†
+k)e−itH
+H
+HBe−iχH
+H
+HB �
+k′
+c′
+k
+�
+ℏ
+2mωk
+(ˆaaak′ + ˆaaa†
+k′)ρρρB)
+=
+�
+k,k′
+ckc′
+k
+2ωk
+TrB(eiχH
+H
+HBeitH
+H
+HB(ˆaaak + ˆaaa†
+k)e−itH
+H
+HBe−iχH
+H
+HB(ˆaaak′ + ˆaaa†
+k′)ρρρB)
+=
+�
+k,k′
+ckc′
+k
+2ωk
+TrB((ˆaaake−iωk(t+χ) + ˆaaa†
+keiωk(t+χ))(ˆaaak′ + ˆaaa†
+k′)ρρρB)
+=
+�
+k
+c2
+k
+2ωk
+[(N(ωk) + 1)e−iωk(t+χ) + N(ωk)eiωk(t+χ)]
+=
+� ∞
+0
+dωJ(ω)[(N(ω) + 1)e−iω(t+χ) + N(ω)eiω(t+χ)]
+(B7)
+N(−ω) =
+1
+e−βω−1 = −(1 +
+1
+e−βω−1), let ω′ = −ω, in the meanwhile, we extend J(ω) to negative values of ω via
+J(−ω) = −J(ω).
+� ∞
+0
+dωJ(ω)N(ω)eiω(t+χ)
+=
+� ∞
+0
+d(−ω′)J(−ω′)N(−ω′)e−iω′(t+χ)
+= −
+� −∞
+0
+dω′(−J(ω′))(−(N(ω′) + 1))e−iω′(t+χ)
+=
+� 0
+−∞
+dω′J(ω′)(N(ω′) + 1)e−iω′(t+χ)
+=
+� 0
+−∞
+dωJ(ω)(N(ω) + 1)e−iω(t+χ)
+(B8)
+Thus, C(−2χ, t) =
+� ∞
+−∞ dωJ(ω)(N(ω) + 1)e−iω(t+χ).
+In the interaction picture, ˜SSS(t) = UUU †(t, 0)SSSUUU(t, 0), where
+UUU(t1, t0) = ⃗TTTe−i
+� t1
+t0 dτH
+H
+HS(τ). Replace them into the above equation and transform the equation back to Schr¨odinger’s
+picture through UUU(t, 0) acting on the left side and UUU †(t, 0) acting on the right side of the equation, we obtain
+iH
+H
+HS(t)ρρρ(χ, t) + ∂tρρρ(χ, t) + ρρρ(χ, t)(−iH
+H
+HS(t)) =
+−
+� ∞
+0
+ds{C(0, s)SSSUUU(t, t − s)SSSUUU †(t, t − s)ρρρ(χ, t)
+− C(−2χ, −s)SSSρρρ(χ, t)UUU(t, t − s)SSSUUU †(t, t − s)
+− C(−2χ, s)UUU(t, t − s)SSSUUU †(t, t − s)ρρρ(χ, t)SSS
++ C(0, −s)ρρρ(χ, t)UUU(t, t − s)SSSUUU †(t, t − s)SSS}
+(B9)
+By using Floquet theorem, UUU(t, t0) = �
+r exp(−iεr(t − t0))|r(t)⟩⟨r(t0)|,
+
+13
+∂tρρρ(χ, t) = −i[H
+H
+HS(t),ρρρ(χ, t)]
+−
+� ∞
+0
+ds{C(0, s)SSS
+�
+r
+exp(−iεrs)|r(t)⟩⟨r(t − s)|SSS
+�
+r′
+exp(iεr′s)|r′(t − s)⟩⟨r′(t)|ρρρ(χ, t)
+− C(−2χ, −s)SSSρρρ(χ, t)
+�
+r
+exp(−iεrs)|r(t)⟩⟨r(t − s)|SSS
+�
+r′
+exp(iεr′s)|r′(t − s)⟩⟨r′(t)|
+− C(−2χ, s)
+�
+r
+exp(−iεrs)|r(t)⟩⟨r(t − s)|SSS
+�
+r′
+exp(iεr′s)|r′(t − s)⟩⟨r′(t)|ρρρ(χ, t)SSS
++ C(0, −s)ρρρ(χ, t)
+�
+r
+exp(−iεrs)|r(t)⟩⟨r(t − s)|SSS
+�
+r′
+exp(iεr′s)|r′(t − s)⟩⟨r′(t)|SSS}
+= −i[H
+H
+HS(t),ρρρ(χ, t)]
+−
+�
+ω
+� ∞
+0
+ds{C(0, s)SSS exp(−iωs)⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)|ρρρ(χ, t)
+− C(−2χ, −s)SSSρρρ(χ, t) exp(−iωs)⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)|
+− C(−2χ, s) exp(−iωs)⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)|ρρρ(χ, t)SSS
++ C(0, −s)ρρρ(χ, t) exp(−iωs)⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)|SSS}
+(B10)
+⟨r(t − s)|SSS|r′(t − s)⟩ is periodic with periodicity T due to the periodicity of the Floquet mode |r(t − s)⟩, we can take
+Fourier transform on it,
+SSSω,n =
+�� T
+0
+d(t − s)
+T
+⟨r(t − s)|SSS e−inωL(t−s)|r′(t − s)⟩
+�
+|r(t)⟩⟨r′(t)|.
+(B11)
+Therefore, ⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)| = �
+n einωL(t−s)SSSω,n. Use C(−2χ, t) = 1
+π
+� ∞
+−∞ dωe−iω(χ+t)J(ω) [1 + Nω]
+and ⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)| = �
+n einωL(t−s)SSSω,n, we arrive at
+∂tρρρ(χ, t) = −i[H
+H
+HS(t),ρρρ(χ, t)]
+−
+�
+n,ω
+einωlt
+� ∞
+0
+ds{C(0, s)SSS exp(−i(ω + nωL)s)SSSω,nρρρ(χ, t)
+− C(−2χ, −s)SSSρρρ(χ, t) exp(−i(ω + nωL)s)SSSω,n
+− C(−2χ, s) exp(−i(ω + nωL)s)SSSω,nρρρ(χ, t)SSS
++ C(0, −s)ρρρ(χ, t) exp(−i(ω + nωL)s)SSSω,nSSS}
+− i[H
+H
+HS(t),ρρρ(χ, t)]
+= −
+�
+n,ω
+{einωLt 1
+π
+� ∞
+−∞
+dω′
+� ∞
+0
+dse−i(ω′+(ω+nωL))sJ(ω′) [1 + Nω′]SSSSSSω,nρρρ(χ, t)
+− 1
+π
+� ∞
+−∞
+dω′
+� ∞
+0
+dse−iω′χei(ω′−(ω+nωL))sJ(ω′) [1 + Nω′]SSSρρρ(χ, t)SSSω,n
+− 1
+π
+� ∞
+−∞
+dω′
+� ∞
+0
+dse−iω′χe−i(ω′+(ω+nωL))sJ(ω′) [1 + Nω′]SSSω,nρρρ(χ, t)SSS
++ 1
+π
+� ∞
+−∞
+dω′
+� ∞
+0
+dsei(ω′−(ω+nωL))sJ(ω′) [1 + Nω′]ρρρ(χ, t)SSSω,nSSS}
+(B12)
+With the help of
+� ∞
+0
+ds eiωs = πδ(ω) + i P 1
+ω and disregarding the principal value P term, J(−ω) = −J(ω), and
+1 + N(−ω) = 1 +
+1
+e−βω−1 =
+1
+1−eβω = −N(ω). We get the generalized master equation finally.
+
+14
+∂tρρρ(χ, t) = −i[H
+H
+HS(t),ρρρ(χ, t)]
+−
+�
+n,ω
+einωlt{J(∆ω,n)
+�
+N∆ω,n
+�
+SSSSSSω,nρρρ(χ, t)
+− e−i∆ω,nχJ(∆ω,n)
+�
+1 + N∆ω,n
+�
+SSSρρρ(χ, t)SSSω,n
+− ei∆ω,nχJ(∆ω,n)
+�
+N∆ω,n
+�
+SSSω,nρρρ(χ, t)SSS
++ J(∆ω,n)
+�
+1 + N∆ω,n
+�
+ρρρ(χ, t)SSSω,nSSS}
+(B13)
+Appendix C: Derivation of the effective system plus system-reservoirs interaction Hamiltonian through flow
+equation approach
+In this section, we derive the effective system plus system-reservoirs interaction Hamiltonian through flow equation
+approach [3]. The method takes advantage of infinitesimal unitary transformation steps, from which renormalization-
+group–like flow equations are derived to derive the effective Hamiltonian. The flow equation is
+dH
+H
+H(s, t)
+ds
+= −VVV (s, t) + i
+� t
+0
+dt1[VVV (s, t1),H
+H
+H(s, t)],
+(C1)
+where s is the flow parameter, H
+H
+H(s, t) and VVV (s, t) are total Hamiltonian and its time-dependent part respectively. It
+should be noted that the family of Hamiltonians H
+H
+H(s, t) represents an interpolation between a starting Hamiltonian
+H
+H
+H(0, t) and a final Hamiltonian H
+H
+H(∞, t). Here, H
+H
+H(∞, t) is the Floquet Hamiltonian H
+H
+HF if VVV (∞, t) = 0. We set
+appropriate boundary conditions by enforcing that s = 0 corresponds to the initial unchanged Hamiltonian. H
+H
+H(s, t)
+can be expressed as a sum of linear operators with coefficients ci(s, t), H
+H
+H(s, t) = �
+i ci(s, t)OOOi. The OOOi operators are
+nothing other than kinetic and potential energy terms appearing in a Hamiltonian. Note that the set of operators
+may include both the original operators and new terms generated from the commutator in Eqn.C1. The coefficients
+ci(s, t) describe the coupling constants (strength) of these terms. In this representation, Eqn.C1 can be written in a
+numerically tractable form,
+dci(s, t)
+dt
+= −gi(t, [cj(s, t′)]),
+t′ ∈ [0, T].
+(C2)
+In [3], Michael Vogl et al. put forward a more analytically tractable equation, which set s = 0 only for the terms
+VVV (s, t).
+dH
+H
+H(s, t)
+ds
+= −VVV (0, t) + i
+� t
+0
+dt1[VVV (0, t1),H
+H
+H(s, t)],
+(C3)
+This corresponds to removing the original time-dependent part VVV (s, t) from the Hamiltonian via the rotating frame
+transformation e−i
+� t
+0 dtVVV (t) while generating other new time dependences. To ensure that this approximation actually
+corresponds to the aforementioned unitary transformation, we also need to restrict s ∈ [0, 1] rather than the previous
+s ∈ [0, ∞). The effective time-independent Hamiltonian is then given by H
+H
+Heff = �
+i ci(1, t)OOOi, where ci(1, t) =
+1
+T
+� T
+0 ci(1, t)dt, if we are only interested in stroboscopic dynamics.
+We now derive the effective Hamiltonian for the model we studied. The system plus system-reservoirs interaction
+Hamiltonian is
+H
+H
+HS(t) + H
+H
+HSB = ωA + K cos (ωLt)
+2
+σσσA
+z + ωB
+2 σσσB
+z + λ(σσσ1
++σσσ2
+− + σσσ1
+−σσσ2
++) + σσσA
+x BBBA + σσσB
+x BBBB,
+(C4)
+where BBBi = �
+K cikxxxik is reservoirs coupling operators and VVV (0, t) = K cos (ωLt)
+2
+σσσA
+z in this case. We make the ansatz
+H
+H
+H(s, t) = C1(s)σσσA
+z + C2(s)σσσB
+z + C3(s)σσσ1
++σσσ2
+− + C4(s)σσσ1
+−σσσ2
++ + C5(s)σσσA
+x BBBA + C6(s)σσσB
+x BBBB + C7(s)σσσA
+y BBBA,
+(C5)
+
+15
+and then find the flow equation is
+dC1(s)
+ds
+= −K cos (ωLt)
+2
+dC2(s)
+ds
+= 0
+dC3(s)
+ds
+= iKC3(s)
+ωL
+sin (ωLt)
+dC4(s)
+ds
+= −iKC4(s)
+ωL
+sin (ωLt)
+dC5(s)
+ds
+= KC7(s)
+ωL
+sin (ωLt)
+dC6(s)
+ds
+= 0
+dC7(s)
+ds
+= −KC5(s)
+ωL
+sin (ωLt)
+(C6)
+with the initial condition
+C1(0) = K cos (ωLt) + ωA
+2
+C2(0) = ωB
+2
+C3(0) = λ
+C4(0) = λ
+C5(0) = 1
+C6(0) = 1
+C7(0) = 0
+(C7)
+Their solutions are
+C1(s) = 1
+2(ωA + K cos(ωLt) − Ks cos(ωLt))
+C2(s) = ωB
+2
+C3(s) = λe
+iKs sin(ωLt)
+ωL
+C4(s) = λe
+−iKs sin(ωLt)
+ωL
+C5(s) = cos(Ks sin(ωLt)/ωL)
+C6(s) = 1
+C7(s) = − sin(Ks sin(ωLt)/ωL)
+(C8)
+After taking an average over one period and set s = 1, we end up with the effective time-independent Hamiltonian
+H
+H
+HS
+eff + H
+H
+HSB
+eff = ωA
+2 σσσA
+z + ωB
+2 σσσB
+z + λJ0(K/ωL)(σσσ1
++σσσ2
+− + σσσ1
+−σσσ2
++) + J0(K/ωL)σσσA
+x BBBA + σσσB
+x BBBB,
+(C9)
+[1] Jon H. Shirley, Solution of the Schr¨odinger Equation with a Hamiltonian Periodic in Time, Phys. Rev. 138 B979 (1965).
+[2] Andr´e Eckardt and Egidijus Anisimovas, High-frequency approximation for periodically driven quantum systems from a
+Floquet-space perspective, New J. Phys 17 093039 (2015).
+[3] Michael Vogl, Pontus Laurell, Aaron D. Barr, and Gregory A. Fiete, Flow Equation Approach to Periodically Driven
+Quantum Systems, Phys. Rev. X 9 021037 (2019).
+[4] T. Oka and H. Aoki, Photovoltaic Hall effect in graphene, Phys. Rev. B 79 081406 (2009).
+[5] T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Topological characterization of periodically driven quantum systems,
+Phys. Rev. B 82 235114 (2010).
+
+16
+[6] Tian-Shi Xiong, Jiangbin Gong, and Jun-Hong An, Towards large-chern-number topological phases by periodic quenching,
+Phys. Rev. B 93 184306 (2016).
+[7] Hui Liu, Tian-Shi Xiong, Wei Zhang, and Jun-Hong An, Floquet engineering of exotic topological phases in systems of cold
+atoms, Phys. Rev. A 100 023622 (2019).
+[8] A. Eckardt, C. Weiss, and M. Holthaus, Superfluid-insulator transition in a periodically driven optical lattice, Phys. Rev.
+Lett. 95 260404 (2005).
+[9] V. M. Bastidas, C. Emary, B. Regler, and T. Brandes, Nonequilibrium quantum phase transitions in the Dicke model,
+Phys. Rev. Lett. 108 043003 (2012).
+[10] M. Aidelsburger, M. Atala, S. Nascimbene, S. Trotzky, Y. A. Chen, and I. Bloch, Experimental realization of strong effective
+magnetic fields in an optical lattice, Phys. Rev. Lett. 107 255301 (2011).
+[11] A. Bermudez, T. Schaetz, and D. Porras, Synthetic gauge fields for vibrational excitations of trapped ions, Phys. Rev. Lett.
+107 150501 (2011).
+[12] J. Struck, C. Olschl¨ager, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Wind-
+passinger, Tunable gauge potential for neutral and spinless particles in driven optical lattices, Phys. Rev. Lett. 108 225304
+(2012).
+[13] D. V. Else, B. Bauer, and C. Nayak, Floquet Time Crystals, Phys. Rev. Lett. 117 090402 (2016).
+[14] Andreu Riera-Campeny, Maria Moreno-Cardoner, and Anna Sanpera, Time crystallinity in open quantum systems, Quan-
+tum 4 270 (2020).
+[15] F. Grossmann, T. Dittrich, P. Jung, and P. H¨anggi, Coherent destruction of tunneling, Phys. Rev. Lett. 67 516 (1991).
+[16] Jose M. Gomez Llorente and Jes´us Plata, Tunneling control in a two-level system, Phys Rev A. 45 R6958(R) (1992).
+[17] Victor Galitski, Ian B. Spielman, Spin–orbit coupling in quantum gases, Nature 494 49–54 (2013).
+[18] J. Struck, J. Simonet, and K. Sengstock, Spin-orbit coupling in periodically driven optical lattices, Nature 90 031601(R)
+(2014).
+[19] J. P. S. Peterson, T. B. Batalhao, M. Herrera, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Experimental
+Characterization of a Spin Quantum Heat Engine , Phys. Rev. Lett. 123 240601 (2019).
+[20] J. P. Pekola and I. M. Khaymovich,, Thermodynamics in single-electron circuits and superconducting qubits, Annu.Rev.
+Condens. Matter Phys. 10 193 (2019).
+[21] A. Ronzani, B. Karimi, J. Senior, Y. C. Chang, J. T. Peltonen, C. Chen, and J. P. Pekola, Tunable photonic heat transport
+in a quantum heat valve, Nat. Phys. 14 991 (2018).
+[22] A. Dechant, N. Kiesel, and E. Lutz, All-Optical Nanomechanical Heat Engine, Phys. Rev. Lett. 114 183602 (2015).
+[23] C. Urgell, W. Yang, S. L. De Bonis, C. Samanta, M. J.Esplandiu, Q. Dong, Y. Jin, and A. Bachtold, Cooling and self-
+oscillation in a nanotube electromechanical resonator,, Nat.Phys. 16 32 (2020).
+[24] J. P. Brantut, C. Grenier, J. Meineke, D. Stadler, S. Krinner, C. Kollath, T. Esslinger, and A. Georges, A thermoelectric
+heat engine with ultracold atoms, Science 342 713 (2013).
+[25] O. Abah, J. Roßnagel, G. Jacob, S. Deffner, F. Schmidt-Kaler, K. Singer, and E. Lutz,Single-Ion Heat Engine at Maximum
+Power, Phys. Rev. Lett. 109 203006 (2012).
+[26] J. Roßnagel, S. T. Dawkins, K. N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, and K. Singer, A single-atom heat engine,
+Science 352 325 (2016).
+[27] Gleb Maslennikov, Shiqian Ding, Roland Habl¨utzel, Jaren Gan, Alexandre Roulet, Stefan Nimmrichter, Jibo Dai, Valerio
+Scarani, Dzmitry Matsukevich, Quantum absorption refrigerator with trapped ions, Nat. Commun. 10 202 (2019).
+[28] James Klatzow, Jonas N. Becker, Patrick M. Ledingham, Christian Weinzetl, Krzysztof T. Kaczmarek, Dylan J. Saunders,
+Joshua Nunn, Ian A. Walmsley, Raam Uzdin, and Eilon Poem, Experimental Demonstration of Quantum Effects in the
+Operation of Microscopic Heat Engines, Phys. Rev. Lett. 122 110601 (2019).
+[29] Sourav Bhattacharjee, Amit Dutta, Quantum thermal machines and batteries, Eur. Phys. J. B 94 239 (2021).
+[30] Wang Zi, Ren Jie, Nonequilibrium thermal transport and thermodynamic geometry in periodically driven systems, Acta
+Physica Sinica 70 230503 (2021).
+[31] Breuer, H. P., and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press (2006).
+[32] Chong Chen, Jun-Hong An, Hong-Gang Luo, C. P. Sun, and C. H. Oh, Floquet control of quantum dissipation in spin
+chains, Phys. Rev. A, 91 052122 (2015).
+[33] W L Yang, W L Song, Jun-Hong An, M Feng, D Suter, and Jiangfeng Du, Floquet engineering to entanglement protection
+of distant nitrogen vacancy centers, New J. Phys., 21 013007 (2019).
+[34] Si-Yuan Bai and Jun-Hong An, Floquet engineering to reactivate a dissipative quantum battery, Phys. Rev. A, 102 060201
+(2020).
+[35] Wan-Lu Song, Jia-Bin You, J.K. Xu, W.L. Yang, and Jun-Hong An, Floquet Engineering of Two Weakly Coupled Super-
+conducting Flux Qubits, Phys. Rev. Applied, 14 054049 (2020).
+[36] T. Shirai, T. Mori, and S. Miyashita, Novel symmetry-broken phase in a driven cavity system in the thermodynamic limit,
+J. Phys. B At. Mol. Opt. Phys., 47 025501 (2014).
+[37] M. Foss-Feig, P. Niroula, J. T. Young, M. Hafezi, A. V. Gorshkov, R. M. Wilson, and M. F. Maghrebi, Emergent equilibrium
+in many-body optical bistability, Phys.Rev. A , 95 043826 (2017).
+[38] S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. B¨uchler, and P. Zoller, Quantum states and phases in driven open
+quantum systems with cold atoms, Nat. Phys., 4 878-883 (2008).
+[39] S. Diehl, E. Rico, M. A. Baranov, and P. Zoller, Topology by dissipation in atomic quantum wires, Nat. Phys., 7 971–977
+(2011).
+[40] D. Vorberg, W. Wustmann, R. Ketzmerick, and A. Eckardt, Generalized Bose-Einstein condensation into multiple states
+
+17
+in driven-dissipative systems, Phys. Rev. Lett., 111 240405 (2013).
+[41] D. Vorberg, W. Wustmann, H. Schomerus, R. Ketzmerick, and A. Eckardt, Nonequilibrium steady states of ideal bosonic
+and fermionic quantum gases, Phys.Rev. E, 92 062119 (2015).
+[42] A. Schnell, R. Ketzmerick, and A. Eckardt, On the number of Bose-selected modes in driven-dissipative ideal Bose gases,
+Phys. Rev. E, 97 032136 (2018).
+[43] Sebastian Restrepo, Javier Cerrillo, Philipp Strasberg and Gernot Schaller, From quantum heat engines to laser cooling:
+Floquet theory beyond the Born–Markov approximation, New J. Phys., 20 053063 (2018).
+[44] C. M. Dai, Z. C. Shi, and X. X. Yi, Floquet theorem with open systems and its applications, Phys. Rev. A , 93 032121
+(2016).
+[45] Tatsuhiko N. Ikeda and Masahiro Sato, General description for nonequilibrium steady states in periodically driven dissi-
+pative quantum systems, Sci. Adv., 6 eabb4019 (2020).
+[46] Massimiliano Esposito, Upendra Harbola, and Shaul Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and
+counting statistics in quantum systems, Rev. Mod. Phys., 81 1665 (2009).
+[47] S Gasparinetti, P Solinas, A Braggio and M Sassetti, Heat-exchange statistics in driven open quantum systems, New J.
+Phys., 161 115001 (2014).
+[48] Hideo Sambe, Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field, Phys. Rev. A, 7
+2203 (1973).
+[49] Wilhelm Magnus, On the exponential solution of differential equations for a linear operator, Communications on Pure and
+Applied Mathematics, 7 649-673 (1954).
+[50] Takahiro Mikami, Sota Kitamura, Kenji Yasuda, Naoto Tsuji, Takashi Oka, and Hideo Aoki, Brillouin-Wigner theory for
+high-frequency expansion in periodically driven systems: Application to Floquet topological insulators, Phys. Rev. B , 93
+144307 (2016).
+[51] Mihail Silaev, Tero T. Heikkil¨a, and Pauli Virtanen, Lindblad-equation approach for the full counting statistics of work and
+heat in driven quantum systems, Phys. Rev. E, 90 022103 (2014).
+[52] Z. Nafari Qaleh and A. T. Rezakhani, Enhancing energy transfer in quantum systems via periodic driving: Floquet master
+equations, Phys. Rev. A, 105 012208 (2022).
+[53] Horodecki R., Horodecki P., Horodecki M., Horodecki,K., Quantum entanglement, Rev. Mod. Phys. 81 865 (2009).
+[54] Zhihai Wang, Wei Wu, and Jin Wang, Steady-state entanglement and coherence of two coupled qubits in equilibrium and
+nonequilibrium environments, Phys. Rev. A 99 042320 (2019).
+
diff --git a/mNAyT4oBgHgl3EQf_vq9/content/tmp_files/load_file.txt b/mNAyT4oBgHgl3EQf_vq9/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c05c7e6786c5e92a86dacbfcb2f12527f1c3ddc0
--- /dev/null
+++ b/mNAyT4oBgHgl3EQf_vq9/content/tmp_files/load_file.txt
@@ -0,0 +1,1259 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf,len=1258
+page_content='Entanglement and work statistics in the driven open system  He Wang1, 2 and Jin Wang3, ∗  1College of Physics, Jilin University,  Changchun 130021, China  2State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry,  Changchun 130021, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  3Department of Chemistry and of Physics and Astronomy, Stony Brook University, Stony Brook,  NY 11794-3400, USA  We study the entanglement and work statistics in a driven two-qubit system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The regulation  of periodic driving has much more versatility and universality in contrast to reservoir engineering  in static systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We found the quasi-steady state entanglement can be amplified effectively by  the external drive in certain parameter regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The drive extends the range of temperatures or  temperature differences at which entanglement can emerge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' From the view of the effective Hamil-  tonian, the addition of the driving alters the inter-qubit coupling and system-bath coupling, which  are crucial in determining the quasi-steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The work statistics are also investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The  driven system, as a continuous quantum thermal machine, output work continuously and steadily  at the quasi-steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' There is a distinct operation of modes and corresponding performance  by changing driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' It can also be understood that the drive changes the effective Hamiltonian,  and further the modes of energy exchanges between the system and the baths as well as the work  reservoir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  ∗ jin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='1@stonybrook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='edu  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='00915v1  [quant-ph]  3 Jan 2023  2  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  INTRODUCTION  For the past few years, the periodically driven quantum system has drawn much attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' This has been a result  of experimental advances in state-of-the-art laser technology, which makes it implementable in the lab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In accordance  with the Floquet theorem [1] and the follow-up theoretical developments [2, 3], physical characteristics of the driven  system are primarily understood by the so-called effective Hamiltonian, which reflects the periodic driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Periodic  driving largely extends the controllability of the systems since time as a new control dimension is introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' It gets  rid of the down-to-earth difficulty of reservoir engineering in static systems that the parameter is hard to change once  the material is prepared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' By designing a suitable driving protocol, one can engineer the effective Hamiltonian, which  empowers us to have desirable properties and functionalities of the physical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Coherent control through periodic  driving (often known as Floquet engineering) has become a commonly used tool in quantum control, which has been  used to realize topologically nontrivial systems [4–7], nonequilibrium phase transitions [8, 9], artificial gauge fields  [10–12], and discrete time crystals [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Additionally, it comes into play in the coherent destruction of tunneling  [15, 16] and the manipulation of spin-orbit coupling [17, 18], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Meanwhile, significant progress has been made  toward the experimental realization of small-scale thermal machines where fluctuations play a significant role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The  thermal machines in the quantum regime have been realized on several platforms [19–26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Specific examples include a  quantum absorption refrigerator with trapped ions [27], quantum heat engines using an ensemble of nitrogen-vacancy  centers [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Continuous thermal machines [29] do not require intermittent couplings and decouplings between the  working fluid and the baths, which are particularly challenging to implement at microscopic scales, in contrast to their  reciprocating counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' As a result, they have greater experimental relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Continuous thermal machines are  typically implemented by a periodic modulation of the system Hamiltonian, which drives the system to a periodic  quasi-steady state in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The temporal driving methods may drive small systems in nonequilibrium quasi-steady  states with far greater versatility and universality than the static manipulation methods, which hinge on steady  nonequilibrium sources such as temperature bias, chemical potential difference, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  A real system is always inevitably influenced by its surroundings and this can lead to the system’s decoherence  eventually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  The environmental effect plays a crucial role in the evolution of the system [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  How to confront  dissipation and decoherence is a fundamental challenge in quantum technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' It has been shown that the dissipation  can be effectively suppressed by the formation of the Floquet bound state under temporal driving [32–34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  The  scheme to generate a maximally entangled state and then protect it based on Floquet engineering is also proposed  [33, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' However, the entanglement of the nonequilibrium quasi-steady state still lacks of investigations based on  our knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Indeed, the balance of the periodic driving and dissipation can yield a variety of nonequilibrium  steady states and phase transitions in various systems including cavity-QED systems [36, 37], cold atoms [38, 39],  ideal Bose gases [40–42], and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A natural question is raised: Is entanglement in the quasi-steady state?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Can we  enhance it with Floquet engineering?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The answer is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The entanglement can be magnified significantly by  the befitting driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The system can become entangled in a wider range of temperatures or temperature differences  as a result of the drive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' From the standpoint of effective Hamiltonian, the existing driving gives rise to the change  of inter-qubit coupling and system-bath coupling, as well as further, modifies steady state entanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The work  statistics of the open system are also of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The net flow from the baths to the system disappears when the static  system approaches the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' When certain external driving is applied, the system can operate continually and  steadily as a continuous quantum thermal machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The different drivings contribute to the various modes of energy  exchanges between the system and the baths as well as the work reservoir (energy source of the external agent which  modulates the system) in the quasi-steady state, which bring about the thermal machine with numerous operation of  modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We quantify the performance efficiency of different operation modes, which is bounded by the Carnot limit  in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  The rest of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In Section II, we introduce our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We then derive a generalized  master equation by means of double-projective measurement protocol and Floquet theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In Section III, the quasi-  steady state entanglement is studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In Section IV, we investigate the work statistics at a quasi-steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Finally,  we draw our conclusions in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  THEORETICAL FRAMEWORK  To start, we first introduce the model we studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The system is composed of a pair of interacting qubits, and each  qubit couples to its own bosonic bath with a certain temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Meanwhile, the system is driven by external field  3  control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The sketch of the model is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The Hamiltonian of the whole system is  H  H  H = H  H  HS(t) + H  H  HB + H  H  HSB  =  �  i=A,B  ωi + Di(t)  2  σσσi  z + λ(σσσA  +σσσB  − + σσσA  −σσσB  +) +  �  i=A,B  �  k  ω2  ikaaa†  ikaaaik +  �  i=A,B  σσσi  x  �  k  cccikxxxik,  (1)  where σσσi  z are Pauli matrices for the i-th qubit, it reads σσσA  z = σσσz  �III for the A qubit or σσσB  z = III �σσσz for the B qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  ωi is the energy spacing of the i-th qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Di(t) is the external field control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' λ measures the coupling interaction  between two qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' aaa†  ik(aaaik) is the creation (annihilation) operator of k-th bosonic mode in i-th bath and satisfies the  commute relation [aaaik,aaa†  i′k′] = δii′δkk′I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The cik are coupling constants that describe the coupling of the i-th qubit  to its own reservoir modes aaaik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' To fully characterize the interaction between the system and baths, we need to define  the spectral density of the baths, which follows  Ji(ω) = π  2  �  k  c2  ik  ωik  δ(ω − ωik)  (2)  A structure-less spectral density (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' linear form  di  ω0 ω) typically empowers a Markovian treatment of the reservoirs  due to the fast decay of its associated correlation functions, while a more structured spectral density (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' strongly  peaked around a frequency  diγω  (ω2−ω2res)2+γ2ω2 ) requires a more involved treatment [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In this paper, we simply take a  structure-less spectral density Ji(ω) = di  ω0 ω into consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  A sketch of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' There are two interacting qubits, which are coupled with individual baths as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The qubit  A is driven by the external field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  The drives Di(t) may be any time-dependent function, but we only take into account an easily implementable drive  scheme: a monochromatic drive with frequency ωL and amplitude K only acts on the qubit A, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', DA(t) = K cos ωLt  and DB(t) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Note that the total Hamiltonian is periodic in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' One can take advantage of the Floquet theorem to solve a  time-periodic Schr¨odinger equation i∂t|ψr(t)⟩ = H  H  HS(t)|ψr(t)⟩, where H  H  HS(t) = H  H  HS(t+T) = �  k eik ωLtH  H  Hk, with period  T =  2π  ωL .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A solution to this Schr¨odinger equation is given by Floquet states |ψr(t)⟩ = e−iεrt|r(t)⟩, where εr are  called quasienergies and |r(t)⟩ = |r(t + T)⟩ are Floquet modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The existence of Floquet states in time-periodically  driven systems follows from the Floquet theorem in a similar way to the existence of Bloch states in spatially periodic  systems [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We also mention that there is a similar Floquet theorem for open systems in [44, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='A,  we review more details on the Floquet theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  To study the heat statistics of the driven system, we follow the full counting statistics formalism in [43, 46, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The  heat moments are expediently described in terms of the characteristic function G(χ) =  �  d∆E e−iχ∆Ep(∆E), which  is based on double-projective measurement of the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' With the help of conditional probability p(E1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' E0),  which one measured the energy of environment E = E0 at time t0, and a follow-up measurement gave E1 at time t1,  and the probability p(E0) to measure E0 at time t0, the probability distribution function for the heat energy exchange  ∆E to be transported to the reservoir between times t = t0 and t = t1 can be expressed as  p(∆E, t) =  �  E1,E0  δ(E1 − E0 − ∆E)p(E1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' E0)p(E0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (3)  Taking account into the projective operator PPP Em and its property PPP EmPPP En = δmnPPP Em, we have  p(E1, E0) = Tr[PPP E1UUU(t)PPP E0ρρρtot(0)PPP E0UUU †(t)PPP E1]  = Tr[UUU †(t)PPP E1UUU(t)PPP E0ρρρtot(0)PPP E0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (4)  4  The generating function is given by  G(χ, t) =  �  d∆E e−iχ∆Ep(∆E)  =  �  d∆E e−iχ∆E �  E1,E0  δ(E1 − E0 − ∆E)p(E1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' E0)p(E0)  =  �  E1,E0  p(E1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' E0)p(E0)e−iχ∆E  (5)  Assume the initial total density matrix ρρρtot(0) = ρρρS(0) ⊗ ρρρB(0) to be factorized into the system density matrix  ρρρS(0) and the thermalized environment density matrix ρρρB(0) = e−βH  H  HB/Z, where Z is the partition function of the  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Particularly, this assumption indicates that all projectors PPP Em commute with ρρρ(0), ensuring that the  dynamics of the reservoir are unaffected by the initial measurement of the observable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  By the use of e−iχH  H  HB =  �  Em PPP Eme−iχEm, we have  G(χ, t) =  �  E1,E0  Tr[UUU †(t)PPP E1UUU(t)PPP E0ρρρtot(0)PPP E0]e−iχ∆E  = Tr[UUU †(t)  �  E1  PPP E1e−iχE1UUU(t)  �  E0  PPP E0eiχE0ρρρtot(0)]  = Tr[UUU †(t)e−iχH  H  HBUUU(t)eiχH  H  HBρρρtot(0)]  = Tr[UUU(χ, t)ρρρtot(0)UUU †(−χ, t)]  = Tr[ρρρtot(χ, t)],  (6)  where UUU(χ, t) = e−iχH  H  HB/2UUU(t)eiχH  H  HB/2 and ρρρtot(χ, t) = UUU(χ, t)ρρρtot(0)UUU †(−χ, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' It enables us to compute the statistics  of the energy transferred between the system and reservoir by straightforward differentiation  ⟨∆En⟩ = −  ∂n  ∂(iχ)n G(χ)|χ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (7)  Utilize the modified time evolution operator UUU(χ, t) and modified density matrix ρρρtot(χ, t), and assume that the  coupling between the system and baths are weak enough such that the Born–Markov approximation is valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We  derive a generalized Markov master equation without secular approximation  ∂tρρρ(χ, t) = LLL(χ, t)ρρρ(χ, t)  = −i [H  H  HS(t),ρρρ(χ, t)]  −  �  {i=1,2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n}  ei∆ω,nt{Ji(∆ω,n)Ni(∆ω,n)SSSi,ω,n(t)SSSiρρρ(χ, t)  − Ji(∆ω,n) [1 + Ni(∆ω,n)]SSSiρρρ(χ, t)SSSi,ω,n(t)ei∆i,ω,nχ  − Ji(∆ω,n)Ni(∆ω,n)SSSi,ω,n(t)ρρρ(χ, t)SSSie−i∆i,ω,nχ  + Ji(∆ω,n) [1 + Ni(∆ω,n)]ρρρ(χ, t)SSSi,ω,n(t)SSSi},  (8)  where SSS1 = σσσA  x and SSS2 = σσσB  x , ∆ω,n = ω + nωL and SSSi,ω,n(t) =  �� T  0  dt  T ⟨r(t)|SSSi e−inωlt|r′(t)⟩  �  |r(t)⟩⟨r′(t)| such that  ω = εr − εr′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' εr is quasi-energy in the first Brillouin zone and |r(t)⟩ corresponds to Floquet modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Ji(ω) and Ni(ω)  are the spectral density and Bose distribution for the i-th baths respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The details are in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Similar  master equations have been derived in different research backgrounds [43, 47, 51, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  ENTANGLEMENT IN THE DRIVEN OPEN SYSTEM  In this section, we will study the entanglement in the quasi-steady state of the driven open system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Note that due  to the periodicity of the Floquet modes |r(t)⟩, the superoperator LLL(χ, t) also has the same periodicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The evolution  5  of the system can be computed just by setting χ = 0 in Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' (8),  ∂tρρρ(t) = − i [H  H  H(t),ρρρ(t)] −  �  {i=1,2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n}  einωLtJi(∆ω,n){Ni(∆ω,n) [SSSiSSSi,ω,n(t)ρρρ(t) − SSSi,ω,n(t)ρρρ(t)SSSi]  + [1 + Ni(∆i,ω,n)] [ρρρ(t)SSSi,ω,n(t)SSSi − SSSiρρρ(t)SSSi,ω,n(t)]}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (9)  Assuming that in the long-time limit the density matrix ρρρ(t) is time-periodic with the same period as the Floquet  modes, in the extended space this equation has the form  ��  k  TTT k ⊗ LLLk − iωLFFF z  �  ⃗ρρρ = 0 ,  (10)  with ⃗ρρρ a vector containing all Fourier components of ρρρ(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The definition of TTT k and FFF z can be found in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Therefore, one can numerically obtain a quasi-steady state by truncating the basis of the temporal space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The number  of basis should be as large enough as possible to ensure that the result converges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' For general two qubits state ρρρ,  the entanglement can be quantified using the concurrence, which is defined as C = max {0, λ1 − λ2 − λ3 − λ4} in  bare basis, where {λ1, λ2, λ3, λ4} are the square roots of the eigenvalues of √ρρρ(σσσy ⊗ σσσy)ρρρ∗(σσσy ⊗ σσσy)√ρρρ sorted in a  descending order [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Entanglement varies w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' (a) the temperatures of baths, (b) the driving amplitude K in one period, and (c) the  driving frequency ωL in one period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The reservoir temperatures are T1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5 and T2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='1 in (a) and (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' And the driving  frequency ωL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5 for (b) and the driving amplitude K = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5 for (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Other parameters are d1 = d2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='001, ω01 = ω02 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  The coupling strength between two qubits is λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='25, and the energy gaps of the qubits are ω1 = ω2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  We first consider what happened provided that K = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', there is no external driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' This is the case shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2(a), which comprises both equilibrium and nonequilibrium scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The steady-state entanglement only survives  in a limited temperature range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The steady-state entanglement varies non-monotonically with both temperatures  or temperature differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  With rising temperatures or temperature differences, the entanglement grows, then  diminishes, and finally vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A similar phenomenon has been found in [54], which can be phenomenologically  explained by the competition between coherence and populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The system has the same period as the external field  when it is driven by an external field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The equilibrium/nonequilibrium steady state is replaced with a nonequilibrium  quasi-steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The entanglement of the nonequilibrium quasi-steady state changes non-monotonically with the  driving amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' If the driving amplitude is low, entanglement does not exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' If the amplitude is tuned higher, one  may be able to harvest more entanglement at certain time slices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Particularly, the entanglement covers the most time  in one period when K ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5 as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The entanglement of the nonequilibrium quasi-steady state also  varies non-monotonically with the driving frequency in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The entanglement disappears if the driving frequency  is less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' One may harvest larger entanglement at some time slices if one tunes the driving frequency properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The  entanglement lasts longest in one period when ωL ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5, which is resonant with the qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Indeed, the nonequilibrium quasi-steady state is a result of the competition between periodic driving and dissipa-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Provided that the drive is weak, the dissipation dominates the quasi-steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' But the quasi-steady state  has periodicity as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' This case is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='3(a,d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Despite being weak, driving still changes the system  significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Entanglement even survives at high temperatures or high-temperature differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Entanglement is  visibly enhanced and lasts for the majority of one period if the driving amplitude is comparative with the energy  gap of the qubit in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='3(b,e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Too dramatic driving can also be damaging to the entanglement of the quasi-steady  state, as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='3(c,f), where the driving dominates the quasi-steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The behavior of the entanglement is  sensitive to temperature changes or variances, therefore the influence of the baths is still considerable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (b)  (c)  (a)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6  K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
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+page_content='8  1  1  0  0  t/S6  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Variation of entanglement w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='t temperatures in (a ∼ c) and temperature differences in (d∼f) with the driving  frequency ωL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5, where K = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5, 5 for (a, d), (b, e), (c, f) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' ∆T = T1 − T2 and T1 increases from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Other  parameters are the same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Similar behaviors also happen when we choose different driving frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A driving frequency that is too strong or  too weak will be not helpful to harvest more entanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' When the frequency is low, the harvesting entanglement is  considerable only at relatively low temperatures or temperature differences depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='4(a,d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Under the Floquet-  Magnus expansion approximation [49, 50], the effective system Hamiltonian is H  H  Heff ≈ H  H  H0 + �  n>0  [H  H  Hn,H  H  H−n]  nωL  + O(ω2  L)  in high frequency regime, where H  H  Hn is the n-th Fourier component of the system Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' One can verify that  H  H  Heff ≈ H  H  H0 in our setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' As a result, when the driving frequency is so high that the system has no time to respond  to the external driving, the quasi-steady state entanglement behavior is very similar to that of steady state without  driving, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='4(c,f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' When the frequency is in the middle value, the drive is quite effective at improving  the entanglement shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='4(b,e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  The behavior in the low and medium frequency regime can also be somewhat understood by the effective Hamilto-  nian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Using the flow equation approach [3], we obtain the effective system plus system-reservoirs interaction Hamil-  tonian (rather than the sole system Hamiltonian)  H  H  HS  eff + H  H  HSB  eff = ωA  2 σσσA  z + ωB  2 σσσB  z + λJ0(K/ωL)(σσσ1  +σσσ2  − + σσσ1  −σσσ2  +) + J0(K/ωL)σσσA  x BBBA + σσσB  x BBBB,  (11)  where J0(x) is the first kind Bessel function and BBBi = �  K cikxxxik are the reservoir coupling operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The derivation  details of Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 11 is in Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The drive affects both the system-reservoirs coupling and the inter-qubit coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Note that J0(0) = 1, we may conclude that the effective Hamiltonian is equal to the original Hamiltonian when the  frequency ωL is set to a very high value and the amplitude K is fixed at a certain finite value, which conforms with  the conclusion we got above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Similar to this, when the frequency ωL is set to a finite value and K is made to be  extremely small, the effective Hamiltonian is identical to the original Hamiltonian as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Therefore, the effect of the  drive is not remarkable in the two kinds of limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' This, however, is not the story for K/ωL being finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' First, the  change of the inter-qubit coupling modifies the eigenenergy of the bare system, resulting in an effect on the population  distribution at the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Second, the change of system-reservoirs coupling alters the dissipative effect of the  environment and further changes the steady coherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' |J0(s)| ≤ 1 indicates that the dissipative effect of one of the  (a)  (b)  (c)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
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+page_content='8  1  0  0  t/2  t/ 2  T37  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Variation of entanglement w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='t temperatures in (a ∼ c) and temperature differences in (d∼f) with the driving  amplitude K = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5, where ωL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5, 5 for (a, d), (b, e), (c, f) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' ∆T = T1 − T2 and T1 increases from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Other  parameters are the same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  baths is weakened and the inter-qubit interaction that induces entanglement within the system diminishes as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The  end result is generated by the combination of these two effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' However, we point out that the effective Hamiltonian  is unable to provide a master equation to propagate the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The reason is also clear: the effective Hamiltonian  can only describe the stroboscopic time evolution, it can not support a continuous time master equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' However,  as we have seen, the effective Hamiltonian still offers certain perspectives for comprehending evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  WORK STATISTICS IN THE DRIVEN OPEN SYSTEM  We investigate work statistics of the driven open system in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Using the counting field and its responding  generalized master equation, the heat flow from the ith bath to the system is obtained by  ˙Qi(t) = −∂t ⟨H  H  HBi⟩ = Tr {(∂iχLLLi(χ, t)) · ρρρ(χ, t)} |χ=0  =  �  {ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n}  einωLt  Tr{−Ji(∆ω,n) [1 + Ni(∆ω,n)] ∆ω,nSSSiρρρ(t)SSSi,ω,n(t)  + Ji(∆ω,n)Ni(∆ω,n)∆ω,nSSSi,ω,n(t)ρρρ(t)SSSi}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (12)  The heat flow, we define, is positive if it flows from the bath to the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The system must abide by the energy  balance at the quasi-steady state, which means ˙QA + ˙QB + ˙W=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5, we plot the variations of the heat flow and  workflow with respect to the amplitude K in (a) and to the frequency in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' If there is no drive, the system relaxes  to the nonequilibrium steady state, and the net flow from the reservoirs to the system vanishes, which also hints that  extracted work ˙Wnd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' By varying the driving amplitude, the heat flow from bath B is always negative while the  heat flow from bath-A drops from a specific positive value to a certain negative value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The combination of the change  of ˙QA and ˙QB determines the ˙W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' As a result, one may classify thermal operation regimes into three modes in K  parameter space in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' When K ∈ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='18) roughly, ˙QA > 0, ˙QB < 0, and ˙W < 0, the system operates as a  (a)  (c)  (b)  1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
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+page_content='8  0  1  1  0  t/  t/  t/ 2元8  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Variation of mean heat flow and work flow w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='t the driving amplitude K in (a) and w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' the driving frequency ωL  in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Variation of performance of operation modes w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='t the driving amplitude K in (c) and w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' the driving frequency ωL  in (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' ωL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5 in (a,c), and K = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='05 in (b,d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' TA = 1 and TB = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Other parameters are the same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  heat engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Additionally, there is a transition region, K ∈ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='18, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='35) approximately, ˙QA > 0, ˙QB < 0, and ˙W > 0,  this operation mode of the system serves no useful purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' When K > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='35, the system functions as a heat pump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Similarly, there are three regimes of thermal operations in ωL parameter space in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' There is a small region  around ωL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5, ˙QA > 0, ˙QB < 0, and  ˙W < 0, the system functions as a heat engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' After going through the  narrow transition regime, the system operates as a heat pump when deviates ωL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5 significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We also quantify  the performance of different operation modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The efficiency of the heat engine is measured by | ˙W/ ˙QA| ≤ η and that  of heat pump as | ˙QA/ ˙W| ≤ η−1, where η = 1 − TB  TA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='99 is Carnot bound in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We can verify that both the  engine and heat pump are bounded by the Carnot limit in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5(c,d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' As the amplitude grows, the engine’s efficiency  increases before declining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' and the heat pump becomes more efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The efficiency of both the heat pump and the  engine fluctuates non-monotonically as a function of frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Variation of mean heat flow and work flow w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='t the temperature in (a) and Variation of performance of operation  modes in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' ωL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5 and K = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='05 in (a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' TA = TB + ∆T and TB = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Other parameters are the same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (b)  (a)  X10-4  6 ,×10-4  10  4  M-  QA  5  QB  Wnd  0  0  2  5  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='52  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='56  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='48  K  (d)  (c)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6  -- engine  heat pump  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='4E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
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+page_content='8  1  △T  △T9  We can also gain some insights into the reason why the system exhibits distinct operation modes and various  performances when we regulate the driving from the perspective of the effective Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The change of inter-  qubits coupling and the system-reservoirs coupling re-determines the heat flow and furthermore leads to output work  being modified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The heat flow is also changed directly by controlling temperature difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' If the drive is fixed, the  system displays various operation modes as the temperature difference changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' When the temperature difference is  less, the system performs as a heat pump;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' after passing through a transition region, the system behaves as a heat  engine at higher temperature differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' This is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The performance efficiency of the heat pump is  lowered as the temperature difference increases, on the contrary, that of the engine increases as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='6(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  CONCLUSION  In conclusion, we computed the nonequilibrium quasi-steady state entanglement within the two-qubit system by  deriving a generalized master equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We have better control over the system with external field regulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The  system may harvest more entanglement from the reservoirs compared with the static system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The driven system  can be entangled even at high temperatures or temperature differences in contrast to the system without driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  We try to get to the bottom of why the driven system behaves differently from the static system from the effective  Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The introduced driving modifies the inter-qubit coupling and system-reservoirs coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The total  effect influences the quasi-steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We also investigate the work statistics in the driven open system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Changing  the drive frequency or amplitude, the system will have different modes of operation, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', heat pump and engine or  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Their performances related to the heat flow from the reservoirs to the system can be changed by modifying  driving and temperature differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  As it stands, our model is likely to be realizable with state-of-the-art laser  technology and quantum simulation platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Further optimization of the model parameters may relax experimental  requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Appendix A: Floquet Theory and the Extended Space  We give a more detailed introduction to Floquet theory in this section [2, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Consider a time-periodic Hamiltonian  H  H  HS(t) = H  H  HS(t + T) = �  k eik ωLtH  H  Hk, with period T =  2π  ωL , according to Floquet theory, a solution to Schr¨odinger  equation i∂t|ψr(t)⟩ = H  H  HS(t)|ψr(t)⟩ is given by Floquet states |ψr(t)⟩ = e−iεrt|r(t)⟩, where εr are dubbed as quasiener-  gies and |r(t)⟩ = |r(t + T)⟩ are Floquet modes (states).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Similar to the way Bloch states exist in spatially periodic  systems, the existence of Floquet states in time-periodically driven systems comes from the Floquet theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  We also mention that there is a similar Floquet theorem for open systems in [44, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  One can ignore the micromotion and focus on the time evolution in a stroboscopic fashion in steps of the driving  period T as long as the dynamics we studied over a time span that is long compared to a single driving period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Such  a stroboscopic time evolution is governed by the time-independent Floquet Hamiltonian H  H  HF  t0, which is defined in a  way that it generates the time evolution over one period,  exp  �  − iTH  H  HF  t0  �  = UUU(t0 + T, t0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A1)  and can be expressed like  H  H  HF  t0 =  �  r  εr|r(t0)⟩⟨r(t0)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A2)  The parametric dependence on the initial time t0 is periodic, H  H  HF  t0+T = H  H  HF  t0, and related to the micromotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' One  can construct a Floquet Hamiltonian for a different initial time t′  0 by applying a unitary transformation, H  H  HF  t′  0 =  UUU †(t0, t′  0)H  H  HF  t0UUU(t0, t′  0), on a Floquet Hamiltonian H  H  HF  t0 obtained for the initial time t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' It is difficult to obtain the  Floquet Hamiltonian in general, however, various methods are developed based on high-frequency expansion [2, 49, 50]  or others [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  We can introduce a unitary operator that describes the periodic time dependence of the Floquet modes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', the  micromotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The corresponding two-point micromotion operator can be defined by  PPP(t2, t1) =  �  r  |r(t2)⟩⟨r(t1)|  (A3)  10  as a result of its construction, it is periodic in both arguments, PPP(t2 + T, t1) = PPP(t2, t1 + T) = PPP(t2, t1), and evolves  the Floquet modes in time,  |r(t2)⟩ = PPP(t2, t1)|r(t1)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A4)  The Floquet Hamiltonian and the micromotion operator can be written down immediately using Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='A2 and  Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='A3 if the Floquet states and their quasienergies are known by diagonalizing the time evolution operator over  one period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' One can then write out the time evolution operator using the Floquet Hamiltonian and the micromotion  operator as  UUU(t2, t1) = e−i(t2−t1)H  H  HF  t2PPP(t2, t1) = PPP(t2, t1)e−i(t2−t1)H  H  HF  t1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A5)  From the above analysis, we can see that quasienergies and Floquet modes are extremely crucial for the evolution  of the driven system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We show how to solve them numerically in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The Floquet modes are time-periodic  and form a complete basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' To find them one solves the eigenvalue problem  (H  H  HS(t) − i∂t) |r(t)⟩ = εr|r(t)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A6)  The periodicity of the Floquet modes enables us to map the eigenvalue problem to a time-independent one in  an extended Hilbert space, also known as Sambe space [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' To do this, an infinite-dimensional space with integer  quantum numbers is introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Its basis is given by  HT = {.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' , | − 3⟩, | − 2⟩, | − 1⟩, |0⟩, |1⟩, |2⟩, |3⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A7)  There are two operators TTT k and FFF z in Sambe space, which are defined as  TTT k|m⟩ = |m + k⟩,  FFF z|m⟩ = m|m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A8)  Combining the basis denoted by HS = {|φ1⟩, |φ2⟩, |φ3⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' |φK⟩} for the quantum system living in original Hilbert  space HS, one can construt the basis of the extended Hilbert space,  H = HT ⊗ HS =  �  |n, φ⟩⟩ |n ∈ Z, i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' , K}  �  ,  (A9)  with the scalar product ⟨⟨u|v⟩⟩ = 1  T  � T  0 dt⟨u(t)|v(t)⟩ = ⟨u(t)|v(t)⟩ in the extended space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We have denoted vectors in  the Sambe space by a double ket notation |r⟩⟩, which corresponds to |r(t)⟩ in HS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Moreover, a periodic time-dependent  operator OOO(t) = �  k OOOkeiωLt in extended space is expressed as  OOOext =  �  k  TTT k ⊗ OOOk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A10)  With the above definitions, we rewrite the operator QQQ = H  H  H(t) − i∂t and solve eigenvalue problem in extended space  as  QQQext =  �  k  TTT k ⊗ H  H  Hk + ωLFFF z ⊗ 111  −→  QQQext|rm⟩⟩ = εrm|rm⟩⟩,  (A11)  where H  H  Hk are the Fourier components of the Hamiltonian H  H  H(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Note that εr is periodic with period ωL because  |r(t)⟩eimωLt is also the eigenstate of Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='A6 with eigenvalue εrm = εr + mωl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' This is the reason why the eigenstates  and quasienergies have been denoted with an additional index m in the extended space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The complete set of solutions  of the quasienergies eigenvalue problem Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='A6 contains a lot of redundant information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' All Floquet states of the  system can, thus, be constructed, for example, from those Floquet modes whose quasienergies lie in a single Brillouin  zone of the ωL periodic quasienergy spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' From now on we will denote Floquet modes in the extended space just  by |r⟩⟩, assuming that all lie in the same Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  One can re-formulate the evolution of any operator with the help of The Floquet modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Take into account an  11  arbitrary operator SSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  SSS(t) = UUU †(t)SSSUUU(t)  = (PPP(t, 0)e−itH  H  HF  0 )†SSSPPP(t, 0)e−itH  H  HF  0  = eitH  H  HF  0 PPP †(t, 0)SSSPPP(t, 0)e−itH  H  HF  0  =  �  r  eitεr|r(0)⟩⟨r(0)|  �  m  |m(0)⟩⟨m(t)|SSS  �  r′  |r′(t)⟩⟨r′(0)|  �  m′  e−itεm′ |m′(0)⟩⟨m′(0)|  =  �  r,r′  eit(εr−εr′)⟨r(t)|SSS|r′(t)⟩|r(0)⟩⟨r′(0)|  =  �  ω,n  eit(ω+nωL)SSSω,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A12)  where SSSω,n =  �� T  0  dt  T ⟨r(t)|S e−inωlt|r′(t)⟩  �  |r(0)⟩⟨r′(0)| and εr − εr′ = ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Due to the periodicity of the Floquet  modes |r(t)⟩(|r′(t)⟩), we can perform the Fourier transform, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' ⟨r(t)|SSS|r′(t)⟩|r(0)⟩⟨r′(0)| = �  k einωLtSSSω,n, where  SSSω,n =  �� T  0  dt  T ⟨r(t)|S e−inωlt|r′(t)⟩  �  |r(0)⟩⟨r′(0)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In extended space, using Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='A8 this is easily computed by  � T  0  dt  T ⟨r(t)|SSS e−inωLt|r′(t)⟩ = ⟨⟨r|TTT −n ⊗ SSS|r⟩⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (A13)  It is now straightforward to obtain a master equation for a driven open quantum system thanks to decomposition  Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='A12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Appendix B: The derivation of the Generalized Master Equation  The total Hamiltonian, including system and reservoir is H  H  Htot = H  H  HS(t) + H  H  HB + H  H  HSB and we assume an initial  factorizing state of the form ρρρtot(0) = ρρρ(0) ⊗ ρρρB, with ρρρB ∼ e−βH  H  HB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Define the modified density matrix  ρρρtot(χ, t) = UUU(χ, t)ρρρtot(0)UUU †(−χ, t),  (B1)  with total (system plus reservoirs) initial density matrix ρρρtot(0) and modified evolution operator UUU(χ, t) =  e−iχH  H  HB/2UUU(t)eiχH  H  HB/2, where UUU(t) is the evolution operator corresponding to Hamiltonian H  H  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  The variable χ is  usually referred to as the counting field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The evolution of operator ρρρtot(χ, t) is given by  ∂tρρρtot(χ, t) = −i [H  H  H(χ, t)ρρρtot(χ, t) − ρρρtot(χ, t)H  H  H(−χ, t)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (B2)  Taking the trace over the reservoir degrees of freedom we define  ρρρ(χ, t) = TrB {ρρρtot(χ, t)} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (B3)  Note that the total density matrix and the reduced density matrix of our system are both recovered by setting χ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Transform Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B2 into the interaction picture by ˜AAA(t) = UUU †  0(t)AAAUUU 0(t), with UUU 0(t) the evolution operator associated  to Hamiltonian H  H  H0(t) = H  H  HS(t) + H  H  HB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' And considering the standard Born–Markov approximations [31], we obtain  ∂t˜ρρρ(χ, t) = −  � ∞  0  dsTrB{ ˜H  H  HI(χ, t) ˜H  H  HI(χ, t − s)˜ρρρ(χ, t)ρρρB − ˜H  H  HI(χ, t)˜ρρρ(χ, t)ρρρB ˜H  H  HI(−χ, t − s)  − ˜H  H  HI(χ, t − s)˜ρρρ(χ, t)ρρρB ˜H  H  HI(−χ, t) + ˜ρρρ(χ, t)ρρρB ˜H  H  HI(−χ, t − s) ˜H  H  HI(−χ, t)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (B4)  We take the interaction Hamiltonian with the form H  H  HSB = SSS ⊗BBB = SSS ⊗�  k ckxxxk and define the correlation function  C(χ, t) ≡ ⟨ ˜BBB(χ, t)BBB⟩ = TrB  �  ˜BBB(χ, t)BBBρρρB  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Using the fact that  �  ˜BBB(χ, t) ˜BBB(ξ, s)  �  =  �  ˜BBB(χ − ξ, t − s)BBB  �  , we have  ∂t˜ρρρ(χ, t) = −  � ∞  0  ds{C(0, s)˜SSS(t)˜SSS(t − s)˜ρρρ(χ, t) − C(−2χ, −s)˜SSS(t)˜ρρρ(χ, t)˜SSS(t − s)  − C(−2χ, s)˜SSS(t − s)˜ρρρ(χ, t)˜SSS(t) + C(0, −s)˜ρρρ(χ, t)˜SSS(t − s)˜SSS(t)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (B5)  12  The correlation functions can actually be written as  C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) =TrB(eiχH  H  HBeitH  H  HBBBBe−itH  H  HBe−iχH  H  HBBBBρρρB)  =TrB(eiχH  H  HBeitH  H  HB �  k  ckxxxke−itH  H  HBe−iχH  H  HB �  k′  c′  kxxx′  kρρρB)  =TrB(eiχH  H  HBeitH  H  HB �  k  ck  �  ℏ  2mω (ˆaaak + ˆaaa†  k)e−itH  H  HBe−iχH  H  HB �  k′  c′  k  �  ℏ  2mω (ˆaaak′ + ˆaaa†  k′)ρρρB)  (B6)  Set ℏ = m = 1 and use ˆaaa†  k(t) = eitH  H  HBˆaaa†  ke−itH  H  HB = ˆaaa†  keiwkt and ˆaaak(t) = eitH  H  HBˆaaake−itH  H  HB = ˆaaake−iwkt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  We derive  ⟨ˆaaak(t)ˆaaak′(t′)⟩ = ⟨ˆaaa†  k(t)ˆaaa†  k′(t′)⟩ = 0, ⟨ˆaaa†  k(t)ˆaaak′(t′)⟩ = δk,k′eiωk(t−t′)N(ωk), and ⟨ˆaaak(t)ˆaaa†  k′(t′)⟩ = δk,k′e−iωk(t−t′)(N(ωk) +  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Going on the derivation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) =TrB(eiχH  H  HBeitH  H  HB �  k  ck  �  ℏ  2mωk  (ˆaaak + ˆaaa†  k)e−itH  H  HBe−iχH  H  HB �  k′  c′  k  �  ℏ  2mωk  (ˆaaak′ + ˆaaa†  k′)ρρρB)  =  �  k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='k′  ckc′  k  2ωk  TrB(eiχH  H  HBeitH  H  HB(ˆaaak + ˆaaa†  k)e−itH  H  HBe−iχH  H  HB(ˆaaak′ + ˆaaa†  k′)ρρρB)  =  �  k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='k′  ckc′  k  2ωk  TrB((ˆaaake−iωk(t+χ) + ˆaaa†  keiωk(t+χ))(ˆaaak′ + ˆaaa†  k′)ρρρB)  =  �  k  c2  k  2ωk  [(N(ωk) + 1)e−iωk(t+χ) + N(ωk)eiωk(t+χ)]  =  � ∞  0  dωJ(ω)[(N(ω) + 1)e−iω(t+χ) + N(ω)eiω(t+χ)]  (B7)  N(−ω) =  1  e−βω−1 = −(1 +  1  e−βω−1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' let ω′ = −ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' in the meanwhile,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' we extend J(ω) to negative values of ω via  J(−ω) = −J(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  � ∞  0  dωJ(ω)N(ω)eiω(t+χ)  =  � ∞  0  d(−ω′)J(−ω′)N(−ω′)e−iω′(t+χ)  = −  � −∞  0  dω′(−J(ω′))(−(N(ω′) + 1))e−iω′(t+χ)  =  � 0  −∞  dω′J(ω′)(N(ω′) + 1)e−iω′(t+χ)  =  � 0  −∞  dωJ(ω)(N(ω) + 1)e−iω(t+χ)  (B8)  Thus, C(−2χ, t) =  � ∞  −∞ dωJ(ω)(N(ω) + 1)e−iω(t+χ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  In the interaction picture, ˜SSS(t) = UUU †(t, 0)SSSUUU(t, 0), where  UUU(t1, t0) = ⃗TTTe−i  � t1  t0 dτH  H  HS(τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Replace them into the above equation and transform the equation back to Schr¨odinger’s  picture through UUU(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 0) acting on the left side and UUU †(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 0) acting on the right side of the equation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' we obtain  iH  H  HS(t)ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) + ∂tρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) + ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)(−iH  H  HS(t)) =  −  � ∞  0  ds{C(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' s)SSSUUU(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t − s)SSSUUU †(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t − s)ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)  − C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' −s)SSSρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)UUU(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t − s)SSSUUU †(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t − s)  − C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' s)UUU(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t − s)SSSUUU †(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t − s)ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSS  + C(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' −s)ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)UUU(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t − s)SSSUUU †(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t − s)SSS}  (B9)  By using Floquet theorem,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' UUU(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t0) = �  r exp(−iεr(t − t0))|r(t)⟩⟨r(t0)|,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  13  ∂tρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) = −i[H  H  HS(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)]  −  � ∞  0  ds{C(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' s)SSS  �  r  exp(−iεrs)|r(t)⟩⟨r(t − s)|SSS  �  r′  exp(iεr′s)|r′(t − s)⟩⟨r′(t)|ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)  − C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' −s)SSSρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)  �  r  exp(−iεrs)|r(t)⟩⟨r(t − s)|SSS  �  r′  exp(iεr′s)|r′(t − s)⟩⟨r′(t)|  − C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' s)  �  r  exp(−iεrs)|r(t)⟩⟨r(t − s)|SSS  �  r′  exp(iεr′s)|r′(t − s)⟩⟨r′(t)|ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSS  + C(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' −s)ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)  �  r  exp(−iεrs)|r(t)⟩⟨r(t − s)|SSS  �  r′  exp(iεr′s)|r′(t − s)⟩⟨r′(t)|SSS}  = −i[H  H  HS(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)]  −  �  ω  � ∞  0  ds{C(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' s)SSS exp(−iωs)⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)|ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)  − C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' −s)SSSρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) exp(−iωs)⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)|  − C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' s) exp(−iωs)⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)|ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSS  + C(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' −s)ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) exp(−iωs)⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)|SSS}  (B10)  ⟨r(t − s)|SSS|r′(t − s)⟩ is periodic with periodicity T due to the periodicity of the Floquet mode |r(t − s)⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' we can take  Fourier transform on it,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n =  �� T  0  d(t − s)  T  ⟨r(t − s)|SSS e−inωL(t−s)|r′(t − s)⟩  �  |r(t)⟩⟨r′(t)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (B11)  Therefore, ⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)| = �  n einωL(t−s)SSSω,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Use C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) = 1  π  � ∞  −∞ dωe−iω(χ+t)J(ω) [1 + Nω]  and ⟨r(t − s)|SSS|r′(t − s)⟩|r(t)⟩⟨r′(t)| = �  n einωL(t−s)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' we arrive at  ∂tρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) = −i[H  H  HS(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)]  −  �  n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ω  einωlt  � ∞  0  ds{C(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' s)SSS exp(−i(ω + nωL)s)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)  − C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' −s)SSSρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) exp(−i(ω + nωL)s)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n  − C(−2χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' s) exp(−i(ω + nωL)s)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSS  + C(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' −s)ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) exp(−i(ω + nωL)s)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nSSS}  − i[H  H  HS(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)]  = −  �  n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ω  {einωLt 1  π  � ∞  −∞  dω′  � ∞  0  dse−i(ω′+(ω+nωL))sJ(ω′) [1 + Nω′]SSSSSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)  − 1  π  � ∞  −∞  dω′  � ∞  0  dse−iω′χei(ω′−(ω+nωL))sJ(ω′) [1 + Nω′]SSSρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n  − 1  π  � ∞  −∞  dω′  � ∞  0  dse−iω′χe−i(ω′+(ω+nωL))sJ(ω′) [1 + Nω′]SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSS  + 1  π  � ∞  −∞  dω′  � ∞  0  dsei(ω′−(ω+nωL))sJ(ω′) [1 + Nω′]ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nSSS}  (B12)  With the help of  � ∞  0  ds eiωs = πδ(ω) + i P 1  ω and disregarding the principal value P term,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' J(−ω) = −J(ω),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' and  1 + N(−ω) = 1 +  1  e−βω−1 =  1  1−eβω = −N(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We get the generalized master equation finally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  14  ∂tρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) = −i[H  H  HS(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)]  −  �  n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ω  einωlt{J(∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n)  �  N∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n  �  SSSSSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)  − e−i∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nχJ(∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n)  �  1 + N∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n  �  SSSρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n  − ei∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nχJ(∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n)  �  N∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n  �  SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSS  + J(∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n)  �  1 + N∆ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='n  �  ρρρ(χ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t)SSSω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='nSSS}  (B13)  Appendix C: Derivation of the effective system plus system-reservoirs interaction Hamiltonian through flow  equation approach  In this section,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' we derive the effective system plus system-reservoirs interaction Hamiltonian through flow equation  approach [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The method takes advantage of infinitesimal unitary transformation steps, from which renormalization-  group–like flow equations are derived to derive the effective Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The flow equation is  dH  H  H(s, t)  ds  = −VVV (s, t) + i  � t  0  dt1[VVV (s, t1),H  H  H(s, t)],  (C1)  where s is the flow parameter, H  H  H(s, t) and VVV (s, t) are total Hamiltonian and its time-dependent part respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' It  should be noted that the family of Hamiltonians H  H  H(s, t) represents an interpolation between a starting Hamiltonian  H  H  H(0, t) and a final Hamiltonian H  H  H(∞, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Here, H  H  H(∞, t) is the Floquet Hamiltonian H  H  HF if VVV (∞, t) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We set  appropriate boundary conditions by enforcing that s = 0 corresponds to the initial unchanged Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' H  H  H(s, t)  can be expressed as a sum of linear operators with coefficients ci(s, t), H  H  H(s, t) = �  i ci(s, t)OOOi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The OOOi operators are  nothing other than kinetic and potential energy terms appearing in a Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Note that the set of operators  may include both the original operators and new terms generated from the commutator in Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The coefficients  ci(s, t) describe the coupling constants (strength) of these terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' In this representation, Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C1 can be written in a  numerically tractable form,  dci(s, t)  dt  = −gi(t, [cj(s, t′)]),  t′ ∈ [0, T].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (C2)  In [3], Michael Vogl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' put forward a more analytically tractable equation, which set s = 0 only for the terms  VVV (s, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  dH  H  H(s, t)  ds  = −VVV (0, t) + i  � t  0  dt1[VVV (0, t1),H  H  H(s, t)],  (C3)  This corresponds to removing the original time-dependent part VVV (s, t) from the Hamiltonian via the rotating frame  transformation e−i  � t  0 dtVVV (t) while generating other new time dependences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' To ensure that this approximation actually  corresponds to the aforementioned unitary transformation, we also need to restrict s ∈ [0, 1] rather than the previous  s ∈ [0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The effective time-independent Hamiltonian is then given by H  H  Heff = �  i ci(1, t)OOOi, where ci(1, t) =  1  T  � T  0 ci(1, t)dt, if we are only interested in stroboscopic dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  We now derive the effective Hamiltonian for the model we studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' The system plus system-reservoirs interaction  Hamiltonian is  H  H  HS(t) + H  H  HSB = ωA + K cos (ωLt)  2  σσσA  z + ωB  2 σσσB  z + λ(σσσ1  +σσσ2  − + σσσ1  −σσσ2  +) + σσσA  x BBBA + σσσB  x BBBB,  (C4)  where BBBi = �  K cikxxxik is reservoirs coupling operators and VVV (0, t) = K cos (ωLt)  2  σσσA  z in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' We make the ansatz  H  H  H(s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' t) = C1(s)σσσA  z + C2(s)σσσB  z + C3(s)σσσ1  +σσσ2  − + C4(s)σσσ1  −σσσ2  + + C5(s)σσσA  x BBBA + C6(s)σσσB  x BBBB + C7(s)σσσA  y BBBA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='(C5)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='and then find the flow equation is  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='dC1(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ds  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='= −K cos (ωLt)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='dC2(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ds  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='= 0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='dC3(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ds  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='= iKC3(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ωL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='sin (ωLt)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='dC4(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ds  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='= −iKC4(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ωL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='sin (ωLt)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='dC5(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ds  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='= KC7(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ωL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='sin (ωLt)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='dC6(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ds  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='= 0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='dC7(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ds  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='= −KC5(s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ωL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='sin (ωLt)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='(C6)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='with the initial condition  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C1(0) = K cos (ωLt) + ωA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C2(0) = ωB  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C3(0) = λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C4(0) = λ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C5(0) = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C6(0) = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C7(0) = 0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='(C7)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='Their solutions are  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C1(s) = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2(ωA + K cos(ωLt) − Ks cos(ωLt))  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C2(s) = ωB  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C3(s) = λe  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='iKs sin(ωLt)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ωL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C4(s) = λe  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='−iKs sin(ωLt)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='ωL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C5(s) = cos(Ks sin(ωLt)/ωL)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C6(s) = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='C7(s) = − sin(Ks sin(ωLt)/ωL)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='(C8)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='After taking an average over one period and set s = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' we end up with the effective time-independent Hamiltonian  H  H  HS  eff + H  H  HSB  eff = ωA  2 σσσA  z + ωB  2 σσσB  z + λJ0(K/ωL)(σσσ1  +σσσ2  − + σσσ1  −σσσ2  +) + J0(K/ωL)σσσA  x BBBA + σσσB  x BBBB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  (C9)  [1] Jon H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Shirley, Solution of the Schr¨odinger Equation with a Hamiltonian Periodic in Time, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 138 B979 (1965).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [2] Andr´e Eckardt and Egidijus Anisimovas, High-frequency approximation for periodically driven quantum systems from a  Floquet-space perspective, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys 17 093039 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [3] Michael Vogl, Pontus Laurell, Aaron D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Barr, and Gregory A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Fiete, Flow Equation Approach to Periodically Driven  Quantum Systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' X 9 021037 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Oka and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Aoki, Photovoltaic Hall effect in graphene, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B 79 081406 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Kitagawa, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Berg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rudner, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Demler, Topological characterization of periodically driven quantum systems,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B 82 235114 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  16  [6] Tian-Shi Xiong, Jiangbin Gong, and Jun-Hong An, Towards large-chern-number topological phases by periodic quenching,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B 93 184306 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [7] Hui Liu, Tian-Shi Xiong, Wei Zhang, and Jun-Hong An, Floquet engineering of exotic topological phases in systems of cold  atoms, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A 100 023622 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Eckardt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Weiss, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Holthaus, Superfluid-insulator transition in a periodically driven optical lattice, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 95 260404 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [9] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Bastidas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Emary, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Regler, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Brandes, Nonequilibrium quantum phase transitions in the Dicke model,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 108 043003 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Aidelsburger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Atala, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Nascimbene, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Trotzky, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Chen, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Bloch, Experimental realization of strong effective  magnetic fields in an optical lattice, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 107 255301 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Bermudez, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Schaetz, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Porras, Synthetic gauge fields for vibrational excitations of trapped ions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  107 150501 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Struck, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Olschl¨ager, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Weinberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Hauke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Simonet, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Eckardt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lewenstein, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Sengstock, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Wind-  passinger, Tunable gauge potential for neutral and spinless particles in driven optical lattices, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 108 225304  (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Else, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Bauer, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Nayak, Floquet Time Crystals, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 117 090402 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [14] Andreu Riera-Campeny, Maria Moreno-Cardoner, and Anna Sanpera, Time crystallinity in open quantum systems, Quan-  tum 4 270 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [15] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Grossmann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Dittrich, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Jung, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' H¨anggi, Coherent destruction of tunneling, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 67 516 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [16] Jose M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Gomez Llorente and Jes´us Plata, Tunneling control in a two-level system, Phys Rev A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 45 R6958(R) (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [17] Victor Galitski, Ian B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Spielman, Spin–orbit coupling in quantum gases, Nature 494 49–54 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Struck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Simonet, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Sengstock, Spin-orbit coupling in periodically driven optical lattices, Nature 90 031601(R)  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Peterson, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Batalhao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Herrera, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Souza, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Sarthour, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Oliveira, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Serra, Experimental  Characterization of a Spin Quantum Heat Engine , Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 123 240601 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Pekola and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Khaymovich,, Thermodynamics in single-electron circuits and superconducting qubits, Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Matter Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 10 193 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Ronzani, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Karimi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Senior, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Chang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Peltonen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Chen, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Pekola, Tunable photonic heat transport  in a quantum heat valve, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 14 991 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Dechant, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Kiesel, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lutz, All-Optical Nanomechanical Heat Engine, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 114 183602 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [23] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Urgell, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' De Bonis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Samanta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='Esplandiu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Dong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Jin, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Bachtold, Cooling and self-  oscillation in a nanotube electromechanical resonator,, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 16 32 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [24] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Brantut, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Grenier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Meineke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Stadler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Krinner, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Kollath, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Esslinger, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Georges, A thermoelectric  heat engine with ultracold atoms, Science 342 713 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [25] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Abah, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Roßnagel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Jacob, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Deffner, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Schmidt-Kaler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Singer, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lutz,Single-Ion Heat Engine at Maximum  Power, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 109 203006 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Roßnagel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Dawkins, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Tolazzi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Abah, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lutz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Schmidt-Kaler, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Singer, A single-atom heat engine,  Science 352 325 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [27] Gleb Maslennikov, Shiqian Ding, Roland Habl¨utzel, Jaren Gan, Alexandre Roulet, Stefan Nimmrichter, Jibo Dai, Valerio  Scarani, Dzmitry Matsukevich, Quantum absorption refrigerator with trapped ions, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 10 202 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [28] James Klatzow, Jonas N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Becker, Patrick M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Ledingham, Christian Weinzetl, Krzysztof T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Kaczmarek, Dylan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Saunders,  Joshua Nunn, Ian A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Walmsley, Raam Uzdin, and Eilon Poem, Experimental Demonstration of Quantum Effects in the  Operation of Microscopic Heat Engines, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 122 110601 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [29] Sourav Bhattacharjee, Amit Dutta, Quantum thermal machines and batteries, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B 94 239 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [30] Wang Zi, Ren Jie, Nonequilibrium thermal transport and thermodynamic geometry in periodically driven systems, Acta  Physica Sinica 70 230503 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [31] Breuer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Petruccione, The Theory of Open Quantum Systems, Oxford University Press (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [32] Chong Chen, Jun-Hong An, Hong-Gang Luo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Sun, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Oh, Floquet control of quantum dissipation in spin  chains, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A, 91 052122 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [33] W L Yang, W L Song, Jun-Hong An, M Feng, D Suter, and Jiangfeng Du, Floquet engineering to entanglement protection  of distant nitrogen vacancy centers, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 21 013007 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [34] Si-Yuan Bai and Jun-Hong An, Floquet engineering to reactivate a dissipative quantum battery, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A, 102 060201  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [35] Wan-Lu Song, Jia-Bin You, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Xu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Yang, and Jun-Hong An, Floquet Engineering of Two Weakly Coupled Super-  conducting Flux Qubits, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Applied, 14 054049 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [36] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Shirai, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Mori, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Miyashita, Novel symmetry-broken phase in a driven cavity system in the thermodynamic limit,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B At.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 47 025501 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [37] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Foss-Feig, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Niroula, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Young, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Hafezi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Gorshkov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Wilson, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Maghrebi, Emergent equilibrium  in many-body optical bistability, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A , 95 043826 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Diehl, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Micheli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Kantian, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Kraus, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B¨uchler, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Zoller, Quantum states and phases in driven open  quantum systems with cold atoms, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 4 878-883 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Diehl, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rico, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Baranov, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Zoller, Topology by dissipation in atomic quantum wires, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 7 971–977  (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [40] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Vorberg, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Wustmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Ketzmerick, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Eckardt, Generalized Bose-Einstein condensation into multiple states  17  in driven-dissipative systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 111 240405 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [41] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Vorberg, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Wustmann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Schomerus, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Ketzmerick, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Eckardt, Nonequilibrium steady states of ideal bosonic  and fermionic quantum gases, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' E, 92 062119 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Schnell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Ketzmerick, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Eckardt, On the number of Bose-selected modes in driven-dissipative ideal Bose gases,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' E, 97 032136 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [43] Sebastian Restrepo, Javier Cerrillo, Philipp Strasberg and Gernot Schaller, From quantum heat engines to laser cooling:  Floquet theory beyond the Born–Markov approximation, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 20 053063 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [44] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Dai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Shi, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Yi, Floquet theorem with open systems and its applications, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A , 93 032121  (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [45] Tatsuhiko N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Ikeda and Masahiro Sato, General description for nonequilibrium steady states in periodically driven dissi-  pative quantum systems, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 6 eabb4019 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [46] Massimiliano Esposito, Upendra Harbola, and Shaul Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and  counting statistics in quantum systems, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 81 1665 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [47] S Gasparinetti, P Solinas, A Braggio and M Sassetti, Heat-exchange statistics in driven open quantum systems, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', 161 115001 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [48] Hideo Sambe, Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A, 7  2203 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [49] Wilhelm Magnus, On the exponential solution of differential equations for a linear operator, Communications on Pure and  Applied Mathematics, 7 649-673 (1954).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [50] Takahiro Mikami, Sota Kitamura, Kenji Yasuda, Naoto Tsuji, Takashi Oka, and Hideo Aoki, Brillouin-Wigner theory for  high-frequency expansion in periodically driven systems: Application to Floquet topological insulators, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' B , 93  144307 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [51] Mihail Silaev, Tero T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Heikkil¨a, and Pauli Virtanen, Lindblad-equation approach for the full counting statistics of work and  heat in driven quantum systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' E, 90 022103 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [52] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Nafari Qaleh and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rezakhani, Enhancing energy transfer in quantum systems via periodic driving: Floquet master  equations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A, 105 012208 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [53] Horodecki R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', Horodecki P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', Horodecki M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', Horodecki,K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=', Quantum entanglement, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' 81 865 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content='  [54] Zhihai Wang, Wei Wu, and Jin Wang, Steady-state entanglement and coherence of two coupled qubits in equilibrium and  nonequilibrium environments, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
+page_content=' A 99 042320 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/mNAyT4oBgHgl3EQf_vq9/content/2301.00915v1.pdf'}
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+WITHIN-GROUP FAIRNESS: A GUIDANCE FOR MORE SOUND
+BETWEEN-GROUP FAIRNESS
+Sara Kim
+Samsung Electronics Co.
+Seoul
+sarah58833@gmail.com
+Kyusang Yu
+Department of Applied Statistics
+Konkuk University
+Seoul
+kyusangu@konkuk.ac.kr
+Yongdai Kim
+Department of Statistics
+Seoul National University
+Seoul
+ydkim0903@gmail.com
+ABSTRACT
+As they have a vital effect on social decision-making, AI algorithms not only should be accurate
+and but also should not pose unfairness against certain sensitive groups (e.g., non-white, women).
+Various specially designed AI algorithms to ensure trained AI models to be fair between sensitive
+groups have been developed. In this paper, we raise a new issue that between-group fair AI models
+could treat individuals in a same sensitive group unfairly. We introduce a new concept of fairness
+so-called within-group fairness which requires that AI models should be fair for those in a same sen-
+sitive group as well as those in different sensitive groups. We materialize the concept of within-group
+fairness by proposing corresponding mathematical definitions and developing learning algorithms to
+control within-group fairness and between-group fairness simultaneously. Numerical studies show
+that the proposed learning algorithms improve within-group fairness without sacrificing accuracy as
+well as between-group fairness.
+1
+Introduction
+Recently, AI (Artificial Intelligence) is being used as decision-making tools in various domains such as credit scoring,
+criminal risk assessment, education of college admissions [1]. As AI has a wide range of influences on human social
+life, issues of transparency and ethics of AI are emerging. However, it is widely known that due to the existence of
+historical bias in data against ethics or regulatory frameworks for fairness, trained AI models based on such biased
+data could also impose bias or unfairness against a certain sensitive group (e.g., non-white, women) [2, 3]. Therefore,
+designing an AI algorithm which is accurate and fair simultaneously has become a crucial research topic.
+Demographic disparities due to AI, which refer to socially unacceptable bias that an AI model favors certain groups
+(e.g., white, men) over other groups (e.g., black, women), have been observed frequently in many applications of AI
+such as COMPAS recidivism risk assessment [1], Amazon’s prime free same-day delivery [4], credit score evaluation
+[5] to name just a few. Many studies have been done recently to develop AI algorithms which remove or alleviate such
+demographic disparities in trained AI models so that they will treat sensitive groups as equally as possible. In general,
+these methods try to search AI models which are not only accurate but also similar between sensitive groups in a certain
+sense. For an example of similarity, it is required that accuracies of an AI model for each sensitive group are similar
+[6]. Hereinafter, criteria of fairness requiring similarity between sensitive groups are referred to as between-groups
+fairness (BGF).
+In this paper, we consider a new concept of fairness so called within-group fairness (WGF) which arises as a new
+problem when we try to enforce BGF into AI algorithms. Generally speaking, within-group unfairness occurs when
+there is an individual who is positively treated compared to others in a same sensitive group by an AI model trained
+without BGF constraints but becomes negatively treated by an AI model trained with BGF constraints.
+For an illustrative example of WGF, consider a college admission problem where gender (men vs women) is a sensitive
+variable. Let X and Y ∈ {0, 1} be the input vector and the corresponding output label where X represents the
+information of a candidate student such as GPA at high school, SAT score, etc. and Y is the admission result where 0
+and 1 mean the rejection and acceptance of the college admission, respectively. The Bayes classifier accepts a student
+arXiv:2301.08375v1  [stat.ML]  20 Jan 2023
+
+Figure 1: A toy example of within-group unfairness: The left panel: without BGF constraints, there exists unfairness
+against the women sensitive group, but with BGF constraints, the scores of the two women become reversed and thus
+within-group unfairness occurs. The right panel: The scores of the two women increase together to achieve BGF
+without within-group unfairness.
+with X = x when Pr(Y = 1|X = x) > 1/2. Suppose that there are two women ‘A’ and ‘B’ with the input vectors
+xA and xB, respectively and the AI model trained without BGF constraints estimates Pr(Y = 1|X = xB) > 1/2 >
+Pr(Y = 1|X = xA). Then, within-group unfairness occurs when an AI model trained with BGF constraints results
+in Pr(Y = 1|X = xA) > 1/2 > Pr(Y = 1|X = xB). In this situation, which is illustrated in the left panel of
+Figure 1, ‘B’ could claim that the AI model trained with BGF constraints mistreats her and so it is unfair. We will
+show in Section 5 that there exists non-negligible within-group unfairness in AI models trained on real data with BGF
+constraints.
+Within-group unfairness arises because most existing learning algorithms for BGF force certain statistics (e.g. rate of
+positive prediction, misclassification error rate, etc.) of a trained AI model being similar across sensitive groups but
+do not care about what happens to individuals in a same sensitive group at all. For within-group fairness, a desirable
+AI model is expected at least to preserve the ranks between Pr(Y = 1|X = xA) and Pr(Y = 1|X = xB) regardless
+of estimating Pr(Y = 1|X = x) with or without BGF constraints, which is depicted in the right panel of Figure 1.
+Our contributions are three folds. We first define the concept of WGF rigorously. Then we develop learning algorithms
+which compromise BGF and WGF as well as accuracy. Finally, we show empirically that the proposed learning
+algorithms improve WGF while maintaining accuracy and BGF.
+Remark. One may argue that training data are prone to bias due to historical prejudices and discriminations, and
+hence a trained AI model is also biased and socially unacceptable. On the other hand, a trained AI model with BGF
+constraints does not have such bias and hence is socially acceptable. Therefore, it would be by no means reasonable
+to claim unfairness based on discrepancies between socially unacceptable and acceptable AI models. However, note
+that historical bias in training data is about bias between sensitive groups but not for individuals in a same sensitive
+group. For WGF, we implicitly assume that no historical bias among individuals in a same sensitive group exists in
+training data, which is not too absurd, and thus there is no reason for a trained AI model without BGF constraints to
+treat individuals in a same sensitive group unfairly. This assumption, of course, needs more debates which we leave
+as future work.
+The paper is organized as follows. In Section 2, we briefly review methods for BGF, and in Sections 3 and 4, we
+propose mathematical definitions of WGF and develop corresponding learning algorithms for classifiers and score
+functions, respectively. The results of numerical studies are presented in Section 5, and remarks about reflecting WGF
+to pre- and post processing algorithms for BGF are given in Section 6. Concluding remarks follow in Section 7.
+2
+Review of between-group fairness
+While it is completely new, the concept of WGF is a by-product of BGF and thus it is helpful to review learning
+methods for BGF. In this section, we review the definitions of BGF and related studies.
+2
+
+Within-group unfair
+Within-group fair
+Estimated
+score
+0.5
+0.5
+BGF
+BGF
+Unconstrained
+Unconstrained
+constrained
+constrained
+men
+women
+rank preserved
+rank changedFAIRNESS CRITERIA
+E
+E′
+DISPARATE IMPACT
+[8]
+1{Cf(X) = 1}
+∅
+EQUAL OPPORTUNITY
+[9]
+1{Cf(X) = 1}
+{Y = 1}
+DISPARATE MISTREATMENT W.R.T. ERROR RATE
+[6]
+1{Cf(X) ̸= Y }
+∅
+MEAN SCORE PARITY
+[10]
+f(X)
+∅
+Table 1: Some group performance functions
+We let D = {(xi, zi, yi)}n
+i=1 be a set of training data of size n which are independent copies of a random vector
+(X, Z, Y ) defined on X × Z × Y, where X ⊂ Rp. We consider a binary classification problem, which means Y =
+{0, 1}, and for notational simplicity, we let Z = {0, 1}, where Z = 0 refers to the unprivileged group and Z = 1 refers
+to the privileged group. Whenever the probability is mentioned, we mean it by either the probability of (X, Z, Y ) or
+its empirical counterpart unless there is any confusion.
+In this paper, we consider AI algorithms which yield a real-valued function f : X → R so called a score function
+which assigns positive labeled instances higher scores than negative labeled instances. An example of the score
+function is the conditional class probability Pr(Y = 1|x = x). In most human-related decision makings, real-valued
+score functions are popularly used (e.g. scores for credit scoring).
+Let F be a given set of score functions, in which we search an optimal score function in a certain sense (e.g. minimizing
+the cross-entropy for classification problems). Examples of F are linear functions, reproducing kernel Hilbert space
+and deep neural networks to name a few. For a given f ∈ F, the corresponding classifier Cf is defined as Cf(x) =
+1(f(x) > 0).
+2.1
+Definition of between-group fairness
+For a given score function f and a sensitive group Z = z, we consider the group performance function of f given as
+qz(f) := E(E|E′, Z = z)
+(1)
+for events E and E′ that might depend on f(X) and Y. The group performance function qz in (1), which is considered
+by [7], includes various performance functions used in fairness AI. We summarize representative group performance
+functions having the form of (1) in Table 1.
+For given group performance functions qz(·), z ∈ {0, 1}, we say that f satisfies the BGF constraint with respect to qz
+if q0(f) = q1(f). A relaxed version of the BGF constraint so called the ϵ-BGF constraint, is frequently considered,
+which requires |q0(f) − q1(f)| < ϵ for a given ϵ > 0. Typically, AI algorithms search an optimal function f among
+those satisfying the ϵ-BGF constraint with respect to given group performance functions qz(·), z ∈ {0, 1}.
+2.2
+Related works
+Several learning algorithms have been proposed to find an accurate model f satisfying a given BGF constraint, which
+are categorized into three groups. In this subsection, we review some methods for each group.
+Pre-processing methods: Pre-processing methods remove bias in training data or find a fair representation with re-
+spect to sensitive variables before the training phase and learn AI models based on de-biased data or fair representation
+[11, 12, 13, 14, 15, 16, 17, 18, 19]. [11] suggested pre-processing methods to eliminate bias in training data by use of
+label changing, reweighing and sampling. Based on the idea that transformed data should not be able to predict the
+sensitive variable, [13] proposed a transformation of input variables for eliminating the disparate impact. To find a fair
+representation, [12, 14] proposed a data transformation mapping for preserving accuracy and alleviating discrimination
+simultaneously. Pre-processing methods for fair learning on text data were studied by [15, 16].
+In-processing methods: In-processing methods generally train an AI model by minimizing a given cost function
+(e.g. the cross-entropy, the sum of squared residuals, the empirical AUC etc.) subject to a ϵ-BGF constraint. Most
+group performance functions qz(·) are not differentiable, and thus various surrogated group performance functions
+and corresponding ϵ-BGF constraints have been proposed [20, 21, 22, 23, 6, 24, 25, 26, 7, 27, 28]. [20] used a
+3
+
+fairness regularizer which is an approximation of the mutual information between the sensitive variable and the target
+variable. [23, 6] proposed covariance-type fairness constraints as tractable proxies targeting the disparate impact and
+the equality of the false positive or negative rate, and [24] used a linear surrogated group performance function for the
+equalized odds. On the other hand, [25, 7] derived an optimal classifier for a constrained fair classification as a form
+of an instance-dependent threshold. Also, for fair score functions, [27] proposed fairness constraints based on ROC
+curves of each sensitive group.
+Post-processing methods: Post-processing methods first learn an AI model without any BGF constraint and then
+transform the decision boundary or score function of the trained AI model for each sensitive group to satisfy given
+BGF criteria [29, 30, 9, 31, 32, 33, 34, 35]. [9, 33] suggested finding sensitive group dependent thresholds to get a fair
+classifier with respect to equal opportunity. [34, 35] developed an algorithm to transform the original score function
+to achieve a BGF constraint.
+3
+Within-group fairness for classifiers
+We assume that there exists a known optimal classifier C⋆ which could be the Bayes classifier or its estimate. For
+example, we can use Cf ⋆ for C⋆, where f ⋆ is the unconstrained minimizer of the cross-entropy on F. We mostly
+focus on in-processing methods for the BGF and explain how to reflect WGF into a learning procedure. Remarks
+about how to reflect WGF to pre- and post-processing methods are given in Section 6.
+3.1
+Definition of within-group fairness
+Conceptually, WGF means that the classifier Cf and C⋆ have the same ranks in each sensitive group. That is, for two
+individuals xA and xB in a same sensitive group with C⋆(xA) > C⋆(xB), WGF requires that Cf(xA) ≥ Cf(xB).
+To materialize this concept of WGF, we define the WGF constraint as
+Pr {C⋆(X) = 0, Cf(X) = 1|Z = z} = 0
+or Pr {C⋆(X) = 1, Cf(X) = 0|Z = z} = 0
+(2)
+for each z ∈ {0, 1}. Similar to the BGF, we relax the constraint (2) by requiring that either of the two probabilities is
+small. That is, we say that f satisfies the δ-WGF constraint for a given δ > 0 if
+max
+z∈{0,1} min{a01|z(f), a10|z(f)} < δ,
+(3)
+where aij|z(f) = Pr{C⋆(X) = i, Cf(X) = j|Z = z}.
+3.2
+Directional within-group fairness
+Many BGF constraints have their own implicit directions toward which the classifier is expected to be guided in the
+training phase. We can design a special WGF constraint reflecting the implicit direction of a given BGF constraint
+which results in more desirable classifiers (better guided, more fair and frequently more accurate). Below, we present
+two such WGF constraints.
+Disparate impact: Note that the disparate impact requires that
+Pr{Cf(X) = 1|Z = 0} = Pr{Cf(X) = 1|Z = 1}.
+Suppose that Pr{C⋆(X) = 1|Z = 0} < Pr{C⋆(X) = 1|Z = 1}. Then, we expect that a desirable classifier Cf
+achieves this BGF constraint by increasing Pr{Cf(X) = 1|Z = 0} from Pr{C⋆(X) = 1|Z = 0} and decreasing
+Pr{Cf(X) = 1|Z = 1} from Pr{C⋆(X) = 1|Z = 1}. To reflect this direction, we can enforce a learning algorithm
+to search a classifier Cf satisfying Pr{C⋆(X) = 1|Z = 0} < Pr{Cf(X) = 1|Z = 0} and Pr{C⋆(X) = 1|Z =
+1} > Pr{Cf(X) = 1|Z = 1}. Based on this argument, we define the directional δ-WGF constraint for the disparate
+impact as
+max{a10|0(f), a01|1(f)} < δ.
+(4)
+Equal opportunity: The equal opportunity constraint is given as
+Pr{Cf(X) = 1|Z = 0, Y = 1} = Pr{Cf(X) = 1|Z = 1, Y = 1}.
+4
+
+Suppose that Pr{C⋆(X) = 1|Z = 0, Y = 1} < Pr{C⋆(X) = 1|Z = 1, Y = 1}. A similar argument for the disparate
+impact leads us to define the directional δ-WGF constraint for the equal opportunity as
+max{a10|01(f), a01|11(f)} < δ
+(5)
+and
+max
+z∈{0,1} min
+�
+a10|z0(f), a01|z0(f)
+�
+< δ,
+(6)
+where
+aij|zy(f) = Pr{C⋆(X) = i, Cf(X) = j|Z = z, Y = y}.
+3.3
+Learning with doubly-group fairness constraints
+We say that f satisfies the (ϵ, δ)-doubly-group fairness constraint if B(f) < ϵ and W(f) < δ, where B is a given BGF
+constraint and W is the corresponding WGF constraint proposed in the previous two subsections. In this section, we
+propose a relaxed version of W(·) for easy computation. As we review in Section 2, many relaxed versions of B(·)
+have been proposed already.
+The WGF constraints considered in Sections 3.1 and 3.2 are hard to be used as themselves in the training phase since
+they are neither convex nor continuous. A standard approach to resolve this problem is to use a convex surrogated
+function. For example, a surrogated version of the WGF constraint (3) is Wsurr(f) < δ, where
+Wsurr(f) := max
+z∈{0,1} min
+�
+E {φ(−f(X))|Z = z, Y ⋆ = 1} p1|z,
+E {φ(f(X))|Z = z, Y ⋆ = 0} p0|z
+�
+,
+(7)
+where Y ⋆ = C⋆(X), py|z = Pr(C⋆(X) = y|Z = z) and φ is a convex surrogated function of the indicator function
+1(z ≥ 0). In this paper, we use the hinge function given as φhinge(z) = (1 + z)+ as a convex surrogated function
+which is popularly used for fair AI [21, 24, 36]. The surrogated versions for the other WGF constraints are derived
+similarly. Finally, we estimate f by ˆf that minimizes the regularized cost function
+L(f) + λBsurr(f) + ηWsurr(f),
+(8)
+where L is a given cost function (e.g. the cross-entropy) and Bsurr and Wsurr are the surrogated constraints of B and
+W, respectively. The nonnegative constants λ and η are regularization parameters which are selected so that ˆf satisfies
+B( ˆf) < ϵ and W( ˆf) < δ.
+3.4
+Related notions with within-group fairness
+There are several fairness concepts which are somehow related to WGF. However, the existing concepts are quite
+different from our WGF.
+1. Unified fairness: [37] used the term ‘within-group fairness’. However, WGF of [37] is different from our
+WGF. [37] measured individual-level benefits of a given prediction model and they defined the model to be
+WGF if the individual benefits in each group are similar. They also illustrated that WGF keeps decreasing as
+BGF increases. Our WGF is nothing to do with individual-level benefits. Our WGF can be high even when
+individual-level benefits are not similar. Also, our WGF can increase even when BGF increases.
+2. Slack consistency: [38] proposed the ‘slack consistency’ which requires that the estimated scores of each
+individual should be monotonic with respect to slack variables used in fairness constraints. Slack consistency
+does not guarantee within-group fairness because the ranks of the estimated scores can change even when
+they move monotonically.
+4
+Within-group fairness for score functions
+Similarly to classifiers, the WGF for score functions requires that f(xA) > f(xB) when f ⋆(xA) > f ⋆(xB) and vice
+versa for two individuals xA and xB in a same sensitive group, where f ⋆ is a known optimal score function such as
+the conditional class probability Pr(Y = 1|X) or its estimate. To realize this concept, we define the WGF constraint
+5
+
+for a score function f as τz(f) = 1 for z ∈ {0, 1}, where τz(·) is the Kendall’s τ between f and f ⋆ conditional on
+Z = z, that is
+τz(f) = E(X1,X2)
+�
+1{(f(X1) − f(X2))(f ⋆(X1) − f ⋆(X2)) > 0}
+���Z = z
+�
+,
+where X1 and X2 are independent copies of X. In turn, the δ-WGF constraint for a score function f is 1 − τz(f) <
+δ, z ∈ {0, 1}.
+Similarly for classifiers, we need a convex surrogated version of the δ-WGF constraint and a candidate would be
+1 − τφ,z(f) < δ, z ∈ {0, 1}, where
+τφ,z(f) = 1 − E(X1,X2)
+�
+φ{(f(X1) − f(X2))(f ⋆(X1) − f ⋆(X2))}
+���Z = z
+�
+and φ is a convex surrogated function of 1(z > 0) such as the φhinge.
+5
+Numerical studies
+We investigate the impacts of the WGF constraints on the prediction accuracy as well as the BGF by analyzing real-
+world datasets. We consider linear logistic and deep neural network (DNN) models for F and use the cross-entropy
+for L. For DNN, fully connected neural networks with one hidden layer and p many hidden nodes are used. We
+train the models by the gradient descent algorithm [39] implemented by Python with related libraries pytorch,
+scikit-learn, numpy. The SGD optimizer is used with momentum 0.9 and a learning rate of either 0.1 or 0.01
+depending on the dataset. We use the unconstrained minimizer of L for f ⋆.
+Datasets. We analyze four real world datasets, which are popularly used in fairness AI research and publicly available:
+(i) The Adult Income dataset (Adult, [5]); (ii) The Bank Marketing dataset(Bank, [5]); (iii) The Law School dataset
+(LSAC, [40]); (iv) The Compas Propublica Risk Assessment dataset (COMPAS, [41]). Except for the dataset Adult,
+we split the training and test datasets randomly by 8:2 ratio and repeat 5 times training/test splits for performance
+evaluation.
+5.1
+Within-group fair classifiers
+We consider following group performance functions for the BGF: the disparate impact (DI) [8] and the disparate
+mistreatment w.r.t. error rate [6], which are defined as
+DI(f) = |Pr(Cf(X) = 1|Z = 1) − Pr(Cf(X) = 1|Z = 0)|
+ME(f) = |Pr(Cf(X) ̸= Y |Z = 0) − Pr(Cf(X) ̸= Y |Z = 1)| .
+Note that the DI is directional while the ME is not. For the surrogated BGF constraints, we replace the indicator
+function with the hinge function in calculating the BGF constraints as is done by [21, 36]. We name the corresponding
+BGF constraints by Hinge-DI and Hinge-ME respectively. The results for other surrogated constraints such as the
+covariance type constraints proposed by [23, 6] and the linear surrogated functions considered in [42] are presented
+in the Supplementary material. In addition, the results for the equal opportunity constraint are summarized in the
+Supplementary material.
+For investigating the impacts of WGF on trained classifiers, we first fix the ϵ for each BGF constraint, and we choose
+the regularization parameters λ and η to make the classifier ˆf minimizing the regularized cost function (8) satisfy the
+ϵ-BGF constraint. Then, we assess the prediction accuracy and the degree of WGF of ˆf.
+5.1.1
+Targeting for disparate impact
+Table 2 presents the three 2 × 2 tables comparing the results of the unconstrained DNN classifier ( ˆY ⋆) and three DNN
+classifiers ( ˆY ) trained on the dataset Adult: (i) only with the DI constraint, (ii) with the DI and WGF constraints and
+(iii) with the DI and directional WGF (dWGF) constraints. We let ϵ be around 0.03. The numbers marked in red
+are subjects treated unfairly with respect to the dWGF. Note that the numbers of unfairly treated subjects are reduced
+much with the WGF and dWGF constraints and the dWGF constraint is more effective. We report that the accuracies
+of the three classifiers on the test data are 0.837, 0.840 and 0.839, respectively, which indicates that the WGF and
+dWGF constraints improve the WGF without hampering the accuracy. Compared to the dWGF, the WGF constraint
+is less effective, which is observed consistently for different datasets when a BGF constraint is directional. See Table
+6
+
+ONLY WITH THE DI CONSTRAINT
+Z = 0
+Z = 1
+ˆY = 0
+ˆY = 1
+ˆY = 0
+ˆY = 1
+ˆY ⋆ = 0
+4,592
+350
+ˆY ⋆ = 0
+7,966
+86
+ˆY ⋆ = 1
+13
+466
+ˆY ⋆ = 1
+945
+1,863
+WITH THE DI AND WGF CONSTRAINTS
+Z = 0
+Z = 1
+ˆY = 0
+ˆY = 1
+ˆY = 0
+ˆY = 1
+ˆY ⋆ = 0
+4,703
+239
+ˆY ⋆ = 0
+8,021
+31
+ˆY ⋆ = 1
+27
+452
+ˆY ⋆ = 1
+1,156
+1,652
+WITH THE DI AND DWGF CONSTRAINTS
+Z = 0
+Z = 1
+ˆY = 0
+ˆY = 1
+ˆY = 0
+ˆY = 1
+ˆY ⋆ = 0
+4,718
+224
+ˆY ⋆ = 0
+8,024
+28
+ˆY ⋆ = 1
+18
+461
+ˆY ⋆ = 1
+1,178
+1,630
+Table 2: Comparison of the results of the three DNN classifiers trained (i) only with the BGF constraint, (ii) with the
+BGF and WGF constraints and (iii) with the BGF and dWGF constraints on the dataset Adult. Marked in red represent
+the numbers of subjects treated unfairly in a same sensitive group.
+LINEAR MODEL
+DNN MODEL
+DATASET
+METHOD
+ACC
+DI
+DWGF
+ACC
+DI
+DWGF
+Adult
+UNCONS.
+0.852
+0.172
+0.000
+0.853
+0.170
+0.000
+HINGE-DI
+0.833
+0.028
+0.005
+0.837
+0.029
+0.008
+HINGE-DI-DF
+0.836
+0.028
+0.003
+0.839
+0.026
+0.003
+Bank
+UNCONS.
+0.908
+0.195
+0.000
+0.904
+0.236
+0.000
+HINGE-DI
+0.901
+0.024
+0.018
+0.899
+0.029
+0.033
+HINGE-DI-DF
+0.904
+0.021
+0.007
+0.905
+0.029
+0.032
+LSAC
+UNCONS.
+0.823
+0.120
+0.000
+0.856
+0.131
+0.000
+HINGE-DI
+0.809
+0.016
+0.014
+0.816
+0.032
+0.064
+HINGE-DI-DF
+0.813
+0.018
+0.009
+0.809
+0.029
+0.047
+COMPAS
+UNCONS.
+0.757
+0.164
+0.000
+0.757
+0.162
+0.000
+HINGE-DI
+0.641
+0.024
+0.153
+0.639
+0.030
+0.142
+HINGE-DI-DF
+0.618
+0.025
+0.145
+0.654
+0.033
+0.120
+Table 3: Results for the DF classifier with the Hinge-DI constraint. Except for the dataset Adult, the average perfor-
+mances are given.
+2 in the Supplementary material for the corresponding numerical results. Thus, hereafter we consider the dWGF only
+for the DI which has an implicit direction.
+Table 3 summarizes the performances of the three classifiers - C⋆ and the two classifiers trained with the DI constraint
+and the DI and dWGF constraints (doubly-fair, DF), respectively. In Table 3, we report the accuracies as well as
+the values of DI and dWGF terms (i.e., DI( ˆf) and max{a10|0( ˆf), a01|1( ˆf)}, respectively). We observe that the DF
+classifier improves the dWGF while keeping that the DI values and accuracies are favorably comparable to those of
+the BGF classifier. For reference, the performances with the WGF constraint are summarized in the Supplementary
+material.
+To investigate the sensitivity of the accuracy to the degree of WGF, the scatter plots between various dWGF values
+and the corresponding accuracies for the DF linear logistic model are given in Figure 2, where the DI value is fixed
+around 0.03. The accuracies are not sensitive to the dWGF values. Moreover, for the datasets Adult, Bank and LSAC,
+the accuracies keep increasing as the dWGF value decreases.
+7
+
+Figure 2: Scatter plots of the accuracies and dWGF values for the DF linear regression model with the DI values
+around 0.03. (Topleft) Adult; (Topright) Bank; (Bottomleft) LSAC; (Bottomright) COMPAS. Red star points in each
+figure represent the results of the BGF classifier.
+While we analyzed the datasets Bank and LSAC, we found an undesirable aspect of the learning algorithm only
+with the DI constraint. The corresponding classifiers improve the DI by decreasing (or increasing) the probabilities
+P( ˆY = 1|Z = 0) and P( ˆY = 1|Z = 1) simultaneously compared to P(Y ⋆ = 1|Z = 0) and P(Y ⋆ = 1|Z = 1).
+A better way to improve the DI would be to increase P( ˆY = 1|Z = 0) and decrease P( ˆY = 1|Z = 1) when
+P(Y ⋆ = 1|Z = 0) < P(Y ⋆ = 1|Z = 1). Figures 3 show that this undesirable aspect disappears when the dWGF
+constraint is considered.
+Figure 3: Comparison of the conditional probabilities of each group for the datasets Bank (Left) and LSAC(Right).
+5.1.2
+Targeting for disparate mistreatment
+The results of the performances of the DF classifier with the ME as a BGF constraint are presented in Table 4. Since
+the ME has no implicit direction, we use the undirectional WGF constraint. The overall conclusions are similar to
+those for the DI and dWGF constraints. That is, the undirectional WGF constraint also works well.
+8
+
+0.836
+0.904
+0.834
+ACC
+CC
+0.902
+0.832
+DF
+DF
+0.830
+BGF
+0.900
+BGF
+0.002
+0.004
+0.010
+0.015
+0.020
+dWGF
+dWGF
+0.816
+0.64
+DF
+BGF
+0.814
+0.63
+CC
+ACC
+A
+0.812
+0.62
+DF
+0.810
+BGF
+0.61
+0.010
+0.012
+0.014
+0.14
+0.15
+0.16
+dWGF
+dWGFZ= 0
+Z = 1
+Z=0
+Z=1
+Uncons.
+Uncons.
+Z=0Z=1
+Z=0Z=1
+BGF
+BGF
+z=0z=1
+Z=0Z=1
+DF
+工
+DF
+0.05
+0.15
+0.25
+0.85
+0.90
+0.95
+Pr(Y= 1|Z = z)
+Pr(Y = 1|Z = z)LINEAR MODEL
+DNN MODEL
+DATASET
+METHOD
+ACC
+ME
+WGF
+ACC
+ME
+WGF
+Adult
+UNCONS.
+0.852
+0.117
+0.000
+0.853
+0.105
+0.000
+HINGE-ME
+0.834
+0.060
+0.005
+0.822
+0.025
+0.059
+HINGE-ME-DF
+0.834
+0.060
+0.005
+0.825
+0.031
+0.026
+Bank
+UNCONS.
+0.908
+0.177
+0.000
+0.904
+0.174
+0.000
+HINGE-ME
+0.740
+0.044
+0.068
+0.902
+0.164
+0.076
+HINGE-ME-DF
+0.749
+0.045
+0.020
+0.897
+0.165
+0.047
+LSAC
+UNCONS.
+0.823
+0.090
+0.000
+0.856
+0.071
+0.000
+HINGE-ME
+0.759
+0.028
+0.038
+0.815
+0.044
+0.040
+HINGE-ME-DF
+0.742
+0.020
+0.017
+0.803
+0.038
+0.001
+COMPAS
+UNCONS.
+0.757
+0.022
+0.000
+0.757
+0.024
+0.000
+HINGE-ME
+0.740
+0.020
+0.018
+0.738
+0.016
+0.018
+HINGE-ME-DF
+0.743
+0.018
+<0.001
+0.757
+0.017
+0.001
+Table 4: Results for the DF classifier with the Hinge-ME constraint. Except for the dataset Adult, average performances
+are given.
+5.2
+Within-group fair for score function
+In this section, we examine the WGF constraint for score functions. We choose the logistic loss (binary cross-entropy,
+BCE) and AUC (area under the ROC) as evaluation metrics for prediction accuracy. For the BGF, we consider the
+mean score parity (MSP, [10]):
+MSP(f) = |E(σ(f(X))|Z = 1) − E(σ(f(X))|Z = 0)| ,
+where σ : x �→ 1/(1 + e−x) is the sigmoid function. To check how much the estimated score function ˆf is within-
+group fair, we calculate the Kendall’s τ between ˆf and the ground-truth score function f ⋆ on the test data for each
+sensitive group, and then we average them, which is denoted by ¯τ in Table 5. We choose the regularization parameters
+λ and η such that ¯τ of ˆf is as close to 1 as possible while maintaining the MSP value around 0.03.
+Table 5 amply shows that the DF score function always improves the degree of WGF (measured by ¯τ) and the accuracy
+in terms of AUC simultaneously while keeping the degree of BGF at a reasonable level. With respect to the BCE, the
+BGF and DF score functions are similar. The superiority of the DF score function in terms of AUC compared with
+the BGF score function is partly because the WGF constraint shrinks the estimated score toward the ground-truth
+score (Uncons. in Table 5) which is expected to be most accurate. Based on these results, we conclude that the WGF
+constraint is a useful guide to find a better score function with respect to AUC as well as the WGF.
+6
+Remarks on within-group fairness for pre- and post-processing methods
+Various pre- and post-processing methods for fair AI have been proposed. An advantage of these methods compared
+to constrained methods is that the methods are simple, computationally efficient but yet reasonably accurate. In this
+section, we briefly explain how to reflect the WGF to pre- and post-processing methods for the BGF.
+6.1
+Pre-processing methods and within-group fairness
+Basically, pre-processing methods transform the training data in a certain way to be between-group fair and train an
+AI model on the transformed data. To reflect the WGF, it suffices to add a WGF constraint in the training phase. Let
+Dtrans be the transformed training data to be between-group fair and let Ltrans be the corresponding cost function. Then,
+we learn a model by minimizing Ltrans(f) + ηWconv(f) for η > 0.
+Table 6 presents the results of the models trained on the pre-processing training data and a WGF constraint for various
+values of η, where the DI is used as the BGF and thus the corresponding dWGF constraint is used. In this experi-
+ment, we use the linear logistic model and the Massaging [11] for the pre-processing. Surprisingly we observed that
+introducing the dWGF constraint to the pre-processing method helps to improve the BGF and WGF simultaneously
+without sacrificing the accuracies much.
+9
+
+LINEAR MODEL
+DNN MODEL
+DATASET
+METHOD
+BCE
+AUC
+MSP
+¯τ
+BCE
+AUC
+MSP
+¯τ
+Adult
+UNCONS.
+0.319
+0.905
+0.173
+1.000
+0.315
+0.908
+0.178
+1.000
+BGF
+0.358
+0.879
+0.037
+0.854
+0.353
+0.879
+0.035
+0.805
+DF
+0.368
+0.882
+0.033
+0.908
+0.364
+0.885
+0.035
+0.891
+Bank
+UNCONS.
+0.214
+0.932
+0.217
+1.000
+0.237
+0.926
+0.237
+1.000
+BGF
+0.235
+0.906
+0.036
+0.706
+0.270
+0.908
+0.033
+0.671
+DF
+0.240
+0.912
+0.039
+0.728
+0.266
+0.917
+0.031
+0.761
+LSAC
+UNCONS.
+0.434
+0.732
+0.125
+1.000
+0.359
+0.831
+0.142
+1.000
+BGF
+0.450
+0.705
+0.033
+0.692
+0.381
+0.803
+0.025
+0.640
+DF
+0.557
+0.717
+0.031
+0.719
+0.383
+0.809
+0.028
+0.738
+COMPAS
+UNCONS.
+0.511
+0.822
+0.122
+1.000
+0.506
+0.824
+0.118
+1.000
+BGF
+0.599
+0.759
+0.035
+0.564
+0.588
+0.753
+0.030
+0.561
+DF
+0.597
+0.792
+0.038
+0.720
+0.597
+0.766
+0.028
+0.623
+Table 5: Results of the DF score functions. Except for the dataset Adult, averages performances are given.
+METHOD
+η
+ACC
+DI
+DWGF
+MASSAGING
+-
+0.837
+0.069
+0.009
+MASSAGING + DWGF
+0.5
+0.837
+0.048
+0.004
+1.0
+0.836
+0.037
+0.003
+Table 6: Comparison of the accuracy and fairnesses of the pre-processing method with and without the dWGF con-
+straint. The results are evaluated on the dataset Adult.
+6.2
+Post-processing methods and within-group fairness
+For the BGF score functions, [35] developed an algorithm to obtain two monotonically nondecreasing transformations
+mz, z ∈ {0, 1} such that m0 ◦ f ⋆ and m1 ◦ f ⋆ are BGF in the sense that the distributions of m0 ◦ f ⋆(X)|Z = 0 and
+m1 ◦ f ⋆(X)|Z = 1 are the same. It is easy to check that the transformed score function mz ◦ f ⋆(x) is a perfectly
+WGF score function even though it depends on the sensitivity group variable z. Note that the algorithm in Section 4
+yields score functions not depending on z.
+7
+Conclusion
+In this paper, we introduced a new concept so called within-group fairness, which should be considered along with
+BGF when fair AI is a concern. Also, we proposed a regularization procedure to control the degree of WGF of
+the estimated classifiers and score functions. By analyzing four real-world datasets, we illustrated that the WGF
+constraints improve the degree of WGF without hampering BGF as well as accuracy. Moreover, in many cases, the
+WGF constraints are helpful to find more accurate prediction models.
+A problem in the proposed learning algorithm for WGF is that using a surrogated constraint for a given WGF constraint
+is sometimes problematic. The learning algorithm can find a DF model which has a lower surrogated WGF value than
+that of a BGF model, but the original WGF value is much higher. See Section A.2 of Appendix for empirical evidence.
+A better surrogated WGF constraint to ensure a lower original WGF value would be useful.
+Acknowledgments
+This work was supported by Institute for Information & communications Technology Planning & Evaluation(IITP)
+grant funded by the Korea government(MSIT) (No. 2019-0-01396, Development of framework for analyzing, detect-
+ing, mitigating of bias in AI model and training data).
+10
+
+References
+[1] Julia Angwin, Jeff Larson, Surya Mattu, and Lauren Kirchner. Machine bias. ProPublica, May, 23:2016, 2016.
+[2] Jon Kleinberg, Jens Ludwig, Sendhil Mullainathan, and Ashesh Rambachan. Algorithmic fairness. In Aea papers
+and proceedings, volume 108, pages 22–27, 2018.
+[3] Ninareh Mehrabi, Fred Morstatter, Nripsuta Saxena, Kristina Lerman, and Aram Galstyan. A survey on bias and
+fairness in machine learning. arXiv preprint arXiv:1908.09635, 2019.
+[4] David Ingold and Spencer Soper. Amazon doesn’t consider the race of its customers. should it. Bloomberg,
+April, 1, 2016.
+[5] Dheeru Dua and Casey Graff. UCI machine learning repository, 2017.
+[6] Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez-Rodriguez, and Krishna P Gummadi. Fairness Con-
+straints: A Flexible Approach for Fair Classification. J. Mach. Learn. Res., 20(75):1–42, 2019.
+[7] L Elisa Celis, Lingxiao Huang, Vijay Keswani, and Nisheeth K Vishnoi. Classification with fairness constraints:
+A meta-algorithm with provable guarantees. In Proceedings of the Conference on Fairness, Accountability, and
+Transparency, pages 319–328, 2019.
+[8] Solon Barocas and Andrew D Selbst. Big data’s disparate impact. Calif. L. Rev., 104:671, 2016.
+[9] Moritz Hardt, Eric Price, and Nati Srebro. Equality of opportunity in supervised learning. In Advances in neural
+information processing systems, pages 3315–3323, 2016.
+[10] Amanda Coston, Karthikeyan Natesan Ramamurthy, Dennis Wei, Kush R Varshney, Skyler Speakman, Zairah
+Mustahsan, and Supriyo Chakraborty. Fair transfer learning with missing protected attributes. In Proceedings of
+the 2019 AAAI/ACM Conference on AI, Ethics, and Society, pages 91–98, 2019.
+[11] Faisal Kamiran and Toon Calders.
+Data preprocessing techniques for classification without discrimination.
+Knowledge and Information Systems, 33(1):1–33, 2012.
+[12] Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork. Learning fair representations. In Inter-
+national Conference on Machine Learning, pages 325–333, 2013.
+[13] Michael Feldman, Sorelle A Friedler, John Moeller, Carlos Scheidegger, and Suresh Venkatasubramanian. Cer-
+tifying and removing disparate impact. In proceedings of the 21th ACM SIGKDD international conference on
+knowledge discovery and data mining, pages 259–268, 2015.
+[14] Flavio Calmon, Dennis Wei, Bhanukiran Vinzamuri, Karthikeyan Natesan Ramamurthy, and Kush R Varshney.
+Optimized pre-processing for discrimination prevention. In Advances in Neural Information Processing Systems,
+pages 3992–4001, 2017.
+[15] Lucas Dixon, John Li, Jeffrey Sorensen, Nithum Thain, and Lucy Vasserman. Measuring and mitigating unin-
+tended bias in text classification. In Proceedings of the 2018 AAAI/ACM Conference on AI, Ethics, and Society,
+pages 67–73, 2018.
+[16] Kellie Webster, Marta Recasens, Vera Axelrod, and Jason Baldridge. Mind the gap: A balanced corpus of
+gendered ambiguous pronouns. Transactions of the Association for Computational Linguistics, 6:605–617, 2018.
+[17] Depeng Xu, Shuhan Yuan, Lu Zhang, and Xintao Wu. Fairgan: Fairness-aware generative adversarial networks.
+In 2018 IEEE International Conference on Big Data (Big Data), pages 570–575. IEEE, 2018.
+[18] Elliot Creager, David Madras, J¨orn-Henrik Jacobsen, Marissa Weis, Kevin Swersky, Toniann Pitassi, and Richard
+Zemel. Flexibly fair representation learning by disentanglement. In International Conference on Machine Learn-
+ing, pages 1436–1445. PMLR, 2019.
+[19] Novi Quadrianto, Viktoriia Sharmanska, and Oliver Thomas. Discovering fair representations in the data domain.
+In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8227–8236,
+2019.
+[20] Toshihiro Kamishima, Shotaro Akaho, Hideki Asoh, and Jun Sakuma. Fairness-aware classifier with preju-
+dice remover regularizer. In Joint European Conference on Machine Learning and Knowledge Discovery in
+Databases, pages 35–50. Springer, 2012.
+[21] Gabriel Goh, Andrew Cotter, Maya Gupta, and Michael P Friedlander. Satisfying real-world goals with dataset
+constraints. In Advances in Neural Information Processing Systems, pages 2415–2423, 2016.
+[22] Yahav Bechavod and Katrina Ligett. Learning fair classifiers: A regularization-inspired approach. arXiv preprint
+arXiv:1707.00044, pages 1733–1782, 2017.
+11
+
+[23] Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez Rogriguez, and Krishna P Gummadi. Fairness constraints:
+Mechanisms for fair classification. In Artificial Intelligence and Statistics, pages 962–970, 2017.
+[24] Michele Donini, Luca Oneto, Shai Ben-David, John S Shawe-Taylor, and Massimiliano Pontil. Empirical risk
+minimization under fairness constraints. In Advances in Neural Information Processing Systems, pages 2791–
+2801, 2018.
+[25] Aditya Krishna Menon and Robert C Williamson. The cost of fairness in binary classification. In Conference on
+Fairness, Accountability and Transparency, pages 107–118, 2018.
+[26] Harikrishna Narasimhan. Learning with complex loss functions and constraints. In International Conference on
+Artificial Intelligence and Statistics, pages 1646–1654. PMLR, 2018.
+[27] Robin Vogel, Aur´elien Bellet, and St´ephan Cl´emenc¸on. Learning Fair Scoring Functions: Fairness Definitions,
+Algorithms and Generalization Bounds for Bipartite Ranking. arXiv preprint arXiv:2002.08159, 2020.
+[28] Jaewoong Cho, Changho Suh, and Gyeongjo Hwang.
+A fair classifier using kernel density estimation.
+In
+34th Conference on Neural Information Processing Systems, NeurIPS 2020. Conference on Neural Information
+Processing Systems, 2020.
+[29] Faisal Kamiran, Asim Karim, and Xiangliang Zhang. Decision theory for discrimination-aware classification. In
+2012 IEEE 12th International Conference on Data Mining, pages 924–929. IEEE, 2012.
+[30] Benjamin Fish, Jeremy Kun, and ´Ad´am D Lelkes. A confidence-based approach for balancing fairness and
+accuracy. In Proceedings of the 2016 SIAM International Conference on Data Mining, pages 144–152. SIAM,
+2016.
+[31] Sam Corbett-Davies, Emma Pierson, Avi Feller, Sharad Goel, and Aziz Huq. Algorithmic decision making and
+the cost of fairness. In Proceedings of the 23rd acm sigkdd international conference on knowledge discovery and
+data mining, pages 797–806, 2017.
+[32] Geoff Pleiss, Manish Raghavan, Felix Wu, Jon Kleinberg, and Kilian Q Weinberger. On fairness and calibration.
+In Advances in Neural Information Processing Systems, pages 5680–5689, 2017.
+[33] Evgenii Chzhen, Christophe Denis, Mohamed Hebiri, Luca Oneto, and Massimiliano Pontil. Leveraging la-
+beled and unlabeled data for consistent fair binary classification. In Advances in Neural Information Processing
+Systems, pages 12760–12770, 2019.
+[34] Dennis Wei, Karthikeyan Natesan Ramamurthy, and Flavio Calmon. Optimized Score Transformation for Fair
+Classification. volume 108 of Proceedings of Machine Learning Research, pages 1673–1683, Online, 26–28
+Aug 2020. PMLR.
+[35] Ray Jiang, Aldo Pacchiano, Tom Stepleton, Heinrich Jiang, and Silvia Chiappa. Wasserstein fair classification.
+In Uncertainty in Artificial Intelligence, pages 862–872. PMLR, 2020.
+[36] Yongkai Wu, Lu Zhang, and Xintao Wu. Fairness-aware Classification: Criterion, Convexity, and Bounds. arXiv
+preprint arXiv:1809.04737, 2018.
+[37] Till Speicher, Hoda Heidari, Nina Grgic-Hlaca, Krishna P Gummadi, Adish Singla, Adrian Weller, and Muham-
+mad Bilal Zafar. A unified approach to quantifying algorithmic unfairness: Measuring individual &group unfair-
+ness via inequality indices. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge
+Discovery & Data Mining, pages 2239–2248, 2018.
+[38] Ofir Nachum and Heinrich Jiang. Group-based fair learning leads to counter-intuitive predictions. arXiv preprint
+arXiv:1910.02097, 2019.
+[39] L´eon Bottou.
+Large-scale machine learning with stochastic gradient descent.
+In Proceedings of COMP-
+STAT’2010, pages 177–186. Springer, 2010.
+[40] Linda F Wightman and Henry Ramsey. LSAC national longitudinal bar passage study. Law School Admission
+Council, 1998.
+[41] Jeff Larson, Surya Mattu, Lauren Kirchner, and Julia Angwin. How we analyzed the COMPAS recidivism
+algorithm. ProPublica (5 2016), 9(1), 2016.
+[42] Manisha Padala and Sujit Gujar. FNNC: Achieving Fairness through Neural Networks. pages 2249–2255, 07
+2020.
+[43] Preethi Lahoti, Alex Beutel, Jilin Chen, Kang Lee, Flavien Prost, Nithum Thain, Xuezhi Wang, and Ed H Chi.
+Fairness without demographics through adversarially reweighted learning. arXiv preprint arXiv:2006.13114,
+2020.
+12
+
+A
+Supplenmetary Material
+A.1
+Additional numerical studies for WGF classification
+A.1.1
+Targeting for disparate impact
+First, we investigate the sensitivity of the prediction accuracy to the degree of dWGF in the DNN model. Figure 4
+shows the scatter plots between various dWGF values and the corresponding accuracies for the DF DNN model, where
+the DI is fixed around 0.03. The accuracies are not very sensitive to the dWGF values like the DF linear logistic model.
+Furthermore, for the datasets Adult, Bank and COMPAS, the DF classifiers have higher accuracies and lower dWGF
+values than the BGF classifier.
+Figure 4: Scatter plots of the accuracies and dWGF values for the DF DNN model with the DI values around 0.03.
+(Topleft) Adult; (Topright) Bank; (Bottomleft) LSAC; (Bottomright) COMPAS. Red star points in each figure represent
+the results of the BGF classifier.
+We also investigate how the dWGF constraint performs with surrogated BGF constraints other than Hinge-DI: (i) the
+covariance type constraint [23, 6], named by COV-DI; and (ii) the linear surrogated function, named by FNNC-DI
+[42]. Table 7 presents the results with various surrogated DI constraints and the dWGF constraint. In most cases,
+COV-DI and FNNC-DI give the results similar to Hinge-DI with or without the dWGF constraint and we consistently
+observe that considering the dWGF constraint together with the DI constraint helps to alleviate within-group fairness
+while maintaining similar levels of the accuracy and the DI. Note that for the dataset Adult, the DNN model with
+COV-DI constraint does not achieve the pre-specified DI value 0.03 regardless of the choice of tuning parameter. In
+contrast, the DNN model trained with the DI and dWGF constraints achieves the DI value 0.03 with a smaller value of
+dWGF. This observation is interesting since it implies that the dWGF constraint is helpful to increase even the BGF.
+Next, we compare the dWGF and WGF constraints when targeting the DI with the hinge surrogated function in Table
+8. In most cases, both the dWGF and WGF constraints are helpful to improve the WGF, while maintaining a similar
+level of accuracy and DI. It is noticeable that the DF classifier with the dWGF constraint is more accurate than that
+with the WGF constraint, which would be mainly because the DI constraint is directional.
+13
+
+0.839
+DF
+0.904
+BGF
+0.838
+ACC
+0.837
+0.902
+0.836
+DF
+0.900
+0.835
+BGF
+0.004
+0.006
+0.008
+0.030
+0.035
+dWGF
+dWGF
+★
+0.815
+0.65
+0.810
+0.64
+CC
+0.63
+0.805
+A
+0.62
+0.800
+DF
+DF
+BGF
+0.61
+BGF
+0.795
+0.04
+0.05
+0.06
+0.12
+0.14
+dWGF
+dWGFLINEAR MODEL
+DNN MODEL
+DATASET
+METHOD
+ACC
+DI
+DWGF
+ACC
+DI
+DWGF
+Adult
+UNCONS.
+0.852
+0.172
+0.000
+0.853
+0.170
+0.000
+COV-DI
+0.837
+0.035
+0.003
+0.845
+0.082
+0.013
+COV-DI-DF
+0.837
+0.030
+0.001
+0.840
+0.025
+0.007
+FNNC-DI
+0.834
+0.023
+0.003
+0.838
+0.023
+0.006
+FNNC-DI-DF
+0.836
+0.025
+0.001
+0.841
+0.025
+0.004
+Bank
+UNCONS.
+0.908
+0.195
+0.000
+0.904
+0.236
+0.000
+COV-DI
+0.904
+0.019
+0.009
+0.906
+0.019
+0.036
+COV-DI-DF
+0.904
+0.020
+0.007
+0.906
+0.020
+0.033
+FNNC-DI
+0.903
+0.020
+0.013
+0.901
+0.020
+0.029
+FNNC-DI-DF
+0.905
+0.020
+0.008
+0.900
+0.010
+0.027
+LSAC
+UNCONS.
+0.823
+0.120
+0.000
+0.856
+0.131
+0.000
+COV-DI
+0.808
+0.015
+0.014
+0.859
+0.052
+0.020
+COV-DI-DF
+0.811
+0.019
+0.010
+0.860
+0.054
+0.014
+FNNC-DI
+0.809
+0.020
+0.014
+0.851
+0.025
+0.023
+FNNC-DI-DF
+0.809
+0.014
+0.010
+0.844
+0.010
+0.019
+COMPAS
+UNCONS.
+0.757
+0.164
+0.000
+0.757
+0.162
+0.000
+COV-DI
+0.640
+0.029
+0.149
+0.661
+0.038
+0.124
+COV-DI-DF
+0.620
+0.024
+0.135
+0.650
+0.028
+0.097
+FNNC-DI
+0.646
+0.037
+0.146
+0.646
+0.032
+0.133
+FNNC-DI-DF
+0.624
+0.034
+0.143
+0.645
+0.021
+0.117
+Table 7: Results for the DF classifier with various surrogated DI constraints. Except for the dataset Adult, average
+performances are described.
+WITH THE DWGF CONSTRAINT
+WITH THE WGF CONSTRAINT
+DATASET
+METHOD
+ACC
+DI
+DWGF
+ACC
+DI
+WGF
+Adult
+HINGE-DI
+0.833
+0.028
+0.005
+0.833
+0.028
+0.005
+HINGE-DI-DF
+0.836
+0.028
+0.003
+0.830
+0.012
+0.005
+Bank
+HINGE-DI
+0.901
+0.024
+0.018
+0.901
+0.024
+0.003
+HINGE-DI-DF
+0.904
+0.021
+0.007
+0.898
+0.017
+0.000
+LSAC
+HINGE-DI
+0.809
+0.017
+0.014
+0.809
+0.017
+0.014
+HINGE-DI-DF
+0.813
+0.018
+0.009
+0.810
+0.016
+0.011
+COMPAS
+HINGE-DI
+0.641
+0.024
+0.153
+0.641
+0.024
+0.136
+HINGE-DI-DF
+0.618
+0.025
+0.145
+0.594
+0.018
+0.088
+Table 8: Comparison of the dWGF and WGF constraints based on the linear logistic model. Except for the dataset
+Adult, average performances are described.
+A.1.2
+Targeting for equal opportunity
+We exam how the dWGF constraint works with the equal opportunity constraint given as
+EOp =
+���Pr( ˆY = 1|Y = 1, Z = 1) − Pr( ˆY = 1|Y = 1, Z = 0)
+��� ,
+and the results are summarized in Table 9. For some cases, the dWGF constraint does not work at all (i.e., the dWGF
+values of the BGF and DF classifiers are the sames). This is partly because the surrogated dWGF constraint does not
+represent the original dWGF well, which is discussed in the following section.
+14
+
+LINEAR MODEL
+DNN MODEL
+DATASET
+METHOD
+ACC
+EOP
+DWGF
+ACC
+EOP
+DWGF
+Adult
+UNCONS.
+0.852
+0.070
+0.000
+0.853
+0.076
+0.000
+HINGE-EOP
+0.851
+0.011
+0.002
+0.854
+0.012
+0.030
+HINGE-EOP-DF
+0.853
+0.016
+0.001
+0.854
+0.015
+0.012
+FNNC-EOP
+0.851
+0.013
+0.012
+0.852
+0.004
+0.021
+FNNC-EOP-DF
+0.852
+0.007
+0.007
+0.852
+0.006
+0.019
+Bank
+UNCONS.
+0.908
+0.099
+0.000
+0.904
+0.082
+0.000
+HINGE-EOP
+0.908
+0.027
+0.007
+0.909
+0.031
+0.122
+HINGE-EOP-DF
+0.908
+0.027
+0.007
+0.909
+0.031
+0.122
+FNNC-EOP
+0.908
+0.027
+0.010
+0.903
+0.037
+0.111
+FNNC-EOP-DF
+0.908
+0.030
+0.010
+0.900
+0.028
+0.107
+LSAC
+UNCONS.
+0.823
+0.041
+0.000
+0.856
+0.038
+0.000
+HINGE-EOP
+0.820
+0.003
+0.004
+0.852
+0.010
+0.015
+HINGE-EOP-DF
+0.820
+0.003
+0.004
+0.851
+0.008
+0.012
+FNNC-EOP
+0.822
+0.011
+0.003
+0.859
+0.010
+0.011
+FNNC-EOP-DF
+0.822
+0.011
+0.003
+0.858
+0.010
+0.010
+COMPAS
+UNCONS.
+0.757
+0.074
+0.000
+0.757
+0.075
+0.000
+HINGE-EOP
+0.713
+0.042
+0.073
+0.719
+0.029
+0.046
+HINGE-EOP-DF
+0.713
+0.042
+0.073
+0.719
+0.029
+0.046
+FNNC-EOP
+0.666
+0.039
+0.197
+0.722
+0.031
+0.056
+FNNC-EOP-DF
+0.706
+0.031
+0.092
+0.725
+0.035
+0.042
+Table 9: Results for targeting EOp-dWGF. Except for the dataset Adult, average performances are described.
+A.2
+Limitations of surrogated WGF constraint
+We have seen that the DF classifier does not improve the dWGF value at all compared to the BGF classifier with respect
+to the equal opportunity constraint for some datasets. We found that these undesirable results would be because the
+surrogated dWGF constraint using the hinge function does not represent the original dWGF constraint. To take a
+closer look at this problem, we investigate relations between the dWGF and Wconv evaluated on the training datasets
+Bank and LSAC in Figure 5. We observe that the DF classifier has lower Wconv values but higher dWGF values than
+the BGF classifier. That is, reducing the Wconv value does not always result in a small value of the original dWGF.
+Alternative surrogated constraints, which resemble the original dWGF closely but are yet computationally easy, are
+needed and we leave this issue for future work.
+Figure 5: Scatter plots of the dWGF and the within-group fairness penalty (Wconv) values for the DF linear logistic
+model with the EOp values around 0.03 evaluated on the training datasets. (Left) Bank; (Right) LSAC. Red star points
+in each figure represent the results of the BGF classifier.
+15
+
+DF
+0.0200
+0.012
+DF
+BGF
+0.0175
+BGF
+0.011
+0.0150
+0.0125
+Mp
+Mp
+0.009
+0.0100
+0.008
+0.0075
+0.0050
+0.007
+0.04
+0.05
+0.06
+0.07
+0.08
+0.09
+0.10
+0.03
+0.04
+0.05
+0.06
+0.07
+Wconv
+WconvMODEL
+DATASET
+ACC
+DI
+EOP
+DM
+LINEAR
+Adult
+0.852
+0.172
+0.070
+0.117
+Bank
+0.908
+0.195
+0.099
+0.176
+LSAC
+0.823
+0.120
+0.041
+0.090
+COMPAS
+0.757
+0.164
+0.074
+0.020
+DNN
+Adult
+0.853
+0.170
+0.076
+0.105
+Bank
+0.904
+0.236
+0.082
+0.174
+LSAC
+0.856
+0.131
+0.038
+0.071
+COMPAS
+0.757
+0.162
+0.075
+0.024
+Table 10: Performances of the unconstrained linear logistic model on the test dataset. Except for Adult, average metrics
+are described.
+A.3
+Datasets and Preprocessing
+Dataset. We conduct our experiments with four real-world datasets, which are popularly used in fairness AI research
+and publicly available:
+• Adult [5]: The Adult Income dataset consists of 32,561 training subjects and 16,281 test subjects with 14
+features and a binary target, which indicates whether income exceeds $50k per a year. The sensitive variable
+is the sex of the subject, Z = 0 for female and Z = 1 for male.
+• Bank [5]: The Bank Marketing dataset contains 41,188 subjects with 20 features (e.g. age, occupation,
+marital status) and a binary target indicating whether or not subjects have subscribed to the product (bank
+term deposit). A discrete age is set as a binary sensitive variable by assigning 0 to subjects aged 25 to 60
+years old and 1 to else.
+• LSAC [40]: The Law School dataset pre-processed by [43] contains 26,551 subjects with 10 input variables
+and a binary target which indicates whether subject passed the bar exam or not. The sensitive variable is set
+by 0 for ‘non-white’ subjects and 1 for ‘white’ subjects.
+• COMPAS [41]: The Compas Propublica Risk Assessment dataset contains 6,172 subjects to predict recidi-
+vism (‘HighScore’ or ‘LowScore’) with 6 variables related to criminal history and demographic information.
+We use racial characteristics as a sensitive variable.
+We transform all categorical variables to dummy variables using one-hot encoding, and standardize to get zero mean
+and 1 standard deviation for each variable. Some variables having serious multicollinearity have been removed in
+order to obtain stable estimation results. The performances of the unconstrained linear logistic model are summarized
+in Table 10.
+A.4
+Implementation details
+For numerical stability, we use the ridge penalty for DNN parameters with the regularization parameter 10−6. All
+experiments are conducted on a GPU server with NVIDIA TITAN Xp GPUs. Also, for each method, we consider
+lr ∈ {0.01, 0.1, 1} and epoch ∈ {10000, 20000}, then we choose the best learning rate and epoch. In addition, we did
+not use a mini-batch for the gradient descent approach, i.e., we set the batch size to the sample size. For each BGF
+constraint, we choose the corresponding regularization parameter so that the value of the BGF constraint (e.g., DI,
+EOp, MSP) reaches a certain level among the following candidate parameters set:
+λ ∈ {0, 0.05, 0.1, 0.35, 0.45, 0.6, 0.75, 1, 2, 5}.
+The hyper-parameters in the doubly-fair algorithm are set to minimize the dWGF (or WGF) value while the BGF level
+remains similar to that of the BGF classifier, among the following candidate parameters sets:
+λ ∈ {0, 0.05, 0.1, 0.35, 0.45, 0.6, 0.75, 1, 2, 5}
+η ∈ {0, 0.1, 0.5, 1, 3, 5}.
+For the WGF score function, we adopt the surrogated version of Kendall’s τ as the WGF constraint. However, the
+surrogated Kendall’s τ requires huge computation since it should process all pairs of the training data. To save
+computing time for calculating the surrogated Kendall’s τ, we use 50,000 pairs of samples randomly selected from the
+training data for each sensitive group.
+16
+
diff --git a/odE_T4oBgHgl3EQf8hwH/content/tmp_files/load_file.txt b/odE_T4oBgHgl3EQf8hwH/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f737367cebfaa47015573d5767506a9457a0a4ad
--- /dev/null
+++ b/odE_T4oBgHgl3EQf8hwH/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf,len=1222
+page_content='WITHIN-GROUP FAIRNESS: A GUIDANCE FOR MORE SOUND  BETWEEN-GROUP FAIRNESS  Sara Kim  Samsung Electronics Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Seoul  sarah58833@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='com  Kyusang Yu  Department of Applied Statistics  Konkuk University  Seoul  kyusangu@konkuk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='kr  Yongdai Kim  Department of Statistics  Seoul National University  Seoul  ydkim0903@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='com  ABSTRACT  As they have a vital effect on social decision-making, AI algorithms not only should be accurate  and but also should not pose unfairness against certain sensitive groups (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', non-white, women).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Various specially designed AI algorithms to ensure trained AI models to be fair between sensitive  groups have been developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In this paper, we raise a new issue that between-group fair AI models  could treat individuals in a same sensitive group unfairly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We introduce a new concept of fairness  so-called within-group fairness which requires that AI models should be fair for those in a same sen-  sitive group as well as those in different sensitive groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We materialize the concept of within-group  fairness by proposing corresponding mathematical definitions and developing learning algorithms to  control within-group fairness and between-group fairness simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Numerical studies show  that the proposed learning algorithms improve within-group fairness without sacrificing accuracy as  well as between-group fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  1  Introduction  Recently, AI (Artificial Intelligence) is being used as decision-making tools in various domains such as credit scoring,  criminal risk assessment, education of college admissions [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' As AI has a wide range of influences on human social  life, issues of transparency and ethics of AI are emerging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' However, it is widely known that due to the existence of  historical bias in data against ethics or regulatory frameworks for fairness, trained AI models based on such biased  data could also impose bias or unfairness against a certain sensitive group (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', non-white, women) [2, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Therefore,  designing an AI algorithm which is accurate and fair simultaneously has become a crucial research topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Demographic disparities due to AI, which refer to socially unacceptable bias that an AI model favors certain groups  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', white, men) over other groups (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', black, women), have been observed frequently in many applications of AI  such as COMPAS recidivism risk assessment [1], Amazon’s prime free same-day delivery [4], credit score evaluation  [5] to name just a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Many studies have been done recently to develop AI algorithms which remove or alleviate such  demographic disparities in trained AI models so that they will treat sensitive groups as equally as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In general,  these methods try to search AI models which are not only accurate but also similar between sensitive groups in a certain  sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For an example of similarity, it is required that accuracies of an AI model for each sensitive group are similar  [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Hereinafter, criteria of fairness requiring similarity between sensitive groups are referred to as between-groups  fairness (BGF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In this paper, we consider a new concept of fairness so called within-group fairness (WGF) which arises as a new  problem when we try to enforce BGF into AI algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Generally speaking, within-group unfairness occurs when  there is an individual who is positively treated compared to others in a same sensitive group by an AI model trained  without BGF constraints but becomes negatively treated by an AI model trained with BGF constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  For an illustrative example of WGF, consider a college admission problem where gender (men vs women) is a sensitive  variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Let X and Y ∈ {0, 1} be the input vector and the corresponding output label where X represents the  information of a candidate student such as GPA at high school, SAT score, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' and Y is the admission result where 0  and 1 mean the rejection and acceptance of the college admission, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The Bayes classifier accepts a student  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='08375v1  [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='ML]  20 Jan 2023  Figure 1: A toy example of within-group unfairness: The left panel: without BGF constraints, there exists unfairness  against the women sensitive group, but with BGF constraints, the scores of the two women become reversed and thus  within-group unfairness occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The right panel: The scores of the two women increase together to achieve BGF  without within-group unfairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  with X = x when Pr(Y = 1|X = x) > 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Suppose that there are two women ‘A’ and ‘B’ with the input vectors  xA and xB, respectively and the AI model trained without BGF constraints estimates Pr(Y = 1|X = xB) > 1/2 >  Pr(Y = 1|X = xA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Then, within-group unfairness occurs when an AI model trained with BGF constraints results  in Pr(Y = 1|X = xA) > 1/2 > Pr(Y = 1|X = xB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In this situation, which is illustrated in the left panel of  Figure 1, ‘B’ could claim that the AI model trained with BGF constraints mistreats her and so it is unfair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We will  show in Section 5 that there exists non-negligible within-group unfairness in AI models trained on real data with BGF  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Within-group unfairness arises because most existing learning algorithms for BGF force certain statistics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' rate of  positive prediction, misclassification error rate, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=') of a trained AI model being similar across sensitive groups but  do not care about what happens to individuals in a same sensitive group at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For within-group fairness, a desirable  AI model is expected at least to preserve the ranks between Pr(Y = 1|X = xA) and Pr(Y = 1|X = xB) regardless  of estimating Pr(Y = 1|X = x) with or without BGF constraints, which is depicted in the right panel of Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Our contributions are three folds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We first define the concept of WGF rigorously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Then we develop learning algorithms  which compromise BGF and WGF as well as accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Finally, we show empirically that the proposed learning  algorithms improve WGF while maintaining accuracy and BGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Remark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' One may argue that training data are prone to bias due to historical prejudices and discriminations, and  hence a trained AI model is also biased and socially unacceptable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' On the other hand, a trained AI model with BGF  constraints does not have such bias and hence is socially acceptable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Therefore, it would be by no means reasonable  to claim unfairness based on discrepancies between socially unacceptable and acceptable AI models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' However, note  that historical bias in training data is about bias between sensitive groups but not for individuals in a same sensitive  group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For WGF, we implicitly assume that no historical bias among individuals in a same sensitive group exists in  training data, which is not too absurd, and thus there is no reason for a trained AI model without BGF constraints to  treat individuals in a same sensitive group unfairly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' This assumption, of course, needs more debates which we leave  as future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Section 2, we briefly review methods for BGF, and in Sections 3 and 4, we  propose mathematical definitions of WGF and develop corresponding learning algorithms for classifiers and score  functions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The results of numerical studies are presented in Section 5, and remarks about reflecting WGF  to pre- and post processing algorithms for BGF are given in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Concluding remarks follow in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  2  Review of between-group fairness  While it is completely new, the concept of WGF is a by-product of BGF and thus it is helpful to review learning  methods for BGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In this section, we review the definitions of BGF and related studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  2  Within-group unfair  Within-group fair  Estimated  score  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='5  BGF  BGF  Unconstrained  Unconstrained  constrained  constrained  men  women  rank preserved  rank changedFAIRNESS CRITERIA  E  E′  DISPARATE IMPACT  [8]  1{Cf(X) = 1}  ∅  EQUAL OPPORTUNITY  [9]  1{Cf(X) = 1}  {Y = 1}  DISPARATE MISTREATMENT W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' ERROR RATE  [6]  1{Cf(X) ̸= Y }  ∅  MEAN SCORE PARITY  [10]  f(X)  ∅  Table 1: Some group performance functions  We let D = {(xi, zi, yi)}n  i=1 be a set of training data of size n which are independent copies of a random vector  (X, Z, Y ) defined on X × Z × Y, where X ⊂ Rp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We consider a binary classification problem, which means Y =  {0, 1}, and for notational simplicity, we let Z = {0, 1}, where Z = 0 refers to the unprivileged group and Z = 1 refers  to the privileged group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Whenever the probability is mentioned, we mean it by either the probability of (X, Z, Y ) or  its empirical counterpart unless there is any confusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In this paper, we consider AI algorithms which yield a real-valued function f : X → R so called a score function  which assigns positive labeled instances higher scores than negative labeled instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' An example of the score  function is the conditional class probability Pr(Y = 1|x = x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In most human-related decision makings, real-valued  score functions are popularly used (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' scores for credit scoring).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Let F be a given set of score functions, in which we search an optimal score function in a certain sense (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' minimizing  the cross-entropy for classification problems).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Examples of F are linear functions, reproducing kernel Hilbert space  and deep neural networks to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For a given f ∈ F, the corresponding classifier Cf is defined as Cf(x) =  1(f(x) > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1  Definition of between-group fairness  For a given score function f and a sensitive group Z = z, we consider the group performance function of f given as  qz(f) := E(E|E′, Z = z)  (1)  for events E and E′ that might depend on f(X) and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The group performance function qz in (1), which is considered  by [7], includes various performance functions used in fairness AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We summarize representative group performance  functions having the form of (1) in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  For given group performance functions qz(·), z ∈ {0, 1}, we say that f satisfies the BGF constraint with respect to qz  if q0(f) = q1(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' A relaxed version of the BGF constraint so called the ϵ-BGF constraint, is frequently considered,  which requires |q0(f) − q1(f)| < ϵ for a given ϵ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Typically, AI algorithms search an optimal function f among  those satisfying the ϵ-BGF constraint with respect to given group performance functions qz(·), z ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2  Related works  Several learning algorithms have been proposed to find an accurate model f satisfying a given BGF constraint, which  are categorized into three groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In this subsection, we review some methods for each group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Pre-processing methods: Pre-processing methods remove bias in training data or find a fair representation with re-  spect to sensitive variables before the training phase and learn AI models based on de-biased data or fair representation  [11, 12, 13, 14, 15, 16, 17, 18, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' [11] suggested pre-processing methods to eliminate bias in training data by use of  label changing, reweighing and sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Based on the idea that transformed data should not be able to predict the  sensitive variable, [13] proposed a transformation of input variables for eliminating the disparate impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' To find a fair  representation, [12, 14] proposed a data transformation mapping for preserving accuracy and alleviating discrimination  simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Pre-processing methods for fair learning on text data were studied by [15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In-processing methods: In-processing methods generally train an AI model by minimizing a given cost function  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' the cross-entropy, the sum of squared residuals, the empirical AUC etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=') subject to a ϵ-BGF constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Most  group performance functions qz(·) are not differentiable, and thus various surrogated group performance functions  and corresponding ϵ-BGF constraints have been proposed [20, 21, 22, 23, 6, 24, 25, 26, 7, 27, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' [20] used a  3  fairness regularizer which is an approximation of the mutual information between the sensitive variable and the target  variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' [23, 6] proposed covariance-type fairness constraints as tractable proxies targeting the disparate impact and  the equality of the false positive or negative rate, and [24] used a linear surrogated group performance function for the  equalized odds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' On the other hand, [25, 7] derived an optimal classifier for a constrained fair classification as a form  of an instance-dependent threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Also, for fair score functions, [27] proposed fairness constraints based on ROC  curves of each sensitive group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Post-processing methods: Post-processing methods first learn an AI model without any BGF constraint and then  transform the decision boundary or score function of the trained AI model for each sensitive group to satisfy given  BGF criteria [29, 30, 9, 31, 32, 33, 34, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' [9, 33] suggested finding sensitive group dependent thresholds to get a fair  classifier with respect to equal opportunity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' [34, 35] developed an algorithm to transform the original score function  to achieve a BGF constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  3  Within-group fairness for classifiers  We assume that there exists a known optimal classifier C⋆ which could be the Bayes classifier or its estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For  example, we can use Cf ⋆ for C⋆, where f ⋆ is the unconstrained minimizer of the cross-entropy on F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We mostly  focus on in-processing methods for the BGF and explain how to reflect WGF into a learning procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Remarks  about how to reflect WGF to pre- and post-processing methods are given in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1  Definition of within-group fairness  Conceptually, WGF means that the classifier Cf and C⋆ have the same ranks in each sensitive group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' That is, for two  individuals xA and xB in a same sensitive group with C⋆(xA) > C⋆(xB), WGF requires that Cf(xA) ≥ Cf(xB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  To materialize this concept of WGF, we define the WGF constraint as  Pr {C⋆(X) = 0, Cf(X) = 1|Z = z} = 0  or Pr {C⋆(X) = 1, Cf(X) = 0|Z = z} = 0  (2)  for each z ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Similar to the BGF, we relax the constraint (2) by requiring that either of the two probabilities is  small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' That is, we say that f satisfies the δ-WGF constraint for a given δ > 0 if  max  z∈{0,1} min{a01|z(f), a10|z(f)} < δ,  (3)  where aij|z(f) = Pr{C⋆(X) = i, Cf(X) = j|Z = z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2  Directional within-group fairness  Many BGF constraints have their own implicit directions toward which the classifier is expected to be guided in the  training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We can design a special WGF constraint reflecting the implicit direction of a given BGF constraint  which results in more desirable classifiers (better guided, more fair and frequently more accurate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Below, we present  two such WGF constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Disparate impact: Note that the disparate impact requires that  Pr{Cf(X) = 1|Z = 0} = Pr{Cf(X) = 1|Z = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Suppose that Pr{C⋆(X) = 1|Z = 0} < Pr{C⋆(X) = 1|Z = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Then, we expect that a desirable classifier Cf  achieves this BGF constraint by increasing Pr{Cf(X) = 1|Z = 0} from Pr{C⋆(X) = 1|Z = 0} and decreasing  Pr{Cf(X) = 1|Z = 1} from Pr{C⋆(X) = 1|Z = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' To reflect this direction, we can enforce a learning algorithm  to search a classifier Cf satisfying Pr{C⋆(X) = 1|Z = 0} < Pr{Cf(X) = 1|Z = 0} and Pr{C⋆(X) = 1|Z =  1} > Pr{Cf(X) = 1|Z = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Based on this argument, we define the directional δ-WGF constraint for the disparate  impact as  max{a10|0(f), a01|1(f)} < δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  (4)  Equal opportunity: The equal opportunity constraint is given as  Pr{Cf(X) = 1|Z = 0, Y = 1} = Pr{Cf(X) = 1|Z = 1, Y = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  4  Suppose that Pr{C⋆(X) = 1|Z = 0, Y = 1} < Pr{C⋆(X) = 1|Z = 1, Y = 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' A similar argument for the disparate  impact leads us to define the directional δ-WGF constraint for the equal opportunity as  max{a10|01(f), a01|11(f)} < δ  (5)  and  max  z∈{0,1} min  �  a10|z0(f), a01|z0(f)  �  < δ,  (6)  where  aij|zy(f) = Pr{C⋆(X) = i, Cf(X) = j|Z = z, Y = y}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='3  Learning with doubly-group fairness constraints  We say that f satisfies the (ϵ, δ)-doubly-group fairness constraint if B(f) < ϵ and W(f) < δ, where B is a given BGF  constraint and W is the corresponding WGF constraint proposed in the previous two subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In this section, we  propose a relaxed version of W(·) for easy computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' As we review in Section 2, many relaxed versions of B(·)  have been proposed already.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  The WGF constraints considered in Sections 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2 are hard to be used as themselves in the training phase since  they are neither convex nor continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' A standard approach to resolve this problem is to use a convex surrogated  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For example, a surrogated version of the WGF constraint (3) is Wsurr(f) < δ, where  Wsurr(f) := max  z∈{0,1} min  �  E {φ(−f(X))|Z = z, Y ⋆ = 1} p1|z,  E {φ(f(X))|Z = z, Y ⋆ = 0} p0|z  �  ,  (7)  where Y ⋆ = C⋆(X), py|z = Pr(C⋆(X) = y|Z = z) and φ is a convex surrogated function of the indicator function  1(z ≥ 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In this paper, we use the hinge function given as φhinge(z) = (1 + z)+ as a convex surrogated function  which is popularly used for fair AI [21, 24, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The surrogated versions for the other WGF constraints are derived  similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Finally, we estimate f by ˆf that minimizes the regularized cost function  L(f) + λBsurr(f) + ηWsurr(f),  (8)  where L is a given cost function (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' the cross-entropy) and Bsurr and Wsurr are the surrogated constraints of B and  W, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The nonnegative constants λ and η are regularization parameters which are selected so that ˆf satisfies  B( ˆf) < ϵ and W( ˆf) < δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='4  Related notions with within-group fairness  There are several fairness concepts which are somehow related to WGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' However, the existing concepts are quite  different from our WGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Unified fairness: [37] used the term ‘within-group fairness’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' However, WGF of [37] is different from our  WGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' [37] measured individual-level benefits of a given prediction model and they defined the model to be  WGF if the individual benefits in each group are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' They also illustrated that WGF keeps decreasing as  BGF increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Our WGF is nothing to do with individual-level benefits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Our WGF can be high even when  individual-level benefits are not similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Also, our WGF can increase even when BGF increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Slack consistency: [38] proposed the ‘slack consistency’ which requires that the estimated scores of each  individual should be monotonic with respect to slack variables used in fairness constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Slack consistency  does not guarantee within-group fairness because the ranks of the estimated scores can change even when  they move monotonically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  4  Within-group fairness for score functions  Similarly to classifiers, the WGF for score functions requires that f(xA) > f(xB) when f ⋆(xA) > f ⋆(xB) and vice  versa for two individuals xA and xB in a same sensitive group, where f ⋆ is a known optimal score function such as  the conditional class probability Pr(Y = 1|X) or its estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' To realize this concept, we define the WGF constraint  5  for a score function f as τz(f) = 1 for z ∈ {0, 1}, where τz(·) is the Kendall’s τ between f and f ⋆ conditional on  Z = z, that is  τz(f) = E(X1,X2)  �  1{(f(X1) − f(X2))(f ⋆(X1) − f ⋆(X2)) > 0}  ���Z = z  �  ,  where X1 and X2 are independent copies of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In turn, the δ-WGF constraint for a score function f is 1 − τz(f) <  δ, z ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Similarly for classifiers, we need a convex surrogated version of the δ-WGF constraint and a candidate would be  1 − τφ,z(f) < δ, z ∈ {0, 1}, where  τφ,z(f) = 1 − E(X1,X2)  �  φ{(f(X1) − f(X2))(f ⋆(X1) − f ⋆(X2))}  ���Z = z  �  and φ is a convex surrogated function of 1(z > 0) such as the φhinge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  5  Numerical studies  We investigate the impacts of the WGF constraints on the prediction accuracy as well as the BGF by analyzing real-  world datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We consider linear logistic and deep neural network (DNN) models for F and use the cross-entropy  for L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For DNN, fully connected neural networks with one hidden layer and p many hidden nodes are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We  train the models by the gradient descent algorithm [39] implemented by Python with related libraries pytorch,  scikit-learn, numpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The SGD optimizer is used with momentum 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='9 and a learning rate of either 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='01  depending on the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We use the unconstrained minimizer of L for f ⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We analyze four real world datasets, which are popularly used in fairness AI research and publicly available:  (i) The Adult Income dataset (Adult, [5]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (ii) The Bank Marketing dataset(Bank, [5]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (iii) The Law School dataset  (LSAC, [40]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (iv) The Compas Propublica Risk Assessment dataset (COMPAS, [41]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Except for the dataset Adult,  we split the training and test datasets randomly by 8:2 ratio and repeat 5 times training/test splits for performance  evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1  Within-group fair classifiers  We consider following group performance functions for the BGF: the disparate impact (DI) [8] and the disparate  mistreatment w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' error rate [6], which are defined as  DI(f) = |Pr(Cf(X) = 1|Z = 1) − Pr(Cf(X) = 1|Z = 0)|  ME(f) = |Pr(Cf(X) ̸= Y |Z = 0) − Pr(Cf(X) ̸= Y |Z = 1)| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Note that the DI is directional while the ME is not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For the surrogated BGF constraints, we replace the indicator  function with the hinge function in calculating the BGF constraints as is done by [21, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We name the corresponding  BGF constraints by Hinge-DI and Hinge-ME respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The results for other surrogated constraints such as the  covariance type constraints proposed by [23, 6] and the linear surrogated functions considered in [42] are presented  in the Supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In addition, the results for the equal opportunity constraint are summarized in the  Supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  For investigating the impacts of WGF on trained classifiers, we first fix the ϵ for each BGF constraint, and we choose  the regularization parameters λ and η to make the classifier ˆf minimizing the regularized cost function (8) satisfy the  ϵ-BGF constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Then, we assess the prediction accuracy and the degree of WGF of ˆf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1  Targeting for disparate impact  Table 2 presents the three 2 × 2 tables comparing the results of the unconstrained DNN classifier ( ˆY ⋆) and three DNN  classifiers ( ˆY ) trained on the dataset Adult: (i) only with the DI constraint, (ii) with the DI and WGF constraints and  (iii) with the DI and directional WGF (dWGF) constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We let ϵ be around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The numbers marked in red  are subjects treated unfairly with respect to the dWGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Note that the numbers of unfairly treated subjects are reduced  much with the WGF and dWGF constraints and the dWGF constraint is more effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We report that the accuracies  of the three classifiers on the test data are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='837, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='840 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='839, respectively, which indicates that the WGF and  dWGF constraints improve the WGF without hampering the accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Compared to the dWGF, the WGF constraint  is less effective, which is observed consistently for different datasets when a BGF constraint is directional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' See Table  6  ONLY WITH THE DI CONSTRAINT  Z = 0  Z = 1  ˆY = 0  ˆY = 1  ˆY = 0  ˆY = 1  ˆY ⋆ = 0  4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='592  350  ˆY ⋆ = 0  7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='966  86  ˆY ⋆ = 1  13  466  ˆY ⋆ = 1  945  1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='863  WITH THE DI AND WGF CONSTRAINTS  Z = 0  Z = 1  ˆY = 0  ˆY = 1  ˆY = 0  ˆY = 1  ˆY ⋆ = 0  4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='703  239  ˆY ⋆ = 0  8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='021  31  ˆY ⋆ = 1  27  452  ˆY ⋆ = 1  1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='156  1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='652  WITH THE DI AND DWGF CONSTRAINTS  Z = 0  Z = 1  ˆY = 0  ˆY = 1  ˆY = 0  ˆY = 1  ˆY ⋆ = 0  4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='718  224  ˆY ⋆ = 0  8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='024  28  ˆY ⋆ = 1  18  461  ˆY ⋆ = 1  1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='630  Table 2: Comparison of the results of the three DNN classifiers trained (i) only with the BGF constraint,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (ii) with the  BGF and WGF constraints and (iii) with the BGF and dWGF constraints on the dataset Adult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Marked in red represent  the numbers of subjects treated unfairly in a same sensitive group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='120  Table 3: Results for the DF classifier with the Hinge-DI constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Except for the dataset Adult, the average perfor-  mances are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  2 in the Supplementary material for the corresponding numerical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Thus, hereafter we consider the dWGF only  for the DI which has an implicit direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Table 3 summarizes the performances of the three classifiers - C⋆ and the two classifiers trained with the DI constraint  and the DI and dWGF constraints (doubly-fair, DF), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Table 3, we report the accuracies as well as  the values of DI and dWGF terms (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', DI( ˆf) and max{a10|0( ˆf), a01|1( ˆf)}, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We observe that the DF  classifier improves the dWGF while keeping that the DI values and accuracies are favorably comparable to those of  the BGF classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For reference, the performances with the WGF constraint are summarized in the Supplementary  material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  To investigate the sensitivity of the accuracy to the degree of WGF, the scatter plots between various dWGF values  and the corresponding accuracies for the DF linear logistic model are given in Figure 2, where the DI value is fixed  around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The accuracies are not sensitive to the dWGF values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Moreover, for the datasets Adult, Bank and LSAC,  the accuracies keep increasing as the dWGF value decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  7  Figure 2: Scatter plots of the accuracies and dWGF values for the DF linear regression model with the DI values  around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Topleft) Adult;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Topright) Bank;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Bottomleft) LSAC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Bottomright) COMPAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Red star points in each  figure represent the results of the BGF classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  While we analyzed the datasets Bank and LSAC, we found an undesirable aspect of the learning algorithm only  with the DI constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The corresponding classifiers improve the DI by decreasing (or increasing) the probabilities  P( ˆY = 1|Z = 0) and P( ˆY = 1|Z = 1) simultaneously compared to P(Y ⋆ = 1|Z = 0) and P(Y ⋆ = 1|Z = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  A better way to improve the DI would be to increase P( ˆY = 1|Z = 0) and decrease P( ˆY = 1|Z = 1) when  P(Y ⋆ = 1|Z = 0) < P(Y ⋆ = 1|Z = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Figures 3 show that this undesirable aspect disappears when the dWGF  constraint is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Figure 3: Comparison of the conditional probabilities of each group for the datasets Bank (Left) and LSAC(Right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2  Targeting for disparate mistreatment  The results of the performances of the DF classifier with the ME as a BGF constraint are presented in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Since  the ME has no implicit direction, we use the undirectional WGF constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The overall conclusions are similar to  those for the DI and dWGF constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' That is, the undirectional WGF constraint also works well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='16  dWGF  dWGFZ= 0  Z = 1  Z=0  Z=1  Uncons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Uncons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='95  Pr(Y= 1|Z = z)  Pr(Y = 1|Z = z)LINEAR MODEL  DNN MODEL  DATASET  METHOD  ACC  ME  WGF  ACC  ME  WGF  Adult  UNCONS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='047  LSAC  UNCONS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='001  Table 4: Results for the DF classifier with the Hinge-ME constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Except for the dataset Adult, average performances  are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2  Within-group fair for score function  In this section, we examine the WGF constraint for score functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We choose the logistic loss (binary cross-entropy,  BCE) and AUC (area under the ROC) as evaluation metrics for prediction accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For the BGF, we consider the  mean score parity (MSP, [10]):  MSP(f) = |E(σ(f(X))|Z = 1) − E(σ(f(X))|Z = 0)| ,  where σ : x �→ 1/(1 + e−x) is the sigmoid function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' To check how much the estimated score function ˆf is within-  group fair, we calculate the Kendall’s τ between ˆf and the ground-truth score function f ⋆ on the test data for each  sensitive group, and then we average them, which is denoted by ¯τ in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We choose the regularization parameters  λ and η such that ¯τ of ˆf is as close to 1 as possible while maintaining the MSP value around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Table 5 amply shows that the DF score function always improves the degree of WGF (measured by ¯τ) and the accuracy  in terms of AUC simultaneously while keeping the degree of BGF at a reasonable level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' With respect to the BCE, the  BGF and DF score functions are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The superiority of the DF score function in terms of AUC compared with  the BGF score function is partly because the WGF constraint shrinks the estimated score toward the ground-truth  score (Uncons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' in Table 5) which is expected to be most accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Based on these results, we conclude that the WGF  constraint is a useful guide to find a better score function with respect to AUC as well as the WGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  6  Remarks on within-group fairness for pre- and post-processing methods  Various pre- and post-processing methods for fair AI have been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' An advantage of these methods compared  to constrained methods is that the methods are simple, computationally efficient but yet reasonably accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In this  section, we briefly explain how to reflect the WGF to pre- and post-processing methods for the BGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1  Pre-processing methods and within-group fairness  Basically, pre-processing methods transform the training data in a certain way to be between-group fair and train an  AI model on the transformed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' To reflect the WGF, it suffices to add a WGF constraint in the training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Let  Dtrans be the transformed training data to be between-group fair and let Ltrans be the corresponding cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Then,  we learn a model by minimizing Ltrans(f) + ηWconv(f) for η > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Table 6 presents the results of the models trained on the pre-processing training data and a WGF constraint for various  values of η, where the DI is used as the BGF and thus the corresponding dWGF constraint is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In this experi-  ment, we use the linear logistic model and the Massaging [11] for the pre-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Surprisingly we observed that  introducing the dWGF constraint to the pre-processing method helps to improve the BGF and WGF simultaneously  without sacrificing the accuracies much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  9  LINEAR MODEL  DNN MODEL  DATASET  METHOD  BCE  AUC  MSP  ¯τ  BCE  AUC  MSP  ¯τ  Adult  UNCONS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='623  Table 5: Results of the DF score functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Except for the dataset Adult, averages performances are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  METHOD  η  ACC  DI  DWGF  MASSAGING 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='003  Table 6: Comparison of the accuracy and fairnesses of the pre-processing method with and without the dWGF con-  straint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The results are evaluated on the dataset Adult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2  Post-processing methods and within-group fairness  For the BGF score functions, [35] developed an algorithm to obtain two monotonically nondecreasing transformations  mz, z ∈ {0, 1} such that m0 ◦ f ⋆ and m1 ◦ f ⋆ are BGF in the sense that the distributions of m0 ◦ f ⋆(X)|Z = 0 and  m1 ◦ f ⋆(X)|Z = 1 are the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' It is easy to check that the transformed score function mz ◦ f ⋆(x) is a perfectly  WGF score function even though it depends on the sensitivity group variable z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Note that the algorithm in Section 4  yields score functions not depending on z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  7  Conclusion  In this paper, we introduced a new concept so called within-group fairness, which should be considered along with  BGF when fair AI is a concern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Also, we proposed a regularization procedure to control the degree of WGF of  the estimated classifiers and score functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' By analyzing four real-world datasets, we illustrated that the WGF  constraints improve the degree of WGF without hampering BGF as well as accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Moreover, in many cases, the  WGF constraints are helpful to find more accurate prediction models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  A problem in the proposed learning algorithm for WGF is that using a surrogated constraint for a given WGF constraint  is sometimes problematic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The learning algorithm can find a DF model which has a lower surrogated WGF value than  that of a BGF model, but the original WGF value is much higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' See Section A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2 of Appendix for empirical evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  A better surrogated WGF constraint to ensure a lower original WGF value would be useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Acknowledgments  This work was supported by Institute for Information & communications Technology Planning & Evaluation(IITP)  grant funded by the Korea government(MSIT) (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' 2019-0-01396, Development of framework for analyzing, detect-  ing, mitigating of bias in AI model and training data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  10  References  [1] Julia Angwin, Jeff Larson, Surya Mattu, and Lauren Kirchner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Machine bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' ProPublica, May, 23:2016, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [2] Jon Kleinberg, Jens Ludwig, Sendhil Mullainathan, and Ashesh Rambachan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Algorithmic fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Aea papers  and proceedings, volume 108, pages 22–27, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [3] Ninareh Mehrabi, Fred Morstatter, Nripsuta Saxena, Kristina Lerman, and Aram Galstyan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' A survey on bias and  fairness in machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' arXiv preprint arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='09635, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [4] David Ingold and Spencer Soper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Amazon doesn’t consider the race of its customers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' should it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Bloomberg,  April, 1, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [5] Dheeru Dua and Casey Graff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' UCI machine learning repository, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [6] Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez-Rodriguez, and Krishna P Gummadi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Fairness Con-  straints: A Flexible Approach for Fair Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', 20(75):1–42, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [7] L Elisa Celis, Lingxiao Huang, Vijay Keswani, and Nisheeth K Vishnoi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Classification with fairness constraints:  A meta-algorithm with provable guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Proceedings of the Conference on Fairness, Accountability, and  Transparency, pages 319–328, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [8] Solon Barocas and Andrew D Selbst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Big data’s disparate impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Calif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', 104:671, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [9] Moritz Hardt, Eric Price, and Nati Srebro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Equality of opportunity in supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Advances in neural  information processing systems, pages 3315–3323, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [10] Amanda Coston, Karthikeyan Natesan Ramamurthy, Dennis Wei, Kush R Varshney, Skyler Speakman, Zairah  Mustahsan, and Supriyo Chakraborty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Fair transfer learning with missing protected attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Proceedings of  the 2019 AAAI/ACM Conference on AI, Ethics, and Society, pages 91–98, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [11] Faisal Kamiran and Toon Calders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Data preprocessing techniques for classification without discrimination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Knowledge and Information Systems, 33(1):1–33, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [12] Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Learning fair representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Inter-  national Conference on Machine Learning, pages 325–333, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [13] Michael Feldman, Sorelle A Friedler, John Moeller, Carlos Scheidegger, and Suresh Venkatasubramanian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Cer-  tifying and removing disparate impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In proceedings of the 21th ACM SIGKDD international conference on  knowledge discovery and data mining, pages 259–268, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [14] Flavio Calmon, Dennis Wei, Bhanukiran Vinzamuri, Karthikeyan Natesan Ramamurthy, and Kush R Varshney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Optimized pre-processing for discrimination prevention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems,  pages 3992–4001, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [15] Lucas Dixon, John Li, Jeffrey Sorensen, Nithum Thain, and Lucy Vasserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Measuring and mitigating unin-  tended bias in text classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Proceedings of the 2018 AAAI/ACM Conference on AI, Ethics, and Society,  pages 67–73, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [16] Kellie Webster, Marta Recasens, Vera Axelrod, and Jason Baldridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Mind the gap: A balanced corpus of  gendered ambiguous pronouns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Transactions of the Association for Computational Linguistics, 6:605–617, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [17] Depeng Xu, Shuhan Yuan, Lu Zhang, and Xintao Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Fairgan: Fairness-aware generative adversarial networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In 2018 IEEE International Conference on Big Data (Big Data), pages 570–575.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [18] Elliot Creager, David Madras, J¨orn-Henrik Jacobsen, Marissa Weis, Kevin Swersky, Toniann Pitassi, and Richard  Zemel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Flexibly fair representation learning by disentanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In International Conference on Machine Learn-  ing, pages 1436–1445.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' PMLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [19] Novi Quadrianto, Viktoriia Sharmanska, and Oliver Thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Discovering fair representations in the data domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8227–8236,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [20] Toshihiro Kamishima, Shotaro Akaho, Hideki Asoh, and Jun Sakuma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Fairness-aware classifier with preju-  dice remover regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Joint European Conference on Machine Learning and Knowledge Discovery in  Databases, pages 35–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Springer, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [21] Gabriel Goh, Andrew Cotter, Maya Gupta, and Michael P Friedlander.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Satisfying real-world goals with dataset  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems, pages 2415–2423, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [22] Yahav Bechavod and Katrina Ligett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Learning fair classifiers: A regularization-inspired approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' arXiv preprint  arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='00044, pages 1733–1782, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  11  [23] Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez Rogriguez, and Krishna P Gummadi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Fairness constraints:  Mechanisms for fair classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Artificial Intelligence and Statistics, pages 962–970, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [24] Michele Donini, Luca Oneto, Shai Ben-David, John S Shawe-Taylor, and Massimiliano Pontil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Empirical risk  minimization under fairness constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems, pages 2791–  2801, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [25] Aditya Krishna Menon and Robert C Williamson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The cost of fairness in binary classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Conference on  Fairness, Accountability and Transparency, pages 107–118, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [26] Harikrishna Narasimhan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Learning with complex loss functions and constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In International Conference on  Artificial Intelligence and Statistics, pages 1646–1654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [27] Robin Vogel, Aur´elien Bellet, and St´ephan Cl´emenc¸on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Learning Fair Scoring Functions: Fairness Definitions,  Algorithms and Generalization Bounds for Bipartite Ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' arXiv preprint arXiv:2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='08159, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [28] Jaewoong Cho, Changho Suh, and Gyeongjo Hwang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  A fair classifier using kernel density estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In  34th Conference on Neural Information Processing Systems, NeurIPS 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Conference on Neural Information  Processing Systems, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [29] Faisal Kamiran, Asim Karim, and Xiangliang Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Decision theory for discrimination-aware classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In  2012 IEEE 12th International Conference on Data Mining, pages 924–929.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' IEEE, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [30] Benjamin Fish, Jeremy Kun, and ´Ad´am D Lelkes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' A confidence-based approach for balancing fairness and  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Proceedings of the 2016 SIAM International Conference on Data Mining, pages 144–152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' SIAM,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [31] Sam Corbett-Davies, Emma Pierson, Avi Feller, Sharad Goel, and Aziz Huq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Algorithmic decision making and  the cost of fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Proceedings of the 23rd acm sigkdd international conference on knowledge discovery and  data mining, pages 797–806, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [32] Geoff Pleiss, Manish Raghavan, Felix Wu, Jon Kleinberg, and Kilian Q Weinberger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' On fairness and calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In Advances in Neural Information Processing Systems, pages 5680–5689, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [33] Evgenii Chzhen, Christophe Denis, Mohamed Hebiri, Luca Oneto, and Massimiliano Pontil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Leveraging la-  beled and unlabeled data for consistent fair binary classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Advances in Neural Information Processing  Systems, pages 12760–12770, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [34] Dennis Wei, Karthikeyan Natesan Ramamurthy, and Flavio Calmon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Optimized Score Transformation for Fair  Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' volume 108 of Proceedings of Machine Learning Research, pages 1673–1683, Online, 26–28  Aug 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [35] Ray Jiang, Aldo Pacchiano, Tom Stepleton, Heinrich Jiang, and Silvia Chiappa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Wasserstein fair classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In Uncertainty in Artificial Intelligence, pages 862–872.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [36] Yongkai Wu, Lu Zhang, and Xintao Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Fairness-aware Classification: Criterion, Convexity, and Bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' arXiv  preprint arXiv:1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='04737, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [37] Till Speicher, Hoda Heidari, Nina Grgic-Hlaca, Krishna P Gummadi, Adish Singla, Adrian Weller, and Muham-  mad Bilal Zafar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' A unified approach to quantifying algorithmic unfairness: Measuring individual &group unfair-  ness via inequality indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge  Discovery & Data Mining, pages 2239–2248, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [38] Ofir Nachum and Heinrich Jiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Group-based fair learning leads to counter-intuitive predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' arXiv preprint  arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='02097, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [39] L´eon Bottou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Large-scale machine learning with stochastic gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  In Proceedings of COMP-  STAT’2010, pages 177–186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Springer, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [40] Linda F Wightman and Henry Ramsey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' LSAC national longitudinal bar passage study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Law School Admission  Council, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [41] Jeff Larson, Surya Mattu, Lauren Kirchner, and Julia Angwin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' How we analyzed the COMPAS recidivism  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' ProPublica (5 2016), 9(1), 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [42] Manisha Padala and Sujit Gujar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' FNNC: Achieving Fairness through Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' pages 2249–2255, 07  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  [43] Preethi Lahoti, Alex Beutel, Jilin Chen, Kang Lee, Flavien Prost, Nithum Thain, Xuezhi Wang, and Ed H Chi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Fairness without demographics through adversarially reweighted learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='13114,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  12  A  Supplenmetary Material  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1  Additional numerical studies for WGF classification  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1  Targeting for disparate impact  First, we investigate the sensitivity of the prediction accuracy to the degree of dWGF in the DNN model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Figure 4  shows the scatter plots between various dWGF values and the corresponding accuracies for the DF DNN model, where  the DI is fixed around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The accuracies are not very sensitive to the dWGF values like the DF linear logistic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Furthermore, for the datasets Adult, Bank and COMPAS, the DF classifiers have higher accuracies and lower dWGF  values than the BGF classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Figure 4: Scatter plots of the accuracies and dWGF values for the DF DNN model with the DI values around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  (Topleft) Adult;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Topright) Bank;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Bottomleft) LSAC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Bottomright) COMPAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Red star points in each figure represent  the results of the BGF classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  We also investigate how the dWGF constraint performs with surrogated BGF constraints other than Hinge-DI: (i) the  covariance type constraint [23, 6], named by COV-DI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' and (ii) the linear surrogated function, named by FNNC-DI  [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Table 7 presents the results with various surrogated DI constraints and the dWGF constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In most cases,  COV-DI and FNNC-DI give the results similar to Hinge-DI with or without the dWGF constraint and we consistently  observe that considering the dWGF constraint together with the DI constraint helps to alleviate within-group fairness  while maintaining similar levels of the accuracy and the DI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Note that for the dataset Adult, the DNN model with  COV-DI constraint does not achieve the pre-specified DI value 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03 regardless of the choice of tuning parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In  contrast, the DNN model trained with the DI and dWGF constraints achieves the DI value 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03 with a smaller value of  dWGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' This observation is interesting since it implies that the dWGF constraint is helpful to increase even the BGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Next, we compare the dWGF and WGF constraints when targeting the DI with the hinge surrogated function in Table  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In most cases, both the dWGF and WGF constraints are helpful to improve the WGF, while maintaining a similar  level of accuracy and DI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' It is noticeable that the DF classifier with the dWGF constraint is more accurate than that  with the WGF constraint, which would be mainly because the DI constraint is directional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='839  DF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='904  BGF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='088  Table 8: Comparison of the dWGF and WGF constraints based on the linear logistic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Except for the dataset  Adult, average performances are described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2  Targeting for equal opportunity  We exam how the dWGF constraint works with the equal opportunity constraint given as  EOp =  ���Pr( ˆY = 1|Y = 1, Z = 1) − Pr( ˆY = 1|Y = 1, Z = 0)  ��� ,  and the results are summarized in Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For some cases, the dWGF constraint does not work at all (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', the dWGF  values of the BGF and DF classifiers are the sames).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' This is partly because the surrogated dWGF constraint does not  represent the original dWGF well, which is discussed in the following section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  14  LINEAR MODEL  DNN MODEL  DATASET  METHOD  ACC  EOP  DWGF  ACC  EOP  DWGF  Adult  UNCONS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='042  Table 9: Results for targeting EOp-dWGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Except for the dataset Adult, average performances are described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='2  Limitations of surrogated WGF constraint  We have seen that the DF classifier does not improve the dWGF value at all compared to the BGF classifier with respect  to the equal opportunity constraint for some datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We found that these undesirable results would be because the  surrogated dWGF constraint using the hinge function does not represent the original dWGF constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' To take a  closer look at this problem, we investigate relations between the dWGF and Wconv evaluated on the training datasets  Bank and LSAC in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We observe that the DF classifier has lower Wconv values but higher dWGF values than  the BGF classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' That is, reducing the Wconv value does not always result in a small value of the original dWGF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Alternative surrogated constraints, which resemble the original dWGF closely but are yet computationally easy, are  needed and we leave this issue for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Figure 5: Scatter plots of the dWGF and the within-group fairness penalty (Wconv) values for the DF linear logistic  model with the EOp values around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='03 evaluated on the training datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Left) Bank;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' (Right) LSAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Red star points  in each figure represent the results of the BGF classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  15  DF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='0200  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='07  Wconv  WconvMODEL  DATASET  ACC  DI  EOP  DM  LINEAR  Adult  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='020  DNN  Adult  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='904  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+page_content='024  Table 10: Performances of the unconstrained linear logistic model on the test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Except for Adult, average metrics  are described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='3  Datasets and Preprocessing  Dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' We conduct our experiments with four real-world datasets, which are popularly used in fairness AI research  and publicly available:  Adult [5]: The Adult Income dataset consists of 32,561 training subjects and 16,281 test subjects with 14  features and a binary target, which indicates whether income exceeds $50k per a year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The sensitive variable  is the sex of the subject, Z = 0 for female and Z = 1 for male.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  Bank [5]: The Bank Marketing dataset contains 41,188 subjects with 20 features (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' age, occupation,  marital status) and a binary target indicating whether or not subjects have subscribed to the product (bank  term deposit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' A discrete age is set as a binary sensitive variable by assigning 0 to subjects aged 25 to 60  years old and 1 to else.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  LSAC [40]: The Law School dataset pre-processed by [43] contains 26,551 subjects with 10 input variables  and a binary target which indicates whether subject passed the bar exam or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The sensitive variable is set  by 0 for ‘non-white’ subjects and 1 for ‘white’ subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  COMPAS [41]: The Compas Propublica Risk Assessment dataset contains 6,172 subjects to predict recidi-  vism (‘HighScore’ or ‘LowScore’) with 6 variables related to criminal history and demographic information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  We use racial characteristics as a sensitive variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  We transform all categorical variables to dummy variables using one-hot encoding, and standardize to get zero mean  and 1 standard deviation for each variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Some variables having serious multicollinearity have been removed in  order to obtain stable estimation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' The performances of the unconstrained linear logistic model are summarized  in Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='4  Implementation details  For numerical stability, we use the ridge penalty for DNN parameters with the regularization parameter 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' All  experiments are conducted on a GPU server with NVIDIA TITAN Xp GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' Also, for each method, we consider  lr ∈ {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1, 1} and epoch ∈ {10000, 20000}, then we choose the best learning rate and epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' In addition, we did  not use a mini-batch for the gradient descent approach, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', we set the batch size to the sample size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' For each BGF  constraint, we choose the corresponding regularization parameter so that the value of the BGF constraint (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=', DI,  EOp, MSP) reaches a certain level among the following candidate parameters set:  λ ∈ {0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='35, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='45, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='75, 1, 2, 5}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  The hyper-parameters in the doubly-fair algorithm are set to minimize the dWGF (or WGF) value while the BGF level  remains similar to that of the BGF classifier, among the following candidate parameters sets:  λ ∈ {0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='35, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='45, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='75, 1, 2, 5}  η ∈ {0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='5, 1, 3, 5}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  For the WGF score function, we adopt the surrogated version of Kendall’s τ as the WGF constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' However, the  surrogated Kendall’s τ requires huge computation since it should process all pairs of the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content=' To save  computing time for calculating the surrogated Kendall’s τ, we use 50,000 pairs of samples randomly selected from the  training data for each sensitive group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
+page_content='  16' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/odE_T4oBgHgl3EQf8hwH/content/2301.08375v1.pdf'}
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+Mon. Not. R. Astron. Soc. 000, 000–000 (0000)
+Printed 30 January 2023
+(MN LATEX style file v2.2)
+Linking the Interiors and Surfaces of Magnetic Stars
+Jim Fuller1⋆ and St´ephane Mathis2
+1TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA
+2Universit´e Paris-Saclay, Universit´e Paris Cit´e, CEA, CNRS, AIM, F-91191, Gif-sur-Yvette, France
+30 January 2023
+ABSTRACT
+Strong magnetic fields are observed in a substantial fraction of upper main se-
+quence stars and white dwarfs. Many such stars are observed to exhibit photometric
+modulations as the magnetic poles rotate in and out of view, which could be a con-
+sequence of magnetic perturbations to the star’s thermal structure. The magnetic
+pressure is typically larger than the gas pressure at the star’s photosphere, but much
+smaller than the gas pressure in the star’s interior, so the expected surface flux pertur-
+bations are not clear. We compute magnetically perturbed stellar structures of young
+3 M⊙ stars that are in both hydrostatic and thermal equilibrium, and which contain
+both poloidal and toroidal components of a dipolar magnetic field as expected for
+stable fossil fields. This provides semi-analytical models of such fields in baroclinic
+stably stratified regions. The star’s internal pressure, temperature, and flux perturba-
+tions can have a range of magnitudes, though we argue the most likely configurations
+exhibit flux perturbations much smaller than the ratio of surface magnetic pressure to
+surface gas pressure, but much larger than the ratio of surface magnetic pressure to
+central gas pressure. The magnetic pole is hotter than the equator in our models, but
+a cooler magnetic pole is possible depending on the magnetic field configuration. The
+expected flux variations for observed field strengths are δL/L ≲ 10−6, much smaller
+than those observed in magnetic stars, suggesting that observed perturbations stem
+from changes to the emergent spectrum rather than changes to the bolometric flux.
+Key words: stars: evolution – stars: magnetic fields
+1
+INTRODUCTION
+Magnetic fields produce a substantial impact on the appear-
+ance of a star. In stars with convective envelopes, star spots
+are well known as regions of high magnetic field strength and
+low temperature. Some stars with radiative envelopes are
+also known to host strong magnetic fields (e.g., Morel et al.
+2014; Wade et al. 2016; Shultz et al. 2019), and such stars
+frequently exhibit photometric variability at their rotation
+periods, suggesting that their emergent flux is altered by the
+magnetic fields. However, it is not clear how the magnetic
+fields actually affect the stellar structure and emergent flux,
+or whether photometric modulations can be used to learn
+about the strength of the star’s internal magnetic fields.
+One might expect magnetic fields to affect the photo-
+spheric temperature if the magnetic pressure is comparable
+to the photospheric gas pressure. Indeed, Cantiello & Braith-
+waite (2011) argued that magnetic spots on massive stars
+should be hot because they would have lower gas pressures
+(and therefore lower densities), allowing us to see deeper into
+⋆ Email: jfuller@caltech.edu
+the star where the temperature is higher. Relatively mod-
+est magnetic fields of B ≳ 100 G are required for large flux
+perturbations in this scenario. Observed photometric mod-
+ulations from stars with stronger magnetic fields, such as
+Ap stars that exhibit photometric modulation with ∼1-3%
+amplitudes (H¨ummerich et al. 2018), are much smaller than
+naively predicted from this scenario.
+The reason is that a star’s radiative flux will change in
+response to the magnetic perturbation (i.e., the magnetic
+hot spot will cool off) until the star finds a new radia-
+tive equilibrium. Long-lived magnetic fields will thus pro-
+duce much different effects than transient fields arising from
+magnetic activity. To compute the perturbed structure of a
+star with a stable magnetic field, we must find a structure
+that is in both hydrostatic equilibrium and radiative equi-
+librium. For rotating stars, it is well known that no state of
+radiative equilibrium exists for solid body rotation, so that
+stars must either have very special rotation profiles (von
+Zeipel 1924; Busse 1981; Rieutord 2006), or have currents
+that advect heat (Eddington 1929; Sweet 1950) and restore a
+state of equilibrium (see Maeder 1999, Decressin et al. 2009,
+Mathis 2013 for useful synopsis). Our goal in this paper is
+© 0000 RAS
+arXiv:2301.11914v1  [astro-ph.SR]  27 Jan 2023
+
+2
+Fuller & Mathis
+to compute the special magnetic field profiles that allow for
+radiative equilibrium without requiring currents within the
+star.
+In addition, the magnetic field configuration must be a
+stable equilibrium that does not unravel via magnetic insta-
+bilities such as those of purely toroidal fields (Tayler 1973)
+and purely poloidal fields (Markey & Tayler 1973). Several
+works (Braithwaite & Spruit 2004; Braithwaite & Nordlund
+2006; Braithwaite 2008; Broderick & Narayan 2008; Lyu-
+tikov 2010; Duez & Mathis 2010; Duez et al. 2010b; Akg¨un
+et al. 2013; Becerra et al. 2022b) have computed stable
+magnetic equilibria through analytic calculations or numer-
+ical simulations. These works agree that purely poloidal or
+toroidal magnetic field configurations are unstable, and that
+stable equilibria require similar toroidal and poloidal field
+strengths (Tayler 1980; Braithwaite 2009). Stable stratifica-
+tion (i.e., non-barotropic stars) is also required for long-term
+stability (Lander & Jones 2012; Akg¨un et al. 2013; Becerra
+et al. 2022a). Magnetic configurations decrease their mag-
+netic energy but approximately conserve their magnetic he-
+licity as they form and evolve (Braithwaite 2008). This is
+the so-called selective decay as observed in plasmas in the
+laboratory (Taylor 1974). Hence, recent works have com-
+puted stable field configurations through variational tech-
+niques that minimize total energy while conserving magnetic
+helicity (Broderick & Narayan 2008; Duez & Mathis 2010).
+However, all of these works have assumed barotropic
+perturbations such that the perturbed temperature is di-
+rectly proportional to the perturbed pressure. While these
+configurations are in hydrostratic equilibrium, they are not
+typically in thermal equlibrium, meaning that heat will be
+transported from high temperature to low temperature re-
+gions, changing the gas pressure and therefore the magnet-
+ically perturbed stellar structure. This heat transport will
+occur on a thermal time (typically ∼106 yr in A-type stars),
+much shorter than Ohmic diffusion time scales (∼ 1010 yr)
+and main sequence life times (∼109 yr). Hence, real stars
+will approach a state close to hydrostatic equilibrium and
+thermal equilibrium, which has not been considered in re-
+cent literature. Accounting for thermal equilibrium is crucial
+for predicting the long-term equilibria of stars (Reiseneg-
+ger 2009), and observational manifestations such as the per-
+turbed surface flux.
+Calculations of equilibrium magnetic configurations
+date back to the 1950s (e.g., Chandrasekhar 1956; Chan-
+drasekhar & Prendergast 1956). Subsequent work included
+the effects of centrifugal distortion and meridional flows
+(e.g., Ostriker & Hartwick 1968; Mestel & Moss 1977). Inter-
+estingly, works dating back to the 1960s (Monaghan 1966;
+Davies 1968; Wright 1969; Moss 1973, 1979; Li et al. 2006)
+have attempted to compute the structures of stars in both
+hydrostatic and thermal equilibrium. However, much of this
+work is either difficult to interpret, does not discuss the per-
+turbed thermal structure and surface flux, does not consider
+fields with both poloidal and toroidal components, or has
+simply been forgotten. The goal of this paper is to provide
+updated calculations of magnetically distorted stars in sta-
+ble hydrostatic and thermal equilibrium for realistic stellar
+structures, and to discuss the observational implications.
+In this paper we primarily focus on application to up-
+per main sequence stars of M ≳1.5 M⊙ with convective cores
+and radiative envelopes. Much of the physics studied here
+could also apply to radiative stars such as white dwarfs and
+the radiative cores of red giants where internal fields can be
+detected through asteroseismology (Garc´ıa et al. 2014; Stello
+et al. 2016; Li et al. 2022) because of their impact on stellar
+oscillations (Fuller et al. 2015; Lecoanet et al. 2017; Loi 2021;
+Bugnet et al. 2021; Mathis et al. 2021). Magnetic upper main
+sequence stars have typical surface field strengths of ∼1 kG
+(see Braithwaite & Spruit 2017 for a review) and surface
+magnetic pressures larger than surface gas pressures, such
+that magnetic forces could be strong. The surface magnetic
+morphologies are observed to be diverse: they can be com-
+plex or simple, axisymmetric or non-axisymmetric, poloidal
+or toroidal (Landstreet & Mathys 2000; Kochukhov et al.
+2011; Shultz et al. 2019). However, as a first step, in this
+work we examine simple dipolar magnetic configurations
+that produce quadrupolar temperature/pressure perturba-
+tions, which likely dominate observable photometric modu-
+lations.
+2
+EQUILIBRIUM STRUCTURE
+Our goal is to calculate the structure of a magnetized star in
+hydrostatic and thermal equilibrium, considering non-force-
+free magnetic fields. We begin from the equation for magne-
+tohydostratic equilibrium
+− ∇P − ρ∇Φ + (∇ × B) × B
+4π
+= 0 ,
+(1)
+where P is the pressure, ρ the density, Φ the gravitational
+potential, and B the magnetic field. We choose to work in
+standard spherical coordinates with r the radius and θ the
+colatitude. Following Duez & Mathis (2010), we decompose
+the magnetic field into a poloidal magnetic stream function
+Ψ and a toroidal magnetic flux F via
+B =
+√
+4π
+r sin θ ∇Ψ × ˆφ +
+√
+4π
+r sin θ F ˆφ .
+(2)
+This means that
+Br =
+√
+4π
+r2 sin θ
+∂Ψ
+∂θ ,
+(3)
+Bθ = −
+√
+4π
+r sin θ
+∂Ψ
+∂r ,
+(4)
+Bφ =
+√
+4π
+r sin θ F .
+(5)
+We consider an axisymmetric magnetic field such that Ψ and
+F are independent of φ. It can easily be verified that this
+field always satisfies ∇ · B = 0.
+The φ-component of equation 1 becomes
+− ∂F
+∂θ
+∂Ψ
+∂r + ∂F
+∂r
+∂Ψ
+∂θ = 0 .
+(6)
+This is always satisfied if F is a function of Ψ, or in other
+words, the poloidal flux Ψ uniquely determines F and hence
+the toroidal field. Broderick & Narayan (2008) and Duez &
+Mathis (2010) show that the lowest energy state has
+F = λ
+RΨ ,
+(7)
+where the constant λ determines the magnetic helicity, and
+R is the stellar radius. This clearly satisfies equation 6. This
+© 0000 RAS, MNRAS 000, 000–000
+
+Magnetic Structure
+3
+also results if we assume that F and Ψ have the same angular
+form, such that equation 6 reduces to
+1
+F
+dF
+dr = 1
+Ψ
+dΨ
+dr .
+(8)
+The solution to this equation is equation 7, for a constant λ
+that is independent of radius.
+Writing out the hydrostatic equilibrium condition and
+using equation 7, the radial component of equation 1 be-
+comes
+−
+1
+r2 sin2 θ
+� λ2
+R2 Ψ + ∆∗Ψ
+�∂Ψ
+∂r = ∂P
+∂r + ρ∂Φ
+∂r ,
+(9)
+while the θ-component is
+−
+1
+r2 sin2 θ
+� λ2
+R2 Ψ + ∆∗Ψ
+�∂Ψ
+∂θ = ∂P
+∂θ + ρ∂Φ
+∂θ .
+(10)
+Here, ∆∗ is the “Grad-Shafranov” or “five-dimensional
+Laplacian” operator, defined as
+∆∗ = ∂2
+∂r2 + sin θ
+r2
+∂
+∂θ
+�
+1
+sin θ
+∂
+∂θ
+�
+= ∂2
+∂r2 + 1 − µ2
+r2
+∂2
+∂µ2 ,
+(11)
+where µ = cos θ.
+It is immediately evident from equations 9 and 10 that
+the field is force-free if
+λ2
+R2 Ψ + ∆∗Ψ = 0 .
+(12)
+This results in a simple linear eigenvalue calculation for the
+magnetic potential Ψ, and is the type of field considered by
+Broderick & Narayan (2008). The work of Duez & Mathis
+(2010) considers a non-force-free field such that
+λ2
+R2 Ψ + ∆∗Ψ = −βρr sin2 θ ,
+(13)
+where β is a constant that determines the strength of the
+magnetic force. As an example, the case with λ = 0 and
+β = 0 corresponds to a force-free poloidal dipole field. This
+can be seen from equation 12, whose solution has Ψ ∝ r−1
+and hence B ∝ r−3 in that case. A non-zero value of β alters
+both the magnetic forces and the radial profile of the field.
+Substitution of equation 13 into equations 9 and 10
+yields
+βρ∇Ψ = ∇P + ρ∇Φ .
+(14)
+Hence there is a direct relationship between the magnetic
+flux and the pressure perturbation for barotropic perturba-
+tions. Remarkably, the non-linear equations 9 and 10 have
+been transformed into a linear relationship between Ψ and
+P. Taking the curl of equation 14 yields
+∇ρ × ∇P = 0 .
+(15)
+This implies that P is a function of ρ, and hence equation
+13 is a solution for a barotropic equation of state such that
+density and pressure perturbations are directly proportional
+to each other.
+In our work, we want to consider non-force-free fields
+that produce non-barotropic density and pressure pertur-
+bations. Hence, we cannot use the approximations made in
+Broderick & Narayan (2008) or Duez & Mathis (2010), and
+we shall see that this generally leads to a series of non-linear
+differential equations that relate the magnetic field to den-
+sity, temperature, and pressure perturbations. In our calcu-
+lations, we parameterize the strength of the magnetic forces
+via a parameter β. Assuming barotropic perturbations en-
+tails that β (as defined in equation 13) is a constant within
+the star. Accounting for radiative diffusion, this is no longer
+the case. Nonetheless, we shall see below that we still require
+a parameter to specify the strength of the magnetic forces,
+which in practice is determined by the boundary conditions.
+Since our stellar model has a convective core where equation
+13 is a good approximation, we label our structures based
+on the resulting β in the convective core.
+2.1
+Electric Currents
+The current density is
+j = ∇ × B
+4π
+=
+λ
+4πRBrˆr +
+λ
+4πRBθ ˆθ −
+1
+√
+4πr sin θ
+∆∗Ψˆφ .
+(16)
+The force-free field of equation 12 occurs when j is parallel
+to B. Force-free fields are also obtained when Ψ = 0 (no
+magnetic field) or from current-free fields, which only occur
+when both λ = 0 and and ∆∗Ψ = 0. Note that the radial
+current is proportional to the radial magnetic field, hence
+a vanishing radial current near the surface of the star re-
+quires a vanishing radial field Br, which in turn requires Ψ
+to vanish at the stellar surface.
+2.2
+Hydrostatic Equilibrium
+In order to determine an equilibrium state, we use a linear
+approximation such that perturbations to background quan-
+tities (ρ, P, etc.) are considered to be small. The linearized
+version of the radial momentum equation (9) is
+−
+1
+r2 sin2 θ
+� λ2
+R2 Ψ+∆∗Ψ
+�∂Ψ
+∂r = ∂
+∂r δP +ρ ∂
+∂r δΦ+gδρ , (17)
+while the θ-component of equation (10) is
+−
+1
+r2 sin2 θ
+� λ2
+R2 Ψ + ∆∗Ψ
+�∂Ψ
+∂θ = ∂
+∂θ δP + ρ ∂
+∂θ δΦ .
+(18)
+Here, δ indicates an Eulerian perturbation, and we have used
+a background in hydrostatic equilibrium with dP/dr = −ρg,
+and g = dΦ/dr.
+We next turn to the angular dependence of the magnetic
+field and the perturbations to the stellar structure. Decom-
+posing Ψ into eigenvalues of the horizontal component of ∆∗
+requires
+(1 − µ2) ∂2
+∂µ2 gℓ(µ) = −ℓ(ℓ + 1)gℓ(µ) ,
+(19)
+where gℓ is the angular eigenfunction corresponding to the
+eigenvalue −ℓ(ℓ + 1) of the operator on the left hand side
+of equation 19. The full response is Ψ = �
+ℓ Ψℓgℓ(µ). As
+discussed in Duez & Mathis (2010), the eigenvalue equation
+above has solutions
+gℓ(µ) = (1 − µ2)Pℓ−1(µ) ,
+(20)
+where Pℓ is a Legendre polynomial.
+For the lowest order (dipole) solution with ℓ = 1, we
+© 0000 RAS, MNRAS 000, 000–000
+
+4
+Fuller & Mathis
+Figure 1. Magnetic field lines of a star for a toroidal field com-
+parable to the poloidal field (λ2 = 10). Magnetic field lines are
+colored by field strength, while the color shading indicates the
+radiative flux perturbation at a given radius.
+have gℓ(µ) = (1 − µ2) and hence Ψ = Ψℓ(r) sin2 θ. Plugging
+this into equation 17 yields
+− sin2(θ)
+r2
+� ∂2
+∂r2 Ψℓ(r) − ℓ(ℓ + 1)
+r2
+Ψℓ(r) + λ2
+R2 Ψℓ(r)
+�∂Ψℓ(r)
+∂r
+= ∂
+∂r δP + ρ ∂
+∂r δΦ + gδρ .
+(21)
+We see that the perturbed density, pressure, and poten-
+tial must have angular form δP
+∝ sin2(θ), which is a
+combination of the ℓ = 2 and ℓ = 0 spherical harmon-
+ics. Hence a dipole magnetic field induces both radial and
+quadrupole components to the star’s distortion. Figure 1
+illustrates the geometry of a dipolar magnetic field with
+helicity λ2 = 10 that induces quadrupolar flux perturba-
+tions. The quadrupole (ℓ = 2) component of the field in-
+duces ℓ = 4, ℓ = 2, and ℓ = 0 components of the stellar
+distortion.
+We thus have the unfortunate situation that the angular
+eigenfunctions of the magnetic and hydrodynamic variables
+are not the same, meaning that the radial and angular parts
+of the response cannot generally be separated. In this work,
+we limit ourselves to dipole magnetic field configurations,
+which induce ℓ = 0 and ℓ = 2 components to the stellar
+structure perturbations. We are not interested in the ℓ = 0
+component of the stellar response, as it is the non-radial
+magnetic distortions that draw our focus. Hence, from here
+forward, we consider a dipole (ℓ = 1) magnetic field and the
+quadrupolar (ℓ = 2) component of the stellar response.
+Letting the pressure response be
+δP = a0δp0(r)Y00(θ) + a2δp2(r)Y20(θ)
+(22)
+and setting the angular dependence equal to sin2 θ requires
+a2 = −
+�
+16π/45. The radial component of the response is
+then a0δp0(r) = (4√π/3)δp2(r). Dropping the (r) depen-
+dence and subscripts of Ψℓ and δp2 for simplicity, equations
+17 and 18 can be written
+� ∂2
+∂r2 Ψ − ℓ(ℓ + 1)
+r2
+Ψ + λ2
+R2 Ψ
+�∂Ψ
+∂r
+= −r2 ∂δp
+∂r − r2ρ ∂
+∂r δΦ − r2gδρ ,
+(23)
+� ∂2
+∂r2 Ψ − ℓ(ℓ + 1)
+r2
+Ψ + λ2
+R2 Ψ
+�
+Ψ = −r2δp − r2ρδΦ ,
+(24)
+and it is now understood that these equations are only valid
+for ℓ = 1 and δp, δΦ etc. refer to the quadrupolar part of
+the stellar response. Equation 24 can be substituted into
+equation 23 to obtain
+�
+δp + ρδΦ
+�∂Ψ
+∂r =
+�∂δp
+∂r + ρ ∂
+∂r δΦ + gδρ
+�
+Ψ .
+(25)
+However, we have divided by Ψ to obtain this equation, so
+we must be wary of solutions that cross Ψ = 0.
+The gravitational potential perturbation is given by
+Poisson’s equation,
+∇2δΦ = 4πGδρ .
+(26)
+This can be written in terms of two first-order equations,
+∂
+∂r δΦ − δΦ′ = 0 ,
+(27)
+∂
+∂r δΦ′ + 2
+r δΦ′ − (ℓ + 1)(ℓ + 2)
+r2
+δΦ − 4πGδρ = 0 .
+(28)
+2.3
+Thermal Equilibrium
+We next turn to the equations of thermal equilibrium. En-
+ergy conservation requires
+ρT ds
+dt = ρϵ − ∇ · F ,
+(29)
+where T is temperature, s is specific entropy, ϵ is the specific
+energy generation rate, and F is the energy flux. In thermal
+equilibrium, the entropy is constant, and the background
+state only has a radial flux 4πr2F = L, which entails that
+dL/dr = 4πρr2ϵ. Additionally, the energy flux is
+F = −χ∇T
+(30)
+where
+χ = 4acT 3
+3κρ
+.
+(31)
+is the thermal diffusivity. This means that the background
+temperature gradient is dT/dr = −L/(4πr2χ).
+For a perturbation in thermal equilibrium, the Eulerian
+perturbation of equation 29 is
+∇ · δF − δρϵ − ρδϵ = 0 .
+(32)
+The Eulerian perturbation of equation 30 is
+δF = −δχdT
+dr ˆr − χ∇δT .
+(33)
+Taking the horizontal divergence of the horizontal part of
+this equation yields
+∇⊥ · δF⊥ = −χ∇2
+⊥δT ,
+(34)
+© 0000 RAS, MNRAS 000, 000–000
+
+0.5
+Flux Perturbation
+-0.5Magnetic Structure
+5
+where ∇2
+⊥ = −(ℓ+1)(ℓ+2)/r2 since we are considering per-
+turbations with spherical harmonics of degree ℓ+1. Plugging
+this into equation 32 and using 4πr2δFr = δL, we obtain
+∂
+∂r δL + 4π(ℓ + 1)(ℓ + 2)χδT − 4πρr2
+�δρ
+ρ ϵ + δϵ
+�
+= 0 . (35)
+This can be rewritten
+r ∂
+∂r
+δL
+Ls + 4π(ℓ + 1)(ℓ + 2)χTr
+Ls
+δT
+T − r
+Ls
+dL
+dr
+�δρ
+ρ + δϵ
+ϵ
+�
+= 0 ,
+(36)
+where Ls is the star’s surface luminosity. The energy gen-
+eration perturbation can be expanded as δϵ/ϵ = ϵT δT/T +
+ϵρδρ/ρ, where ϵT = (∂ ln ϵ/∂ ln T)ρ and ϵρ = (∂ ln ϵ/∂ ln ρ)T ,
+yielding
+r ∂
+∂r
+δL
+Ls + 4π(ℓ + 1)(ℓ + 2)χTr
+Ls
+δT
+T
+− r
+Ls
+dL
+dr
+�
+(1 + ϵρ)δρ
+ρ + ϵT δT
+T
+�
+= 0 .
+(37)
+The radial component of equation 33 can be written
+δFr
+F
+=
+�
+3δT
+T − δκ
+κ − δρ
+ρ
+�
+− χ
+F
+∂δT
+∂r .
+(38)
+Using
+δκ/κ
+=
+κT δT/T
++ κρδρ/ρ,
+where
+κT
+=
+(∂ ln κ/∂ ln T)ρ and κρ = (∂ ln κ/∂ ln ρ)T , this can be writ-
+ten as
+r ∂
+∂r
+�δT
+T
+�
++
+L
+4πrχT
+�δL
+L − (4 − κT )∂T
+T + (1 + κρ)δρ
+ρ
+�
+= 0.
+(39)
+Finally, we require an equation of state to close the
+system of equations. This is given by
+δP
+P − χT δT
+T − χρ δρ
+ρ = 0 ,
+(40)
+where χT = (∂ ln P/∂ ln T)ρ and χρ = (∂ ln P/∂ ln ρ)T and
+are determined by the equation of state. This is valid if the
+composition is uniform, otherwise there will be an additional
+term in equation 40, which we discuss in Section 4.
+2.4
+Equations and Boundary Conditions
+Putting everything together, we have a system of equations
+that can be solved for six variables: Ψ and its radial deriva-
+tive Ψ′ = ∂Ψ/∂r, and the Eulerian perturbations δP, δρ,
+δT, and δL. The equations can be written
+∂
+∂r Ψ − Ψ′ = 0 ,
+(41)
+r2Ψ ∂
+∂r Ψ′+
+�λ2r2
+R2 −ℓ(ℓ+1)
+�
+Ψ2+r4P δP
+P +r4ρδΦ = 0 , (42)
+rΨ ∂
+∂r
+δP
+P + ρgr
+P ΨδP
+P + rρ
+P Ψ ∂
+∂r δΦ + ρgr
+P Ψδρ
+ρ
+− rΨ′
+�δP
+P + ρδΦ
+P
+�
+= 0 ,
+(43)
+r ∂
+∂r
+�δT
+T
+�
++
+L
+4πrχT
+�δL
+L − (4 − κT )δT
+T + (1 + κρ)δρ
+ρ
+�
+= 0 ,
+(44)
+r ∂
+∂r
+δL
+Ls + 4π(ℓ + 1)(ℓ + 2)χTr
+Ls
+δT
+T
+− r
+Ls
+dL
+dr
+�
+(1 + ϵρ)δρ
+ρ + ϵT δT
+T
+�
+= 0 ,
+(45)
+along with Poisson’s equation (equations 27 and 28) and the
+equation of state (equation 40). This system contains seven
+first-order differential equations, two of which are non-linear.
+They depend on the field geometry ℓ (assumed to be ℓ = 1
+here), and the magnetic helicity λ.
+This system of equations requires seven boundary con-
+ditions in order to be solved. At the inner boundary, we
+require
+Ψ = 0
+(46)
+δP
+P
+= 0 ,
+(47)
+and
+δΦ = 0 ,
+(48)
+These ensure that δT/T, δρ/ρ, and δL/Ls are also zero at
+the center of the star.
+At the surface, we require the blackbody radiation con-
+dition
+∆L
+Ls − 4∆T
+T
+− 2ξr
+r = 0 ,
+(49)
+where
+∆
+indicates
+a
+Lagrangian
+perturbation.
+Using
+dL/dr = 0 at the surface, and the surface pressure boundary
+condition ∆P = 0, which becomes (P/ρgr)δP/P = ξr/r ≪
+δP/P, we can drop the last term, and this can be written as
+δL
+Ls − 4δT
+T + 4∇δP
+P
+= 0 ,
+(50)
+where ∇ = d ln T/d ln P. At the outer boundary we require
+a decaying potential perturbation:
+δΦ′ = −ℓ + 2
+r
+Φ .
+(51)
+Additionally, the amplitude of the response can be chosen
+with a normalization condition at the surface, e.g.,
+Ψ =
+√
+GM 2 .
+(52)
+Finally, we require another boundary condition at the
+surface that determines the amplitude of another variable
+(e.g., δT/T or δL/Ls), relative to Ψ. This boundary condi-
+tion will determine the amplitude of the surface flux pertur-
+bation and can be considered to be a measure of the strength
+of the magnetic forces within the star. It is similar to speci-
+fying the strength of the magnetic forces in barotropic stars
+with a β parameter as described in Duez & Mathis (2010)
+and in Section 2.5. In practice, we set the luminosity per-
+turbation at the outer boundary in order to determine an
+effective value of β. Setting δL = 0 at the outer boundary
+would be equivalent to setting β = 0.
+We pause to note a few important points. First, the dis-
+placement vector ξ does not appear anywhere in our system
+of equations. Lagrangian perturbations cannot be calculated
+from this system of equations, except at the surface where
+ξr/r = (P/ρgr)δP/P. Physically this arises from the fact
+that in a thermally relaxed system of uniform composition,
+there are an infinite number of combinations of radial and
+© 0000 RAS, MNRAS 000, 000–000
+
+6
+Fuller & Mathis
+horizontal displacements ξr and ξ⊥ that could give rise to
+a given density perturbation δρ/ρ. This is discussed further
+in Section 4.
+A second important point is that we have not imposed a
+surface boundary condition in which the poloidal or toroidal
+component of the magnetic field goes to zero. This is quite
+different from the fields studied in Broderick & Narayan
+(2008) and Duez & Mathis (2010). A non-zero toroidal field
+requires a current to flow at the surface of the star, which is
+often assumed to be zero due to the vanishing density and
+temperature. Real stars, however, do not have zero tem-
+perature or density in their photospheres or coronae, which
+can support currents and toroidal fields (Kochukhov et al.
+2011; Shulyak et al. 2007, 2010). Therefore, we do not im-
+pose Ψ = 0 at the surface. A consequence of relaxing this
+condition is that λ is no longer an eigenvalue, and the system
+of equations can now be solved for any value of λ.
+Alternatively, one could argue that the radial compo-
+nent of the electric current (Equation 16) should vanish at
+the surface of the star. This would require Br = 0 and hence
+Ψ = 0 as discussed in Section 2.1, and imposed by Broderick
+& Narayan (2008) and Duez & Mathis (2010). This eighth
+boundary condition would transform our system of seven
+differential equations into an eigenvalue problem that could
+only be solved for certain combinations of λ and the surface
+flux perturbation. We discuss this further in Section 3 and
+4.
+2.5
+Convective Zones
+In convective zones, the radiative diffusion equation no
+longer applies, and equations 44 and 45 are not valid. In-
+stead, we assume that the perturbation to the entropy is
+nearly zero, as convective heat flux will quickly smooth out
+any entropy gradients. We therefore have
+d ln T
+d ln P = ∇ad = Γ3 − 1
+Γ1
+.
+(53)
+Perturbing this yields
+δT
+T − Γ3 − 1
+Γ1
+δP
+P
+= 0 .
+(54)
+and
+δP
+P − Γ1 δρ
+ρ = 0 .
+(55)
+Since the perturbations are barotropic, the system of
+equations 41-43 simplifies, as discussed above. In this case,
+the system of equations reduces to that of Duez & Mathis
+(2010):
+∂
+∂r Ψ − Ψ′ = 0 ,
+(56)
+∂
+∂r Ψ′ +
+� λ2
+R2 − ℓ(ℓ + 1)
+r2
+�
+Ψ + βr2ρ = 0 .
+(57)
+Here, β is a constant that determines the magnitude of the
+magnetic force. Comparison with equation 14 shows that the
+pressure perturbation is
+δP
+P + ρδΦ
+P
+= βρΨ
+P
+.
+(58)
+Equations 56 and 57 combine into a linear wave equation:
+∂2
+∂r2 Ψ +
+� λ2
+R2 − ℓ(ℓ + 1)
+r2
+�
+Ψ + βr2ρ = 0 .
+(59)
+2.6
+Linking Convective and Radiative Zones
+In this work we only consider stars with convective cores
+and radiative envelopes. To solve for the magnetic field in
+the full star, we choose a value of λ and a surface flux per-
+turbation δL/L, which effectively sets the magnetic forces
+and the value of β within the convective zone. Within the
+convective zone, we replace equation 44 with equation 54,
+and we replace equation 45 with ∂δL/∂r = 0. However, the
+value of δL is not defined in the convective zone, only within
+the radiative zone above it. In our solutions, we verify that
+equation 58 is approximately satisfied within the convective
+region. We then label our solutions by the corresponding
+value of β.
+2.7
+Solving the Equations
+We solve the system of equations above in a stellar model
+generated with the MESA stellar evolution code (Paxton
+et al. 2011). We choose a M = 3 M⊙ star at the start of the
+main sequence, with a radius of R = 2.1 R⊙, a surface tem-
+perature of Teff = 11, 800 K, and a convective core bound-
+ary at r/R = 0.13. This model resembles typical magnetic
+Ap/Bp stars that are observed to harbor strong magnetic
+fields. Our model has nearly uniform stellar composition so
+that the equation of state (equation 40) is a good approxi-
+mation.
+We use a relaxation technique from Numerical Recipes
+(Press et al. 2007) to solve the system of equations in Sec-
+tion 2.4. We solve the equations on the same grid as the
+underlying MESA model. A good initial guess is often re-
+quired in order reliably to converge to a solution. Spurious
+solutions (involving sudden jumps in the derivatives of δP
+and Ψ) are often found, so caution is required. There may be
+other physical solutions that exist that we do not examine
+in this work.
+3
+SOLUTIONS
+In our models, both λ and β are free parameters. Physi-
+cally, λ represents the magnetic helicity which is determined
+by the dynamo process that created the field, and which is
+roughly conserved during subsequent turbulent relaxation
+(Braithwaite 2008; Duez & Mathis 2010). The lowest en-
+ergy stable field configurations have λ ∼ 1, so λ values in
+the range of 1-10 are reasonable expectations for real stars,
+though larger values are possible. The value of β determines
+the relative strength of magnetic forces as described in the
+previous section.
+Figure 2 and 3 show the magnetic field configuration
+for a model with λ2 = β = 10. The poloidal field is largest
+at the center of the star, where its field strength is roughly
+four times larger than the surface value. The toroidal field
+is largest at r/R ≈ 0.7. We shall see below that β = 10 is
+small such that the magnetic field is similar to a force-free
+field. For this value of λ, there is a null point (where Bθ = 0
+© 0000 RAS, MNRAS 000, 000–000
+
+Magnetic Structure
+7
+Figure 2. Meridional slices of a star, with color shading indicating the strength of the toroidal magnetic field (left) and poloidal
+magnetic field (right) normalized to the maximum magnetic field. Orange lines show magnetic field lines of the poloidal field. This model
+has magnetic helicity λ2 = 10 and magnetic force β = 10.
+Radius
+0
+2
+4
+Magnetic Field
+λ 2 = 10
+β = 10
+Br
+Bθ
+Bφ
+0
+10
+20
+Magnetic Field
+λ 2 = 17
+β = 10
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Radius
+0
+10
+20
+30
+Magnetic Field
+λ 2 = 10
+β = 110
+Figure 3. Radial profiles of the r, θ, and φ-components of the
+magnetic field, scaled to the radial field at the surface, for models
+with β = 10. Panels are labeled by their values of λ2 and β.
+Note that the field is much more centrally concentrated for higher
+values of λ or β.
+and the field lines converge to closed loops at the equator)
+at r/R ≃ 0.85. Both the poloidal and toroidal fields extend
+above the surface of the star, where the field is force-free but
+is not current-free.
+Figure 4, 5, and 6 show the magnetic potential Ψ, pres-
+sure perturbation δP/P, and luminosity perturbation δL/L
+as a function of radius. In Figure 4, each curve has a dif-
+ferent value of λ. Higher values of λ cause more oscillatory
+variation of Ψ, as can be seen in equation 59 where the
+radial wavenumber of Ψ is roughly
+�
+λ2/R2 − ℓ(ℓ + 1)/r2.
+Higher values of λ push the null point and toroidal field
+maximum deeper into the star, and also cause the central
+field strengths to become larger relative to the surface field
+strength, as shown in Figure 3. In this stellar model, a value
+of λ ≃ 20 is the first value of λ for which Ψ = 0 at the sur-
+face. From equation 42 we see that Ψ = 0 requires δP = 0,
+so the Eulerian pressure perturbation is always zero where
+the radial component of the field is zero.
+For larger values of λ or β, the values of Ψ and δP
+approach zero somewhere within the model. When this hap-
+pens, the numerical solutions exhibit strange behavior. The
+values of Ψ′ and ∂δP/∂r sometimes exhibit discontinuous
+jumps at the zero-crossings of Ψ. However, the radial mag-
+netic field, pressure perturbation, and temperature pertur-
+bations are all continuous across these zero-crossings (only
+their derivatives are discontinuous). It is unclear if these so-
+lutions are physical or numerical artifacts. Physically, these
+solutions would exhibit a discontinuity in the θ-component
+of the magnetic field, an associated current sheet, and a
+discontinuity in both the magnetic force and the pressure
+force. Because the physicality of these solutions is unclear
+and they also sometimes cause numerical convergence prob-
+lems, we will not investigate them further in this work.
+More highly oscillatory solutions also represent higher en-
+ergy states (Broderick & Narayan 2008) and may be less
+© 0000 RAS, MNRAS 000, 000–000
+
+Toroidal Field
+Poloidal Field
+1.0
+1.0
+0.8
+0.5
+0.6
+R
+0.0
+Z
+0.4 B
+-0.5
+0.2
+-1.0
+0
+0
+x/R
+x/R8
+Fuller & Mathis
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Ψ
+10−1
+100
+101
+102
+103
+δP/P
+λ 2 =2.0
+λ 2 =5.0
+λ 2 =10.0
+λ 2 =14.0
+λ 2 =17.0
+λ 2 =19.6
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Radius
+−20
+−15
+−10
+−5
+0
+5
+δL
+Figure 4. Profiles of the magnetic potential Ψ, relative pressure
+perturbation δP/P, and luminosity perturbation δL (in units of
+Lsurf) as a function of radius for a model with β = 10 and varying
+values of the helicity λ. All quantities are normalized so that Ψ =
+1 at its maximum. Stronger toroidal fields (larger λ) create more
+oscillatory magnetic fields, but the associated surface luminosity
+perturbation varies only slightly. The large values of δP/P near
+the surface are discussed in Section 3.5.
+likely to exist in stars that have relaxed to a minimum en-
+ergy state.
+In Figure 4, the relatively small value of β = 10 means
+that the pressure and density terms in equation 42 are neg-
+ligible relative to the magnetic terms, and the field is nearly
+force-free. The magnetic solutions are thus similar to the
+force-free solutions of Broderick & Narayan (2008). In this
+limit, the perturbed pressure, temperature, etc. have a value
+that is proportional to β, with a radial dependence that is
+determined only by λ and the structure of the star. This
+can be seen from equation 58, such that the value of δP,
+δT, and δL are roughly proportional to β at the radiative
+convective interface, and hence within the bulk of the ra-
+diative zone. It is demonstrated in Figure 5 and 6, where
+the pressure and luminosity fluctuations have similar pro-
+files and increase linearly with β, as long as β ≲ 100. Hence,
+a wide range in surface temperature and flux variations are
+possible for a given surface field, depending on the strength
+of the magnetic forces, parameterized by β in these models.
+For larger values of β, however, the pressure/density
+terms in equation 42 become comparable to the magnetic
+terms. Physically this means that gas pressure forces begin
+competing with magnetic forces, altering the profile of the
+magnetic field. Large values of β have a similar effect to
+larger values of λ, causing more oscillatory behavior of the
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Ψ
+10−1
+100
+101
+102
+103
+δP/P
+β =4.2
+β =23
+β =61
+β =110
+β =160
+β =200
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Radius
+−400
+−200
+0
+200
+δL
+Figure 5. Same as Figure 4, but for a model with λ2 = 10 and
+varying values of β. Larger magnetic forces (higher values of β)
+create larger surface luminosity perturbations and more oscilla-
+tory magnetic fields.
+magnetic potential Ψ. The surface pressure and luminosity
+perturbations reach a maximum when β ∼ 200, and decrease
+at larger values. This is because Ψ (and hence δP) become
+smaller near the surface at large values of β as gas pressure
+forces start backreacting on the magnetic field profile. The
+magnitude of β needed to have a large influence on the field
+profile can be seen from equation 59: β must be large enough
+for the last term to be comparable to the second term. Deep
+within the star, this requires β ∼ ℓ(ℓ+1)Ψ/(ρr4), which typ-
+ically has a value of a couple hundred for our stellar model
+and normalization.
+From Figure 4-6, we see that δP/P typically approaches
+very large values near the surface of the star, because P
+reaches very small values. However, the value of δP ap-
+proaches very small values δP ≃ ρgξr near the surface, such
+that the Lagrangian pressure perturbation ∆P = δP − ρgξr
+smoothly approaches zero at the surface. The value of δP/P
+thus approaches δP/P ≃ ξr/H at the star’s surface, which
+becomes large as the pressure scale height H becomes small.
+Although δP/P peaks near the surface, the value of δP
+peaks at radii of r/R ≃ 0.2, as can be seen in Figure 7.
+The values of δρ and δΦ show similar behavior.
+In contrast, the value of δT increases within the con-
+vective zone and then maintains a roughly constant profile
+throughout the star. The derivative of δT has a discontinuity
+at the convective interface due to the change in structure and
+energy transport mechanism. Within the convective core, δT
+is directly proportional to δP which is proportional to Ψ
+© 0000 RAS, MNRAS 000, 000–000
+
+Magnetic Structure
+9
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Ψ
+10−1
+100
+101
+102
+103
+δP/P
+β =8.7
+β =79
+β =140
+β =220
+β =270
+β =290
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Radius
+−600
+−400
+−200
+0
+200
+400
+δL
+Figure 6. Same as Figure 5, but for a model with λ2 = 2. Al-
+though the magnetic structure is somewhat different, the surface
+luminosity perturbations are similar to the case in Figure 5 with
+stronger toroidal fields.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Radius
+−20
+−10
+0
+10
+20
+30
+Ψ×30
+δP
+δT ×20
+δρ
+δL
+δΦ×3
+Figure 7. The magnetic potential Ψ (units of
+√
+GM2), pressure
+perturbation δP (units of GM2/R4), temperature perturbation
+δT (units of Tcen), density perturbation δρ (units of M/R3), lumi-
+nosity perturbation δL (units of Lsurf), and gravitational poten-
+tial perturbation δΦ (units of GM/R) for a model with λ2 = 10,
+β = 10. The kinks at r = 0.13 occur at the boundary of the
+convective core.
+(equations 54 and 58), but in the radiative zone δT is de-
+termined by the thermal equilibrium conditions (equations
+44 and 45). This causes oscillatory variations in δT in the
+outer layers of the star, due to variations in the thermal dif-
+fusivity χ caused by opacity variations in partial ionization
+zones near the surface.
+Nevertheless, the luminosity perturbation δL always
+changes smoothly and gradually throughout the star. Phys-
+ically this occurs because sudden changes in δL would be
+smoothed out by radiative diffusion. Mathematically this
+can be seen from equation 45, because the values of χTr/L
+and d ln L/d ln r become very small near the surface of the
+star, preventing sudden variation in δL, despite large values
+of δP/P and δT/T. Interestingly, in all of our models, the
+luminosity perturbation switches sign at r/R ≃ 0.23 within
+the radiative region above the convective core.
+3.1
+Surface Flux Perturbation
+All of our models have negative surface luminosity pertur-
+bations δL2 as shown in the figures. However, the quadrupo-
+lar component of the physical response (see equation 22) is
+δL = δL2(1/3−cos2 θ). Hence, a negative value of δL2 trans-
+lates to a positive flux perturbation at the magnetic pole
+and a negative flux perturbation at the magnetic equator,
+as shown in Figure 1. This is consistent with the heuristic
+idea that strong magnetic pressure at the star’s pole causes
+the gas pressure and density to be smaller, allowing us to see
+deeper into the star such that magnetic spots are brighter
+(Cantiello & Braithwaite 2011). However, it is also possible
+for our models to produce a negative flux perturbation at
+the magnetic pole if we consider negative values of β, so in
+principle it is possible for the magnetic pole to be either hot
+or cool. Below we argue that a hot magnetic pole is more
+likely.
+The value of the surface flux perturbation in our models
+is δL/L ∼ βΨ2
+max, where Ψmax is the maximum value of Ψ
+reached within the model. Since we have normalized Ψmax
+to units of
+√
+GM 2, this implies
+δL
+L ∼ β
+4π
+B2
+maxr4
+max
+GM 2
+,
+(60)
+where Bmax and rmax are the magnetic field and radius
+where Ψ peaks. In our models, this roughly translates to
+δL
+L ∼ 10−11β
+�Bsurf
+1kG
+�2� R
+R⊙
+�4� M
+M⊙
+�−2
+,
+(61)
+where Bsurf is the magnetic field at the star’s surface. Clearly
+this is too small to be detected in main sequence stars un-
+less extremely large values of β are assumed. Equation 61
+is consistent with a naive estimate from the von Zeipel the-
+orem applied to the star’s interior. The smoothly varying
+magnetic fields of our models produce magnetic forces of
+order fmag ∼ βB2/(ρr). Using the average stellar density
+ρ ∼ M/R3 and gravitational force g ∼ GM/R2 yields the
+von Zeipel estimate of δF/F ∼ fmag/g ∼ βB2R4/GM 2.
+3.2
+Most likely field configurations
+As mentioned in Section 2.1, the radial current jr may be
+expected to be close to zero near the surface of the star
+so that current does not flow into the star’s low-density
+© 0000 RAS, MNRAS 000, 000–000
+
+10
+Fuller & Mathis
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Ψ
+10−1
+101
+103
+δP/P
+λ 2 =10.0
+λ 2 =9.0
+λ 2 =8.0
+λ 2 =7.0
+λ 2 =5.0
+λ 2 =2.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Radius
+−600
+−400
+−200
+0
+200
+400
+δL
+Figure 8. Magnetic structures for models whose poloidal com-
+ponent has a potential profile (Ψ ∝ r−ℓ) at the outer boundary,
+for various magnetic helicities λ. This outer boundary condition
+effectively sets the strength of magnetic forces, β. Configurations
+similar to these may be more likely to exist in real stars.
+corona. From equation 16, the only way this can happen
+is when λ2 = 0 or Ψ = 0 at the surface of the star. If
+there are near-surface toroidal fields, Ψ (and hence Br) must
+be zero to have a non-zero current flowing out of the star.
+Hence there is a critical value β0 such that Ψ = 0 at the
+star’s surface. Figure 5 indicates this occurs at β0 ≃200 and
+δL/L ∼ −400 for λ2 = 10 in our stellar model, or β0 ≃ 300
+and δL/L ∼ −500 for λ2 = 2 (Figure 6). Hence, those so-
+lutions are arguably the most physically probable amongst
+the possibilities shown here. Fireffig:magstrucvis shows the
+predicted surface flux variations for β = β0. Even though
+the large values of β increase the surface flux perturbation
+above the naive estimate discussed above, it is too small to
+be detected with current instruments.
+Another possibility is that the value of λ2 is not con-
+stant within the star due to dissipative effects near the sur-
+face. In that case, one may expect the value of λ to de-
+crease near the star’s surface, allowing the radial current
+to vanish and still have a large value of Ψ and hence a
+non-zero radial magnetic field. If the electric currents de-
+crease to zero near or above the surface, the field must ap-
+proach a potential configuration. Potential force-free fields
+have ∂Ψ/∂r2 = ℓ(ℓ + 1)Ψ/r2, and an outwardly decreasing
+field has Ψ ∝ r−ℓ and hence B ∝ r−(ℓ+2), i.e., a dipole field
+for our assumed value of ℓ = 1. To model this case, we set
+the outer boundary condition to ∂Ψ/∂r = −ℓΨ/r. The fixed
+103
+104
+105
+106
+Surface Poloidal Field Strength (G)
+10−8
+10−7
+10−6
+10−5
+10−4
+10−3
+Surface Luminosity Perturbation
+λ 2 = 10, β = β0
+λ 2 = 2, β = β0
+λ 2 = 9, β = βpot
+λ 2 = 2, β = βpot
+Figure 9. The surface luminosity perturbation as a function of
+surface magnetic field strength for models with β = β0, such that
+the radial component of the magnetic field and electric current
+vanish at the surface. We also plot luminosity perturbations for
+β = βpot such that the poloidal field has a potential profile at the
+surface. In either case, very strong magnetic fields are required for
+detectable luminosity perturbations in main sequence stars. Ob-
+served photometric variations of magnetic stars likely arise from
+variations in the emergent spectrum rather than variations in the
+bolometric flux.
+slope at the outer boundary effectively sets the value of β,
+which we refer to as βpot.
+Figure 8 shows the results of this calculation for several
+values of λ2. The required values of βpot are typically sim-
+ilar to (but smaller than) β0, i.e., values on the order of a
+hundred. For λ2 ≃ 10, a nearly force-free field satisfies the
+potential outer boundary condition, such that βpot ≃ 0. For
+larger values of λ, the required βpot is negative. However,
+we find those solutions almost always have a zero-crossing
+somewhere in the star, and cause numerical problems, so we
+do not investigate them further in this work. We note that
+they would likely entail surface flux perturbations of the
+opposite sign, i.e., a cool magnetic pole and hot magnetic
+equator. Figure 9 shows the surface luminosity perturba-
+tions for β = βpot, which are a similar magnitude to those
+with β = β0, and not detectable for observed magnetic field
+strengths.
+3.3
+Shape of Distorted Star
+The sign of the pressure/density perturbations near the sur-
+face of the star determine wither it becomes oblate (smaller
+photospheric radius at magnetic pole) or prolate (larger
+radius at magnetic pole). As discussed above, we believe
+negative Eulerian pressure perturbations at the magnetic
+pole are most likely, which means the surface displacement
+ξr = δP/(ρg) is also negative at the magnetic pole. Hence,
+magnetically distorted stars are likely to be oblate. Heuris-
+tically, this is consistent with the idea that high magnetic
+pressure at the star’s pole (or magnetic tension near the
+equator) squeezes the star into a flattened shape.
+© 0000 RAS, MNRAS 000, 000–000
+
+Magnetic Structure
+11
+The star’s ellipticity is
+ε = ξr,surf
+R
+= δP
+P
+H
+R
+∼ β × 10−10
+�Bsurf
+1kG
+�2� R
+R⊙
+�4� M
+M⊙
+�−2
+.
+(62)
+Similar to the flux perturbations, this is too small to detect.
+The quadrupole moment of the star is
+Q =
+�
+δρr4Y ∗
+20dΩdr
+MR2
+∼ β × 10−12
+�Bsurf
+1kG
+�2� R
+R⊙
+�4� M
+M⊙
+�−2
+.
+(63)
+The quadrupole moment of the star is even tinier than other
+perturbations because the density perturbation is largest
+near r ∼ 0.2, providing a small lever arm for the quadrupole
+moment.
+3.4
+Ohmic Heating and Poynting Flux
+Our models ignore non-ideal effects such as Ohmic heating
+that will inevitably cause the field to decay. As long as these
+effects are small, our approximations are suitable. We first
+investigate the effect of Ohmic heating in our models. The
+heating rate per unit volume is
+ρϵOhm = 4πηj2
+(64)
+where the current density j is given in equation 16. Hence
+the heating rate is
+ρϵOhm = η
+λ2
+4πR2
+�
+B2
+r + B2
+θ
+�
++
+η
+r2 sin2 θ (∆∗Ψ)2 .
+(65)
+Using equations 3, 5, and manipulating equation 18, this can
+be expressed
+ρϵOhm = η sin2 θ
+r2
+� −4
+r2R2 Ψ2 + 1
+R2 Ψ′2
++
+�r2(δP + ρδΦ)
+Ψ
++ λ2
+R2 Ψ
+�2�
+.
+(66)
+The angular dependence is sin2 θ, and we have removed a
+spherically symmetric term since we are only interested in
+the non-spherical component.
+Equation 66 can be compared to other sources of heat
+generation and/or heat diffusion in equation 45. We find that
+the Ohmic heating term is roughly three orders of magni-
+tude smaller than the heat diffusion term (second term in
+equation 45) for all the models shown in this paper. Hence,
+Ohmic heating is irrelevant for these models.
+Likely a more important effect is that the Ohmic diffu-
+sion time tOhm = r2/η drops sharply near the surface of the
+star, falling to ∼ 1 Gyr near the surface of our model. The
+diffusion time scale is even shorter in the atmosphere of the
+star and could be shorter than the star’s lifetime. Conse-
+quently, the fields will dissipate or change their morphology
+within the star’s atmosphere until they approach a current-
+free (and force-free configuration). This will bend the field
+lines and hence create magnetic forces within the star until
+it approaches a new (quasi)-equilibrium.
+Another way of seeing this is by examining the Poynting
+flux (see Duez et al. 2010a):
+Fpoy = ∇ ·
+�
+ηFmag
+�
+(67)
+where Fmag = (∇ × B) × B/4π is the Lorentz force. The
+Poynting flux represents the decrease of electromagnetic en-
+ergy per unit volume, and it has the same order of magnitude
+as the Ohmic heating rate. As the fields dissipate, their en-
+ergy density changes until the Poynting flux is nearly zero,
+which happens on Ohmic diffusion time scales. Landstreet
+(1987) discusses the importance of magnetic forces arising
+due to Ohmic dissipation, finding they are likely negligible
+for main sequence stars. However, over long time scales, the
+morphology of the magnetic field will be altered away from
+the solutions we have computed, which could also affect the
+emerging luminosity perturbations.
+3.5
+Linearity and near-surface effects
+Since the value of δP/P can become very large near the sur-
+face of the star (Figure 5-8), non-linear effects may also start
+to be important in the near-surface layers. In our models, the
+δP/P eigenfunction is 1-2 orders of magnitude larger than
+the surface luminosity perturbation δL/L, which is plotted
+as a function of surface field strength in Figure 9. Hence,
+δP/P remains very small except for unphysically large sur-
+face field strengths B ≳ 105 G.
+However, we placed the outer boundary at a radius of
+r/R ≃ 0.99 in our calculations. This allowed us to avoid
+uncertainties associated with the response of near-surface
+convective layers above our outer boundary. The value of
+δP/P likely continues to increase towards the surface (be-
+cause P drops sharply), so it is possible that non-linear ef-
+fects start to become important near the surface. It is un-
+likely that this affects the luminosity perturbation, which
+changes smoothly with radius and cannot be greatly affected
+in the near-surface layers. Hence, the magnetic field profiles
+and luminosity perturbations that we calculate are probably
+robust, but the near-surface pressure and temperature pro-
+files could be affected by these surface effects. In principle,
+this could affect the spectrum of the star, which is sensitive
+the atmospheric temperature profile.
+4
+DISCUSSION
+4.1
+Stability of Equilibrium
+The magnetic field configurations we have computed are
+in hydrostatic and radiative equilibrium, but we have not
+investigated whether these equilibria are stable or unsta-
+ble. Braithwaite (2009) (see also Akg¨un et al. 2013; Becerra
+et al. 2022b) showed that stable magnetic equilibria require
+Etor ≳ 0.25Epol, where Etor and Epol are the toroidal and
+poloidal magnetic field energies. All of our models satisfy
+this criterion (they typically have Etor/Epol ∼ 1) except for
+the λ2 = 2 models. They also fall below the upper limit for
+stability, Emag ≲ (1/10)GM 2/R for surface field strengths
+less than ∼ 1 MG. Nonetheless, it is possible that some of
+our models are unstable, which should be examined in fu-
+ture work using 3D numerical simulations (Duez et al. 2010b;
+Kaufman et al. 2022).
+© 0000 RAS, MNRAS 000, 000–000
+
+12
+Fuller & Mathis
+4.2
+More Realistic Field Configurations
+A limitation of our work is the assumption of a field with
+purely dipole structure, whereas real fields likely have a
+more complicated angular structure that changes with ra-
+dius. As discussed above, real fields likely have vanishing
+current above the photosphere which (according to our solu-
+tions, equation 16) require vanishing Br or vanishing λ. The
+first conflicts with observations of real stars (Landstreet &
+Mathys 2000; Oksala et al. 2018; Shultz et al. 2019) while the
+second implies purely poloidal fields which are well known
+to be unstable (Markey & Tayler 1973). It is likely that a
+real star has a more complicated angular and radial field
+dependence, such that the electric currents vanish in the
+near-vacuum outside the star. In these configurations, the
+toroidal magnetic field vanishes on magnetic field lines that
+penetrate the surface of the star (Lyutikov 2010).
+These sorts of configurations have been computed near
+the surface of a star in Raadu (1971); Milsom & Wright
+(1976), or in the interior for parameterized field configu-
+rations (Lyutikov 2010; Akg¨un et al. 2013; Becerra et al.
+2022b). However, these configurations are not in thermal
+equilibrium and therefore not stable over thermal time
+scales. Computing such fields in the bulk of a star and ac-
+counting for thermal and hydrostatic equilibrium will re-
+quire the solutions of partial differential equations, which is
+beyond the scope of this work. We suspect that such con-
+figurations (which appear qualitatively similar to those we
+compute) will alter our results by a factor of order unity,
+but will not greatly change any of our conclusions.
+4.3
+Estimating the Perturbed Surface Flux
+Our solutions which map onto Br = 0 or Br ∝ r−(ℓ+2)
+may resemble more realistic magnetic field configurations.
+We find that large values of β ∼200 are required for typical
+toroidal fluxes of λ2 ∼ 1 − 10. This entails internal temper-
+ature, pressure, and flux perturbations that are ∼200 times
+larger than a naive estimate of ∼B2/(GM 2/R4). Nonethe-
+less, even for the strongest observed fields of B ∼ 10 kG in
+main sequence stars, the bolometric luminosity variation is
+δL/L ≲ 10−6 (Figure 9) and is not detectable even with
+high-quality space-based photometry.
+Applying von Zeipel’s law near the surface of the star,
+one might expect magnetic fields to produce flux perturba-
+tions of order
+δL
+L ∼ fmag
+fgrav ∼ B2
+surf
+4πρRg .
+(68)
+This translates to
+δL
+L ∼ 0.004
+�Bsurf
+1 kG
+�2�
+ρ
+10−8g/cm3
+�−1� M
+M⊙
+�−1� R
+R⊙
+�
+.
+(69)
+This is several orders of magnitude larger than our calcula-
+tions, clearly ruling out this expectation. Even though mag-
+netic forces can be comparable to gravity near the star’s
+surface, this applies only in a very thin layer near the photo-
+sphere. The deep interior (where the outgoing thermal flux is
+determined) has much higher density and is only weakly dis-
+torted, leading to a flux perturbation on the order of equa-
+tion 61, which is the von Zeipel expectation applied to the
+deep interior. The even more naive estimate
+δL
+L ∼ Pmag
+Pgas ∼ 4
+�Bsurf
+1 kG
+�2�
+Pgas
+104erg cm−3
+�−1
+(70)
+can be ruled out for the same reasons.
+It would be useful to relate the observed flux perturba-
+tion or surface magnetic field strength to a star’s internal
+magnetic field strength. This will be difficult to accomplish
+from flux perturbations until a better understanding of their
+cause is established. Our results suggest that central mag-
+netic field strengths can be anywhere from ∼3-50 larger than
+surface field strengths (see Figure 3) which is in qualita-
+tive agreement with numerical simulations by Braithwaite
+(2008) (see Figure 8 of that work), with higher central field
+strengths for higher magnetic forces or helicity. The force
+will be difficult to observationally quantify but the helicity
+could potentially be determined if the star’s surface toroidal
+field can be measured (e.g., Figure 6 in Kochukhov et al.
+2011).
+The effects of magnetic fields are very different for sys-
+tems not in thermal equilibrium. In stars with transient
+magnetic activity (e.g., spots in magnetically active stars),
+magnetic spot life times can be much shorter than the star’s
+local thermal time, depending on the depth of the spots.
+Magnetic fields can also temporarily disrupt convective en-
+ergy transport, which also occurs on a thermal time. This
+is why the Sun’s spots can appear dark: they are not in
+thermal equilibrium with underlying layers. In our work, we
+predict that magnetic poles of radiative stars can be either
+hot or cool, although we have argued they are more likely
+to be hot for realistic magnetic field configurations. This
+agrees with the sign predicted by Cantiello & Braithwaite
+(2011), who examined spots in hydrostatic equilibrium but
+not thermal equilibrium. However, thermal diffusion could
+drastically reduce the flux perturbation below their estimate
+(essentially equation 70), for spots that live longer than the
+local thermal time.
+4.4
+Limitations
+For the most part, our methods are general and are applica-
+ble to nearly any type of radiative star, such as massive stars
+or white dwarfs. However, there are a few modifications that
+need to be made depending on the circumstances.
+In this work, we did not compute the physical displace-
+ment vector ξ, which does not appear anywhere in our set
+of equations. The reason for this is that the final state of the
+system (i.e., the perturbed pressure, temperature, etc.) and
+its final energy is independent of the displacements needed
+to reach that configuration. There are infinite combinations
+of ξr and ξ⊥ that satisfy the continuity equation
+δρ + ∇ ·
+�
+ρξ
+�
+= 0 .
+(71)
+However, we assumed uniform composition in our equation
+of state (equation 40), a good approximation for young main
+sequence stars. In stars with composition differences, the
+equation of state will contain an extra χµ(δµ/µ) term, where
+µ is the mean molecular weight. If composition does not
+diffuse, we have δµ ∼ −ξrdµ/dr, and hence the perturbed
+state will depend explicitly on the displacement vector. The
+equilibrium configuration is then presumably given by the
+© 0000 RAS, MNRAS 000, 000–000
+
+Magnetic Structure
+13
+displacement which minimizes the total energy of the per-
+turbed system. This should be accounted for when consider-
+ing stars with composition gradients (e.g., evolved stars and
+white dwarfs).
+Another issue we have neglected is anisotropic conduc-
+tion induced by magnetic fields. In main sequence stars, this
+effect is only important in the surface layers where the elec-
+tron mean-free path increases and becomes comparable to
+the Larmor radius. However, it may be important in the deep
+interiors of white dwarfs where electrons conduct most of the
+heat (Potekhin 1999; Potekhin & Yakovlev 2001; Chang &
+Quataert 2010) and have fairly long mean free paths due to
+the high electron degeneracy. We hope to examine this effect
+in future work.
+We have also neglected any magnetically induced
+changes to opacity. These could be important near a star’s
+surface because magnetic fields split the energy levels of
+atomic transitions, changing the opacity from bound-bound,
+bound-free absorption, and free-free absorption (e.g., Jordan
+1992). We suspect that this will not alter our conclusions re-
+garding the perturbation to the bolometric surface flux, be-
+cause effects limited to the surface layers cannot change the
+emerging flux from below. This can be seen from equation
+45, because the second term is of order unity near the sur-
+face, and will only change the emerging flux by an amount
+∼ ∆r/r, where ∆r is the width over which near-surface ef-
+fects are important.
+What is more likely is that the star’s emergent spec-
+trum is altered by magnetic changes to opacity, or by com-
+position differences between the magnetic pole and equator.
+Even with no perturbation to the bolometric flux, a chang-
+ing spectrum could create large differences in, e.g., g-band or
+r-band fluxes as the magnetic pole rotates in and out of view.
+As an example, Caiazzo in prep. finds large changes in the
+composition and spectrum as a function of rotational phase
+in the magnetic WD ZTF J203349.8+322901.1 (“Janus”),
+even though there is no clear variation in the bolomet-
+ric flux. Similar photometric variations (typically ∼1-3% in
+amplitude) are observed in chemically peculiar magnetic A
+type stars (H¨ummerich et al. 2018). Compositional inho-
+mogeneities could naturally arise due to the perturbed gas
+pressure in the near-surface layers, which will alter atomic
+diffusion processes. This process should be studied in more
+detail.
+5
+CONCLUSIONS
+We have computed the effects of strong magnetic fields on
+the structures of radiative main sequence stars. Our focus
+is the perturbed surface temperature and radiative flux in-
+duced by the magnetic field, which can produce photomet-
+ric modulation as the star rotates. Unlike most prior work,
+we have computed structures in both hydrostatic and ther-
+mal equilibrium, which applies to stars with long-lived fossil
+fields, such as magnetic Ap stars. Our models have simple
+dipolar angular structure and include toroidal fields with
+associated magnetic helicity λ.
+We find that magnetic fields at observed field strengths
+of ∼ 1 kG produce negligible bolometric flux perturbations,
+δL/L ≲ 10−6. Even though such fields are large enough to
+produce significant perturbations to the photospheric gas
+pressure and hydrostatic force balance, the radiative flux
+is determined by deeper layers of the star where magnetic
+forces are negligible. The perturbed surface flux is compa-
+rable to the von Zeipel theorem estimate δL/L ∼ fmag/(ρg)
+only when evaluated in the deep interior. Depending on their
+helicity and magnetic force, internal magnetic fields are typ-
+ically a factor of ∼10 larger than surface magnetic fields.
+The size of the magnetic perturbation depends on the
+strength of the magnetic forces, parameterized by β, which
+is zero for a force-free field. Relatively large values of β ∼200
+are needed for significant modification of the magnetic field
+profile relative to a force-free configuration. We have argued
+that these values of β are most likely to occur in real stars
+such that the magnetic profile matches onto boundary condi-
+tions minimizing electric current near the surface. This leads
+to photometric modulations that are a few hundred times
+larger than a naive estimate of δL/L∼B2
+surfR4/(GM 2), but
+still too small to be observed. Photometric modulations ob-
+served in magnetic stars likely arise from changes in the
+emergent spectrum rather than changes in the bolometric
+flux. Although we have focused on a young 3 M⊙ model in
+this work, the same method can be applied to other types of
+predominantly radiative stars, such as moderately evolved
+massive stars or white dwarfs.
+Our work can be improved in several ways. First, real-
+istic magnetic configurations likely have toroidal fields con-
+fined to closed poloidal surfaces within the star such that
+current does not flow into the atmosphere and dissipate
+the magnetic field. Incorporating this condition will require
+more complicated magnetic topologies and non-separable
+solutions to the hydrostatic balance and radiative diffu-
+sion equations. The impacts of rotation, where the rotation
+and magnetic axis are often misaligned, and of the associ-
+ated centrifugal forces have also been neglected in this work
+(Monaghan 1973; Galea & Wood 1985). Our models do not
+account for composition gradients within a star, which may
+significantly affect the magnetic perturbations in evolved
+stars and white dwarfs. Finally, magnetic changes to opac-
+ity and anisotropic conduction should be included in future
+models in order to better interpret observable photometric
+and spectroscopic variations of magnetic stars.
+ACKNOWLEDGMENTS
+JF is thankful for support through an Innovator Grant
+from The Rose Hills Foundation. S.M. acknowledges sup-
+port from CNES SOHO, PLATO, and LISA grants at
+CEA/IRFU/DAp.
+DATA AVAILABILITY
+The relaxation code to compute magnetic perturbations is
+available upon request.
+REFERENCES
+Akg¨un T., Reisenegger A., Mastrano A., Marchant P.,
+2013, MNRAS, 433, 2445
+Becerra L., Reisenegger A., Valdivia J. A., Gusakov M. E.,
+2022a, MNRAS, 511, 732
+© 0000 RAS, MNRAS 000, 000–000
+
+14
+Fuller & Mathis
+Becerra L., Reisenegger A., Valdivia J. A., Gusakov M.,
+2022b, MNRAS, 517, 560
+Braithwaite J., 2008, Mon. Not. R. Astron. Soc., 386, 1947
+Braithwaite J., 2009, MNRAS, 397, 763
+Braithwaite J., Nordlund ˚A., 2006, Astronomy & Astro-
+physics, 450, 1077
+Braithwaite J., Spruit H. C., 2004, Nature, 431, 819
+Braithwaite J., Spruit H. C., 2017, Royal Society Open
+Science, 4, 160271
+Broderick A. E., Narayan R., 2008, MNRAS, 383, 943
+Bugnet L., et al., 2021, A&A, 650, A53
+Busse F. H., 1981, Geophysical and Astrophysical Fluid
+Dynamics, 17, 215
+Cantiello M., Braithwaite J., 2011, A&A, 534, A140
+Chandrasekhar S., 1956, ApJ, 124, 232
+Chandrasekhar S., Prendergast K. H., 1956, Proceedings of
+the National Academy of Science, 42, 5
+Chang P., Quataert E., 2010, MNRAS, 403, 246
+Davies G. F., 1968, Australian Journal of Physics, 21, 293
+Decressin T., Mathis S., Palacios A., Siess L., Talon S.,
+Charbonnel C., Zahn J. P., 2009, A&A, 495, 271
+Duez V., Mathis S., 2010, A&A, 517, A58
+Duez V., Mathis S., Turck-Chi`eze S., 2010a, MNRAS, 402,
+271
+Duez V., Braithwaite J., Mathis S., 2010b, ApJ, 724, L34
+Eddington A. S., 1929, MNRAS, 90, 54
+Fuller J., Cantiello M., Stello D., Garcia R. A., Bildsten L.,
+2015, Science, 350, 423
+Galea E. R., Wood W. P., 1985, MNRAS, 217, 633
+Garc´ıa R. A., et al., 2014, Astron. Astrophys., 563, A84
+H¨ummerich S., et al., 2018, A&A, 619, A98
+Jordan S., 1992, A&A, 265, 570
+Kaufman E., Lecoanet D., Anders E. H., Brown B. P., Vasil
+G. M., Oishi J. S., Burns K. J., 2022, MNRAS, 517, 3332
+Kochukhov O., Lundin A., Romanyuk I., Kudryavtsev D.,
+2011, ApJ, 726, 24
+Lander S. K., Jones D. I., 2012, MNRAS, 424, 482
+Landstreet J. D., 1987, MNRAS, 225, 437
+Landstreet J. D., Mathys G., 2000, A&A, 359, 213
+Lecoanet D., Vasil G. M., Fuller J., Cantiello M., Burns
+K. J., 2017, MNRAS, 466, 2181
+Li L. H., Ventura P., Basu S., Sofia S., Demarque P., 2006,
+ApJS, 164, 215
+Li G., Deheuvels S., Ballot J., Ligni`eres F., 2022, Nature,
+610, 43
+Loi S. T., 2021, MNRAS, 504, 3711
+Lyutikov M., 2010, MNRAS, 402, 345
+Maeder A., 1999, A&A, 347, 185
+Markey P., Tayler R. J., 1973, MNRAS, 163, 77
+Mathis S., 2013, in Goupil M., Belkacem K., Neiner C.,
+Ligni`eres F., Green J. J., eds, , Vol. 865, Lecture Notes in
+Physics, Berlin Springer Verlag. p. 23, doi:10.1007/978-3-
+642-33380-4˙2
+Mathis S., Bugnet L., Prat V., Augustson K., Mathur S.,
+Garcia R. A., 2021, A&A, 647, A122
+Mestel L., Moss D. L., 1977, MNRAS, 178, 27
+Milsom F., Wright G. A. E., 1976, MNRAS, 174, 307
+Monaghan F. F., 1966, MNRAS, 132, 1
+Monaghan J. J., 1973, MNRAS, 163, 423
+Morel T., et al., 2014, The Messenger, 157, 27
+Moss D. L., 1973, MNRAS, 164, 33
+Moss D., 1979, MNRAS, 187, 601
+Oksala M. E., Silvester J., Kochukhov O., Neiner C., Wade
+G. A., MiMeS Collaboration 2018, MNRAS, 473, 3367
+Ostriker J. P., Hartwick F. D. A., 1968, ApJ, 153, 797
+Paxton B., Bildsten L., Dotter A., Herwig F., Lesaffre P.,
+Timmes F., 2011, ApJS, 192, 3
+Potekhin A. Y., 1999, A&A, 351, 787
+Potekhin A. Y., Yakovlev D. G., 2001, A&A, 374, 213
+Press W. H., Teukolsky S. A., Vetterling W. T., Flannery
+B. P., 2007, Numerical Recipes 3rd Edition: The Art of
+Scientific Computing, 3 edn. Cambridge University Press,
+USA
+Raadu M. A., 1971, Ap&SS, 14, 464
+Reisenegger A., 2009, A&A, 499, 557
+Rieutord M., 2006, EAS Publ. Ser., 21, 275
+Shultz M. E., et al., 2019, MNRAS, 490, 274
+Shulyak D., et al., 2007, A&A, 464, 1089
+Shulyak D., Kochukhov O., Valyavin G., Lee B. C.,
+Galazutdinov G., Kim K. M., Han I., Burlakova T., 2010,
+A&A, 509, A28
+Stello D., Cantiello M., Fuller J., Huber D., Garc´ıa R. A.,
+Bedding T. R., Bildsten L., Silva Aguirre V., 2016, Na-
+ture, 529, 364
+Sweet P. A., 1950, MNRAS, 110, 548
+Tayler R. J., 1973, MNRAS, 161, 365
+Tayler R. J., 1980, MNRAS, 191, 151
+Taylor J. B., 1974, Phys. Rev. Lett., 33, 1139
+Wade G. A., et al., 2016, MNRAS, 456, 2
+Wright G. A. E., 1969, MNRAS, 146, 197
+von Zeipel H., 1924, MNRAS, 84, 665
+© 0000 RAS, MNRAS 000, 000–000
+
diff --git a/q9FKT4oBgHgl3EQf0C6i/content/tmp_files/load_file.txt b/q9FKT4oBgHgl3EQf0C6i/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf,len=913
+page_content='Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 000, 000–000 (0000)  Printed 30 January 2023  (MN LATEX style file v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2)  Linking the Interiors and Surfaces of Magnetic Stars  Jim Fuller1⋆ and St´ephane Mathis2  1TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA  2Universit´e Paris-Saclay, Universit´e Paris Cit´e, CEA, CNRS, AIM, F-91191, Gif-sur-Yvette, France  30 January 2023  ABSTRACT  Strong magnetic fields are observed in a substantial fraction of upper main se-  quence stars and white dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Many such stars are observed to exhibit photometric  modulations as the magnetic poles rotate in and out of view, which could be a con-  sequence of magnetic perturbations to the star’s thermal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The magnetic  pressure is typically larger than the gas pressure at the star’s photosphere, but much  smaller than the gas pressure in the star’s interior, so the expected surface flux pertur-  bations are not clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We compute magnetically perturbed stellar structures of young  3 M⊙ stars that are in both hydrostatic and thermal equilibrium, and which contain  both poloidal and toroidal components of a dipolar magnetic field as expected for  stable fossil fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This provides semi-analytical models of such fields in baroclinic  stably stratified regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The star’s internal pressure, temperature, and flux perturba-  tions can have a range of magnitudes, though we argue the most likely configurations  exhibit flux perturbations much smaller than the ratio of surface magnetic pressure to  surface gas pressure, but much larger than the ratio of surface magnetic pressure to  central gas pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The magnetic pole is hotter than the equator in our models, but  a cooler magnetic pole is possible depending on the magnetic field configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The  expected flux variations for observed field strengths are δL/L ≲ 10−6, much smaller  than those observed in magnetic stars, suggesting that observed perturbations stem  from changes to the emergent spectrum rather than changes to the bolometric flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Key words: stars: evolution – stars: magnetic fields  1  INTRODUCTION  Magnetic fields produce a substantial impact on the appear-  ance of a star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In stars with convective envelopes, star spots  are well known as regions of high magnetic field strength and  low temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Some stars with radiative envelopes are  also known to host strong magnetic fields (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Morel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Wade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Shultz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2019), and such stars  frequently exhibit photometric variability at their rotation  periods, suggesting that their emergent flux is altered by the  magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, it is not clear how the magnetic  fields actually affect the stellar structure and emergent flux,  or whether photometric modulations can be used to learn  about the strength of the star’s internal magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  One might expect magnetic fields to affect the photo-  spheric temperature if the magnetic pressure is comparable  to the photospheric gas pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Indeed, Cantiello & Braith-  waite (2011) argued that magnetic spots on massive stars  should be hot because they would have lower gas pressures  (and therefore lower densities), allowing us to see deeper into  ⋆ Email: jfuller@caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='edu  the star where the temperature is higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Relatively mod-  est magnetic fields of B ≳ 100 G are required for large flux  perturbations in this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Observed photometric mod-  ulations from stars with stronger magnetic fields, such as  Ap stars that exhibit photometric modulation with ∼1-3%  amplitudes (H¨ummerich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2018), are much smaller than  naively predicted from this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  The reason is that a star’s radiative flux will change in  response to the magnetic perturbation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', the magnetic  hot spot will cool off) until the star finds a new radia-  tive equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Long-lived magnetic fields will thus pro-  duce much different effects than transient fields arising from  magnetic activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' To compute the perturbed structure of a  star with a stable magnetic field, we must find a structure  that is in both hydrostatic equilibrium and radiative equi-  librium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' For rotating stars, it is well known that no state of  radiative equilibrium exists for solid body rotation, so that  stars must either have very special rotation profiles (von  Zeipel 1924;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Busse 1981;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Rieutord 2006), or have currents  that advect heat (Eddington 1929;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Sweet 1950) and restore a  state of equilibrium (see Maeder 1999, Decressin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2009,  Mathis 2013 for useful synopsis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Our goal in this paper is  © 0000 RAS  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='11914v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='SR]  27 Jan 2023  2  Fuller & Mathis  to compute the special magnetic field profiles that allow for  radiative equilibrium without requiring currents within the  star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  In addition, the magnetic field configuration must be a  stable equilibrium that does not unravel via magnetic insta-  bilities such as those of purely toroidal fields (Tayler 1973)  and purely poloidal fields (Markey & Tayler 1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Several  works (Braithwaite & Spruit 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Braithwaite & Nordlund  2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Braithwaite 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Broderick & Narayan 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Lyu-  tikov 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Duez & Mathis 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Duez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2010b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Akg¨un  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Becerra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2022b) have computed stable  magnetic equilibria through analytic calculations or numer-  ical simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' These works agree that purely poloidal or  toroidal magnetic field configurations are unstable, and that  stable equilibria require similar toroidal and poloidal field  strengths (Tayler 1980;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Braithwaite 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Stable stratifica-  tion (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', non-barotropic stars) is also required for long-term  stability (Lander & Jones 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Akg¨un et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Becerra  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Magnetic configurations decrease their mag-  netic energy but approximately conserve their magnetic he-  licity as they form and evolve (Braithwaite 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This is  the so-called selective decay as observed in plasmas in the  laboratory (Taylor 1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence, recent works have com-  puted stable field configurations through variational tech-  niques that minimize total energy while conserving magnetic  helicity (Broderick & Narayan 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Duez & Mathis 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  However, all of these works have assumed barotropic  perturbations such that the perturbed temperature is di-  rectly proportional to the perturbed pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' While these  configurations are in hydrostratic equilibrium, they are not  typically in thermal equlibrium, meaning that heat will be  transported from high temperature to low temperature re-  gions, changing the gas pressure and therefore the magnet-  ically perturbed stellar structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This heat transport will  occur on a thermal time (typically ∼106 yr in A-type stars),  much shorter than Ohmic diffusion time scales (∼ 1010 yr)  and main sequence life times (∼109 yr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence, real stars  will approach a state close to hydrostatic equilibrium and  thermal equilibrium, which has not been considered in re-  cent literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Accounting for thermal equilibrium is crucial  for predicting the long-term equilibria of stars (Reiseneg-  ger 2009), and observational manifestations such as the per-  turbed surface flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Calculations of equilibrium magnetic configurations  date back to the 1950s (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Chandrasekhar 1956;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Chan-  drasekhar & Prendergast 1956).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Subsequent work included  the effects of centrifugal distortion and meridional flows  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Ostriker & Hartwick 1968;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Mestel & Moss 1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Inter-  estingly, works dating back to the 1960s (Monaghan 1966;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Davies 1968;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Wright 1969;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Moss 1973, 1979;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2006)  have attempted to compute the structures of stars in both  hydrostatic and thermal equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, much of this  work is either difficult to interpret, does not discuss the per-  turbed thermal structure and surface flux, does not consider  fields with both poloidal and toroidal components, or has  simply been forgotten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The goal of this paper is to provide  updated calculations of magnetically distorted stars in sta-  ble hydrostatic and thermal equilibrium for realistic stellar  structures, and to discuss the observational implications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  In this paper we primarily focus on application to up-  per main sequence stars of M ≳1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5 M⊙ with convective cores  and radiative envelopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Much of the physics studied here  could also apply to radiative stars such as white dwarfs and  the radiative cores of red giants where internal fields can be  detected through asteroseismology (Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Stello  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2022) because of their impact on stellar  oscillations (Fuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Lecoanet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Loi 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Bugnet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Mathis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Magnetic upper main  sequence stars have typical surface field strengths of ∼1 kG  (see Braithwaite & Spruit 2017 for a review) and surface  magnetic pressures larger than surface gas pressures, such  that magnetic forces could be strong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The surface magnetic  morphologies are observed to be diverse: they can be com-  plex or simple, axisymmetric or non-axisymmetric, poloidal  or toroidal (Landstreet & Mathys 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Kochukhov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Shultz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, as a first step, in this  work we examine simple dipolar magnetic configurations  that produce quadrupolar temperature/pressure perturba-  tions, which likely dominate observable photometric modu-  lations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2  EQUILIBRIUM STRUCTURE  Our goal is to calculate the structure of a magnetized star in  hydrostatic and thermal equilibrium, considering non-force-  free magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We begin from the equation for magne-  tohydostratic equilibrium  − ∇P − ρ∇Φ + (∇ × B) × B  4π  = 0 ,  (1)  where P is the pressure, ρ the density, Φ the gravitational  potential, and B the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We choose to work in  standard spherical coordinates with r the radius and θ the  colatitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Following Duez & Mathis (2010), we decompose  the magnetic field into a poloidal magnetic stream function  Ψ and a toroidal magnetic flux F via  B =  √  4π  r sin θ ∇Ψ × ˆφ +  √  4π  r sin θ F ˆφ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (2)  This means that  Br =  √  4π  r2 sin θ  ∂Ψ  ∂θ ,  (3)  Bθ = −  √  4π  r sin θ  ∂Ψ  ∂r ,  (4)  Bφ =  √  4π  r sin θ F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (5)  We consider an axisymmetric magnetic field such that Ψ and  F are independent of φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' It can easily be verified that this  field always satisfies ∇ · B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  The φ-component of equation 1 becomes  − ∂F  ∂θ  ∂Ψ  ∂r + ∂F  ∂r  ∂Ψ  ∂θ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (6)  This is always satisfied if F is a function of Ψ, or in other  words, the poloidal flux Ψ uniquely determines F and hence  the toroidal field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Broderick & Narayan (2008) and Duez &  Mathis (2010) show that the lowest energy state has  F = λ  RΨ ,  (7)  where the constant λ determines the magnetic helicity, and  R is the stellar radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This clearly satisfies equation 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This  © 0000 RAS, MNRAS 000, 000–000  Magnetic Structure  3  also results if we assume that F and Ψ have the same angular  form, such that equation 6 reduces to  1  F  dF  dr = 1  Ψ  dΨ  dr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (8)  The solution to this equation is equation 7, for a constant λ  that is independent of radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Writing out the hydrostatic equilibrium condition and  using equation 7, the radial component of equation 1 be-  comes  −  1  r2 sin2 θ  � λ2  R2 Ψ + ∆∗Ψ  �∂Ψ  ∂r = ∂P  ∂r + ρ∂Φ  ∂r ,  (9)  while the θ-component is  −  1  r2 sin2 θ  � λ2  R2 Ψ + ∆∗Ψ  �∂Ψ  ∂θ = ∂P  ∂θ + ρ∂Φ  ∂θ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (10)  Here, ∆∗ is the “Grad-Shafranov” or “five-dimensional  Laplacian” operator, defined as  ∆∗ = ∂2  ∂r2 + sin θ  r2  ∂  ∂θ  �  1  sin θ  ∂  ∂θ  �  = ∂2  ∂r2 + 1 − µ2  r2  ∂2  ∂µ2 ,  (11)  where µ = cos θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  It is immediately evident from equations 9 and 10 that  the field is force-free if  λ2  R2 Ψ + ∆∗Ψ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (12)  This results in a simple linear eigenvalue calculation for the  magnetic potential Ψ, and is the type of field considered by  Broderick & Narayan (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The work of Duez & Mathis  (2010) considers a non-force-free field such that  λ2  R2 Ψ + ∆∗Ψ = −βρr sin2 θ ,  (13)  where β is a constant that determines the strength of the  magnetic force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' As an example, the case with λ = 0 and  β = 0 corresponds to a force-free poloidal dipole field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This  can be seen from equation 12, whose solution has Ψ ∝ r−1  and hence B ∝ r−3 in that case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A non-zero value of β alters  both the magnetic forces and the radial profile of the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Substitution of equation 13 into equations 9 and 10  yields  βρ∇Ψ = ∇P + ρ∇Φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (14)  Hence there is a direct relationship between the magnetic  flux and the pressure perturbation for barotropic perturba-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Remarkably, the non-linear equations 9 and 10 have  been transformed into a linear relationship between Ψ and  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Taking the curl of equation 14 yields  ∇ρ × ∇P = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (15)  This implies that P is a function of ρ, and hence equation  13 is a solution for a barotropic equation of state such that  density and pressure perturbations are directly proportional  to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  In our work, we want to consider non-force-free fields  that produce non-barotropic density and pressure pertur-  bations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence, we cannot use the approximations made in  Broderick & Narayan (2008) or Duez & Mathis (2010), and  we shall see that this generally leads to a series of non-linear  differential equations that relate the magnetic field to den-  sity, temperature, and pressure perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In our calcu-  lations, we parameterize the strength of the magnetic forces  via a parameter β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Assuming barotropic perturbations en-  tails that β (as defined in equation 13) is a constant within  the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Accounting for radiative diffusion, this is no longer  the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Nonetheless, we shall see below that we still require  a parameter to specify the strength of the magnetic forces,  which in practice is determined by the boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Since our stellar model has a convective core where equation  13 is a good approximation, we label our structures based  on the resulting β in the convective core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='1  Electric Currents  The current density is  j = ∇ × B  4π  =  λ  4πRBrˆr +  λ  4πRBθ ˆθ −  1  √  4πr sin θ  ∆∗Ψˆφ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (16)  The force-free field of equation 12 occurs when j is parallel  to B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Force-free fields are also obtained when Ψ = 0 (no  magnetic field) or from current-free fields, which only occur  when both λ = 0 and and ∆∗Ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Note that the radial  current is proportional to the radial magnetic field, hence  a vanishing radial current near the surface of the star re-  quires a vanishing radial field Br, which in turn requires Ψ  to vanish at the stellar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  Hydrostatic Equilibrium  In order to determine an equilibrium state, we use a linear  approximation such that perturbations to background quan-  tities (ρ, P, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=') are considered to be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The linearized  version of the radial momentum equation (9) is  −  1  r2 sin2 θ  � λ2  R2 Ψ+∆∗Ψ  �∂Ψ  ∂r = ∂  ∂r δP +ρ ∂  ∂r δΦ+gδρ , (17)  while the θ-component of equation (10) is  −  1  r2 sin2 θ  � λ2  R2 Ψ + ∆∗Ψ  �∂Ψ  ∂θ = ∂  ∂θ δP + ρ ∂  ∂θ δΦ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (18)  Here, δ indicates an Eulerian perturbation, and we have used  a background in hydrostatic equilibrium with dP/dr = −ρg,  and g = dΦ/dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  We next turn to the angular dependence of the magnetic  field and the perturbations to the stellar structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Decom-  posing Ψ into eigenvalues of the horizontal component of ∆∗  requires  (1 − µ2) ∂2  ∂µ2 gℓ(µ) = −ℓ(ℓ + 1)gℓ(µ) ,  (19)  where gℓ is the angular eigenfunction corresponding to the  eigenvalue −ℓ(ℓ + 1) of the operator on the left hand side  of equation 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The full response is Ψ = �  ℓ Ψℓgℓ(µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' As  discussed in Duez & Mathis (2010), the eigenvalue equation  above has solutions  gℓ(µ) = (1 − µ2)Pℓ−1(µ) ,  (20)  where Pℓ is a Legendre polynomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  For the lowest order (dipole) solution with ℓ = 1, we  © 0000 RAS, MNRAS 000, 000–000  4  Fuller & Mathis  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Magnetic field lines of a star for a toroidal field com-  parable to the poloidal field (λ2 = 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Magnetic field lines are  colored by field strength, while the color shading indicates the  radiative flux perturbation at a given radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  have gℓ(µ) = (1 − µ2) and hence Ψ = Ψℓ(r) sin2 θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Plugging  this into equation 17 yields  − sin2(θ)  r2  � ∂2  ∂r2 Ψℓ(r) − ℓ(ℓ + 1)  r2  Ψℓ(r) + λ2  R2 Ψℓ(r)  �∂Ψℓ(r)  ∂r  = ∂  ∂r δP + ρ ∂  ∂r δΦ + gδρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (21)  We see that the perturbed density, pressure, and poten-  tial must have angular form δP  ∝ sin2(θ), which is a  combination of the ℓ = 2 and ℓ = 0 spherical harmon-  ics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence a dipole magnetic field induces both radial and  quadrupole components to the star’s distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Figure 1  illustrates the geometry of a dipolar magnetic field with  helicity λ2 = 10 that induces quadrupolar flux perturba-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The quadrupole (ℓ = 2) component of the field in-  duces ℓ = 4, ℓ = 2, and ℓ = 0 components of the stellar  distortion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  We thus have the unfortunate situation that the angular  eigenfunctions of the magnetic and hydrodynamic variables  are not the same, meaning that the radial and angular parts  of the response cannot generally be separated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In this work,  we limit ourselves to dipole magnetic field configurations,  which induce ℓ = 0 and ℓ = 2 components to the stellar  structure perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We are not interested in the ℓ = 0  component of the stellar response, as it is the non-radial  magnetic distortions that draw our focus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence, from here  forward, we consider a dipole (ℓ = 1) magnetic field and the  quadrupolar (ℓ = 2) component of the stellar response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Letting the pressure response be  δP = a0δp0(r)Y00(θ) + a2δp2(r)Y20(θ)  (22)  and setting the angular dependence equal to sin2 θ requires  a2 = −  �  16π/45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The radial component of the response is  then a0δp0(r) = (4√π/3)δp2(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Dropping the (r) depen-  dence and subscripts of Ψℓ and δp2 for simplicity, equations  17 and 18 can be written  � ∂2  ∂r2 Ψ − ℓ(ℓ + 1)  r2  Ψ + λ2  R2 Ψ  �∂Ψ  ∂r  = −r2 ∂δp  ∂r − r2ρ ∂  ∂r δΦ − r2gδρ ,  (23)  � ∂2  ∂r2 Ψ − ℓ(ℓ + 1)  r2  Ψ + λ2  R2 Ψ  �  Ψ = −r2δp − r2ρδΦ ,  (24)  and it is now understood that these equations are only valid  for ℓ = 1 and δp, δΦ etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' refer to the quadrupolar part of  the stellar response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Equation 24 can be substituted into  equation 23 to obtain  �  δp + ρδΦ  �∂Ψ  ∂r =  �∂δp  ∂r + ρ ∂  ∂r δΦ + gδρ  �  Ψ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (25)  However, we have divided by Ψ to obtain this equation, so  we must be wary of solutions that cross Ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  The gravitational potential perturbation is given by  Poisson’s equation,  ∇2δΦ = 4πGδρ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (26)  This can be written in terms of two first-order equations,  ∂  ∂r δΦ − δΦ′ = 0 ,  (27)  ∂  ∂r δΦ′ + 2  r δΦ′ − (ℓ + 1)(ℓ + 2)  r2  δΦ − 4πGδρ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (28)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='3  Thermal Equilibrium  We next turn to the equations of thermal equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' En-  ergy conservation requires  ρT ds  dt = ρϵ − ∇ · F ,  (29)  where T is temperature, s is specific entropy, ϵ is the specific  energy generation rate, and F is the energy flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In thermal  equilibrium, the entropy is constant, and the background  state only has a radial flux 4πr2F = L, which entails that  dL/dr = 4πρr2ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Additionally, the energy flux is  F = −χ∇T  (30)  where  χ = 4acT 3  3κρ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (31)  is the thermal diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This means that the background  temperature gradient is dT/dr = −L/(4πr2χ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  For a perturbation in thermal equilibrium, the Eulerian  perturbation of equation 29 is  ∇ · δF − δρϵ − ρδϵ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (32)  The Eulerian perturbation of equation 30 is  δF = −δχdT  dr ˆr − χ∇δT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (33)  Taking the horizontal divergence of the horizontal part of  this equation yields  ∇⊥ · δF⊥ = −χ∇2  ⊥δT ,  (34)  © 0000 RAS, MNRAS 000, 000–000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5  Flux Perturbation  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5Magnetic Structure  5  where ∇2  ⊥ = −(ℓ+1)(ℓ+2)/r2 since we are considering per-  turbations with spherical harmonics of degree ℓ+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Plugging  this into equation 32 and using 4πr2δFr = δL, we obtain  ∂  ∂r δL + 4π(ℓ + 1)(ℓ + 2)χδT − 4πρr2  �δρ  ρ ϵ + δϵ  �  = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' (35)  This can be rewritten  r ∂  ∂r  δL  Ls + 4π(ℓ + 1)(ℓ + 2)χTr  Ls  δT  T − r  Ls  dL  dr  �δρ  ρ + δϵ  ϵ  �  = 0 ,  (36)  where Ls is the star’s surface luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The energy gen-  eration perturbation can be expanded as δϵ/ϵ = ϵT δT/T +  ϵρδρ/ρ, where ϵT = (∂ ln ϵ/∂ ln T)ρ and ϵρ = (∂ ln ϵ/∂ ln ρ)T ,  yielding  r ∂  ∂r  δL  Ls + 4π(ℓ + 1)(ℓ + 2)χTr  Ls  δT  T  − r  Ls  dL  dr  �  (1 + ϵρ)δρ  ρ + ϵT δT  T  �  = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (37)  The radial component of equation 33 can be written  δFr  F  =  �  3δT  T − δκ  κ − δρ  ρ  �  − χ  F  ∂δT  ∂r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (38)  Using  δκ/κ  =  κT δT/T  + κρδρ/ρ,  where  κT  =  (∂ ln κ/∂ ln T)ρ and κρ = (∂ ln κ/∂ ln ρ)T , this can be writ-  ten as  r ∂  ∂r  �δT  T  �  +  L  4πrχT  �δL  L − (4 − κT )∂T  T + (1 + κρ)δρ  ρ  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (39)  Finally, we require an equation of state to close the  system of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This is given by  δP  P − χT δT  T − χρ δρ  ρ = 0 ,  (40)  where χT = (∂ ln P/∂ ln T)ρ and χρ = (∂ ln P/∂ ln ρ)T and  are determined by the equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This is valid if the  composition is uniform, otherwise there will be an additional  term in equation 40, which we discuss in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  Equations and Boundary Conditions  Putting everything together, we have a system of equations  that can be solved for six variables: Ψ and its radial deriva-  tive Ψ′ = ∂Ψ/∂r, and the Eulerian perturbations δP, δρ,  δT, and δL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The equations can be written  ∂  ∂r Ψ − Ψ′ = 0 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (41)  r2Ψ ∂  ∂r Ψ′+  �λ2r2  R2 −ℓ(ℓ+1)  �  Ψ2+r4P δP  P +r4ρδΦ = 0 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' (42)  rΨ ∂  ∂r  δP  P + ρgr  P ΨδP  P + rρ  P Ψ ∂  ∂r δΦ + ρgr  P Ψδρ  ρ  − rΨ′  �δP  P + ρδΦ  P  �  = 0 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (43)  r ∂  ∂r  �δT  T  �  +  L  4πrχT  �δL  L − (4 − κT )δT  T + (1 + κρ)δρ  ρ  �  = 0 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (44)  r ∂  ∂r  δL  Ls + 4π(ℓ + 1)(ℓ + 2)χTr  Ls  δT  T  − r  Ls  dL  dr  �  (1 + ϵρ)δρ  ρ + ϵT δT  T  �  = 0 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (45)  along with Poisson’s equation (equations 27 and 28) and the  equation of state (equation 40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This system contains seven  first-order differential equations, two of which are non-linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  They depend on the field geometry ℓ (assumed to be ℓ = 1  here), and the magnetic helicity λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  This system of equations requires seven boundary con-  ditions in order to be solved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' At the inner boundary, we  require  Ψ = 0  (46)  δP  P  = 0 ,  (47)  and  δΦ = 0 ,  (48)  These ensure that δT/T, δρ/ρ, and δL/Ls are also zero at  the center of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  At the surface, we require the blackbody radiation con-  dition  ∆L  Ls − 4∆T  T  − 2ξr  r = 0 ,  (49)  where  ∆  indicates  a  Lagrangian  perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Using  dL/dr = 0 at the surface, and the surface pressure boundary  condition ∆P = 0, which becomes (P/ρgr)δP/P = ξr/r ≪  δP/P, we can drop the last term, and this can be written as  δL  Ls − 4δT  T + 4∇δP  P  = 0 ,  (50)  where ∇ = d ln T/d ln P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' At the outer boundary we require  a decaying potential perturbation:  δΦ′ = −ℓ + 2  r  Φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (51)  Additionally, the amplitude of the response can be chosen  with a normalization condition at the surface, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  Ψ =  √  GM 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (52)  Finally, we require another boundary condition at the  surface that determines the amplitude of another variable  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', δT/T or δL/Ls), relative to Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This boundary condi-  tion will determine the amplitude of the surface flux pertur-  bation and can be considered to be a measure of the strength  of the magnetic forces within the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' It is similar to speci-  fying the strength of the magnetic forces in barotropic stars  with a β parameter as described in Duez & Mathis (2010)  and in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In practice, we set the luminosity per-  turbation at the outer boundary in order to determine an  effective value of β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Setting δL = 0 at the outer boundary  would be equivalent to setting β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  We pause to note a few important points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' First, the dis-  placement vector ξ does not appear anywhere in our system  of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Lagrangian perturbations cannot be calculated  from this system of equations, except at the surface where  ξr/r = (P/ρgr)δP/P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Physically this arises from the fact  that in a thermally relaxed system of uniform composition,  there are an infinite number of combinations of radial and  © 0000 RAS, MNRAS 000, 000–000  6  Fuller & Mathis  horizontal displacements ξr and ξ⊥ that could give rise to  a given density perturbation δρ/ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This is discussed further  in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  A second important point is that we have not imposed a  surface boundary condition in which the poloidal or toroidal  component of the magnetic field goes to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This is quite  different from the fields studied in Broderick & Narayan  (2008) and Duez & Mathis (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A non-zero toroidal field  requires a current to flow at the surface of the star, which is  often assumed to be zero due to the vanishing density and  temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Real stars, however, do not have zero tem-  perature or density in their photospheres or coronae, which  can support currents and toroidal fields (Kochukhov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Shulyak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2007, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Therefore, we do not im-  pose Ψ = 0 at the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A consequence of relaxing this  condition is that λ is no longer an eigenvalue, and the system  of equations can now be solved for any value of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Alternatively, one could argue that the radial compo-  nent of the electric current (Equation 16) should vanish at  the surface of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This would require Br = 0 and hence  Ψ = 0 as discussed in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='1, and imposed by Broderick  & Narayan (2008) and Duez & Mathis (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This eighth  boundary condition would transform our system of seven  differential equations into an eigenvalue problem that could  only be solved for certain combinations of λ and the surface  flux perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We discuss this further in Section 3 and  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5  Convective Zones  In convective zones, the radiative diffusion equation no  longer applies, and equations 44 and 45 are not valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In-  stead, we assume that the perturbation to the entropy is  nearly zero, as convective heat flux will quickly smooth out  any entropy gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We therefore have  d ln T  d ln P = ∇ad = Γ3 − 1  Γ1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (53)  Perturbing this yields  δT  T − Γ3 − 1  Γ1  δP  P  = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (54)  and  δP  P − Γ1 δρ  ρ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (55)  Since the perturbations are barotropic, the system of  equations 41-43 simplifies, as discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In this case,  the system of equations reduces to that of Duez & Mathis  (2010):  ∂  ∂r Ψ − Ψ′ = 0 ,  (56)  ∂  ∂r Ψ′ +  � λ2  R2 − ℓ(ℓ + 1)  r2  �  Ψ + βr2ρ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (57)  Here, β is a constant that determines the magnitude of the  magnetic force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Comparison with equation 14 shows that the  pressure perturbation is  δP  P + ρδΦ  P  = βρΨ  P  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (58)  Equations 56 and 57 combine into a linear wave equation:  ∂2  ∂r2 Ψ +  � λ2  R2 − ℓ(ℓ + 1)  r2  �  Ψ + βr2ρ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (59)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  Linking Convective and Radiative Zones  In this work we only consider stars with convective cores  and radiative envelopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' To solve for the magnetic field in  the full star, we choose a value of λ and a surface flux per-  turbation δL/L, which effectively sets the magnetic forces  and the value of β within the convective zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Within the  convective zone, we replace equation 44 with equation 54,  and we replace equation 45 with ∂δL/∂r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, the  value of δL is not defined in the convective zone, only within  the radiative zone above it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In our solutions, we verify that  equation 58 is approximately satisfied within the convective  region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We then label our solutions by the corresponding  value of β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='7  Solving the Equations  We solve the system of equations above in a stellar model  generated with the MESA stellar evolution code (Paxton  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We choose a M = 3 M⊙ star at the start of the  main sequence, with a radius of R = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='1 R⊙, a surface tem-  perature of Teff = 11, 800 K, and a convective core bound-  ary at r/R = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This model resembles typical magnetic  Ap/Bp stars that are observed to harbor strong magnetic  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Our model has nearly uniform stellar composition so  that the equation of state (equation 40) is a good approxi-  mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  We use a relaxation technique from Numerical Recipes  (Press et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2007) to solve the system of equations in Sec-  tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We solve the equations on the same grid as the  underlying MESA model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A good initial guess is often re-  quired in order reliably to converge to a solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Spurious  solutions (involving sudden jumps in the derivatives of δP  and Ψ) are often found, so caution is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' There may be  other physical solutions that exist that we do not examine  in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  3  SOLUTIONS  In our models, both λ and β are free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Physi-  cally, λ represents the magnetic helicity which is determined  by the dynamo process that created the field, and which is  roughly conserved during subsequent turbulent relaxation  (Braithwaite 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Duez & Mathis 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The lowest en-  ergy stable field configurations have λ ∼ 1, so λ values in  the range of 1-10 are reasonable expectations for real stars,  though larger values are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The value of β determines  the relative strength of magnetic forces as described in the  previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Figure 2 and 3 show the magnetic field configuration  for a model with λ2 = β = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The poloidal field is largest  at the center of the star, where its field strength is roughly  four times larger than the surface value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The toroidal field  is largest at r/R ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We shall see below that β = 10 is  small such that the magnetic field is similar to a force-free  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' For this value of λ, there is a null point (where Bθ = 0  © 0000 RAS, MNRAS 000, 000–000  Magnetic Structure  7  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Meridional slices of a star, with color shading indicating the strength of the toroidal magnetic field (left) and poloidal  magnetic field (right) normalized to the maximum magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Orange lines show magnetic field lines of the poloidal field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This model  has magnetic helicity λ2 = 10 and magnetic force β = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Radius  0  2  4  Magnetic Field  λ 2 = 10  β = 10  Br  Bθ  Bφ  0  10  20  Magnetic Field  λ 2 = 17  β = 10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Radius  0  10  20  30  Magnetic Field  λ 2 = 10  β = 110  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Radial profiles of the r, θ, and φ-components of the  magnetic field, scaled to the radial field at the surface, for models  with β = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Panels are labeled by their values of λ2 and β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Note that the field is much more centrally concentrated for higher  values of λ or β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  and the field lines converge to closed loops at the equator)  at r/R ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Both the poloidal and toroidal fields extend  above the surface of the star, where the field is force-free but  is not current-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Figure 4, 5, and 6 show the magnetic potential Ψ, pres-  sure perturbation δP/P, and luminosity perturbation δL/L  as a function of radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In Figure 4, each curve has a dif-  ferent value of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Higher values of λ cause more oscillatory  variation of Ψ, as can be seen in equation 59 where the  radial wavenumber of Ψ is roughly  �  λ2/R2 − ℓ(ℓ + 1)/r2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Higher values of λ push the null point and toroidal field  maximum deeper into the star, and also cause the central  field strengths to become larger relative to the surface field  strength, as shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In this stellar model, a value  of λ ≃ 20 is the first value of λ for which Ψ = 0 at the sur-  face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' From equation 42 we see that Ψ = 0 requires δP = 0,  so the Eulerian pressure perturbation is always zero where  the radial component of the field is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  For larger values of λ or β, the values of Ψ and δP  approach zero somewhere within the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' When this hap-  pens, the numerical solutions exhibit strange behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The  values of Ψ′ and ∂δP/∂r sometimes exhibit discontinuous  jumps at the zero-crossings of Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, the radial mag-  netic field, pressure perturbation, and temperature pertur-  bations are all continuous across these zero-crossings (only  their derivatives are discontinuous).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' It is unclear if these so-  lutions are physical or numerical artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Physically, these  solutions would exhibit a discontinuity in the θ-component  of the magnetic field, an associated current sheet, and a  discontinuity in both the magnetic force and the pressure  force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Because the physicality of these solutions is unclear  and they also sometimes cause numerical convergence prob-  lems, we will not investigate them further in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  More highly oscillatory solutions also represent higher en-  ergy states (Broderick & Narayan 2008) and may be less  © 0000 RAS, MNRAS 000, 000–000  Toroidal Field  Poloidal Field  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  R  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Z  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4 B  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0  0  x/R  x/R8  Fuller & Mathis  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Ψ  10−1  100  101  102  103  δP/P  λ 2 =2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Radius  −20  −15  −10  −5  0  5  δL  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Profiles of the magnetic potential Ψ, relative pressure  perturbation δP/P, and luminosity perturbation δL (in units of  Lsurf) as a function of radius for a model with β = 10 and varying  values of the helicity λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' All quantities are normalized so that Ψ =  1 at its maximum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Stronger toroidal fields (larger λ) create more  oscillatory magnetic fields, but the associated surface luminosity  perturbation varies only slightly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The large values of δP/P near  the surface are discussed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  likely to exist in stars that have relaxed to a minimum en-  ergy state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  In Figure 4, the relatively small value of β = 10 means  that the pressure and density terms in equation 42 are neg-  ligible relative to the magnetic terms, and the field is nearly  force-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The magnetic solutions are thus similar to the  force-free solutions of Broderick & Narayan (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In this  limit, the perturbed pressure, temperature, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' have a value  that is proportional to β, with a radial dependence that is  determined only by λ and the structure of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This  can be seen from equation 58, such that the value of δP,  δT, and δL are roughly proportional to β at the radiative  convective interface, and hence within the bulk of the ra-  diative zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' It is demonstrated in Figure 5 and 6, where  the pressure and luminosity fluctuations have similar pro-  files and increase linearly with β, as long as β ≲ 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence,  a wide range in surface temperature and flux variations are  possible for a given surface field, depending on the strength  of the magnetic forces, parameterized by β in these models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  For larger values of β, however, the pressure/density  terms in equation 42 become comparable to the magnetic  terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Physically this means that gas pressure forces begin  competing with magnetic forces, altering the profile of the  magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Large values of β have a similar effect to  larger values of λ, causing more oscillatory behavior of the  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Ψ  10−1  100  101  102  103  δP/P  β =4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  β =23  β =61  β =110  β =160  β =200  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Radius  −400  −200  0  200  δL  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Same as Figure 4, but for a model with λ2 = 10 and  varying values of β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Larger magnetic forces (higher values of β)  create larger surface luminosity perturbations and more oscilla-  tory magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  magnetic potential Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The surface pressure and luminosity  perturbations reach a maximum when β ∼ 200, and decrease  at larger values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This is because Ψ (and hence δP) become  smaller near the surface at large values of β as gas pressure  forces start backreacting on the magnetic field profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The  magnitude of β needed to have a large influence on the field  profile can be seen from equation 59: β must be large enough  for the last term to be comparable to the second term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Deep  within the star, this requires β ∼ ℓ(ℓ+1)Ψ/(ρr4), which typ-  ically has a value of a couple hundred for our stellar model  and normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  From Figure 4-6, we see that δP/P typically approaches  very large values near the surface of the star, because P  reaches very small values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, the value of δP ap-  proaches very small values δP ≃ ρgξr near the surface, such  that the Lagrangian pressure perturbation ∆P = δP − ρgξr  smoothly approaches zero at the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The value of δP/P  thus approaches δP/P ≃ ξr/H at the star’s surface, which  becomes large as the pressure scale height H becomes small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Although δP/P peaks near the surface, the value of δP  peaks at radii of r/R ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2, as can be seen in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  The values of δρ and δΦ show similar behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  In contrast, the value of δT increases within the con-  vective zone and then maintains a roughly constant profile  throughout the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The derivative of δT has a discontinuity  at the convective interface due to the change in structure and  energy transport mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Within the convective core, δT  is directly proportional to δP which is proportional to Ψ  © 0000 RAS, MNRAS 000, 000–000  Magnetic Structure  9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Ψ  10−1  100  101  102  103  δP/P  β =8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='7  β =79  β =140  β =220  β =270  β =290  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Radius  −600  −400  −200  0  200  400  δL  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Same as Figure 5, but for a model with λ2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Al-  though the magnetic structure is somewhat different, the surface  luminosity perturbations are similar to the case in Figure 5 with  stronger toroidal fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Radius  −20  −10  0  10  20  30  Ψ×30  δP  δT ×20  δρ  δL  δΦ×3  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The magnetic potential Ψ (units of  √  GM2), pressure  perturbation δP (units of GM2/R4), temperature perturbation  δT (units of Tcen), density perturbation δρ (units of M/R3), lumi-  nosity perturbation δL (units of Lsurf), and gravitational poten-  tial perturbation δΦ (units of GM/R) for a model with λ2 = 10,  β = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The kinks at r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='13 occur at the boundary of the  convective core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (equations 54 and 58), but in the radiative zone δT is de-  termined by the thermal equilibrium conditions (equations  44 and 45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This causes oscillatory variations in δT in the  outer layers of the star, due to variations in the thermal dif-  fusivity χ caused by opacity variations in partial ionization  zones near the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Nevertheless, the luminosity perturbation δL always  changes smoothly and gradually throughout the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Phys-  ically this occurs because sudden changes in δL would be  smoothed out by radiative diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Mathematically this  can be seen from equation 45, because the values of χTr/L  and d ln L/d ln r become very small near the surface of the  star, preventing sudden variation in δL, despite large values  of δP/P and δT/T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Interestingly, in all of our models, the  luminosity perturbation switches sign at r/R ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='23 within  the radiative region above the convective core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='1  Surface Flux Perturbation  All of our models have negative surface luminosity pertur-  bations δL2 as shown in the figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, the quadrupo-  lar component of the physical response (see equation 22) is  δL = δL2(1/3−cos2 θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence, a negative value of δL2 trans-  lates to a positive flux perturbation at the magnetic pole  and a negative flux perturbation at the magnetic equator,  as shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This is consistent with the heuristic  idea that strong magnetic pressure at the star’s pole causes  the gas pressure and density to be smaller, allowing us to see  deeper into the star such that magnetic spots are brighter  (Cantiello & Braithwaite 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, it is also possible  for our models to produce a negative flux perturbation at  the magnetic pole if we consider negative values of β, so in  principle it is possible for the magnetic pole to be either hot  or cool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Below we argue that a hot magnetic pole is more  likely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  The value of the surface flux perturbation in our models  is δL/L ∼ βΨ2  max, where Ψmax is the maximum value of Ψ  reached within the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Since we have normalized Ψmax  to units of  √  GM 2, this implies  δL  L ∼ β  4π  B2  maxr4  max  GM 2  ,  (60)  where Bmax and rmax are the magnetic field and radius  where Ψ peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In our models, this roughly translates to  δL  L ∼ 10−11β  �Bsurf  1kG  �2� R  R⊙  �4� M  M⊙  �−2  ,  (61)  where Bsurf is the magnetic field at the star’s surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Clearly  this is too small to be detected in main sequence stars un-  less extremely large values of β are assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Equation 61  is consistent with a naive estimate from the von Zeipel the-  orem applied to the star’s interior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The smoothly varying  magnetic fields of our models produce magnetic forces of  order fmag ∼ βB2/(ρr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Using the average stellar density  ρ ∼ M/R3 and gravitational force g ∼ GM/R2 yields the  von Zeipel estimate of δF/F ∼ fmag/g ∼ βB2R4/GM 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  Most likely field configurations  As mentioned in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='1, the radial current jr may be  expected to be close to zero near the surface of the star  so that current does not flow into the star’s low-density  © 0000 RAS, MNRAS 000, 000–000  10  Fuller & Mathis  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Ψ  10−1  101  103  δP/P  λ 2 =10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  λ 2 =2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='0  Radius  −600  −400  −200  0  200  400  δL  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Magnetic structures for models whose poloidal com-  ponent has a potential profile (Ψ ∝ r−ℓ) at the outer boundary,  for various magnetic helicities λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This outer boundary condition  effectively sets the strength of magnetic forces, β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Configurations  similar to these may be more likely to exist in real stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' From equation 16, the only way this can happen  is when λ2 = 0 or Ψ = 0 at the surface of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' If  there are near-surface toroidal fields, Ψ (and hence Br) must  be zero to have a non-zero current flowing out of the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Hence there is a critical value β0 such that Ψ = 0 at the  star’s surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Figure 5 indicates this occurs at β0 ≃200 and  δL/L ∼ −400 for λ2 = 10 in our stellar model, or β0 ≃ 300  and δL/L ∼ −500 for λ2 = 2 (Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence, those so-  lutions are arguably the most physically probable amongst  the possibilities shown here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Fireffig:magstrucvis shows the  predicted surface flux variations for β = β0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Even though  the large values of β increase the surface flux perturbation  above the naive estimate discussed above, it is too small to  be detected with current instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Another possibility is that the value of λ2 is not con-  stant within the star due to dissipative effects near the sur-  face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In that case, one may expect the value of λ to de-  crease near the star’s surface, allowing the radial current  to vanish and still have a large value of Ψ and hence a  non-zero radial magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' If the electric currents de-  crease to zero near or above the surface, the field must ap-  proach a potential configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Potential force-free fields  have ∂Ψ/∂r2 = ℓ(ℓ + 1)Ψ/r2, and an outwardly decreasing  field has Ψ ∝ r−ℓ and hence B ∝ r−(ℓ+2), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', a dipole field  for our assumed value of ℓ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' To model this case, we set  the outer boundary condition to ∂Ψ/∂r = −ℓΨ/r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The fixed  103  104  105  106  Surface Poloidal Field Strength (G)  10−8  10−7  10−6  10−5  10−4  10−3  Surface Luminosity Perturbation  λ 2 = 10, β = β0  λ 2 = 2, β = β0  λ 2 = 9, β = βpot  λ 2 = 2, β = βpot  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The surface luminosity perturbation as a function of  surface magnetic field strength for models with β = β0, such that  the radial component of the magnetic field and electric current  vanish at the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We also plot luminosity perturbations for  β = βpot such that the poloidal field has a potential profile at the  surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In either case, very strong magnetic fields are required for  detectable luminosity perturbations in main sequence stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Ob-  served photometric variations of magnetic stars likely arise from  variations in the emergent spectrum rather than variations in the  bolometric flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  slope at the outer boundary effectively sets the value of β,  which we refer to as βpot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Figure 8 shows the results of this calculation for several  values of λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The required values of βpot are typically sim-  ilar to (but smaller than) β0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', values on the order of a  hundred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' For λ2 ≃ 10, a nearly force-free field satisfies the  potential outer boundary condition, such that βpot ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' For  larger values of λ, the required βpot is negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However,  we find those solutions almost always have a zero-crossing  somewhere in the star, and cause numerical problems, so we  do not investigate them further in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We note that  they would likely entail surface flux perturbations of the  opposite sign, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', a cool magnetic pole and hot magnetic  equator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Figure 9 shows the surface luminosity perturba-  tions for β = βpot, which are a similar magnitude to those  with β = β0, and not detectable for observed magnetic field  strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='3  Shape of Distorted Star  The sign of the pressure/density perturbations near the sur-  face of the star determine wither it becomes oblate (smaller  photospheric radius at magnetic pole) or prolate (larger  radius at magnetic pole).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' As discussed above, we believe  negative Eulerian pressure perturbations at the magnetic  pole are most likely, which means the surface displacement  ξr = δP/(ρg) is also negative at the magnetic pole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence,  magnetically distorted stars are likely to be oblate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Heuris-  tically, this is consistent with the idea that high magnetic  pressure at the star’s pole (or magnetic tension near the  equator) squeezes the star into a flattened shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  © 0000 RAS, MNRAS 000, 000–000  Magnetic Structure  11  The star’s ellipticity is  ε = ξr,surf  R  = δP  P  H  R  ∼ β × 10−10  �Bsurf  1kG  �2� R  R⊙  �4� M  M⊙  �−2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (62)  Similar to the flux perturbations, this is too small to detect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  The quadrupole moment of the star is  Q =  �  δρr4Y ∗  20dΩdr  MR2  ∼ β × 10−12  �Bsurf  1kG  �2� R  R⊙  �4� M  M⊙  �−2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (63)  The quadrupole moment of the star is even tinier than other  perturbations because the density perturbation is largest  near r ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2, providing a small lever arm for the quadrupole  moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  Ohmic Heating and Poynting Flux  Our models ignore non-ideal effects such as Ohmic heating  that will inevitably cause the field to decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' As long as these  effects are small, our approximations are suitable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We first  investigate the effect of Ohmic heating in our models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The  heating rate per unit volume is  ρϵOhm = 4πηj2  (64)  where the current density j is given in equation 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence  the heating rate is  ρϵOhm = η  λ2  4πR2  �  B2  r + B2  θ  �  +  η  r2 sin2 θ (∆∗Ψ)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (65)  Using equations 3, 5, and manipulating equation 18, this can  be expressed  ρϵOhm = η sin2 θ  r2  � −4  r2R2 Ψ2 + 1  R2 Ψ′2  +  �r2(δP + ρδΦ)  Ψ  + λ2  R2 Ψ  �2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (66)  The angular dependence is sin2 θ, and we have removed a  spherically symmetric term since we are only interested in  the non-spherical component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Equation 66 can be compared to other sources of heat  generation and/or heat diffusion in equation 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We find that  the Ohmic heating term is roughly three orders of magni-  tude smaller than the heat diffusion term (second term in  equation 45) for all the models shown in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence,  Ohmic heating is irrelevant for these models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Likely a more important effect is that the Ohmic diffu-  sion time tOhm = r2/η drops sharply near the surface of the  star, falling to ∼ 1 Gyr near the surface of our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The  diffusion time scale is even shorter in the atmosphere of the  star and could be shorter than the star’s lifetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Conse-  quently, the fields will dissipate or change their morphology  within the star’s atmosphere until they approach a current-  free (and force-free configuration).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This will bend the field  lines and hence create magnetic forces within the star until  it approaches a new (quasi)-equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Another way of seeing this is by examining the Poynting  flux (see Duez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2010a):  Fpoy = ∇ ·  �  ηFmag  �  (67)  where Fmag = (∇ × B) × B/4π is the Lorentz force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The  Poynting flux represents the decrease of electromagnetic en-  ergy per unit volume, and it has the same order of magnitude  as the Ohmic heating rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' As the fields dissipate, their en-  ergy density changes until the Poynting flux is nearly zero,  which happens on Ohmic diffusion time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Landstreet  (1987) discusses the importance of magnetic forces arising  due to Ohmic dissipation, finding they are likely negligible  for main sequence stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, over long time scales, the  morphology of the magnetic field will be altered away from  the solutions we have computed, which could also affect the  emerging luminosity perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='5  Linearity and near-surface effects  Since the value of δP/P can become very large near the sur-  face of the star (Figure 5-8), non-linear effects may also start  to be important in the near-surface layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In our models, the  δP/P eigenfunction is 1-2 orders of magnitude larger than  the surface luminosity perturbation δL/L, which is plotted  as a function of surface field strength in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence,  δP/P remains very small except for unphysically large sur-  face field strengths B ≳ 105 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  However, we placed the outer boundary at a radius of  r/R ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='99 in our calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This allowed us to avoid  uncertainties associated with the response of near-surface  convective layers above our outer boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The value of  δP/P likely continues to increase towards the surface (be-  cause P drops sharply), so it is possible that non-linear ef-  fects start to become important near the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' It is un-  likely that this affects the luminosity perturbation, which  changes smoothly with radius and cannot be greatly affected  in the near-surface layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Hence, the magnetic field profiles  and luminosity perturbations that we calculate are probably  robust, but the near-surface pressure and temperature pro-  files could be affected by these surface effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In principle,  this could affect the spectrum of the star, which is sensitive  the atmospheric temperature profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  4  DISCUSSION  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='1  Stability of Equilibrium  The magnetic field configurations we have computed are  in hydrostatic and radiative equilibrium, but we have not  investigated whether these equilibria are stable or unsta-  ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Braithwaite (2009) (see also Akg¨un et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Becerra  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2022b) showed that stable magnetic equilibria require  Etor ≳ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='25Epol, where Etor and Epol are the toroidal and  poloidal magnetic field energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' All of our models satisfy  this criterion (they typically have Etor/Epol ∼ 1) except for  the λ2 = 2 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' They also fall below the upper limit for  stability, Emag ≲ (1/10)GM 2/R for surface field strengths  less than ∼ 1 MG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Nonetheless, it is possible that some of  our models are unstable, which should be examined in fu-  ture work using 3D numerical simulations (Duez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2010b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Kaufman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  © 0000 RAS, MNRAS 000, 000–000  12  Fuller & Mathis  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='2  More Realistic Field Configurations  A limitation of our work is the assumption of a field with  purely dipole structure, whereas real fields likely have a  more complicated angular structure that changes with ra-  dius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' As discussed above, real fields likely have vanishing  current above the photosphere which (according to our solu-  tions, equation 16) require vanishing Br or vanishing λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The  first conflicts with observations of real stars (Landstreet &  Mathys 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Oksala et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Shultz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2019) while the  second implies purely poloidal fields which are well known  to be unstable (Markey & Tayler 1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' It is likely that a  real star has a more complicated angular and radial field  dependence, such that the electric currents vanish in the  near-vacuum outside the star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In these configurations, the  toroidal magnetic field vanishes on magnetic field lines that  penetrate the surface of the star (Lyutikov 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  These sorts of configurations have been computed near  the surface of a star in Raadu (1971);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Milsom & Wright  (1976), or in the interior for parameterized field configu-  rations (Lyutikov 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Akg¨un et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Becerra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, these configurations are not in thermal  equilibrium and therefore not stable over thermal time  scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Computing such fields in the bulk of a star and ac-  counting for thermal and hydrostatic equilibrium will re-  quire the solutions of partial differential equations, which is  beyond the scope of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We suspect that such con-  figurations (which appear qualitatively similar to those we  compute) will alter our results by a factor of order unity,  but will not greatly change any of our conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='3  Estimating the Perturbed Surface Flux  Our solutions which map onto Br = 0 or Br ∝ r−(ℓ+2)  may resemble more realistic magnetic field configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  We find that large values of β ∼200 are required for typical  toroidal fluxes of λ2 ∼ 1 − 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This entails internal temper-  ature, pressure, and flux perturbations that are ∼200 times  larger than a naive estimate of ∼B2/(GM 2/R4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Nonethe-  less, even for the strongest observed fields of B ∼ 10 kG in  main sequence stars, the bolometric luminosity variation is  δL/L ≲ 10−6 (Figure 9) and is not detectable even with  high-quality space-based photometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Applying von Zeipel’s law near the surface of the star,  one might expect magnetic fields to produce flux perturba-  tions of order  δL  L ∼ fmag  fgrav ∼ B2  surf  4πρRg .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (68)  This translates to  δL  L ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='004  �Bsurf  1 kG  �2�  ρ  10−8g/cm3  �−1� M  M⊙  �−1� R  R⊙  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (69)  This is several orders of magnitude larger than our calcula-  tions, clearly ruling out this expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Even though mag-  netic forces can be comparable to gravity near the star’s  surface, this applies only in a very thin layer near the photo-  sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The deep interior (where the outgoing thermal flux is  determined) has much higher density and is only weakly dis-  torted, leading to a flux perturbation on the order of equa-  tion 61, which is the von Zeipel expectation applied to the  deep interior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The even more naive estimate  δL  L ∼ Pmag  Pgas ∼ 4  �Bsurf  1 kG  �2�  Pgas  104erg cm−3  �−1  (70)  can be ruled out for the same reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  It would be useful to relate the observed flux perturba-  tion or surface magnetic field strength to a star’s internal  magnetic field strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This will be difficult to accomplish  from flux perturbations until a better understanding of their  cause is established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Our results suggest that central mag-  netic field strengths can be anywhere from ∼3-50 larger than  surface field strengths (see Figure 3) which is in qualita-  tive agreement with numerical simulations by Braithwaite  (2008) (see Figure 8 of that work), with higher central field  strengths for higher magnetic forces or helicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The force  will be difficult to observationally quantify but the helicity  could potentially be determined if the star’s surface toroidal  field can be measured (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Figure 6 in Kochukhov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  The effects of magnetic fields are very different for sys-  tems not in thermal equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In stars with transient  magnetic activity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', spots in magnetically active stars),  magnetic spot life times can be much shorter than the star’s  local thermal time, depending on the depth of the spots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Magnetic fields can also temporarily disrupt convective en-  ergy transport, which also occurs on a thermal time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This  is why the Sun’s spots can appear dark: they are not in  thermal equilibrium with underlying layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In our work, we  predict that magnetic poles of radiative stars can be either  hot or cool, although we have argued they are more likely  to be hot for realistic magnetic field configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This  agrees with the sign predicted by Cantiello & Braithwaite  (2011), who examined spots in hydrostatic equilibrium but  not thermal equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, thermal diffusion could  drastically reduce the flux perturbation below their estimate  (essentially equation 70), for spots that live longer than the  local thermal time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='4  Limitations  For the most part, our methods are general and are applica-  ble to nearly any type of radiative star, such as massive stars  or white dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, there are a few modifications that  need to be made depending on the circumstances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  In this work, we did not compute the physical displace-  ment vector ξ, which does not appear anywhere in our set  of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The reason for this is that the final state of the  system (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', the perturbed pressure, temperature, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=') and  its final energy is independent of the displacements needed  to reach that configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' There are infinite combinations  of ξr and ξ⊥ that satisfy the continuity equation  δρ + ∇ ·  �  ρξ  �  = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  (71)  However, we assumed uniform composition in our equation  of state (equation 40), a good approximation for young main  sequence stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In stars with composition differences, the  equation of state will contain an extra χµ(δµ/µ) term, where  µ is the mean molecular weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' If composition does not  diffuse, we have δµ ∼ −ξrdµ/dr, and hence the perturbed  state will depend explicitly on the displacement vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The  equilibrium configuration is then presumably given by the  © 0000 RAS, MNRAS 000, 000–000  Magnetic Structure  13  displacement which minimizes the total energy of the per-  turbed system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This should be accounted for when consider-  ing stars with composition gradients (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', evolved stars and  white dwarfs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Another issue we have neglected is anisotropic conduc-  tion induced by magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' In main sequence stars, this  effect is only important in the surface layers where the elec-  tron mean-free path increases and becomes comparable to  the Larmor radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' However, it may be important in the deep  interiors of white dwarfs where electrons conduct most of the  heat (Potekhin 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Potekhin & Yakovlev 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Chang &  Quataert 2010) and have fairly long mean free paths due to  the high electron degeneracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We hope to examine this effect  in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  We have also neglected any magnetically induced  changes to opacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' These could be important near a star’s  surface because magnetic fields split the energy levels of  atomic transitions, changing the opacity from bound-bound,  bound-free absorption, and free-free absorption (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Jordan  1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We suspect that this will not alter our conclusions re-  garding the perturbation to the bolometric surface flux, be-  cause effects limited to the surface layers cannot change the  emerging flux from below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This can be seen from equation  45, because the second term is of order unity near the sur-  face, and will only change the emerging flux by an amount  ∼ ∆r/r, where ∆r is the width over which near-surface ef-  fects are important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  What is more likely is that the star’s emergent spec-  trum is altered by magnetic changes to opacity, or by com-  position differences between the magnetic pole and equator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Even with no perturbation to the bolometric flux, a chang-  ing spectrum could create large differences in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', g-band or  r-band fluxes as the magnetic pole rotates in and out of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  As an example, Caiazzo in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' finds large changes in the  composition and spectrum as a function of rotational phase  in the magnetic WD ZTF J203349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='8+322901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='1 (“Janus”),  even though there is no clear variation in the bolomet-  ric flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Similar photometric variations (typically ∼1-3% in  amplitude) are observed in chemically peculiar magnetic A  type stars (H¨ummerich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Compositional inho-  mogeneities could naturally arise due to the perturbed gas  pressure in the near-surface layers, which will alter atomic  diffusion processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This process should be studied in more  detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  5  CONCLUSIONS  We have computed the effects of strong magnetic fields on  the structures of radiative main sequence stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Our focus  is the perturbed surface temperature and radiative flux in-  duced by the magnetic field, which can produce photomet-  ric modulation as the star rotates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Unlike most prior work,  we have computed structures in both hydrostatic and ther-  mal equilibrium, which applies to stars with long-lived fossil  fields, such as magnetic Ap stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Our models have simple  dipolar angular structure and include toroidal fields with  associated magnetic helicity λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  We find that magnetic fields at observed field strengths  of ∼ 1 kG produce negligible bolometric flux perturbations,  δL/L ≲ 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Even though such fields are large enough to  produce significant perturbations to the photospheric gas  pressure and hydrostatic force balance, the radiative flux  is determined by deeper layers of the star where magnetic  forces are negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The perturbed surface flux is compa-  rable to the von Zeipel theorem estimate δL/L ∼ fmag/(ρg)  only when evaluated in the deep interior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Depending on their  helicity and magnetic force, internal magnetic fields are typ-  ically a factor of ∼10 larger than surface magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  The size of the magnetic perturbation depends on the  strength of the magnetic forces, parameterized by β, which  is zero for a force-free field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Relatively large values of β ∼200  are needed for significant modification of the magnetic field  profile relative to a force-free configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' We have argued  that these values of β are most likely to occur in real stars  such that the magnetic profile matches onto boundary condi-  tions minimizing electric current near the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' This leads  to photometric modulations that are a few hundred times  larger than a naive estimate of δL/L∼B2  surfR4/(GM 2), but  still too small to be observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Photometric modulations ob-  served in magnetic stars likely arise from changes in the  emergent spectrum rather than changes in the bolometric  flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Although we have focused on a young 3 M⊙ model in  this work, the same method can be applied to other types of  predominantly radiative stars, such as moderately evolved  massive stars or white dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  Our work can be improved in several ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' First, real-  istic magnetic configurations likely have toroidal fields con-  fined to closed poloidal surfaces within the star such that  current does not flow into the atmosphere and dissipate  the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Incorporating this condition will require  more complicated magnetic topologies and non-separable  solutions to the hydrostatic balance and radiative diffu-  sion equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' The impacts of rotation, where the rotation  and magnetic axis are often misaligned, and of the associ-  ated centrifugal forces have also been neglected in this work  (Monaghan 1973;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Galea & Wood 1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Our models do not  account for composition gradients within a star, which may  significantly affect the magnetic perturbations in evolved  stars and white dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Finally, magnetic changes to opac-  ity and anisotropic conduction should be included in future  models in order to better interpret observable photometric  and spectroscopic variations of magnetic stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  JF is thankful for support through an Innovator Grant  from The Rose Hills Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' acknowledges sup-  port from CNES SOHO, PLATO, and LISA grants at  CEA/IRFU/DAp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  DATA AVAILABILITY  The relaxation code to compute magnetic perturbations is  available upon request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='  REFERENCES  Akg¨un T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Reisenegger A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Mastrano A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Marchant P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  2013, MNRAS, 433, 2445  Becerra L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Reisenegger A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Valdivia J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Gusakov M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  2022a, MNRAS, 511, 732  © 0000 RAS, MNRAS 000, 000–000  14  Fuller & Mathis  Becerra L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Reisenegger A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Valdivia J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Gusakov M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  2022b, MNRAS, 517, 560  Braithwaite J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2008, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 386, 1947  Braithwaite J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2009, MNRAS, 397, 763  Braithwaite J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Nordlund ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2006, Astronomy & Astro-  physics, 450, 1077  Braithwaite J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Spruit H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2004, Nature, 431, 819  Braithwaite J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Spruit H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2017, Royal Society Open  Science, 4, 160271  Broderick A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Narayan R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2008, MNRAS, 383, 943  Bugnet L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2021, A&A, 650, A53  Busse F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1981, Geophysical and Astrophysical Fluid  Dynamics, 17, 215  Cantiello M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Braithwaite J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2011, A&A, 534, A140  Chandrasekhar S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1956, ApJ, 124, 232  Chandrasekhar S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Prendergast K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1956, Proceedings of  the National Academy of Science, 42, 5  Chang P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Quataert E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2010, MNRAS, 403, 246  Davies G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1968, Australian Journal of Physics, 21, 293  Decressin T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Mathis S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Palacios A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Siess L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Talon S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  Charbonnel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Zahn J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2009, A&A, 495, 271  Duez V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Mathis S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2010, A&A, 517, A58  Duez V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Mathis S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Turck-Chi`eze S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2010a, MNRAS, 402,  271  Duez V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Braithwaite J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Mathis S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2010b, ApJ, 724, L34  Eddington A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1929, MNRAS, 90, 54  Fuller J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Cantiello M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Stello D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Garcia R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Bildsten L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  2015, Science, 350, 423  Galea E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Wood W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1985, MNRAS, 217, 633  Garc´ıa R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2014, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 563, A84  H¨ummerich S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2018, A&A, 619, A98  Jordan S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1992, A&A, 265, 570  Kaufman E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Lecoanet D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Anders E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Brown B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Vasil  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Oishi J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Burns K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2022, MNRAS, 517, 3332  Kochukhov O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Lundin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Romanyuk I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Kudryavtsev D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  2011, ApJ, 726, 24  Lander S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Jones D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2012, MNRAS, 424, 482  Landstreet J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1987, MNRAS, 225, 437  Landstreet J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Mathys G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2000, A&A, 359, 213  Lecoanet D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Vasil G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Fuller J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Cantiello M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Burns  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2017, MNRAS, 466, 2181  Li L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Ventura P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Basu S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Sofia S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Demarque P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2006,  ApJS, 164, 215  Li G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Deheuvels S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Ballot J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Ligni`eres F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2022, Nature,  610, 43  Loi S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2021, MNRAS, 504, 3711  Lyutikov M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2010, MNRAS, 402, 345  Maeder A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1999, A&A, 347, 185  Markey P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Tayler R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1973, MNRAS, 163, 77  Mathis S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2013, in Goupil M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Belkacem K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Neiner C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  Ligni`eres F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Green J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', eds, , Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 865, Lecture Notes in  Physics, Berlin Springer Verlag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' 23, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content='1007/978-3-  642-33380-4˙2  Mathis S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Bugnet L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Prat V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Augustson K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Mathur S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  Garcia R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2021, A&A, 647, A122  Mestel L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Moss D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1977, MNRAS, 178, 27  Milsom F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Wright G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1976, MNRAS, 174, 307  Monaghan F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1966, MNRAS, 132, 1  Monaghan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1973, MNRAS, 163, 423  Morel T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2014, The Messenger, 157, 27  Moss D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1973, MNRAS, 164, 33  Moss D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1979, MNRAS, 187, 601  Oksala M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Silvester J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Kochukhov O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Neiner C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Wade  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', MiMeS Collaboration 2018, MNRAS, 473, 3367  Ostriker J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Hartwick F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1968, ApJ, 153, 797  Paxton B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Bildsten L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Dotter A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Herwig F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Lesaffre P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  Timmes F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2011, ApJS, 192, 3  Potekhin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1999, A&A, 351, 787  Potekhin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Yakovlev D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2001, A&A, 374, 213  Press W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Teukolsky S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Vetterling W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Flannery  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2007, Numerical Recipes 3rd Edition: The Art of  Scientific Computing, 3 edn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Cambridge University Press,  USA  Raadu M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1971, Ap&SS, 14, 464  Reisenegger A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2009, A&A, 499, 557  Rieutord M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2006, EAS Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 21, 275  Shultz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2019, MNRAS, 490, 274  Shulyak D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2007, A&A, 464, 1089  Shulyak D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Kochukhov O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Valyavin G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Lee B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  Galazutdinov G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Kim K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Han I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Burlakova T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2010,  A&A, 509, A28  Stello D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Cantiello M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Fuller J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Huber D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Garc´ıa R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=',  Bedding T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Bildsten L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', Silva Aguirre V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2016, Na-  ture, 529, 364  Sweet P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1950, MNRAS, 110, 548  Tayler R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1973, MNRAS, 161, 365  Tayler R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1980, MNRAS, 191, 151  Taylor J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1974, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 33, 1139  Wade G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 2016, MNRAS, 456, 2  Wright G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1969, MNRAS, 146, 197  von Zeipel H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
+page_content=', 1924, MNRAS, 84, 665  © 0000 RAS, MNRAS 000, 000–000' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9FKT4oBgHgl3EQf0C6i/content/2301.11914v1.pdf'}
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+RF Injection Locking of THz Metasurface Quantum-
+Cascade VECSEL 
+Yu Wu,1* Christopher A. Curwen,2 Mohammad Shahili,1 John L. Reno,3 
+Benjamin S. Williams1  
+1Department of Electrical and Computer Engineering, University of California Los Angeles, Los Angeles, 
+California 90095, USA 
+2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA 
+3Sandia National Laboratories, Center of Integrated Nanotechnologies, MS 1303, Albuquerque, New Mexico 
+87185, USA 
+*Corresponding author: ywu17@ucla.edu 
+ 
+Abstract: RF injection locking and spectral broadening of a terahertz (THz) 
+quantum-cascade 
+vertical-external-cavity 
+surface-emitting 
+laser 
+(QC-
+VECSEL) is demonstrated. An intra-cryostat VECSEL focusing cavity design 
+is used to enable continuous-wave lasing with a cavity length over 30 mm which 
+corresponds to a round-trip frequency near 5 GHz. Strong RF current 
+modulation is injected to the QC-metasurface electrical bias to pull and lock 
+the round-trip frequency. The injection locking range at various RF injection 
+powers is recorded and compared with the injection locking theory. Moreover, 
+the lasing spectrum broadens from 14 GHz in free-running mode to a maximum 
+spectral width around 100 GHz with 20 dBm of injected RF power. This 
+experimental setup is suitable for further exploration of active mode-locking 
+and picosecond pulse generation in THz QC-VECSELs.  
+1. Introduction  
+The terahertz (THz) spectral region has a need for high-resolution, high-speed 
+spectroscopy techniques, as many gas phase polar molecular species have strong 
+characteristic rotational lines there. Examples include applications in industrial and 
+environmental monitoring,[1,2] chemical detection and identification,[3,4] combustion 
+diagnostics.[5] The quantum cascade (QC) laser is well suited for spectroscopic 
+applications as it has been demonstrated as a compact, electrically pumped 
+semiconductor source which gives high power, broadband, coherent THz 
+radiation.[6–8] Its inherently high optical nonlinearity induces self-phase locking 
+through four-wave mixing, which promotes the generation of spontaneous frequency 
+combs; these have been demonstrated in waveguide-based Fabry-Pérot[9–11] and ring 
+QC-lasers.[12,13] Based on that, THz dual-comb spectroscopy has been demonstrated, 
+surpassing the precision and speed of traditional Fourier spectrometers by several 
+orders of magnitude.[14–17]  
+
+In separate experiments, THz quantum-cascade lasers have recently been 
+implemented in the vertical-external-cavity surface-emitting laser (VECSEL) 
+architecture, which exhibits watt-level output power, near diffraction-limited beam 
+quality, and ~20% continuous fractional single-mode tuning.[18–20] The key 
+component of a QC-VECSEL is an amplifying reflectarray metasurface of metal-
+metal waveguide antennas that are loaded with QC-gain material. It is further paired 
+with a partially transmissive output coupler to form the laser cavity. In contrast to 
+ridge-waveguide QC-lasers, experiments have shown that QC-VECSELs tend to 
+operate in single-mode regime despite having large gain bandwidths. For example, 
+we have developed an intra-cryostat focusing VECSEL cavity to reduce the intra-
+cavity diffraction loss and enable continuous-wave (CW) lasing at 3.4 THz with a 
+cavity length of ∼30 mm.[21] Even though the gain bandwidth of the metasurface 
+used was at least 100 times larger than the free spectral range, only a single lasing 
+mode was observed. This is mainly due to a lack of spatial hole burning within the 
+QC-VECSEL metasurface which suppresses multi-mode instabilities,[22] although it 
+is perhaps compounded by the fact that no effort towards dispersion engineering has 
+Figure 1. (a) Schematic of the QC-VECSEL based on an intra-cryostat focusing cavity design. (b) 
+Scanning electron microscopy image of the fabricated QC-metasurface. The inset shows the 
+dimension and E-field distribution in a single ridge antenna. (c) FEM simulated active metasurface 
+reflectance, output coupler transmittance and GDD contributed by the two components. Shaded 
+area indicates the frequency range where lasing is observed. (d) Schematic of experimental setup 
+for RF injection locking. THz lasing spectrum (e) and beat note spectra (f) of the free-running QC-
+device in existence of optical feedback are collected at a DC bias of 0.235 mA, where optical 
+feedback is provided by the moving FTIR mirror. The beat note spectra are measured in both 
+Average (solid) and Max Hold modes (dashed) with a RBW of 2 kHz.  
+
+(a)
+Outputcoupler
+(b)
+IEI at 3.36 THz
+X104
+(c)
+21.5
+QC-gain
+FEM
+Exp
+10日
+L80.2
+Biasarea
+d=0.4mm
+41.7μm
+MS+OC
+OC
+Off-axis
+(sd)
+0.5
+MS
+paraboloid
+GDD (
+QC-metasurface
+mirror
+-0.5
+2.5
+3
+3.5
+4
+Frequency (THz)
+100
+Intensity (a.u.)
+(e)
+(d)
+Directional
+Microwave
+RF synthesizer
+FTIR
+Bias-T
+coupler
+amplifier
+10-2
+SMA
+3.3
+3.4
+3.5
+3.6
+Optical
+Frequency(THz)
+feedback
+Intensity (dBm)
+60
+Cryostat
+(f)
+50kH
+-80
+DCpower
+8kHz
+Average
+MaxHold
+supply
+Spectrum
+-100
+analyzer
+BN
+4852.4
+4852.6
+4852.8
+Frequency(MHz)yet been attempted. Despite these challenges, there is strong interest in achieving 
+active mode-locked QCLs and frequency combs within the QC-VECSEL 
+architecture.  
+Radiofrequency (RF) current modulation of QC-lasers has been demonstrated to 
+promote the generation of sidemodes; by injecting a RF signal near the cavity round-
+trip frequency, the generated sidemodes will lock existing adjacent free-running 
+lasing modes or seed new ones, which allows for the stabilization and tuning of 
+frequency comb states.[23–26] RF modulation and injection locking is also an 
+important mechanism for active mode-locking in QC-lasers;  pulses as narrow as 4-
+5 ps have been reported.[27,28]  
+In this article, we demonstrate the emergence of spectral broadening and 
+multimoding in THz QC-VECSEL as we inject strong RF current modulation to the 
+QC-metasurface at a frequency close to the cavity round-trip frequency; at the same 
+time, round-trip frequency pulling and locking to the injected RF signal is observed. 
+The lasing bandwidth and injection locking range increase monotonically with the 
+injected RF power. Lasing modes spanning ~100 GHz are demonstrated under an 
+injected RF power of 20 dBm at 4852.7 MHz, along with a locking range ~5 MHz.  
+2. Sample and experimental setup 
+The QC-VECSEL used for all measurements is based on an intra-cryostat focusing 
+cavity design, as sketched in Figure 1(a). An off-axis paraboloid (OAP) mirror with 
+a focal length of 12.7 mm is introduced into the VECSEL cavity to reduce the intra-
+cavity diffraction loss and enable CW lasing using small metasurfaces in long lasing 
+cavities.[21] The QC-metasurface used in this paper is the same one as reported in ref 
+[21], with a small bias area of diameter d = 0.4 mm for reduced injection current. It is 
+designed to be resonant at 3.3 THz and consists of an array of ridges of width 12.2 
+µm repeated with a period of 41.7 µm (Figure 1(b)). An output coupler with ROC ≈ 
+95% is used in pair with the metasurface to form a laser cavity. Both two components 
+are dispersive and contribute to the group delay dispersion (GDD) over one round 
+trip - it exhibits a maximum value exceeding 0.35 ps2 in the frequency range where 
+lasing occurs. The simulated spectral response of the metasurface and the output 
+coupler are plotted in Figure 1(c) based on full-wave 2D finite-element (FEM) 
+electromagnetic reflectance simulation (Ansys HFSS). Detailed information of the 
+active region design and simulation parameters can be found in the Supporting 
+Information.  
+The experimental setup for RF injection locking is depicted in Figure 1(d). All the 
+measurements were performed in vacuum at a temperature of 77 K. We note that 
+formable semi-rigid coaxial cable is used within the cryostat up to the chip carrier 
+package (see Supporting Information). Due to impedance mismatch between the 
+
+50Ω SMA port and the QC-device, the spectrum analyzer collects not only the 
+generated beat note from the QC-device fBN (blue arrow), but also the RF injection 
+signal reflected at the interface of SMA/QC-device fRF (green arrow). 
+In free-running case, although only single-mode lasing was observed using the 
+same QC-device in ref [21], here we note that the existence of optical feedback can 
+induce multi-mode operation.[29–31] Due to the temporally varying small feedback 
+from the scanning Fourier-transform infrared spectrometer (FTIR, Nicolet 8700) 
+mirrors, we observed at least two lasing modes separated by ~14 GHz in the emission 
+spectrum (Figure 1(e)). Additional low intensity sidemodes may also exist but 
+cannot be resolved by the limited FTIR resolution of 7.5 GHz. This phenomenon is 
+similar as that observed in ref [30], where additional lasing modes are observed in a 
+Mid-IR QC-laser under tilted optical feedback. Through nonlinear mixing of the 
+free-running lasing modes, a weak electrical beat note signal is observed. It is 
+collected using the spectrum analyzer (Agilent N9020a) both in Average mode and 
+in Max Hold mode over 30 seconds, which indicates a round-trip frequency fBN ≈ 
+4852.7 MHz and an equivalent cavity length around 31 mm (Figure 1(f)). A narrow 
+8-kHz -3dB linewidth in Average mode and 60-kHz linewidth in Max Hold mode of 
+the intermodal beat note is on the same order as the free-running linewidth of the 
+single THz lasing mode measured in [21]; it is likely contributed by only two (or a 
+few) lasing modes. Furthermore, recent study of optical feedback has highlighted its 
+effect on THz QC-lasers combs.[32–34] Here, we experimentally demonstrate that 
+optical feedback plays an important role in determining not only the free-running 
+beat note frequency but also the injection locking range (see Supporting 
+Information).  
+3. RF injection locking 
+With the knowledge of an accurate round-trip frequency, we are able to 
+systematically study the modulation-dependent behavior of this QC-device. We 
+swept the RF modulation frequency around the round-trip frequency at various 
+modulation powers from -20 dBm to 20 dBm. All RF powers indicated in this paper 
+refer to the nominal output level of the RF synthesizer (Hewlett-Packard 83650B) 
+or after a 20 dBm amplifier (Hewlett-Packard 8349B). The DC bias is fixed at a 
+current of 0.235 mA (≈1.17×Ith), and the THz emission spectra as well as intermodal 
+beat note are collected and plotted in Figure 2.  
+At the lowest power level of -20 dBm, the spectral map in Figure 2(a) clearly shows 
+that the beat note is pulled toward the injection signal and finally locked. A locking 
+range of 30 kHz is demonstrated which increases with respect to the RF injection 
+power. Starting from an RF power of -2.5 dBm, injection locking occurs before the 
+beat note is fully pulled to meet the injected signal fRF (Figure 2(b)); at the same 
+
+time, lasing bandwidth broadening is observed in the THz emission spectra. This 
+spectral broadening increases with respect to RF power as shown in Figure 2(d). The 
+maximum RF injection power used in this measurement is 20 dBm limited by the 
+max allowable power of the bias-Tee. THz emission and RF beat note spectral maps 
+in this case are plotted in Figure 2(e-f). The maximum spectral broadening occurs at 
+fRF = 4852.7 MHz with lasing modes spanning around 100 GHz (Figure 2(g)). 
+However, due to the limited FTIR resolution of 7.5 GHz, we were not able to 
+spectrally resolve individual lasing modes. The corresponding power and voltage vs. 
+current (P-I-V) curves are plotted in Figure 2(h) (solid curve). A maximum output 
+power around 10 mW was collected using a pyroelectric detector (GentecEO). 
+Compared with the P-I characteristic in the free-running case (dashed curve), the 
+output power, as well as the lasing threshold, is slightly lower. It is noticed from 
+Figure 2(e) that the symmetry of the lasing spectrum is highest at fRF = 4852.7 MHz, 
+where the maximum bandwidth is observed with relative low THz output power 
+obtained from the P-I curve. At injection frequencies above/below this value, the 
+optical power increases – still smaller than that in free-running case – and 
+concentrates toward lower/higher portion of the spectrum. This phenomenon is 
+Figure 2. Beat note spectral map under constant RF injection power of -20 dBm (a) and -2.5 dBm 
+(b) with RF modulation frequency sweeping around the round-trip frequency. (c) Experimental 
+injection locking range at different RF injection powers (blue stars), following a 0.5-slope 
+dependence in log–log scale (red dashed line). The free-running beat note frequency was shifted 
+from ~ 4842 MHz in (a-c) to ~ 4853 MHz in (d-h) as the movement of cryostat changes the amount 
+of optical feedback. (d) THz lasing spectra at increasing RF power when fRF is fixed at 4852.7 MHz. 
+(e) Lasing spectral and (f) beat note maps of the device under constant RF injection power of 20 
+dBm. The estimated locking range is pointed out by the red arrows. The maximum spectral 
+broadening occurs at fRF = 4852.7 MHz (white dashed line) and the THz lasing spectrum and P-I-
+V curves in this case are plotted in (g-h). 
+
+4842.1
+(a)
+dBm
+(d)
+(e)
+20dBm
+(f)
+20 dBm
+-40
+4842.05
+20dBm
+-20dBm
+60
+19dBm
+Locking
+(MHz)
+80
+18dBm
+4842
+17dBm
+injection freg (
+4854
+Range
+100
+freq
+-120
+16dBm
+=4852.7MHz
+15dBm
+4841.9
+4842
+4842.1
+RF Inj.
+RF injection f
+14dBm
+Frequency (MHz)
+4852
+Signal fr
+13dBm
+800
+dBm
+(b)
+dBm
+12dBm
+600
+Beat note fen
+20
+4842.2
+-20
+11dBm
+40
+-2.5 dBm
+48
+Intensity (a.u.)
+10dBm
+4850
+400
+60
+4842
+9dBm
+200
+80
+8dBm
+100
+4841.8
+100
+Z dBm
+6dBm
+3.33.353.43.453.5
+4848
+4852
+4856
+4841.5
+4842
+4842.5
+5dBm
+Frequency(THz)
+Frequency(MHz)
+Frequency (MHz)
+4dBm
+3dBm
+(h)
+Current (A)
+range(kHz)
+(c)
+2dBm
+(g)
+1dBm
+Atm
+0
+0.1
+0.2
+103
+OdBm
+('ne)
+absorption
+10
+1dBm
+-2dBm
+M
+Intensity
+10
+-3dBm
+-4dBm
+6
+-5dBm
+~100GHz
+4
+5
+(mW)
+Expt.
+-6dBm
+-7dBm
+-RFoff
+Adler's Eq.
+-8dBm
+2
+fr=4852.7MHz
+101
+-9dBm
+0
+20.dBm
+0
+-20
+-10
+0
+10
+20
+3.35
+3.45
+3.55
+3.3
+3.4
+3.5
+3.6
+0
+200
+400
+600
+RFpower(dBm)
+Freguency(THz)
+Freguency (THz)
+CurrentDensity(A/cm2)similar as that reported in ref [26] and a possible explanation can be found in ref [35] 
+due to phase mismatch between the modulation period and group round-trip time. In 
+Figure 2(f), although there is no beat note pulling observed, it is notable that the 
+emission spectrum undergoes distinct change as the beat note disappears (pointed 
+out by red arrows) – it is believed that this is a signature of injection locking and 
+occurs in our measurements under different RF powers.  
+The experimental locking range at various RF injection powers is plotted in Figure 
+2(c). To analyze the phenomenon of RF injection locking, Adler’s equation is 
+commonly used with a locking bandwidth given by:[23,36] 
+𝛥𝜈 = 2𝜈0
+𝑄 √𝑃𝑖𝑛𝑗
+𝑃0
+,                                                     (1) 
+where Q is the cold-cavity quality factor, 𝜈0 and P0 are the frequency and power of 
+a free-running longitudinal mode, while Pinj is the power of the injected sideband 
+induced by RF injection. Adler’s equation indicates a square root dependence of the 
+locking bandwidth on the RF power and fits our experimental results well at low RF 
+powers (red dashed line). However, our experimental locking range deviates from 
+Adler’s equation towards higher values under strong RF modulation. This may 
+indicate the limitation of Adler’s equation in explaining RF injection locking 
+especially in the case when multiple new lasing modes are excited at RF powers > 
+−2.5 dBm. Adler’s equation assumes a weak injection signal where amplitude 
+perturbation induced by the injection signal is not considered; a more rigorous 
+derivation of the locking range is therefore needed.  
+Moreover, we studied the behavior of this QC-device at various DC biases ranging 
+from the lasing threshold to near the NDR point. Figure 3(a) shows the lasing spectra 
+under 20 dBm RF injection at a frequency of fRF = 4852.7 MHz. Significant spectral 
+Figure 3. (a) THz lasing spectra at various biases when RF signal at 4852.7 MHz is injected into the 
+QC-device, the RF power used is 20 dBm for significant spectral broadening. (b) Injection locking 
+range as a function of bias current under -15 dBm RF power in the cases of different 
+length/strength/angle of optical feedback.  
+
+120
+(a.u.)
+(a)
+(b)
+247 mA
+244mA
+(ZH>) 
+Intensity
+100
+240mA
+235mA
+range
+230 mA
+80
+Normalized
+225 mA
+Locking 
+219mA
+60
+213 mA
+207 mA
+201 mA
+40
+3.3
+3.4
+3.5
+3.6
+0.2
+0.210.220.230.240.25
+Frequency (THz)
+Biascurrent (A)broadening is observed at all the applied biases, and the lasing bandwidth increases 
+only slightly with respect to the bias current as more modes are brought above the 
+lasing threshold. 
+As a next step, the effects of device bias on the injection locking bandwidth were 
+investigated. We swept the RF modulation frequency around the round-trip 
+frequency at a fixed injection power of -15 dBm and measured the injection locking 
+bandwidth at various biases. Small injection power was used so the locking range 
+can be more clearly observed. Additionally, we repeated such bias sweeps while 
+providing different magnitude, phase, and angle of feedback light from an external 
+mirror, the corresponding locking ranges are indicated by different colored curves 
+in Figure 3(b). Our experimental observation reveals that the relationship between 
+locking range and device bias is related to the condition of optical feedback, i.e. 
+feedback length (phase), strength and tilted angle. This is significantly different from 
+previous demonstrations using ridge-waveguide QC-lasers, where the locking range 
+became smaller with increasing bias.[23,37] In our system, we could make a simple 
+assumption that there are two free-running modes, where mode ω1 is induced by 
+optical feedback around the main lasing peak ω0 and is locked by the RF-excited 
+sideband of the latter. The ratio of Pinj/P0 in Adler’s equation can be estimated as the 
+ratio of the free-running power of mode ω0 and that of mode ω1 as the injected RF 
+power is fixed, which determines the injection locking range. How the locking range 
+changes is therefore determined by how the relative power of two lasing modes 
+develops with respect to bias. Unfortunately, this is not able to be observed 
+experimentally limited by the resolution of our FTIR. In theory, the spectral 
+characteristics of the device versus applied bias is expected to be affected by the 
+changes of threshold gain induced by optical feedback and the alignment of 
+compound-cavity modes formed in the external cavity with respect to gain, which is 
+related to not only the length and strength of optical feedback, but also the tilt angle 
+of external mirror.[31] To fully understand this phenomenon, a theoretical study of 
+laser dynamics and instabilities of QC-VECSELs under optical feedback and 
+systematic experiments of the RF-injected system with well-controlled, adjustable 
+optical feedback will be needed and are beyond the scope of this paper. 
+4. Discussion and conclusion  
+The injection locking range obtained in this paper is considerably smaller 
+compared with those demonstrated in RF injection-locked Fabry-Pérot waveguide 
+QC-lasers at same level of RF power.[23,25] One of the reasons is that QC-VECSELs 
+have higher quality factors compared with ridge waveguide QC-lasers. Our 
+VECSEL has a 31 mm-long external cavity and low loss from the ~95% reflectance 
+output coupler; using a coupled-cavity model we estimate a cold-cavity linewidth of 
+
+ν0/Q ≈ 70 MHz. This is around 300 times smaller than a value of 25 GHz estimated 
+in ref [23]. In addition, intrinsic and technical issues with our QC-VECSEL setup 
+result in a low efficiency of RF power transfer at ~4.8 GHz from the synthesizer to 
+the QC-metasurface bias terminal. First, due to parasitic capacitances contributed by 
+unbiased regions, the QC-metasurface itself exhibits a larger RC time-constant 
+compared with a narrow ridge waveguide. Second, the electrical packaging has not 
+been optimized for RF operation, where wire bonds and wire bonding pads 
+contribute parasitic inductance and capacitance respectively. Consequently, there is 
+a huge impedance mismatch between the 50Ω SMA port and the QC-device, the 
+resulting transmittance of RF signal through the SMA/QC-package boundary is 
+simulated to be ~4% at a target frequency of 4.8 GHz (see Supporting Information), 
+only part of which will be applied to modulate the gain material. To make things 
+worse, an additional ~8 dB RF attenuation has been characterized accounting for 
+losses through cables and directional coupler from the synthesizer to the SMA 
+connector. In contrast to other demonstrations of ridge waveguide QC-lasers using 
+RF coplanar probes,[23,38] RF launchers,[39] or custom high-frequency PCB mounts[28] 
+to achieve modulation of QC-lasers up to 35 GHz, microwave rectification technique 
+indicates a significant roll-off at frequency higher than 3 GHz in our QC-device (see 
+Supporting Information). 
+In conclusion, we demonstrate RF injection locking in a THz QC-VECSEL based 
+on intra-cryostat focusing cavity design. Round-trip frequency pulling and locking 
+against an RF injection signal is observed. Furthermore, the RF amplitude 
+modulation leads to broadening of the lasing spectrum up to a spectral width of 100 
+GHz. This is particularly notable, as multi-mode lasing in QC-VECSELs has been 
+extremely difficult to achieve due to the lack of spatial hole burning within the 
+metasurface; before now at most 9 lasing modes had been observed.[22] There are 
+several obvious avenues for improvement. First, RF attenuation and impedance 
+mismatch severely limits the modulation efficiency, and strong RF reflections 
+impede the detection of the electrical beat note signal using a spectrum analyzer. 
+This can be improved by optimizing the electrical packaging of the QC-device, i.e. 
+reducing the capacitance and inductance portion of the equivalent circuit by 1) 
+redesigning the QC-metasurface with reduced unbiased area and an improved RF 
+feed structure; 2) replacing the electrical contact pad with a well-designed PCB 50Ω 
+transmission line feed up to the edge of the metasurface chip with minimal wire bond 
+length. Second, we note that no particular effort to provide dispersion compensation 
+has been attempted here; further engineering of GDD within the QC-VECSEL cavity 
+may be needed to increase the lasing across the entire ~1 THz gain bandwidth. 
+Finally, given measurements of ridge-waveguide THz QC-lasers under strong RF 
+modulation, it is quite likely that this device is generating short pulses in an active 
+mode-locking regime.[27,28] Further characterization techniques such as shifted-wave 
+
+interference Fourier-transform spectroscopy (SWIFTs)[10,40,41] or asynchronous 
+electro-optical sampling will be needed to recover the time-domain structure of the 
+field.[42,43] 
+ 
+Supporting Information  
+Supporting Information is available from the author. 
+Acknowledgments  
+The authors thank David Burghoff, Andres Forrer, Giacomo Scalari, and Stefano 
+Barbieri for valuable conversations. Microfabrication was performed at the UCLA 
+Nanoelectronics Research Facility, wire bonding was performed at the UCLA 
+Center for High Frequency Electronics. This work was performed, in part, at the 
+Center for Integrated Nanotechnologies, an Office of Science User Facility operated 
+for the U.S. Department of Energy (DOE) Office of Science. Sandia National 
+Laboratories is a multimission laboratory managed and operated by National 
+Technology and Engineering Solution of Sandia, LLC., a wholly owned subsidiary 
+of Honeywell International, Inc., for the U.S. Department of Energy's National 
+Nuclear Security Administration under contract DE-NA-0003525. Partial funding 
+was provided by the National Science Foundation (2041165), and the National 
+Aeronautics and Space Administration (80NSSC19K0700). 
+References 
+[1] 
+D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, M. C. Nuss, Appl. Phys. B 
+Lasers Opt. 1998, 67, 379. 
+[2] 
+A. Cuisset, F. Hindle, G. Mouret, R. Bocquet, J. Bruckhuisen, J. Decker, A. Pienkina, C. Bray, É. 
+Fertein, V. Boudon, Appl. Sci. 2021, 11, 1229. 
+[3] 
+H. Zhong, A. Redo-Sanchez, X.-C. Zhang, Opt. Express 2006, 14, 9130. 
+[4] 
+I. R. Medvedev, C. F. Neese, G. M. Plummer, F. C. De Lucia, Opt. Lett. 2010, 35, 1533. 
+[5] 
+M. Araki, K. Matsuyama, Curr. Appl. Phys. 2022, 36, 83. 
+[6] 
+R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. 
+C. Iotti, F. Rossi, Nature 2002, 417, 156. 
+[7] 
+L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, E. H. Linfield, Electron. Lett. 
+2017, 53, 799. 
+[8] 
+D. Turčinková, G. Scalari, F. Castellano, M. I. Amanti, M. Beck, J. Faist, Appl. Phys. Lett. 2011, 
+99, 191104. 
+[9] 
+M. Rösch, G. Scalari, M. Beck, J. Faist, Nat. Photonics 2014, 9, 42. 
+[10] 
+D. Burghoff, T. Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J. R. Gao, J. L. 
+Reno, Q. Hu, Nat. Photonics 2014, 8, 462. 
+[11] 
+A. Forrer, Y. Wang, M. Beck, A. Belyanin, J. Faist, G. Scalari, Appl. Phys. Lett. 2021, 118, 
+131112. 
+[12] 
+M. Piccardo, B. Schwarz, D. Kazakov, M. Beiser, N. Opačak, Y. Wang, S. Jha, J. Hillbrand, M. 
+Tamagnone, W. T. Chen, A. Y. Zhu, L. L. Columbo, A. Belyanin, F. Capasso, Nature 2020, 582, 
+360. 
+[13] 
+M. Jaidl, N. Opačak, M. A. Kainz, S. Schönhuber, D. Theiner, B. Limbacher, M. Beiser, M. 
+Giparakis, A. M. Andrews, G. Strasser, B. Schwarz, J. Darmo, K. Unterrainer, Optica 2021, 8, 
+780. 
+
+[14] 
+M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, J. Faist, Appl. Phys. Lett. 2016, 108, 
+171104. 
+[15] 
+L. A. Sterczewski, J. Westberg, Y. Yang, D. Burghoff, J. Reno, Q. Hu, G. Wysocki, Optica 2019, 
+6, 766. 
+[16] 
+H. Li, Z. Li, W. Wan, K. Zhou, X. Liao, S. Yang, C. Wang, J. C. Cao, H. Zeng, ACS Photonics 
+2020, 7, 49. 
+[17] 
+L. Consolino, M. Nafa, M. De Regis, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. 
+Davies, E. H. Linfield, M. S. Vitiello, S. Bartalini, P. De Natale, Commun. Phys. 2020, 3, 1. 
+[18] 
+L. Xu, C. A. Curwen, P. W. C. Hon, Q.-S. Chen, T. Itoh, B. S. Williams, Appl. Phys. Lett. 2015, 
+107, 221105. 
+[19] 
+C. A. Curwen, J. L. Reno, B. S. Williams, Appl. Phys. Lett. 2018, 113, 011104. 
+[20] 
+C. A. Curwen, J. L. Reno, B. S. Williams, Nat. Photonics 2019, 13, 855. 
+[21] 
+Y. Wu, C. Curwen, J. L. Reno, B. Williams, Appl. Phys. Lett. 2022, 121, 191106. 
+[22] 
+Y. Wu, S. Addamane, J. L. Reno, B. S. Williams, Appl. Phys. Lett. 2021, 119, 111103. 
+[23] 
+P. Gellie, S. Barbieri, J. F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. 
+H. Linfield, H. E. Beere, D. A. Ritchie, Opt. Express 2010, 18, 20799. 
+[24] 
+H. Li, P. Laffaille, D. Gacemi, M. Apfel, C. Sirtori, J. Leonardon, G. Santarelli, M. Rösch, G. 
+Scalari, M. Beck, J. Faist, W. Hänsel, R. Holzwarth, S. Barbieri, Opt. Express 2015, 23, 33270. 
+[25] 
+A. Forrer, L. Bosco, M. Beck, J. Faist, G. Scalari, Photonics 2020, 7, 9. 
+[26] 
+B. Schneider, F. Kapsalidis, M. Bertrand, M. Singleton, J. Hillbrand, M. Beck, J. Faist, Laser 
+Photonics Rev. 2021, 15, 2100242. 
+[27] 
+A. Mottaghizadeh, D. Gacemi, P. Laffaille, H. Li, M. Amanti, C. Sirtori, G. Santarelli, W. Hänsel, 
+R. Holzwart, L. H. Li, E. H. Linfield, S. Barbieri, Optica 2017, 4, 168. 
+[28] 
+U. Senica, A. Forrer, T. Olariu, P. Micheletti, S. Cibella, G. Torrioli, M. Beck, Jerome Faist, G. 
+Scalari, arXiv:2207.06737 [physics.optics]. 
+[29] 
+X. Qi, K. Bertling, T. Taimre, G. Agnew, Y. L. Lim, Phys. Rev. A 2021, 103, 033504. 
+[30] 
+X. G. Wang, B. Bin Zhao, Y. Deng, V. Kovanis, C. Wang, Phys. Rev. A 2021, 103, 23528. 
+[31] 
+D. S. Seo, J. D. Park, J. G. Mcinerney, M. Osinski, IEEE J. Quantum Electron. 1989, 25, 2229. 
+[32] 
+M. Wienold, B. Röben, L. Schrottke, H. T. Grahn, Opt. Express 2014, 22, 30410. 
+[33] 
+X. Liao, X. Wang, K. Zhou, W. Guan, Z. Li, X. Ma, C. Wang, J. C. Cao, C. Wang, H. Li, Opt. 
+Express 2022, 30, 35937. 
+[34] 
+M. Piccardo, P. Chevalier, T. S. Mansuripur, D. Kazakov, Y. Wang, N. A. Rubin, L. 
+Meadowcroft, A. Belyanin, F. Capasso, Opt. Express 2018, 26, 9464. 
+[35] 
+Y. Wang, A. Belyanin, Opt. Express 2015, 23, 4173. 
+[36] 
+M. R. St-Jean, M. I. Amanti, A. Bernard, A. Calvar, A. Bismuto, E. Gini, M. Beck, J. Faist, 
+H.C.Liu, Carlo Sirtori, Laser Photon. Rev. 2014, 8, 443. 
+[37] 
+F. P. Mezzapesa, K. Garrasi, J. Schmidt, L. Salemi, V. Pistore, L. Li, A. G. Davies, E. H. Linfield, 
+M. Riesch, C. Jirauschek, T. Carey, F. Torrisi, A. C. Ferrari, M. S. Vitiello, ACS Photonics 2020, 
+7, 3489. 
+[38] 
+B. Hinkov, A. Hugi, M. Beck, J. Faist, Opt. Express 2016, 24, 3294. 
+[39] 
+E. Rodriguez, A. Mottaghizadeh, D. Gacemi, M. Jeannin, Z. Asghari, A. Vasanelli, Y. Todorov, 
+Q. J. Wang, C. Sirtori, Laser Photonics Rev. 2020, 14, 1900389. 
+[40] 
+D. Burghoff, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, Q. Hu, Opt. Express 2015, 23, 1190. 
+[41] 
+F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. 
+Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, S. Bartalini, Nat. 
+Photonics 2019, 13, 562. 
+[42] 
+D. Oustinov, N. Jukam, R. Rungsawang, J. Madéo, S. Barbieri, P. Filloux, C. Sirtori, X. Marcadet, 
+J. Tignon, S. Dhillon, Nat. Commun. 2010, 1, 69. 
+[43] 
+S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. 
+Linfield, A. G. Davies, Nat. Photonics 2011, 5, 306. 
+
+Supplementary material of “RF Injection Locking of THz 
+Metasurface Quantum-Cascade VECSEL” 
+Yu Wu,1* Christopher A. Curwen,2 Mohammad Shahili,1 John L. Reno,3 
+Benjamin S. Williams1 
+ 
+S1. Modeling of QC-metasurface and output coupler 
+The QC-metasurface shown in Figure 1 is modelled using full-wave 2D finite-
+element (FEM) simulation (Ansys HFSS), assuming it is infinite in extent, where a 
+single metal-metal waveguide antenna is simulated with periodic boundary 
+conditions. Simulated losses in the metal thin films are estimated using the Drude 
+model (nAu = 5.9 × 1022 cm-3, τAu,77 K = 39 fs [1]), while for the semiconductor layer, 
+band diagram is simulated to obtain the intersubband gain provided by the active 
+material. The QC-active material is grown 10-μm thick by molecular beam epitaxy 
+(wafer number VB0739). The active region is based upon a hybrid bound-to-
+continuum/ resonant-phonon design scheme and exhibits over 1 THz gain bandwidth 
+peaking at 3.4 THz, the same one as used in Refs [2,3]. It consists of an 
+GaAs/Al0.15Ga0.85As heterostructure where, starting from the injection barrier, the 
+layer thicknesses in Å are 51/103/17/107/37/88/37/172 (barrier layers are bold). The 
+central 88 Å of the underlined well is Si-doped at 5 × 1016 cm−3. We simulated the 
+band diagram for one module of the active region using a self-consistent 
+Schrödinger-Poisson solver at the bias providing maximum gain (Figure S1(a)) and 
+obtained its permittivity along the growth direction (Figure S1(b)). The dominant 
+intersubband transition occurs between the upper lasing state 5 and the lower lasing 
+state 4 at a frequency of 𝜈54 = 3.4 THz with oscillator strength of f54 = 0.427, where 
+the population inversion takes up 25% of the total doping concentration. A good 
+Figure. S1. (a) Conduction band diagram of the active region at the bias of 58 mV/module. (b) 
+The real and imaginary part of the permittivity of the active region simulated using the 
+Schrödinger-Poisson solver (red solid curves), and fitting based on Lorentz model (blue dashed 
+curves).  
+
+a
+Bias = 58 mV/module, T=77 K
+0.2
+(b)
+0.1
+180
+Real
+0
+(meV)
+-0.1
+140
+Energy (
+-0.2
+- Lorentz model
+100
+0
+Schrodinger solver
+3
+-0.1
+Imag(
+60
+1
+-0.2
+-0.3
+20
+0
+10
+20
+30
+40
+50
+60
+2.5
+3
+3.5
+4
+z (nm)
+Freguency(THz)qualitative fitting of the permittivity is obtained by considering only the 5 → 4 
+transition using a Lorentz oscillator model (Figure S1(b), dashed lines): 
+                                       𝜀𝑧(𝜔) = 𝜀𝑐𝑜𝑟𝑒 + 𝑁𝐼𝑆𝐵𝑒2
+𝑚∗𝐿𝑚𝑜𝑑
+𝑓54
+𝜔2 − 𝜔54
+2 + 𝑖𝜔𝛾,                                (1) 
+where NISB is the population inversion sheet density per module, εcore is the 
+semiconductor permittivity excluding free carrier contributions, m* is the GaAs 
+electron effective mass, Lmod is the length of one module of the active region and γ 
+is the damping term which is set as 2π × 700 GHz for best fit. The resonance 
+frequency offset between the Lorentz model and Schrödinger simulation results can 
+be explained by uncertainties in growth thicknesses and compositions of the QC-
+material. This permittivity is brought into FEM simulation, where the simulated 
+reflectance and GDD are plotted in Figure 1(c). 
+The output coupler used to form a laser cavity is the same type that has been used 
+in previous QC-VECSEL experiments [4,5]. It is made of an inductive Ti/Au mesh 
+evaporated on a 100-μm-thick double-side-polished z-cut quartz substrate. The mesh 
+is designed with a period of 13 μm and width of 3 μm, which determines the overall 
+transmittance magnitude.  
+ 
+S2. Effects of optical feedback 
+We experimentally found that optical feedback, even weak feedback originating 
+from the FTIR mirrors, induces few-mode lasing in free-running QC-VECSELs. 
+This can be useful, as it provides exact information on round-trip frequency from an 
+observed beat note (Figure 1(e-f)) – without feedback, the device lases in single-
+Figure. S2. (a-c) Beat note spectral maps under constant RF injection power of -15 dBm in the 
+case when the strength of optical feedback is reduced controlled by the rotational angle from 
+“90°” to “70°”. (d) The free-running beat note frequency is shifted with reduced strength of 
+optical feedback. 
+
+4987.7
+(a) 90°
+(b) 80°
+4987.7
+. Freq (MHz)
+Locking
+Locking
+Range
+Range
+dBm
+4987.6
+dBm
+4987.6
+~50kHz
+40
+64kHz
+Inj.
+40
+60
+Inj.
+60
+RF
+-80
+-80
+100
+100
+4987.5
+4987.5
+4987.44987.64987.8
+4987.44987.64987.8
+Frequency(MHz)
+Frequency(MHz)
+4987.7
+50
+(c)70°
+(d)
+Inj.Freq (MHz)
+Intensity (dBm)
+0
+Locking
+4987.6
+Range
+dBm
+~72kHz
+-40
+-50
+-60
+80
+30
+-100
+-100
+4987.5
+20
+4987.44987.64987.8
+4987.6
+4987.8
+Freguency（(MHz)
+Frequency(MHz)mode regime with no beat note detected. It is believed that the performances (e.g. 
+output power, spectral characteristics, injection locking range) of QC-lasers will be 
+affected by the strength, length (phase) and the tilted angle of the optical feedback 
+[6–9]. A systematic study will be needed using a motorized translational and rotational 
+stage that can precisely control the optical feedback length and angle, and a rotatable 
+polarizer that adjusts optical feedback strength.  
+Here, we did a simple experiment to qualitatively demonstrate the effects of optical 
+feedback strength on free-running beat note frequency as well as the RF injection 
+locking range. We put a flat mirror in front of the cryostat window (approximately 
+15 cm from the device) and a rotatable wire-grid polarizer in between. THz radiation 
+coming from the QC-VECSEL has a polarization perpendicular to the ridge antennas 
+and the QC-metasurface only interacts with light at that polarization. We label it as 
+“90°” for the case when 100% of the THz radiation passes through the polarizer. As 
+the polarizer was rotated from “90°” to “70°”, the amount of light feedbacked back 
+into the QC-device was reduced. The collected beat note spectral maps under a 
+constant RF power of -15 dBm are plotted in Figure S2(a-c) which indicate an 
+increasing locking range with respect to the reduced optical feedback strength. 
+Moreover, the free-running beat notes were also collected in Figure S2(d) showing 
+frequency shift as optical feedback strength was changed.  
+ 
+S3. Transmission loss in the QC-device   
+To estimate the transmission loss in the QC-device due to impedance mismatch, 
+an FEM simulation is used accounting for the finite dimension of the metasurface 
+including its electrical packaging. Figure S3(a) shows the QC-device mounted in the 
+focusing cavity that is modelled using Ansys HFSS in Figure S3(b). Only the 
+electrically biased ridges are modelled with metal layers loaded with Drude loss; the 
+circular biased area is assumed to be loaded with GaAs with a shunt conductivity 
+derived from experimental dI/dV curve while the unbiased area is defined as bulk 
+GaAs. Two 1-mil bond wires of approximately 2 mm length electrically connect the 
+metasurface to a “gold pad”: a 2.5 mm × 4.5 mm × 0.254 mm thick Al2O3 pad coated 
+with Au above and below. The pad is soldered to the center pin of an SMA connector 
+on the other side.  The E-field distribution along one of the biased ridges is simulated 
+at 5 GHz which indicates the injected RF signal propagating along the QC-
+metasurface has an effective wavelength much longer than its dimension. The 
+simulated power dissipation with a 50 Ω excitation port is plotted in Figure S3(c), 
+which gives an estimated power transfer of 4% from the SMA into the QC-device 
+and shows good agreement with circuit model result (see section S4) except at lower 
+frequencies. The frequency of the electrical resonance is determined by the 
+dimensions of the gold pad and bond wires. 
+
+ 
+S4. Microwave rectification measurement and equivalent lumped element 
+circuit model 
+To experimentally characterize the response of QC-device to injected RF signal, 
+microwave rectification technique has been applied as described in Ref. [10–12]. The 
+RF signal generated from the synthesizer is amplitude modulated at a frequency of 
+10 kHz and injected into the QC-device, while the latter is biased at a constant 
+current. The variation in DC rectification voltage is measured using a lock-in 
+amplifier referenced to the amplitude modulation. The injected RF power is kept 
+constant at -10 dBm, and the normalized rectification voltage (proportional to |VRF|2) 
+is plotted in Figure S4 at bias current of 0.235 mA. The result is well described by a 
+lumped-element circuit model described in more details below. Notably, an 
+electrical resonance is present at 3 GHz (associated with the LC parasitics) and the 
+3-dB cutoff frequency is 3.7 GHz followed by a rapid roll-off at higher frequencies. 
+Consequently, the rectification voltage of the QC-device at the target frequency of 
+4.8 GHz is reduced to ~5% of that at lower frequencies.   
+An equivalent lumped-element circuit is introduced to model the QC-device and 
+explain the rectification measurement. The QC-metasurface used in this paper has a 
+dimension much smaller than the RF operation wavelength as shown in Figure S3(b) 
+and is therefore represented as a parallel plate capacitor in parallel with a resistor 
+Figure. S3. (a) Image of QC metasurface device mounted in the focusing cavity. (b) Electrical 
+packaging structure that is modelled in Ansys HFSS including the gold pad and bond wires. Their 
+dimensions are labeled and the simulated E-field distribution along one of the biased ridges at 5 
+GHz is plotted. (c) Transmission coefficient simulated within HFSS assuming an excitation port of 
+50 Ω (blue) and calculated using the lumped element circuit model (red).  
+
+(a)
+(c)
+1
+HFSS
+0.8
+Circuit model
+QC device
+~.0.6
+0.15
+SMA
+0.4
+0.1
+~4%
+0.05
+0.2
+0
+Off-axismirror
+4
+5
+6
+0
+Frequency (GHz)
+10-1
+100
+101
+Frequency(GHz)
+(b)
+2.5mm
+4.5mm
+Wire-bond area
+1.5mm
+QC-metasurface
+(biased ridges)
+Gold pad
+0.254mm
+Biasdiameter0.4mm
+Wire bonds
+E-field at5GHz
+Circular
+bias areacoming from the effect of QC-active material. The capacitance CMS is calculated 
+based on the dimension and thickness of the metasurface assuming the permittivity 
+of 12.5 for the GaAs/AlGaAs active region. The differential shunt resistance RAR is 
+obtained based on the experimental slope of I-V curve at the bias point. Lwire is the 
+inductance of the two wire bonds connected in series with the RC circuit and is 
+estimated based upon the rule of thumb of ~1nH/mm/wire. Cgold pad is the capacitance 
+of the gold pad whose value is estimated based on its dimension and the permittivity 
+of Al2O3. The gold pad is connected to the RF source with a 50Ω generator 
+impedance Rg, which provides a RF power of PRF and an equivalent RF voltage of 
+𝑉𝑅𝐹 = 2√𝑅𝑔𝑃𝑅𝐹.  
+The rectification voltage of the QC-device can be calculated according to Ref. [11]: 
+𝑉𝑟𝑒𝑐𝑡 = 1
+2 |𝑉′′|𝐼0𝐼𝑅𝐹,𝑄𝐶𝐿
+2
+,
+(S1) 
+where V’’ is the second derivative of the I-V curve at DC bias current I0. IRF, QCL is 
+the RF modulation current injected into the QC-active material: 
+𝐼𝑅𝐹,𝑄𝐶𝐿 = 𝑉𝑅𝐹
+𝑅𝐿
+𝑅𝐴𝑅(𝑍𝑄𝐶𝐿 + 𝑅𝐿)
+𝑍𝑀𝑆
+(𝑗𝜔𝐿 + 𝑍𝑀𝑆) ,
+(S2) 
+where the impedance of the QC-device ZQCL and the metasurface ZMS is pointed out 
+in Figure S4 inset. The theoretical rectification voltage is plotted in dashed line using 
+values of: CMS = 6.1 pF, RAR = 16 Ω, Cgold pad = 3.8 pF, Lwire = 1nH.  
+ 
+References: 
+[1] 
+N. Laman, D. Grischkowsky, Appl. Phys. Lett. 2008, 93, 051105. 
+[2] 
+C. A. Curwen, J. L. Reno, B. S. Williams, Nat. Photonics 2019, 13, 855. 
+[3] 
+C. A. Curwen, J. L. Reno, B. S. Williams, Electron. Lett. 2020, 56, 1264. 
+Figure. S4. Normalized rectification curves (solid line) measured at bias current of 0.235 mA, 
+together with the theoretical fits (dashed line) obtained based on lumped element circuit model. 
+Inset: equivalent lumped element circuit model. Blue and red dashed boxes point out the 
+impedances of the QC-device and metasurface. 
+
+101
+Measurement
+Lumpedmodel
+(a.u.)
+100
+rectification
+RF source
+R.
+I Z
+wire
+10-1
+>
+MS
+Norm.
+P
+RF
+10-2
+gold pad
+R
+1
+2
+3
+4
+5
+6
+7 8
+Frequency(GHz)[4] 
+L. Xu, C. A. Curwen, J. L. Reno, B. S. Williams, Appl. Phys. Lett. 2017, 111, 101101. 
+[5] 
+Y. Wu, S. Addamane, J. L. Reno, B. S. Williams, Appl. Phys. Lett. 2021, 119, 111103. 
+[6] 
+M. Wienold, B. Röben, L. Schrottke, H. T. Grahn, Opt. Express 2014, 22, 30410. 
+[7] 
+X. Liao, X. Wang, K. Zhou, W. Guan, Z. Li, X. Ma, C. Wang, J. C. Cao, C. Wang, H. Li, Opt. 
+Express 2022, 30, 35937. 
+[8] 
+D. S. Seo, J. D. Park, J. G. Mcinerney, M. Osinski, IEEE J. Quantum Electron. 1989, 25, 2229. 
+[9] 
+X. G. Wang, B. Bin Zhao, Y. Deng, V. Kovanis, C. Wang, Phys. Rev. A 2021, 103, 23528. 
+[10] 
+E. Rodriguez, A. Mottaghizadeh, D. Gacemi, M. Jeannin, Z. Asghari, A. Vasanelli, Y. Todorov, 
+Q. J. Wang, C. Sirtori, Laser Photonics Rev. 2020, 14, 1900389. 
+[11] 
+B. Hinkov, A. Hugi, M. Beck, J. Faist, Opt. Express 2016, 24, 3294. 
+[12] 
+L. Gu, W. J. Wan, Y. H. Zhu, Z. L. Fu, H. Li, J. C. Cao, J. Opt. (United Kingdom) 2017, 19, 
+065706. 
+ 
+ 
+ 
+
diff --git a/qdE3T4oBgHgl3EQf8QuK/content/tmp_files/load_file.txt b/qdE3T4oBgHgl3EQf8QuK/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf,len=1020
+page_content='RF Injection Locking of THz Metasurface Quantum-  Cascade VECSEL  Yu Wu,1* Christopher A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen,2 Mohammad Shahili,1 John L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno,3  Benjamin S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams1  1Department of Electrical and Computer Engineering, University of California Los Angeles, Los Angeles,  California 90095, USA  2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA  3Sandia National Laboratories, Center of Integrated Nanotechnologies, MS 1303, Albuquerque, New Mexico  87185, USA  Corresponding author: ywu17@ucla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='edu  Abstract: RF injection locking and spectral broadening of a terahertz (THz)  quantum-cascade  vertical-external-cavity  surface-emitting  laser  (QC-  VECSEL) is demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' An intra-cryostat VECSEL focusing cavity design  is used to enable continuous-wave lasing with a cavity length over 30 mm which  corresponds to a round-trip frequency near 5 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Strong RF current  modulation is injected to the QC-metasurface electrical bias to pull and lock  the round-trip frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The injection locking range at various RF injection  powers is recorded and compared with the injection locking theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Moreover,  the lasing spectrum broadens from 14 GHz in free-running mode to a maximum  spectral width around 100 GHz with 20 dBm of injected RF power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This  experimental setup is suitable for further exploration of active mode-locking  and picosecond pulse generation in THz QC-VECSELs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Introduction  The terahertz (THz) spectral region has a need for high-resolution, high-speed  spectroscopy techniques, as many gas phase polar molecular species have strong  characteristic rotational lines there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Examples include applications in industrial and  environmental monitoring,[1,2] chemical detection and identification,[3,4] combustion  diagnostics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [5] The quantum cascade (QC) laser is well suited for spectroscopic  applications as it has been demonstrated as a compact, electrically pumped  semiconductor source which gives high power, broadband, coherent THz  radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [6–8] Its inherently high optical nonlinearity induces self-phase locking  through four-wave mixing, which promotes the generation of spontaneous frequency  combs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' these have been demonstrated in waveguide-based Fabry-Pérot[9–11] and ring  QC-lasers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [12,13] Based on that, THz dual-comb spectroscopy has been demonstrated,  surpassing the precision and speed of traditional Fourier spectrometers by several  orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [14–17]  In separate experiments, THz quantum-cascade lasers have recently been  implemented in the vertical-external-cavity surface-emitting laser (VECSEL)  architecture, which exhibits watt-level output power, near diffraction-limited beam  quality, and ~20% continuous fractional single-mode tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [18–20] The key  component of a QC-VECSEL is an amplifying reflectarray metasurface of metal-  metal waveguide antennas that are loaded with QC-gain material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' It is further paired  with a partially transmissive output coupler to form the laser cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' In contrast to  ridge-waveguide QC-lasers, experiments have shown that QC-VECSELs tend to  operate in single-mode regime despite having large gain bandwidths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' For example,  we have developed an intra-cryostat focusing VECSEL cavity to reduce the intra-  cavity diffraction loss and enable continuous-wave (CW) lasing at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4 THz with a  cavity length of ∼30 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [21] Even though the gain bandwidth of the metasurface  used was at least 100 times larger than the free spectral range, only a single lasing  mode was observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This is mainly due to a lack of spatial hole burning within the  QC-VECSEL metasurface which suppresses multi-mode instabilities,[22] although it  is perhaps compounded by the fact that no effort towards dispersion engineering has  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (a) Schematic of the QC-VECSEL based on an intra-cryostat focusing cavity design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (b)  Scanning electron microscopy image of the fabricated QC-metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The inset shows the  dimension and E-field distribution in a single ridge antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (c) FEM simulated active metasurface  reflectance, output coupler transmittance and GDD contributed by the two components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Shaded  area indicates the frequency range where lasing is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (d) Schematic of experimental setup  for RF injection locking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' THz lasing spectrum (e) and beat note spectra (f) of the free-running QC-  device in existence of optical feedback are collected at a DC bias of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='235 mA, where optical  feedback is provided by the moving FTIR mirror.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The beat note spectra are measured in both  Average (solid) and Max Hold modes (dashed) with a RBW of 2 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  (a)  Outputcoupler  (b)  IEI at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='36 THz  X104  (c)  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  QC-gain  FEM  Exp  10日  L80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='2  Biasarea  d=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4mm  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7μm  MS+OC  OC  Off-axis  (sd)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  MS  paraboloid  GDD (  QC-metasurface  mirror  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  4  Frequency (THz)  100  Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=')  (e)  (d)  Directional  Microwave  RF synthesizer  FTIR  Bias-T  coupler  amplifier  10-2  SMA  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  Optical  Frequency(THz)  feedback  Intensity (dBm)  60  Cryostat  (f)  50kH  80  DCpower  8kHz  Average  MaxHold  supply  Spectrum  100  analyzer  BN  4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4  4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8  Frequency(MHz)yet been attempted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Despite these challenges, there is strong interest in achieving  active mode-locked QCLs and frequency combs within the QC-VECSEL  architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Radiofrequency (RF) current modulation of QC-lasers has been demonstrated to  promote the generation of sidemodes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' by injecting a RF signal near the cavity round-  trip frequency, the generated sidemodes will lock existing adjacent free-running  lasing modes or seed new ones, which allows for the stabilization and tuning of  frequency comb states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [23–26] RF modulation and injection locking is also an  important mechanism for active mode-locking in QC-lasers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  pulses as narrow as 4-  5 ps have been reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [27,28]  In this article, we demonstrate the emergence of spectral broadening and  multimoding in THz QC-VECSEL as we inject strong RF current modulation to the  QC-metasurface at a frequency close to the cavity round-trip frequency;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' at the same  time, round-trip frequency pulling and locking to the injected RF signal is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  The lasing bandwidth and injection locking range increase monotonically with the  injected RF power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lasing modes spanning ~100 GHz are demonstrated under an  injected RF power of 20 dBm at 4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 MHz, along with a locking range ~5 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sample and experimental setup  The QC-VECSEL used for all measurements is based on an intra-cryostat focusing  cavity design, as sketched in Figure 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' An off-axis paraboloid (OAP) mirror with  a focal length of 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 mm is introduced into the VECSEL cavity to reduce the intra-  cavity diffraction loss and enable CW lasing using small metasurfaces in long lasing  cavities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [21] The QC-metasurface used in this paper is the same one as reported in ref  [21], with a small bias area of diameter d = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4 mm for reduced injection current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' It is  designed to be resonant at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='3 THz and consists of an array of ridges of width 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='2  µm repeated with a period of 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 µm (Figure 1(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' An output coupler with ROC ≈  95% is used in pair with the metasurface to form a laser cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Both two components  are dispersive and contribute to the group delay dispersion (GDD) over one round  trip - it exhibits a maximum value exceeding 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='35 ps2 in the frequency range where  lasing occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The simulated spectral response of the metasurface and the output  coupler are plotted in Figure 1(c) based on full-wave 2D finite-element (FEM)  electromagnetic reflectance simulation (Ansys HFSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Detailed information of the  active region design and simulation parameters can be found in the Supporting  Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  The experimental setup for RF injection locking is depicted in Figure 1(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' All the  measurements were performed in vacuum at a temperature of 77 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' We note that  formable semi-rigid coaxial cable is used within the cryostat up to the chip carrier  package (see Supporting Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Due to impedance mismatch between the  50Ω SMA port and the QC-device, the spectrum analyzer collects not only the  generated beat note from the QC-device fBN (blue arrow), but also the RF injection  signal reflected at the interface of SMA/QC-device fRF (green arrow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  In free-running case, although only single-mode lasing was observed using the  same QC-device in ref [21], here we note that the existence of optical feedback can  induce multi-mode operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [29–31] Due to the temporally varying small feedback  from the scanning Fourier-transform infrared spectrometer (FTIR, Nicolet 8700)  mirrors, we observed at least two lasing modes separated by ~14 GHz in the emission  spectrum (Figure 1(e)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Additional low intensity sidemodes may also exist but  cannot be resolved by the limited FTIR resolution of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This phenomenon is  similar as that observed in ref [30], where additional lasing modes are observed in a  Mid-IR QC-laser under tilted optical feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Through nonlinear mixing of the  free-running lasing modes, a weak electrical beat note signal is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' It is  collected using the spectrum analyzer (Agilent N9020a) both in Average mode and  in Max Hold mode over 30 seconds, which indicates a round-trip frequency fBN ≈  4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 MHz and an equivalent cavity length around 31 mm (Figure 1(f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A narrow  8-kHz -3dB linewidth in Average mode and 60-kHz linewidth in Max Hold mode of  the intermodal beat note is on the same order as the free-running linewidth of the  single THz lasing mode measured in [21];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' it is likely contributed by only two (or a  few) lasing modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Furthermore, recent study of optical feedback has highlighted its  effect on THz QC-lasers combs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [32–34] Here, we experimentally demonstrate that  optical feedback plays an important role in determining not only the free-running  beat note frequency but also the injection locking range (see Supporting  Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' RF injection locking  With the knowledge of an accurate round-trip frequency, we are able to  systematically study the modulation-dependent behavior of this QC-device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' We  swept the RF modulation frequency around the round-trip frequency at various  modulation powers from -20 dBm to 20 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' All RF powers indicated in this paper  refer to the nominal output level of the RF synthesizer (Hewlett-Packard 83650B)  or after a 20 dBm amplifier (Hewlett-Packard 8349B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The DC bias is fixed at a  current of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='235 mA (≈1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='17×Ith), and the THz emission spectra as well as intermodal  beat note are collected and plotted in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  At the lowest power level of -20 dBm, the spectral map in Figure 2(a) clearly shows  that the beat note is pulled toward the injection signal and finally locked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A locking  range of 30 kHz is demonstrated which increases with respect to the RF injection  power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Starting from an RF power of -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 dBm, injection locking occurs before the  beat note is fully pulled to meet the injected signal fRF (Figure 2(b));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' at the same  time, lasing bandwidth broadening is observed in the THz emission spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This  spectral broadening increases with respect to RF power as shown in Figure 2(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The  maximum RF injection power used in this measurement is 20 dBm limited by the  max allowable power of the bias-Tee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' THz emission and RF beat note spectral maps  in this case are plotted in Figure 2(e-f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The maximum spectral broadening occurs at  fRF = 4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 MHz with lasing modes spanning around 100 GHz (Figure 2(g)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  However, due to the limited FTIR resolution of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 GHz, we were not able to  spectrally resolve individual lasing modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The corresponding power and voltage vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  current (P-I-V) curves are plotted in Figure 2(h) (solid curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A maximum output  power around 10 mW was collected using a pyroelectric detector (GentecEO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Compared with the P-I characteristic in the free-running case (dashed curve), the  output power, as well as the lasing threshold, is slightly lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' It is noticed from  Figure 2(e) that the symmetry of the lasing spectrum is highest at fRF = 4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 MHz,  where the maximum bandwidth is observed with relative low THz output power  obtained from the P-I curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' At injection frequencies above/below this value, the  optical power increases – still smaller than that in free-running case – and  concentrates toward lower/higher portion of the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This phenomenon is  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beat note spectral map under constant RF injection power of -20 dBm (a) and -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 dBm  (b) with RF modulation frequency sweeping around the round-trip frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (c) Experimental  injection locking range at different RF injection powers (blue stars), following a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5-slope  dependence in log–log scale (red dashed line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The free-running beat note frequency was shifted  from ~ 4842 MHz in (a-c) to ~ 4853 MHz in (d-h) as the movement of cryostat changes the amount  of optical feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (d) THz lasing spectra at increasing RF power when fRF is fixed at 4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  (e) Lasing spectral and (f) beat note maps of the device under constant RF injection power of 20  dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The estimated locking range is pointed out by the red arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The maximum spectral  broadening occurs at fRF = 4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 MHz (white dashed line) and the THz lasing spectrum and P-I-  V curves in this case are plotted in (g-h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  4842.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='1  (a)  dBm  (d)  (e)  20dBm  (f)  20 dBm  40  4842.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='05  20dBm  20dBm  60  19dBm  Locking  (MHz)  80  18dBm  4842  17dBm  injection freg (  4854  Range  100  freq  120  16dBm  =4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7MHz  15dBm  4841.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='9  4842  4842.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='1  RF Inj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  RF injection f  14dBm  Frequency (MHz)  4852  Signal fr  13dBm  800  dBm  (b)  dBm  12dBm  600  Beat note fen  20  4842.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='2  20  11dBm  40  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 dBm  48  Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=')  10dBm  4850  400  60  4842  9dBm  200  80  8dBm  100  4841.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8  100  Z dBm  6dBm  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  4848  4852  4856  4841.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  4842  4842.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  5dBm  Frequency(THz)  Frequency(MHz)  Frequency (MHz)  4dBm  3dBm  (h)  Current (A)  range(kHz)  (c)  2dBm  (g)  1dBm  Atm  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content="2  103  OdBm  ('ne)  absorption  10  1dBm  2dBm  M  Intensity  10  3dBm  4dBm  6  5dBm  ~100GHz  4  5  (mW)  Expt." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content="  6dBm  7dBm  RFoff  Adler's Eq." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  8dBm  2  fr=4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7MHz  101  9dBm  0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='dBm  0  20  10  0  10  20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='35  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='45  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='55  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  0  200  400  600  RFpower(dBm)  Freguency(THz)  Freguency (THz)  CurrentDensity(A/cm2)similar as that reported in ref [26] and a possible explanation can be found in ref [35]  due to phase mismatch between the modulation period and group round-trip time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' In  Figure 2(f), although there is no beat note pulling observed, it is notable that the  emission spectrum undergoes distinct change as the beat note disappears (pointed  out by red arrows) – it is believed that this is a signature of injection locking and  occurs in our measurements under different RF powers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  The experimental locking range at various RF injection powers is plotted in Figure  2(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' To analyze the phenomenon of RF injection locking, Adler’s equation is  commonly used with a locking bandwidth given by:[23,36]  𝛥𝜈 = 2𝜈0  𝑄 √𝑃𝑖𝑛𝑗  𝑃0  ,                                                     (1)  where Q is the cold-cavity quality factor, 𝜈0 and P0 are the frequency and power of  a free-running longitudinal mode, while Pinj is the power of the injected sideband  induced by RF injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Adler’s equation indicates a square root dependence of the  locking bandwidth on the RF power and fits our experimental results well at low RF  powers (red dashed line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' However, our experimental locking range deviates from  Adler’s equation towards higher values under strong RF modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This may  indicate the limitation of Adler’s equation in explaining RF injection locking  especially in the case when multiple new lasing modes are excited at RF powers >  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Adler’s equation assumes a weak injection signal where amplitude  perturbation induced by the injection signal is not considered;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' a more rigorous  derivation of the locking range is therefore needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Moreover, we studied the behavior of this QC-device at various DC biases ranging  from the lasing threshold to near the NDR point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Figure 3(a) shows the lasing spectra  under 20 dBm RF injection at a frequency of fRF = 4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Significant spectral  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (a) THz lasing spectra at various biases when RF signal at 4852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 MHz is injected into the  QC-device, the RF power used is 20 dBm for significant spectral broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (b) Injection locking  range as a function of bias current under -15 dBm RF power in the cases of different  length/strength/angle of optical feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  120  (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=')  (a)  (b)  247 mA  244mA  (ZH>)  Intensity  100  240mA  235mA  range  230 mA  80  Normalized  225 mA  Locking  219mA  60  213 mA  207 mA  201 mA  40  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='25  Frequency (THz)  Biascurrent (A)broadening is observed at all the applied biases, and the lasing bandwidth increases  only slightly with respect to the bias current as more modes are brought above the  lasing threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  As a next step, the effects of device bias on the injection locking bandwidth were  investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' We swept the RF modulation frequency around the round-trip  frequency at a fixed injection power of -15 dBm and measured the injection locking  bandwidth at various biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Small injection power was used so the locking range  can be more clearly observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Additionally, we repeated such bias sweeps while  providing different magnitude, phase, and angle of feedback light from an external  mirror, the corresponding locking ranges are indicated by different colored curves  in Figure 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Our experimental observation reveals that the relationship between  locking range and device bias is related to the condition of optical feedback, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  feedback length (phase), strength and tilted angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This is significantly different from  previous demonstrations using ridge-waveguide QC-lasers, where the locking range  became smaller with increasing bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [23,37] In our system, we could make a simple  assumption that there are two free-running modes, where mode ω1 is induced by  optical feedback around the main lasing peak ω0 and is locked by the RF-excited  sideband of the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The ratio of Pinj/P0 in Adler’s equation can be estimated as the  ratio of the free-running power of mode ω0 and that of mode ω1 as the injected RF  power is fixed, which determines the injection locking range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' How the locking range  changes is therefore determined by how the relative power of two lasing modes  develops with respect to bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Unfortunately, this is not able to be observed  experimentally limited by the resolution of our FTIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' In theory, the spectral  characteristics of the device versus applied bias is expected to be affected by the  changes of threshold gain induced by optical feedback and the alignment of  compound-cavity modes formed in the external cavity with respect to gain, which is  related to not only the length and strength of optical feedback, but also the tilt angle  of external mirror.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [31] To fully understand this phenomenon, a theoretical study of  laser dynamics and instabilities of QC-VECSELs under optical feedback and  systematic experiments of the RF-injected system with well-controlled, adjustable  optical feedback will be needed and are beyond the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Discussion and conclusion  The injection locking range obtained in this paper is considerably smaller  compared with those demonstrated in RF injection-locked Fabry-Pérot waveguide  QC-lasers at same level of RF power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [23,25] One of the reasons is that QC-VECSELs  have higher quality factors compared with ridge waveguide QC-lasers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Our  VECSEL has a 31 mm-long external cavity and low loss from the ~95% reflectance  output coupler;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' using a coupled-cavity model we estimate a cold-cavity linewidth of  ν0/Q ≈ 70 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This is around 300 times smaller than a value of 25 GHz estimated  in ref [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' In addition, intrinsic and technical issues with our QC-VECSEL setup  result in a low efficiency of RF power transfer at ~4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8 GHz from the synthesizer to  the QC-metasurface bias terminal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' First, due to parasitic capacitances contributed by  unbiased regions, the QC-metasurface itself exhibits a larger RC time-constant  compared with a narrow ridge waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Second, the electrical packaging has not  been optimized for RF operation, where wire bonds and wire bonding pads  contribute parasitic inductance and capacitance respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Consequently, there is  a huge impedance mismatch between the 50Ω SMA port and the QC-device, the  resulting transmittance of RF signal through the SMA/QC-package boundary is  simulated to be ~4% at a target frequency of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8 GHz (see Supporting Information),  only part of which will be applied to modulate the gain material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' To make things  worse, an additional ~8 dB RF attenuation has been characterized accounting for  losses through cables and directional coupler from the synthesizer to the SMA  connector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' In contrast to other demonstrations of ridge waveguide QC-lasers using  RF coplanar probes,[23,38] RF launchers,[39] or custom high-frequency PCB mounts[28]  to achieve modulation of QC-lasers up to 35 GHz, microwave rectification technique  indicates a significant roll-off at frequency higher than 3 GHz in our QC-device (see  Supporting Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  In conclusion, we demonstrate RF injection locking in a THz QC-VECSEL based  on intra-cryostat focusing cavity design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Round-trip frequency pulling and locking  against an RF injection signal is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Furthermore, the RF amplitude  modulation leads to broadening of the lasing spectrum up to a spectral width of 100  GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This is particularly notable, as multi-mode lasing in QC-VECSELs has been  extremely difficult to achieve due to the lack of spatial hole burning within the  metasurface;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' before now at most 9 lasing modes had been observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [22] There are  several obvious avenues for improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' First, RF attenuation and impedance  mismatch severely limits the modulation efficiency, and strong RF reflections  impede the detection of the electrical beat note signal using a spectrum analyzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  This can be improved by optimizing the electrical packaging of the QC-device, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  reducing the capacitance and inductance portion of the equivalent circuit by 1)  redesigning the QC-metasurface with reduced unbiased area and an improved RF  feed structure;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2) replacing the electrical contact pad with a well-designed PCB 50Ω  transmission line feed up to the edge of the metasurface chip with minimal wire bond  length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Second, we note that no particular effort to provide dispersion compensation  has been attempted here;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' further engineering of GDD within the QC-VECSEL cavity  may be needed to increase the lasing across the entire ~1 THz gain bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Finally, given measurements of ridge-waveguide THz QC-lasers under strong RF  modulation, it is quite likely that this device is generating short pulses in an active  mode-locking regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [27,28] Further characterization techniques such as shifted-wave  interference Fourier-transform spectroscopy (SWIFTs)[10,40,41] or asynchronous  electro-optical sampling will be needed to recover the time-domain structure of the  field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [42,43]  Supporting Information  Supporting Information is available from the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Acknowledgments  The authors thank David Burghoff, Andres Forrer, Giacomo Scalari, and Stefano  Barbieri for valuable conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Microfabrication was performed at the UCLA  Nanoelectronics Research Facility, wire bonding was performed at the UCLA  Center for High Frequency Electronics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This work was performed, in part, at the  Center for Integrated Nanotechnologies, an Office of Science User Facility operated  for the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Department of Energy (DOE) Office of Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sandia National  Laboratories is a multimission laboratory managed and operated by National  Technology and Engineering Solution of Sandia, LLC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=', a wholly owned subsidiary  of Honeywell International, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=', for the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=" Department of Energy's National  Nuclear Security Administration under contract DE-NA-0003525." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Partial funding  was provided by the National Science Foundation (2041165), and the National  Aeronautics and Space Administration (80NSSC19K0700).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  References  [1]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mittleman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Jacobsen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Neelamani, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Baraniuk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Nuss, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' B  Lasers Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 1998, 67, 379.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [2]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cuisset, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hindle, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mouret, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bocquet, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bruckhuisen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Decker, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Pienkina, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bray, É.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Fertein, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Boudon, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2021, 11, 1229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [3]  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Zhong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Redo-Sanchez, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Zhang, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2006, 14, 9130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [4]  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Medvedev, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Neese, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Plummer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' De Lucia, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2010, 35, 1533.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [5]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Araki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Matsuyama, Curr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2022, 36, 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [6]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Kohler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Tredicucci, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beltram, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beere, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Linfield, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Davies, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Ritchie, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Iotti, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rossi, Nature 2002, 417, 156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [7]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Freeman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Salih, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Dean, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Davies, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Linfield, Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  2017, 53, 799.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [8]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Turčinková, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Scalari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Castellano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Amanti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2011,  99, 191104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [9]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rösch, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Scalari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Photonics 2014, 9, 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [10]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Burghoff, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Kao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Han, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Chan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Yang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hayton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Reno, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hu, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Photonics 2014, 8, 462.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [11]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Forrer, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Belyanin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Scalari, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2021, 118,  131112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [12]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Piccardo, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Schwarz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Kazakov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beiser, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Opačak, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Jha, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hillbrand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Tamagnone, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Zhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Columbo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Belyanin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Capasso, Nature 2020, 582,  360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [13]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Jaidl, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Opačak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Kainz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Schönhuber, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Theiner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Limbacher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beiser, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Giparakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Andrews, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Strasser, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Schwarz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
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+page_content=' Unterrainer, Optica 2021, 8,  780.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [14]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rösch, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
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+page_content=' Villares, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bosco, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2016, 108,  171104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [15]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sterczewski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Westberg, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Yang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Burghoff, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
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+page_content='  [16]  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
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+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Zeng, ACS Photonics  2020, 7, 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [17]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Consolino, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Nafa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' De Regis, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cappelli, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Garrasi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mezzapesa, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Davies, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Linfield, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Vitiello, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bartalini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' De Natale, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2020, 3, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [18]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Xu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hon, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Itoh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2015,  107, 221105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [19]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2018, 113, 011104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [20]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Photonics 2019, 13, 855.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [21]  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2022, 121, 191106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [22]  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Addamane, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2021, 119, 111103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [23]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gellie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Barbieri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lampin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Filloux, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Manquest, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sirtori, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sagnes, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Khanna, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Linfield, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beere, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Ritchie, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2010, 18, 20799.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [24]  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Laffaille, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gacemi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Apfel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sirtori, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Leonardon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Santarelli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rösch, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Scalari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hänsel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Holzwarth, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Barbieri, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2015, 23, 33270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [25]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Forrer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bosco, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Scalari, Photonics 2020, 7, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [26]  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Schneider, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Kapsalidis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bertrand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Singleton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hillbrand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, Laser  Photonics Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2021, 15, 2100242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [27]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mottaghizadeh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gacemi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Laffaille, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Amanti, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sirtori, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Santarelli, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hänsel,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Holzwart, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Linfield, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Barbieri, Optica 2017, 4, 168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [28]  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Senica, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Forrer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Olariu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Micheletti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cibella, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Torrioli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, Jerome Faist, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Scalari, arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='06737 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='optics].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [29]  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Qi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bertling, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Taimre, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Agnew, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lim, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A 2021, 103, 033504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [30]  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bin Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Deng, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Kovanis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A 2021, 103, 23528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [31]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Seo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mcinerney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Osinski, IEEE J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Quantum Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 1989, 25, 2229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [32]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wienold, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Röben, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Schrottke, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Grahn, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2014, 22, 30410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [33]  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Liao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Zhou, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Guan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Ma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Express 2022, 30, 35937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [34]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Piccardo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Chevalier, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mansuripur, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Kazakov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rubin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Meadowcroft, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Belyanin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Capasso, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2018, 26, 9464.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [35]  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Belyanin, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2015, 23, 4173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [36]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' St-Jean, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Amanti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bernard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Calvar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bismuto, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='Liu, Carlo Sirtori, Laser Photon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2014, 8, 443.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [37]  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mezzapesa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Garrasi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Schmidt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Salemi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Pistore, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Davies, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Linfield,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Riesch, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Jirauschek, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Carey, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Torrisi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Ferrari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Vitiello, ACS Photonics 2020,  7, 3489.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [38]  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hinkov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hugi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2016, 24, 3294.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [39]  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rodriguez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mottaghizadeh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gacemi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Jeannin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Asghari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Vasanelli, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Todorov,  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sirtori, Laser Photonics Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2020, 14, 1900389.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [40]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Burghoff, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Yang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hayton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hu, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2015, 23, 1190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [41]  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cappelli, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Consolino, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Campo, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Galli, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mazzotti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Campa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Siciliani de Cumis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Cancio Pastor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Eramo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rösch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Scalari, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' De Natale, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bartalini, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Photonics 2019, 13, 562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [42]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Oustinov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Jukam, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rungsawang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Madéo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Barbieri, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Filloux, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sirtori, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Marcadet,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Tignon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Dhillon, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2010, 1, 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [43]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Barbieri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Ravaro, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gellie, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Santarelli, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Manquest, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sirtori, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Khanna, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Linfield, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Davies, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Photonics 2011, 5, 306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Supplementary material of “RF Injection Locking of THz  Metasurface Quantum-Cascade VECSEL”  Yu Wu,1* Christopher A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen,2 Mohammad Shahili,1 John L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno,3  Benjamin S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams1  S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Modeling of QC-metasurface and output coupler  The QC-metasurface shown in Figure 1 is modelled using full-wave 2D finite-  element (FEM) simulation (Ansys HFSS), assuming it is infinite in extent, where a  single metal-metal waveguide antenna is simulated with periodic boundary  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Simulated losses in the metal thin films are estimated using the Drude  model (nAu = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='9 × 1022 cm-3, τAu,77 K = 39 fs [1]), while for the semiconductor layer,  band diagram is simulated to obtain the intersubband gain provided by the active  material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The QC-active material is grown 10-μm thick by molecular beam epitaxy  (wafer number VB0739).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The active region is based upon a hybrid bound-to-  continuum/ resonant-phonon design scheme and exhibits over 1 THz gain bandwidth  peaking at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4 THz, the same one as used in Refs [2,3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' It consists of an  GaAs/Al0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='15Ga0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='85As heterostructure where, starting from the injection barrier, the  layer thicknesses in Å are 51/103/17/107/37/88/37/172 (barrier layers are bold).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The  central 88 Å of the underlined well is Si-doped at 5 × 1016 cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' We simulated the  band diagram for one module of the active region using a self-consistent  Schrödinger-Poisson solver at the bias providing maximum gain (Figure S1(a)) and  obtained its permittivity along the growth direction (Figure S1(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The dominant  intersubband transition occurs between the upper lasing state 5 and the lower lasing  state 4 at a frequency of 𝜈54 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4 THz with oscillator strength of f54 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='427, where  the population inversion takes up 25% of the total doping concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A good  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (a) Conduction band diagram of the active region at the bias of 58 mV/module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (b)  The real and imaginary part of the permittivity of the active region simulated using the  Schrödinger-Poisson solver (red solid curves), and fitting based on Lorentz model (blue dashed  curves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  a  Bias = 58 mV/module, T=77 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='2  (b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='1  180  Real  0  (meV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='1  140  Energy (  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='2  Lorentz model  100  0  Schrodinger solver  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='1  Imag(  60  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='3  20  0  10  20  30  40  50  60  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  4  z (nm)  Freguency(THz)qualitative fitting of the permittivity is obtained by considering only the 5 → 4  transition using a Lorentz oscillator model (Figure S1(b),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' dashed lines):  𝜀𝑧(𝜔) = 𝜀𝑐𝑜𝑟𝑒 + 𝑁𝐼𝑆𝐵𝑒2  𝑚∗𝐿𝑚𝑜𝑑  𝑓54  𝜔2 − 𝜔54  2 + 𝑖𝜔𝛾,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='                                (1)  where NISB is the population inversion sheet density per module,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' εcore is the  semiconductor permittivity excluding free carrier contributions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' m* is the GaAs  electron effective mass,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lmod is the length of one module of the active region and γ  is the damping term which is set as 2π × 700 GHz for best fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The resonance  frequency offset between the Lorentz model and Schrödinger simulation results can  be explained by uncertainties in growth thicknesses and compositions of the QC-  material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' This permittivity is brought into FEM simulation, where the simulated  reflectance and GDD are plotted in Figure 1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  The output coupler used to form a laser cavity is the same type that has been used  in previous QC-VECSEL experiments [4,5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' It is made of an inductive Ti/Au mesh  evaporated on a 100-μm-thick double-side-polished z-cut quartz substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The mesh  is designed with a period of 13 μm and width of 3 μm, which determines the overall  transmittance magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Effects of optical feedback  We experimentally found that optical feedback, even weak feedback originating  from the FTIR mirrors, induces few-mode lasing in free-running QC-VECSELs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  This can be useful, as it provides exact information on round-trip frequency from an  observed beat note (Figure 1(e-f)) – without feedback, the device lases in single-  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (a-c) Beat note spectral maps under constant RF injection power of -15 dBm in the  case when the strength of optical feedback is reduced controlled by the rotational angle from  “90°” to “70°”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (d) The free-running beat note frequency is shifted with reduced strength of  optical feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7  (a) 90°  (b) 80°  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Freq (MHz)  Locking  Locking  Range  Range  dBm  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  dBm  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  ~50kHz  40  64kHz  Inj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  40  60  Inj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  60  RF  80  80  100  100  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='44987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='64987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='44987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='64987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8  Frequency(MHz)  Frequency(MHz)  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7  50  (c)70°  (d)  Inj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='Freq (MHz)  Intensity (dBm)  0  Locking  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  Range  dBm  ~72kHz  40  50  60  80  30  100  100  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5  20  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='44987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='64987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  4987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8  Freguency（(MHz)  Frequency(MHz)mode regime with no beat note detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' It is believed that the performances (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  output power, spectral characteristics, injection locking range) of QC-lasers will be  affected by the strength, length (phase) and the tilted angle of the optical feedback  [6–9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A systematic study will be needed using a motorized translational and rotational  stage that can precisely control the optical feedback length and angle, and a rotatable  polarizer that adjusts optical feedback strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Here, we did a simple experiment to qualitatively demonstrate the effects of optical  feedback strength on free-running beat note frequency as well as the RF injection  locking range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' We put a flat mirror in front of the cryostat window (approximately  15 cm from the device) and a rotatable wire-grid polarizer in between.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' THz radiation  coming from the QC-VECSEL has a polarization perpendicular to the ridge antennas  and the QC-metasurface only interacts with light at that polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' We label it as  “90°” for the case when 100% of the THz radiation passes through the polarizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' As  the polarizer was rotated from “90°” to “70°”, the amount of light feedbacked back  into the QC-device was reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The collected beat note spectral maps under a  constant RF power of -15 dBm are plotted in Figure S2(a-c) which indicate an  increasing locking range with respect to the reduced optical feedback strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Moreover, the free-running beat notes were also collected in Figure S2(d) showing  frequency shift as optical feedback strength was changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Transmission loss in the QC-device  To estimate the transmission loss in the QC-device due to impedance mismatch,  an FEM simulation is used accounting for the finite dimension of the metasurface  including its electrical packaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Figure S3(a) shows the QC-device mounted in the  focusing cavity that is modelled using Ansys HFSS in Figure S3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Only the  electrically biased ridges are modelled with metal layers loaded with Drude loss;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' the  circular biased area is assumed to be loaded with GaAs with a shunt conductivity  derived from experimental dI/dV curve while the unbiased area is defined as bulk  GaAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Two 1-mil bond wires of approximately 2 mm length electrically connect the  metasurface to a “gold pad”: a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 mm × 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 mm × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='254 mm thick Al2O3 pad coated  with Au above and below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The pad is soldered to the center pin of an SMA connector  on the other side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The E-field distribution along one of the biased ridges is simulated  at 5 GHz which indicates the injected RF signal propagating along the QC-  metasurface has an effective wavelength much longer than its dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The  simulated power dissipation with a 50 Ω excitation port is plotted in Figure S3(c),  which gives an estimated power transfer of 4% from the SMA into the QC-device  and shows good agreement with circuit model result (see section S4) except at lower  frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The frequency of the electrical resonance is determined by the  dimensions of the gold pad and bond wires.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Microwave rectification measurement and equivalent lumped element  circuit model  To experimentally characterize the response of QC-device to injected RF signal,  microwave rectification technique has been applied as described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [10–12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The  RF signal generated from the synthesizer is amplitude modulated at a frequency of  10 kHz and injected into the QC-device, while the latter is biased at a constant  current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The variation in DC rectification voltage is measured using a lock-in  amplifier referenced to the amplitude modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The injected RF power is kept  constant at -10 dBm, and the normalized rectification voltage (proportional to |VRF|2)  is plotted in Figure S4 at bias current of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='235 mA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The result is well described by a  lumped-element circuit model described in more details below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Notably, an  electrical resonance is present at 3 GHz (associated with the LC parasitics) and the  3-dB cutoff frequency is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='7 GHz followed by a rapid roll-off at higher frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Consequently, the rectification voltage of the QC-device at the target frequency of  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8 GHz is reduced to ~5% of that at lower frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  An equivalent lumped-element circuit is introduced to model the QC-device and  explain the rectification measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The QC-metasurface used in this paper has a  dimension much smaller than the RF operation wavelength as shown in Figure S3(b)  and is therefore represented as a parallel plate capacitor in parallel with a resistor  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (a) Image of QC metasurface device mounted in the focusing cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (b) Electrical  packaging structure that is modelled in Ansys HFSS including the gold pad and bond wires.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Their  dimensions are labeled and the simulated E-field distribution along one of the biased ridges at 5  GHz is plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (c) Transmission coefficient simulated within HFSS assuming an excitation port of  50 Ω (blue) and calculated using the lumped element circuit model (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  (a)  (c)  1  HFSS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8  Circuit model  QC device  ~.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='15  SMA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='1  ~4%  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='2  0  Off-axismirror  4  5  6  0  Frequency (GHz)  10-1  100  101  Frequency(GHz)  (b)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5mm  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5mm  Wire-bond area  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5mm  QC-metasurface  (biased ridges)  Gold pad  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='254mm  Biasdiameter0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='4mm  Wire bonds  E-field at5GHz  Circular  bias areacoming from the effect of QC-active material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The capacitance CMS is calculated  based on the dimension and thickness of the metasurface assuming the permittivity  of 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='5 for the GaAs/AlGaAs active region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The differential shunt resistance RAR is  obtained based on the experimental slope of I-V curve at the bias point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lwire is the  inductance of the two wire bonds connected in series with the RC circuit and is  estimated based upon the rule of thumb of ~1nH/mm/wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cgold pad is the capacitance  of the gold pad whose value is estimated based on its dimension and the permittivity  of Al2O3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The gold pad is connected to the RF source with a 50Ω generator  impedance Rg, which provides a RF power of PRF and an equivalent RF voltage of  𝑉𝑅𝐹 = 2√𝑅𝑔𝑃𝑅𝐹.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  The rectification voltage of the QC-device can be calculated according to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' [11]:  𝑉𝑟𝑒𝑐𝑡 = 1  2 |𝑉′′|𝐼0𝐼𝑅𝐹,𝑄𝐶𝐿  2  ,  (S1)  where V’’ is the second derivative of the I-V curve at DC bias current I0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' IRF, QCL is  the RF modulation current injected into the QC-active material:  𝐼𝑅𝐹,𝑄𝐶𝐿 = 𝑉𝑅𝐹  𝑅𝐿  𝑅𝐴𝑅(𝑍𝑄𝐶𝐿 + 𝑅𝐿)  𝑍𝑀𝑆  (𝑗𝜔𝐿 + 𝑍𝑀𝑆) ,  (S2)  where the impedance of the QC-device ZQCL and the metasurface ZMS is pointed out  in Figure S4 inset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' The theoretical rectification voltage is plotted in dashed line using  values of: CMS = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='1 pF, RAR = 16 Ω, Cgold pad = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='8 pF, Lwire = 1nH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  References:  [1]  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Laman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Grischkowsky, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2008, 93, 051105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [2]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Photonics 2019, 13, 855.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [3]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2020, 56, 1264.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Normalized rectification curves (solid line) measured at bias current of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='235 mA,  together with the theoretical fits (dashed line) obtained based on lumped element circuit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Inset: equivalent lumped element circuit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Blue and red dashed boxes point out the  impedances of the QC-device and metasurface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  101  Measurement  Lumpedmodel  (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=')  100  rectification  RF source  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  I Z  wire  10-1  >  MS  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  P  RF  10-2  gold pad  R  1  2  3  4  5  6  7 8  Frequency(GHz)[4]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Xu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Curwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2017, 111, 101101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [5]  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Addamane, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Reno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Williams, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2021, 119, 111103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [6]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wienold, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Röben, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Schrottke, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Grahn, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2014, 22, 30410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [7]  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Liao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Zhou, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Guan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Ma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  Express 2022, 30, 35937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [8]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Seo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mcinerney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Osinski, IEEE J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Quantum Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 1989, 25, 2229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [9]  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Bin Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Deng, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Kovanis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' A 2021, 103, 23528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [10]  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Rodriguez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Mottaghizadeh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gacemi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Jeannin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Asghari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Vasanelli, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Todorov,  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Sirtori, Laser Photonics Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' 2020, 14, 1900389.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [11]  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hinkov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Hugi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Beck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Faist, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Express 2016, 24, 3294.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content='  [12]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Gu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Wan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Fu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Cao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
+page_content=' (United Kingdom) 2017, 19,  065706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE3T4oBgHgl3EQf8QuK/content/2301.04806v1.pdf'}
diff --git a/rtAzT4oBgHgl3EQfA_rZ/content/tmp_files/2301.00937v1.pdf.txt b/rtAzT4oBgHgl3EQfA_rZ/content/tmp_files/2301.00937v1.pdf.txt
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+Draft version January 4, 2023
+Typeset using LATEX twocolumn style in AASTeX62
+FEASTS: IGM cooling triggered by tidal interactions through the diffuse HI phase around NGC 4631
+Jing Wang (王菁),1 Dong Yang (杨冬),1 S-H. Oh,2 Lister Staveley-Smith,3, 4 Jie Wang,5 Q. Daniel Wang,6
+Kelley M. Hess,7, 8 Luis C. Ho,1, 9 Ligang Hou,5 Yingjie Jing,5 Peter Kamphuis,10 Fujia Li,11, 12
+Xuchen Lin (林旭辰),1 Ziming Liu,5 Li Shao,5 Shun Wang (王舜),1 and Ming Zhu5
+1 Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China
+2Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, Republic of Korea
+3International Centre for Radio Astronomy Research, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
+4ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
+5National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, People’s Republic of
+China
+6Astronomy Department, University of Massachusetts, Amherst, MA 01003, USA
+7Instituto de Astrof´ısica de Andaluc´ıa (CSIC), Glorieta de la Astronom´ıa s/n, 18008 Granada, Spain
+8ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands
+9Department of Astronomy, School of Physics, Peking University, Beijing 100871, People’s Republic of China
+10Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute, 44780 Bochum, Germany
+11CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of
+China, Hefei 230026, People’s Republic of China
+12 School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, People’s Republic of China
+ABSTRACT
+We use the single-dish radio telescope FAST to map the Hi in the tidally interacting NGC 4631
+group with a resolution of 3.24′ (7 kpc), reaching a 5-σ column density limit of 1017.9 cm−2 assuming
+a line width of 20 km s−1. Taking the existing interferometric Hi image from the HALOGAS project
+of WSRT as reference, we are able to identify and characterize a significant excess of large-scale, low-
+density, and diffuse Hi in the group. This diffuse Hi extends for more than 120 kpc across, and accounts
+for more than one fourth of the total Hi detected by FAST in and around the galaxy NGC 4631. In the
+region of the tidal tails, the diffuse Hi has a typical column density above 1019.5 cm−2, and is highly
+turbulent with a velocity dispersion around 50 km s−1. It increases in column density with the dense
+Hi, and tends to be associated with the kinematically “hotter” part of the dense Hi. Through simple
+modeling, we find that the majority of the diffuse Hi in the tail region is likely to induce cooling out
+of the hot IGM instead of evaporating or being radiatively ionized. Given these relations of gas in
+different phases, the diffuse Hi may represent a condensing phase of the IGM. Active tidal interactions
+on-going and in the past may have produced the wide-spreading Hi distribution, and triggered the gas
+accretion to NGC 4631 through the phase of the diffuse Hi.
+Keywords: Galaxy evolution, interstellar medium
+1. INTRODUCTION
+The loss and gain of Hi are important drivers of galac-
+tic evolution, as Hi is in the phase where the star-
+forming gas starts to cool and settle down onto a galactic
+Corresponding author: Jing Wang
+jwang astro@pku.edu.cn
+Corresponding author: S-H. Oh
+seheonoh@kasi.re.kr
+disk. Although Hi disks can be several times more ex-
+tended from the galactic center than the optical disks
+where most star formation occurs (Swaters et al. 2002;
+Wang et al. 2013), the integral Hi richness is correlated
+with the amount of Hi on optical disks (Wang et al. 2020;
+Yu et al. 2022), and further with the specific star forma-
+tion rate (SFR) (Saintonge et al. 2017; Guo et al. 2021).
+Such a link of SFR with Hi far away extends further into
+the circum-galactic medium, indicated by the strengths
+of Lyman-α absorbers (Borthakur et al. 2016; Lan &
+arXiv:2301.00937v1  [astro-ph.GA]  3 Jan 2023
+
+2
+Mo 2018). These correlations imply a quasi-equilibrium
+state of baryonic flow through galaxies, and supports the
+role of Hi as the reservoir of raw material for forming
+stars.
+Tidal interactions are significant channels for galax-
+ies to both gain and lose Hi (Putman 2017; Verdes-
+Montenegro et al. 2001), but the net effects on the
+whole and in each step of physical processes remain to
+be studied. For example, Hi tails and clouds possibly
+of tidal origin are often found, including the Magellanic
+stream and at least some of the high-velocity cloud com-
+plexes around the Milky Way (Putman et al. 2012).
+They indicate a redistribution of gas between galaxies
+due to tidal interactions.
+These extra-planar Hi fea-
+tures should be prone to thermal evaporation (Cowie &
+McKee 1977), radiative ionisation, and dispersal due to
+Kelvin-Helmholtz instability and Rayleigh-Taylor insta-
+bility, but long-lasting ones have been found in massive
+clusters (Chung et al. 2007), loose groups (Koopmann
+et al. 2008; Zhu et al. 2021), and compact groups (Serra
+et al. 2013). It indicates a complex interplay between
+the Hi gas and the circum(inter)-galactic environment.
+For another example, starbursts are often found in gas-
+rich interacting pairs (Ellison et al. 2013; Chown et al.
+2019), possibly caused by gas inflows driven by tidal
+shocks, torques, and instabilities (Blumenthal & Barnes
+2018). Despite the enhanced consumption of gas, the
+integral Hi masses of mergers and post-mergers are not
+found to decrease compared to control samples (Ellison
+et al. 2018; Zuo et al. 2018; Shangguan et al. 2019).
+This unexpected consistency in Hi amount may be due
+to a boosted CGM cooling out of thermal instabilities,
+or suppressed atomic-to-molecular conversion efficiency
+out of turbulent Hi, but the exact reason is unclear. In
+most of the puzzles of this type, a major difficulty arises
+from the physical nature that various gravitational and
+hydrodynamic effects are involved and interact, and that
+gas exchanges between phases.
+Sorting out the response of Hi during tidal interac-
+tions is important for a refined evolutionary theory of
+galaxies of different types and in different environments.
+Semi-analytical models of galaxy evolution have been
+plagued by the fact that environmental and internal ef-
+fects have a strong degeneracy when reproducing the
+observed Hi or SFR scaling relations of satellite galaxies
+(Stevens & Brown 2017). Because different environmen-
+tal mechanisms co-exist, it is hard to separate and assess
+the role of each (Boselli & Gavazzi 2006; Cortese et al.
+2021), even in groups and the outskirts of clusters where
+tidal interactions should dominate other environmental
+effects (Boselli et al. 2022). The most promising way
+forward may be a more detailed analysis of existing and
+newly observed data.
+Characterizing the distribution
+and kinematics of Hi in prominent tidally interacting
+galaxy samples will help us identify signatures to sep-
+arate the tidal effects from other environmental effects;
+comparing quantified properties with physical models,
+and formulating empirical relations to be implemented
+into semi-analytical models, will help us break the de-
+generacy between internal and external causes.
+Luckily, there have been long-lasting efforts in this di-
+rection of characterizing detailed Hi properties in tidal
+interactions (e.g.
+Rand 1994; Yun et al. 1994; Wolfe
+et al. 2013; Lee-Waddell et al. 2019; Sorgho et al. 2019;
+Namumba et al. 2021).
+A highlight among them are
+the systematic research on compact groups (Verdes-
+Montenegro et al. 2001, 2005; Borthakur et al. 2010;
+Serra et al. 2013; Hess et al. 2017; Jones et al. 2019).
+Built upon these benchmarking papers, in this paper
+we study in detail one classical interacting system, the
+NGC 4631 group (N4631g). We contribute the following
+unique inputs. We use the Five hundred meter Aperture
+Spherical Telescope (FAST, Jiang et al. 2019) to obtain
+an Hi image with a high sensitivity, and moderate reso-
+lution. A first impression of the N4631g and its Hi distri-
+bution can be obtained from Figure 1. The FAST data
+reveals and spatially resolves a significant excess of Hi
+compared to a previous deep interferometric observation
+with the Westerbork Synthesis Radio Telescope (WSRT)
+by Hydrogen Accretion in LOcal GAlaxieS (HALOGAS)
+survey (Heald et al. 2011). This paper thus addresses
+in particular the existence of such an extended Hi enve-
+lope around NGC 4631, which the WSRT observations
+miss because it is too faint and too extended. The com-
+bined data show this well and allow an assessment of
+how much there is, how it is distributed, what its kine-
+matics are and how it is connected to the higher density
+Hi that the HALOGAS project found. The amount tells
+us about the total gas reservoir around galaxies, while
+the detailed properties tells us about the tidal interac-
+tion and the physics of the IGM (intra-galactic medium),
+CGM (circum-galactic medium), and ISM (inter-stellar
+medium) connection that are essential to gas accretion
+and depletion.
+The combination of single dish data and synthesis
+data, which is essential to obtain the new results in this
+paper, is a known but difficult problem (Stanimirovic
+2002). This paper demonstrates the power of FAST as
+compared to existing attempts to add extended emis-
+sion restricted to other single-dish telescopes (e.g. GBT
+and Parkes, de Blok et al. 2018; Das et al. 2020), which
+have much smaller dishes and hence have less overlap in
+u,v space with the synthesis data, or relatively signif-
+icant side-lobes (e.g. Arecibo, Heiles et al. 2001; Hess
+
+3
+et al. 2017). Closely relevant to this paper, Richter et al.
+(2018) used Hi image taken by the GBT in combination
+with the WSRT image. Limited by the resolution of the
+GBT image, the two types of Hi data were compared
+mainly in a qualitative way, and the focus of that work
+was instead on one line-of-sight with ultraviolet spectro-
+scopic data taken by the Hubble Space Telescope (HST).
+The FAST image used in this work has three times bet-
+ter resolution than the GBT image, has a much wider
+uv coverage in common with the WSRT data, and there-
+fore enables a relatively better quantified characteriza-
+tion and comparison of the Hi properties throughout the
+tidally interacting region in the group.
+This paper is organized as follows. We introduce the
+sample, the Hi data , and the multi-wavelength data in
+section 2. Particularly, we describe the observation and
+reduction of the FAST Hi data. In section 3, we ver-
+ify that the flux calibrations are consistent between the
+FAST and WSRT data, and show globally the existence
+of excess Hi detected by FAST. In section 4, we con-
+duct detailed analysis of the excess Hi, which is likely
+large-scale and low-density diffuse Hi. We quantify the
+distribution and localized kinematics of it, and its rela-
+tion to the dense Hi detected by WSRT. In section 5,
+we quantify the hydrodynamic and gravitational envi-
+ronment around the galaxy NGC 4631, and discuss the
+fate and motion of the (diffuse) Hi in the IGM. Finally
+we summarize in section 6. Throughout the paper, we
+assume a Chabrier (2003) initial mass function to esti-
+mate the stellar mass and SFR.
+2. DATA AND ANALYSIS
+2.1. The NGC 4631 galaxy and group
+The galaxy NGC 4631, known as the Whale galaxy,
+is an edge-on spiral galaxy, and has remarkable Hi tidal
+structures (Weliachew et al. 1978; Rand 1994).
+It is
+centered at α2000 = 190.9905◦, δ2000 = 32.1682◦, ac-
+cording to the 2MASS Extended Source Catalog (Jar-
+rett et al. 2000). It has a heliocentric systematic velocity
+of 615 km s−1 (Rand 1994). We take the error weighted
+mean of luminosity distances derived with the TRGB
+method in the literature (Seth et al. 2005; Tully et al.
+2013; Radburn-Smith et al. 2011; Monachesi et al. 2016),
+which is 7.53 Mpc.
+The members of N4631g have a velocity dispersion σc
+of 217 km s−1 (Kourkchi & Tully 2017). As the brightest
+galaxy of the N4631g, NGC 4631 has two major com-
+panions, NGC 4656 and NGC 4627, 70.5 and 5.6 kpc
+away in projected distance respectively, the interaction
+with which should have produced most of the Hi tidal
+structures around NGC 4631. Its interaction with NGC
+4656 might start only a few hundreds of million years
+ago, as suggested by the age of a tidal dwarf near NGC
+4656 (Schechtman-Rook & Hess 2012), and the simula-
+tion of Combes (1978) in an attempt to reproduce its
+Hi tidal tails. It also has many other fainter dwarf com-
+panions, and stellar tidal tails which do not correspond
+to the Hi tails (Mart´ınez-Delgado et al. 2015). These
+properties indicate a dynamic, actively interacting envi-
+ronment around NGC 4631.
+NGC 4631 has an active star formation possibly due
+to the active tidal interaction with neighbors. The ac-
+tive star formation may have triggered powerful outflows
+of mass and energy. These outflows reveal themselves
+as super-shells and anomalous velocity features in the
+Hi (Rand 1994) and CO images (Rand 2000), filamen-
+tary structures of dust (Mel´endez et al. 2015), ionized
+gas (Golla et al. 1996; Martin & Kern 2001; Strickland
+et al. 2004; T¨ullmann et al. 2006) extending above the
+disk plane, and magnetic fields perpendicular to the disk
+plane (Mora-Partiarroyo et al. 2019a,b).
+The present
+and past outflows may have built the prominent hot
+gaseous halo that is bright in the radio continuum (Ek-
+ers & Sancisi 1977; Irwin et al. 2012) and X-ray (Wang
+et al. 1995, 2001). But we point out that, the Hi struc-
+ture detected in this work which is large than 60 kpc
+in radius extends much further than the X-ray emitting
+hot gas halo which is roughly 10 kpc in radius.
+2.2. The FAST HI observation
+The FAST Hi observations of NGC 4631 were
+carried out on 2022 March 25/26/27 (proposal ID:
+PT2021 0071) as part of the FAST Extended Atlas
+of Selected Targets Survey (FEASTS)1. The zenith an-
+gles were < 15.7◦ during the observation. A rectangle
+of 1.6◦ × 1.5◦ is targeted around α2000 = 190.7027◦,
+δ2000 = 32.4058◦, an arbitrary position (grey cross in
+top panel of Figure 3) between NGC 4631 and NGC
+4656. The rectangle is scanned in the on-the-fly (OTF)
+mode with six passes, evenly divided into vertical and
+horizontal ones to achieve basket weaving. The scans are
+conducted with the L-band (1.05 - 1.45 GHz) 19-beam
+receiver rotated by 23.4/53.4◦(horizontal/vertical), and
+the spacing of scanning stripes set to be 21.66′.
+We
+show in the left panel of Figure 2 how these stripes are
+arranged. They cover extra regions on the four sides, in
+order to achieve relatively uniform sampling densities in
+the targeted region.
+The full width half maximum (FWHM) of the raw
+beam is ∼ 2.9′ at a frequency of 1.42 GHz (Jiang et al.
+2020).
+The effective angular separation between scan
+lines is 1.15′, and the effective integration time per po-
+1 https://github.com/FEASTS/LVgal/wiki
+
+4
+Figure 1.
+A false color image demonstrating the NGC 4631 group and its Hi gas. On top of the optical image, the blue
+colored halo shows the diffuse Hi flux imaged by FAST (beam FWHM=3.24′ or 7 kpc) in this study, while the light-blue finer
+structures are the denser Hi previously detected in the WSRT HALOGAS (Heald et al. 2011) observation (beam FWHM=40′′
+or 1.46 kpc). The names of 6 relatively prominent member galaxies are denoted.
+sition is 235.8 s. The total integration time is 4.47 h.
+The observation is accompanied by a 10-K noise diode
+turned on for 1 s every 60 s. The data is recorded by
+the Spec (W+N) backend, with a sampling time of 1 s,
+and channel width of 7.63 kHz, or 1.61 km/s for Hi 21
+cm observations.
+2.3. The FAST data reduction
+We extract a low-redshift frequency slice of 1408.7-
+1425.2 MHz (equivalent to 76-1609 km s−1), and focus
+on this part of the data. The data reduction is carried
+out with a pipeline developed following the standard
+procedures of reducing radio single-dish image data, par-
+ticularly those from Arecibo Legacy Fast ALFA Survey
+(ALFALFA, Haynes et al. 2018) and HI Parkes All Sky
+Survey (HIPASS, Barnes et al. 2001). It has 4 major
+modules, including RFI flagging, calibration, imaging,
+and baseline flattening. Many of these steps go back-
+ward and iterate till convergency. We briefly introduce
+
+Keeler 529
+NGC4627
+Dwarf A
+NGC4631
+MCG+06-28-022
+NGC4656
+FAST
+WSRT
+10 kpc5
+the steps below. An early version of the pipeline is also
+described in Zuo et al. (2022).
+1. RFI flagging.
+We flag the radio frequency in-
+terferences (RFIs) in two major steps. Firstly, we
+use the conventional waterfall map, which is distri-
+bution of flux in the diagram of frequency versus
+time, to identify outstanding stripes.
+Secondly,
+the whole image region is scanned with 6 passes,
+so that after gridding the data by sky position for
+each of the 6 passes, we can use a median and 3-
+σ based outlier finder to reject RFI contaminated
+data for the same sky position. The whole RFI
+flagging procedure is reviewed again after the steps
+of bandpass removal and flux calibration in the cal-
+ibration module. The RFI contamination rate is
+minimal in the FAST data used in this paper.
+2. Calibration. The bandpass is derived per beam
+for each stripe of the scan.
+The Hi emission is
+masked from the waterfall map with a best effort.
+The mask starts with a subjective, rough region
+with knowledge of Hi distribution from the litera-
+ture (Rand 1994), and is adjusted later with rms
+level based criterion after the first round of cal-
+ibration. Tests are conducted to decide an opti-
+mized smoothing width of 240 s for determining
+the bandpasses. The data and bandpass are cali-
+brated against the bandpass-removed sampling of
+the noise diode. The mask of the Hi emission is up-
+dated with the bandpass-removed and scaled data
+with the criterion of at least 200 connected pixels
+above 2-σ threshold. The procedure goes back to
+the step of determining the bandpasses and is it-
+erated for 3 times. Finally, the bandpass-removed
+and scaled data is corrected for a zenith angle
+dependent effective gain value of 13.5-16 to ac-
+count for scaling differences from the perfect gain
+and aperture efficiency at almost zero zenith angle
+(Jiang et al. 2020).
+3. Imaging. For the analysis of this paper, we pro-
+duce two sets of data cubes. The first set is a con-
+ventional FAST cube, with pixel size of of 30′′, and
+the channel width of 1.61 km/s. The second set is
+a projected FAST cube, gridded to match the area
+and WCS system of the WSRT HALOGAS data
+(see section 2.5). A Gaussian kernel with FWHM
+equivalent to half the FWHM of the raw beam
+is used to grid the data into channel maps. The
+FWHM of the raw beam is taken to be 2.9′, the
+median value of the 19 beams typically at the se-
+lected frequency (Jiang et al. 2020). This gridding
+process effectively smoothes the data, increasing
+the FWHM of the actual beam to 3.24′. The right
+panel of Figure 2 displays the the relative sampling
+densities of the observed data when gridding them
+into pixels. The density is roughly uniform with a
+1-σ scatter of 3.48% around the median value.
+4. Baseline flattening. We remove the continuum
+in the full range 1408.7-1425.2 MHz of the se-
+lected frequency slice by modeling it with a first-
+order polynomial function. Before removing the
+continuum, the Hi emissions are masked using a
+mask file generated by SoFiA (Serra et al. 2015).
+We then remove the residual continuum, standing
+waves, and other global irregularities in the spec-
+tra, which are referred to together as the resid-
+ual continuum. The residual continuum is mod-
+eled with the S-G filter with an effective poly-
+nomial order of 2, and a width of 480 km s−1
+(or 2.274 MHz), which are optimized after exper-
+iments.
+For reference, the major standing wave
+due to reflection between the dish and the receiver
+bin is ∼ 200 km s−1 (∼ 1 MHz) for FAST (Jiang
+et al. 2020). This module is iterated for 3 times.
+2.4. The FAST data cube
+We use SoFiA (Serra et al. 2015) on the conven-
+tional FAST cube to generate the detection mask for Hi
+emission. We use the threshold-based smooth+clipping
+source finding algorithm. The threshold is set to be 3-
+σ, and the smoothing kernels have widths of 0, 3, and 5
+pixels in the sky direction, and of 0 and 3 channels in the
+velocity direction. The reliability module is used with a
+threshold of 0.99 to exclude false detections. The result-
+ing mask is used to project the cube into moment maps
+and integral spectrum, and also to select emission-free
+regions to derive the rms level. The FAST data cube
+has an rms level of 0.965 mJy b−1
+F , where bF denotes
+the beam area of FAST. It corresponds to a 5-σ column
+density limit of 8.0×1017 cm−2, assuming a line width of
+20 km s−1, or a 5-σ point source mass limit of 105.9 M⊙,
+assuming a line width of 150 km s−1.
+We show the column density map derived from the
+moment-0 images in Figure 3. Apparent from the mo-
+ment images are the main target NGC 4631, its major
+satellite NGC 4656 to the south-east, and a known op-
+tically faint companion Dwarf A to the north-west. An-
+other two Hi bearing dwarfs previously detected in the
+WSRT cube of Rand (1994), Keeler 529 and MCG+06-
+28-022, are blended into the tidal feature on the north
+and south-east. Due to their relatively small Hi masses
+(each ∼ 107.15 M⊙, Rand 1994), we will not distinguish
+
+6
+192.0°
+191.5°
+191.0°
+190.5°
+190.0°
+189.5°
+33.5°
+33.0°
+32.5°
+32.0°
+31.5°
+RA(deg)
+DEC(deg)
+scan track
+Cut_region
+191.3°
+191.0°
+190.7°
+190.3°
+190.0°
+33.0°
+32.7°
+32.3°
+32.0°
+31.7°
+RA(deg)
+Dec(deg)
+sampling density
+0.85
+0.90
+0.95
+1.00
+1.05
+1.10
+1.15
+Figure 2. Left: one set of vertical and horizontal scanning stripes of the observation. Lines of different colors represent different
+IDs of the 19 beams. The blue square represents the imaging region of the final data cube. One can see that the scanning mode
+is not the traditional basket weaving, but using evenly distributed horizontal and vertical scans to micmic a basket weaving.
+Right: the relative sampling density of the whole observed data set when gridding them into pixels. The densities are normalized
+to the median value.
+them from the tidal structures in the analysis later. We
+also show the moment-1 and -2 images in Figure 4. De-
+spite the relatively low spatial resolution, the moment-1
+image shows velocity gradients in the disk regions of
+NGC 4631 and NGC 4656. It also shows several steep
+gradients in the region of tidal tails, possibly reflect-
+ing sharp turning in the direction of motions.
+These
+steep gradients are accompanied by high values in the
+moment-2 image, where the relative large beam of FAST
+tends to mix velocity structures. In the moment-2 im-
+age, the particularly high values are also caused by over-
+lapping structures that are separated in velocity space.
+We run SoFiA similarly for the projected FAST cube,
+but the smoothing kernels have widths of 0, 3, 11, and
+41 pixels in the sky direction instead. In unit of arcsec,
+the maximum extents of smoothing are actually similar
+for the conventional and projected FAST cubes. Expect-
+edly, the depths and moment images from the projected
+FAST cube are similar to those from the conventional
+FAST cube.
+2.5. The WSRT data cube
+We use the naturally weighted data cube from the
+WSRT HALOGAS project (Heald et al. 2011). It was
+observed with an integration time of 10×12h. The obser-
+vation has the shortest and longest baselines of WSRT
+around 36 m and 2.7 km, corresponding to a nominal
+largest and smallest angular scale of 24.5′ and 19.6′′, re-
+spectively. The data cube has a synthesis beam major
+and minor axes of 45.0′′ and 39.1′′. It has a pixel size
+of 4′′, and a channel width of 4.12 km s−1. The WSRT
+data cube covers an area of roughly 1◦×1◦ around NGC
+4631, so the companion NGC 4656 is near the edge of
+the image, and quite some of the tidal Hi is near or
+beyond the FWHM of the WSRT primary beam (PB)
+which has a size of 0.3◦.
+We run SoFiA on the WSRT cube to generate the
+detection mask.
+The parameter setting is similar to
+that for the projected FAST cube.
+With the SoFiA
+mask, we produce the moment images and integral spec-
+tra, and derive the rms level. The moment images are
+close to those published in Richter et al. (2018). The
+column density map derived from the moment-0 im-
+age is displayed in the bottom-left panel of Figure 3.
+The WSRT cube has a rms level σW of 0.257 mJy b−1,
+where b denotes the beam area of the WSRT data. This
+rms level corresponds to a 5-σ column density limit of
+7.32 × 1018 cm−2 assuming a line width of 20 km s−1
+and 5-σ point source mass limit of 105.54 M⊙ assuming
+a line width of 150 km s−1.
+Through visual inspection, we find noticeable so-called
+“negative bowl” artifacts throughout the cube indicative
+of missing short-spacing information, particularly in the
+
+7
+12h44m
+42m
+40m
+33°00'
+32°40'
+20'
+00'
+ra (deg)
+dec (deg)
+FAST
+18.0
+18.5
+19.0
+19.5
+20.0
+20.5
+21.0
+21.5
+logNHI(cm
+2)
+12h44m
+43m
+42m
+41m
+40m
+33°00'
+32°45'
+30'
+15'
+00'
+ra (deg)
+dec (deg)
+WSRT
+18.0
+18.5
+19.0
+19.5
+20.0
+20.5
+21.0
+21.5
+22.0
+logNHI(cm
+2)
+12h44m
+43m
+42m
+41m
+40m
+33°00'
+32°45'
+30'
+15'
+00'
+ra (deg)
+dec (deg)
+FAST+WSRT
+18.0
+18.5
+19.0
+19.5
+20.0
+20.5
+21.0
+21.5
+22.0
+logNHI(cm
+2)
+Figure 3.
+The Hi column density maps of NGC 4631 field. The maps are derived from the FAST cube (top), WSRT cube
+(bottom-left), and the FAST+WSRT combined cube (bottom-right). In the top panel, the center of the FAST observational
+field is marked with a grey cross. In the bottom-left panel, the FWHM of the WSRT PB is shown as the grey dashed circle.
+In the bottom-right panel, the grey dashed circle has a diameter equal to the critical angular scale for WSRT to miss extended
+Hi (see section 3.2). The bottom-right image does not look like the sum of the other two because the combination is done in
+the Fourier space thus the FAST flux is conserved, and because the PB attenuation effect of the WSRT cube is applied (see
+section 4.1). Beam shapes are denoted as green and open ellipses at the bottom left corner of each map.
+velocity range between 500 and 700 km s−1 where tidal
+features are strong. They highlight the need of single-
+dish image to fill this missing part, but also add un-
+certainties and complexities when we directly compare
+the FAST and WSRT images to characterize the spatial
+distribution of the large-scale Hi. Luckily, the typical
+absolute level of those “negative bowl” is around 1-σ of
+the WSRT data cube, and as we will show in section 4.2
+and Figure 8, the associated cumulative absolute flux is
+low compared to the excess Hi detected by FAST. These
+facts mitigate the problem, but future investigation of
+optimized strategy of combining the single-dish and in-
+terferometric data in the uv space may better solve this
+problem.
+2.6. Derived cubes
+For convenience of comparison, we produce a few de-
+rived cubes to control for the effects of the PSF (i.e. the
+FAST beam and the WSRT synthesis beam) and the
+WSRT PB attenuation.
+We use the equation from Wang et al. (2015) to pro-
+duce a data cube of PB attenuation levels (the PB cube
+hereafter). The equation is a function of the distance
+from the image center, and was calibrated using con-
+
+8
+12h44m
+42m
+40m
+33°00'
+32°40'
+20'
+00'
+31°40'
+ra (deg)
+dec (deg)
+450
+500
+550
+600
+650
+700
+750
+v (km/s)
+12h44m
+42m
+40m
+33°00'
+32°40'
+20'
+00'
+31°40'
+ra (deg)
+dec (deg)
+10
+20
+30
+40
+50
+60
+70
+v (km/s)
+Figure 4.
+Moment 1 (top) and 2 (bottom) images of the
+NGC 4631 field.
+The images are derived from the FAST
+cube. The column density contour of the WSRT data at the
+level of 1019.5cm−2 is plotted on top to guide the eye.
+tinuum sources from NRAO VLA Sky Survey (NVSS,
+Condon et al. 1998) and Faint Images of the Radio Sky
+at Twenty centimeters (FIRST, Becker et al. 1995). We
+produce the PB-corrected WSRT cube by dividing the
+original WSRT cube by the PB cube.
+We produce the smoothed WSRT cube by convolving
+the channel maps of the WSRT cube with the FAST
+beam. The beam image of the FAST is derived by stack-
+ing point source images of the 19 beams with data from
+Jiang et al. (2020). More details and discussion regard-
+ing the beam image can be found in appendix A. The
+flux of the smoothed WSRT cube is converted to the
+unit of Jy b−1
+F .
+We produce the PB-attenuated FAST cube by mul-
+tiplying the projected FAST cube with the PB cube.
+We subtract the smoothed WSRT cube from the PB-
+attenuated FAST cube, and obtain the PB-attenuated
+excess Hi cube2. We apply PB correction to the PB-
+attenuated excess Hi cube, and obtain the PB-free excess
+Hi cube. The PB-free excess Hi cube is largely positive,
+and the very few negative regions (most apparent ones
+are the two small white patches near the N4631 disk
+in the top panel of Figure 9) are likely due to point-
+ing uncertainties, deviation of real FAST beam from the
+adopted averaged one, and noise.
+The PB-attenuated excess Hi cube has the advantage
+of a relatively uniform rms level, convenient for thresh-
+old based analysis, while the PB-free one has the advan-
+tage of reflecting the actual amount of excess Hi. We
+will show in section 4 that, the PB-free excess Hi cube
+is practically the diffuse HI cube.
+2.7. Definition of regions
+We define the NGC 4631 region. We take the SoFiA
+mask of the projected FAST cube, exclude the region
+of Dwarf A, and separate the region of NGC 4631 and
+NGC 4656 by arbitrarily drawing a line roughly along
+the disk direction of NGC 4656. The line and the resul-
+tant NGC 4631 region to the north-west are shown in
+Figure 5. This region is delineated in order to study the
+distribution of any excess Hi detected by FAST (sec-
+tion 4.2). We exclude NGC 4656 because it is at the
+corner of the WSRT field of view, where the PB atten-
+uation factor reaches 0.1 and where the rms level will
+thus be increased by 10 times after PB correction.
+We separate the WSRT-detected NGC 4631 region
+into the disk region and the tail region. The disk and tail
+regions are defined to compare the localized kinemat-
+ics and distribution of Hi fluxes detected by FAST and
+WSRT (section 4.4 and 4.3). The tail region is further
+divided into the regions of four tails to study their bulk
+motions (section 5.2). These regions are defined based
+on the SoFiA mask of the WSRT cube and the tilted
+ring model of the NGC 4631 disk from Rand (1994),
+and through the watershed algorithm. The technique
+details are presented in appendix B. The sky projected
+view of these regions are displayed in Figure 5.
+We exclude the disk region from the NGC 4631 re-
+gion, and define the IGM region. This region is mainly
+2
+Strictly
+speaking,
+we
+should
+compare
+(FAST
+cube) ∗
+(WSRT beam) with (WSRT cube)∗(FAST beam), where ∗ is the
+sign of operation for convolution. We thus also tried smoothing
+the projected FAST cube with the WSRT beam, before applying
+the PB attenuation. We find the two products do not differ much
+due to the relatively small size of the WSRT beam.
+
+9
+12h44m
+43m
+42m
+41m
+40m
+33°00'
+32°45'
+30'
+15'
+00'
+ra (deg)
+dec (deg)
+region labels
+0
+1
+2
+3
+4
+5
+6
+7
+8
+Region
+Figure 5. Label of regions in the WSRT cube. The id from
+1 to 7 (color from dark blue to brown) corresponds to tail
+1, tail 2, tail 3, tail 4, NGC 4656, Dwarf A, and NGC 4631
+disk region respectively. The light blue color (id 0) marks
+the region detected in Hi by the projected FAST cube. The
+white dashed line separates the NGC 4631 and NGC 4656
+regions.
+for highlighting where the excess Hi dominates the Hi
+detected by FAST (section 4.2), and discussing the hy-
+drodynamical effects in the IGM (section 5.1).
+2.8. Multi-wavelength measurements from the literature
+We derive the stellar mass for NGC 4631 with Spitzer
+IRAC1 and 2 (3.6 and 4.5 µm) fluxes from the Local Vol-
+ume Legacy (LVL) project (Dale et al. 2009). We use
+the equation from Querejeta et al. (2015), to derive the
+IRAC1−IRAC2 color dependent IRAC1 mass-to-light
+ratio. The equation was calibrated using fluxes decom-
+posed into stellar and non-stellar components through
+independent component analysis. The estimated stellar
+mass log M∗/M⊙ = 10.25 ± 0.1. We use the star for-
+mation rates (SFR) derived in Lee et al. (2011) based
+on the far-ultraviolet and the total-infrared luminosi-
+ties.
+The total-infrared luminosity accounts for the
+dust attenuation of the far-ultraviolet luminosity, and
+was derived through spectral energy distribution fit-
+ting of mid- and far-infrared bands taken by Spitzer
+as part of the LVL project (Dale et al. 2009).
+The
+SFR= 4.19 ± 0.25 M⊙yr−1. We also obtain these two
+parameters for NGC 4656 from the same datasets, with
+log M∗/M⊙ = 9.15±0.1, and SFR= 1.17±0.07 M⊙yr−1.
+We summarize from the literature and estimate more
+properties about the N4631g in the appendix. Partic-
+ularly, in appendix D, we show that, based on the the
+local grouping of satellites, the characteristic radius r200
+within which the averaged density is 200 times the cos-
+mic critical density is around 249 kpc. Accordingly the
+virial temperature of the IGM should be around 8× 105
+K, though the near-disk outflowing hot gas reaches a
+temperature of nearly 2×106 K (Wang et al. 1995). A
+single-β model of the density profile of the IGM hot gas
+is presented and discussed in appendix E.
+3. COMPARING THE FAST AND WSRT DATA
+In this section, we provide integral spectra, fluxes and
+masses of Hi for galaxies in N4631g, and analyze Hi dis-
+tribution on different angular scales (inverse of spatial
+frequency) in the FAST and WSRT data. The difference
+of the integral measurements for galaxies between the
+two datasets provides a first-order measure of the excess
+Hi detected by FAST. Comparing integral fluxes of com-
+pact sources, and comparing amplitudes in an angular-
+scale range corresponding to overlapping region in the
+uv space help verify the consistency of flux calibrations
+between the two datasets, which is the basis for char-
+acterizing any excess Hi detected by FAST. Through
+comparing the amplitudes of the two datasets on large
+angular scales, we can further derive the critical angular
+scale for WSRT to miss extended Hi.
+3.1. The integral spectra and integrated fluxes
+In Figure 6, we show the integral Hi spectra of the
+N4631g from the FAST data, and compare it with those
+from the WSRT data.
+The conventional FAST spectrum is slightly higher
+than the projected FAST spectrum at the high velocity
+end, consistent with the truncation of the galaxy NGC
+4656 at the edge of the field of view of the WSRT ob-
+servation. The projected FAST Hi flux is in excess of
+the PB-corrected WSRT one throughout the velocity
+range.
+The integral fluxes from the FAST data, the
+projected FAST data, the WSRT cube, and the PB-
+corrected WSRT data are 1345.9±134.6, 1314.6±131.5,
+593.8±59.4, and 852.1±85.2 Jy km s−1 respectively.
+The error bars are dominated by an assumed flux cali-
+bration uncertainty of 10%.
+From the FAST cube, the Hi masses of NGC 4631,
+its major satellite NGC 4656, and dwarf companion
+Dwarf A are 1010.08±0.04, 109.77±0.04, and 107.77±0.04 M⊙
+(all assuming the distance of NGC 4656) respectively.
+In comparison, the corresponding values from the PB-
+corrected WSRT cube are 109.90±0.04, 109.38±0.04, and
+107.82±0.04 M⊙. To show the very little influence of reso-
+
+10
+400
+450
+500
+550
+600
+650
+700
+750
+800
+vel (km/s)
+0
+1
+2
+3
+4
+5
+6
+7
+f (Jy)
+FAST
+FAST (proj)
+WSRT
+WSRT (PBc)
+Figure 6.
+Integral Hi spectra of N4631g from different
+cubes. The spectra from the FAST cube, the projected FAST
+cube, the WSRT cube, and the PB-corrected WSRT cube are
+plotted in red, pink, green and purple, respectively.
+lution in this comparison, we also derive the correspond-
+ing values from the PB-corrected smoothed WSRT cube,
+which are are 109.90±0.04, 109.39±0.04, and 107.76±0.04
+M⊙.
+There is clear excess Hi detected by FAST for NGC
+4631 and NGC 4656.
+The excess Hi may be caused
+by the existence of diffuse Hi, which has large angular
+size or low surface densities 3. There is no excess Hi
+detected by FAST for Dwarf A, which is relatively small
+in angular size.
+3.2. Comparing the amplitude spectra
+One concern that arises when comparing the FAST
+and WSRT data is whether the flux calibrations are con-
+sistent. The consistent integral fluxes of Dwarf A sup-
+port it, but we further justify it by comparing the am-
+plitude spectra between the PB-attenuated FAST cube
+and the smoothed WSRT cube.
+The analysis exploits modified scripts from the pack-
+age uvcombine 4. Each channel image is Fourier trans-
+formed, and becomes a complex image of amplitudes and
+phases where the position of a pixel reflects the spatial
+frequency (inverse of the angular scale). The relation
+between the amplitude A and the angular scale is called
+the amplitude spectrum. The right panel of Figure 7
+shows the amplitude spectra for both datasets at a se-
+lected channel. The two spectra converge at intermedi-
+ate angular scales, largely between a lower and upper
+3 We note that, when the definition of low-surface density is
+based on the rms level of the WSRT cube, it is influenced by the
+effect of PB attenuation. We will discuss more on this point in
+section 4.2
+4 https://github.com/radio-astro-tools/uvcombine/
+limit angular scales of 4′ and 24.5′. The lower limit is
+just slightly (1.25 times) higher than the FWHM of the
+FAST beam, while the upper one corresponds to the
+shortest baseline (36 m) of the WSRT array. We select
+the data points of the two datasets between the limiting
+angular scales, and compare their spectral amplitudes
+as well as the related real and imaginary parts in the
+left panel of Figure 7. The data points all lie close to
+the one-to-one line. We select the channels (in total 50)
+where the maximum FAST amplitudes are higher than
+0.15 Jy, and derive the average linear scaling factor of
+FAST amplitudes over the WSRT amplitudes for each
+of these channels (more details in appendix F and left
+panel of Figure 20). The average scaling factors have a
+median value and standard deviation of 0.98 and 0.02
+respectively. They strongly support the consistency of
+fluxes from FAST and WSRT observations on the se-
+lected overlapping angular scales. We do not correct for
+this 1.02 scaling difference, but if we do so the amount of
+excess Hi derived in this work should be systematically
+enlarged by 2%.
+In the left panel of Figure 7, we see a hint of the FAST
+amplitudes exceeding the WSRT amplitudes on the high
+amplitude end. It indicates the start of the regime where
+the WSRT tends to miss large-scale diffuse flux. In order
+to investigate whether this hint is really, we select chan-
+nels (50 in total) where the PB-attenuated FAST inten-
+sity is higher than 0.15 Jy and higher than the WSRT
+intensity by more than 10%. For each channel, we derive
+the critical angular scale above which the FAST A are
+higher than the WSRT A by more than 1%. The critical
+angular scales have a relative narrow range, and a mean
+value of 13.6′ ± 1.9′ (more details in appendix F and
+right panel of Figure 20), corresponding to a baseline of
+65 m and a physical scale of 29.7 kpc. This critical an-
+gular scale is roughly half the theoretical value derived
+from the shortest baseline of the WSRT array, possibly
+due to a combined effect of the PB attenuation, and the
+limited WSRT sampling density of the shortest baseline
+which can be exacerbated by RFI flagging.
+4. THE DIFFUSE HI DETECTED BY FAST
+This section characterizes the diffuse Hi detected by
+FAST, including how much there is, how it is dis-
+tributed, what its kinematics are, and how it is con-
+nected to the higher density Hi that the HALOGAS
+project detected.
+4.1. Combining the HI data
+Because the FAST beam has a relatively low side-
+lobe level of around 1% beyond a radius of ∼ 3.5′ (ap-
+pendix A), we use the MIRIAD procedure immerge to
+
+11
+2
+1
+0
+1
+2
+AWSRT
+2
+1
+0
+1
+2
+AFAST
+channel-31
+imag
+real
+A
+103
+Angular scale (arcsec)
+10
+4
+10
+3
+10
+2
+10
+1
+100
+A
+smoothed WSRT
+PB attenuated FAST
+Figure 7.
+An example of amplitude spectral analysis of channel maps. The two channel maps analyzed have the same channel
+number 31 (corresponding to a velocity of 477.7 km s−1), but are from the PB-attenuated FAST cube and the smoothed WSRT
+cube. Left: a one-to-one comparison in amplitudes (purple), the real parts (yellow), and the imaginary parts (green) between
+the two types of data, selected to have angular scales between the limiting values marked in the right panel. The dashed line
+is the y = x line. The solid line shows the best-fit linear relation between the two types of amplitudes. Right: the amplitude
+spectra of the amplitude (A) as a function of the angular scale, for the FAST (red dots) and WSRT data (blue dots). The two
+black, thick, vertical lines mark the limiting angular scales of 4′ and 24.5′, between which both FAST and WSRT data should
+have relatively good sensitivity. Here this channel 31 is arbitrarily chosen, and the emission of that channel map is relatively
+compact in morphology. In Figure 20 of appendix F, we show a similar comparison between the FAST and WSRT datasets
+with data from all channels which have significant flux (FAST amplitudes>0.15 Jy) putting together.
+combine the projected FAST and WSRT cubes, which
+uses the Gaussian functions to approximate beams. The
+procedure immerge combines the two types of data in
+the Fourier domain, with a unit weight for the projected
+FAST data and a tapering for the WSRT data. The ef-
+fect of the tappering is to make a Gaussian beam equiv-
+alent to the WSRT synthesis beam, after adding the
+tapered WSRT synthesis beam to the FAST beam in
+the Fourier domain. The output is an image combining
+the spatial information of both data, but with the same
+PB attenuation effect as the WSRT data. The proce-
+dure also derives a calibration factor of WSRT flux over
+FAST flux to be 0.98, consistent with the result from
+our amplitude spectral analysis.
+The combined data give us a visual impression where
+and how significant FAST detects the diffuse Hi that
+is lacking in the WSRT observations.
+The combined
+moment-0 image is displayed in the bottom-right panel
+of Figure 3. FAST detects an excess of Hi widely sur-
+rounding the denser tidal structures previously detected
+by WSRT, typically on a scale larger than the critical
+angular scale for WSRT to miss extended fluxes (see
+section 3.2). The immerge process adds not only a lot
+of new, diffuse Hi near the WSRT detection limit of
+1018.86 cm−2, but also thickens the structures at a rel-
+atively higher column density of 1020 cm−2 (i.e. FAST
+also detects more relatively high-density gas).
+Because the side-lobe level of the FAST beam cannot
+be ignored (appendix A), the combined data cube and
+image are mainly for visual inspection here and later
+in section 5.2. In the following, we analyze the FAST-
+detected excess, diffuse Hi combining the two datasets,
+but not directly based on the immerge combined data.
+4.2. Relating the diffuse HI to large-angular scale gas
+We classify and quantify the distribution of excess Hi
+detected in the FAST data with respect to the WSRT
+data. Unless otherwise specified, we focus on the NGC
+4631 region in this section, as NGC 4656 is heavily at-
+tenuated by the PB effects. In the NGC 4631 region,
+26.3% of the flux from the PB-attenuated FAST cube
+are missed by the WSRT cube. The missed part may be
+related to the existence of low-surface density or large-
+angular scale Hi, which we refer to together as the diffuse
+Hi.
+We use the rms level of the WSRT data, to separate
+the PB-attenuated excess Hi into the low-surface density
+and the large-angular scale types. We remind that, the
+noise level of the PB-attenuated FAST cube decreases
+as a function of radius from the image center while that
+of the WSRT cube remains roughly constant, so the rel-
+ative level of low-surface density Hi that is missed by
+WSRT for being below the rms-based threshold should
+increase toward large radius. This effect biases our anal-
+ysis toward attributing excess Hi to the low-surface den-
+sity type at large radius, and undermines the detection
+of large-angular scale type.
+
+12
+In Figure 8, we study the cumulative distribution of
+the PB-attenuated excess Hi as a function of the asso-
+ciated flux in the PB-attenuated FAST cube. The 3-σ
+detection threshold line of the smoothed WSRT cube is
+marked in the figure. The distribution to the left of the
+positive threshold line (i.e. the right-side edge of the
+cyan band) reflects the part of PB-attenuated excess Hi
+missed by WSRT due to its low-surface density. There is
+only 10.3% of PB-attenuated excess Hi in this part. The
+remaining part (89.7%) of PB-attenuated excess Hi is
+likely missed by WSRT due to its large-angular scale dis-
+tribution. Because the periphery of large-angular scale
+Hi distribution naturally has low densities, and because
+of the PB attenuation effects described above, the ac-
+tual fraction of large-angular scale Hi missed by WSRT
+should be higher than this value of 89.7%. Thus, the
+majority of the diffuse Hi are invisible to WSRT not
+because of the limited sensitivity, but because of the
+limited shortest baseline.
+We display the column density maps of the diffuse
+Hi (PB-free excess Hi), its low-surface density part (the
+part below the WSRT detection threshold before apply-
+ing the correction for PB attenuation), and the large-
+angular scale part (the diffuse Hi minus the low-surface
+density part) for the NGC 4631 region in Figure 9.
+As discussed before, the low-surface density and large-
+angular scale parts displayed here are upper and lower
+limits of the actual parts. The displayed large-angular
+scale Hi is almost always higher in level than the dis-
+played low-surface density Hi, except for the periphery
+of the whole region and a small region on the south-
+west.
+It confirms that, a considerable fraction of the
+low-surface density Hi is attached to the large-angular
+scale Hi in the outskirts. The majority of the excess Hi
+is by nature the large-angular scale Hi.
+It is still questionable whether the diffuse Hi primar-
+ily overlaps with or is beyond the region of dense Hi
+detected in the WSRT cube.
+In Figure 8, the right
+panel is similar to the left panel, but the x-axis is re-
+placed by the associated flux of the smoothed WSRT
+cube. The distribution to the left of the positive thresh-
+old line now reflects the part of PB-attenuated excess Hi
+residing in regions where the WSRT data detects no Hi.
+Only 40.3% of the PB-attenuated excess Hi are found in
+blank regions of the WSRT data. More than half of the
+PB-attenuated excess Hi overlaps in regions with where
+the WSRT detects the dense Hi (i.e. disk region+tail
+region). Another noticeable feature in the right panel of
+Figure 8 is that, the WSRT flux distribution is peaked
+at a value below zero (∼ −1.5 mJy b−1
+F ), likely related
+to the “negative bowl” artifacts discussed in section 2.5.
+Multiplying this absolute peak value with the number of
+voxels which have smoothed WSRT flux below 3-σ but
+non-zero excess Hi provides a rough estimate of the re-
+lated uncertainty for the fraction 40.3% derived above,
+which is 12.5%.
+If we further limit the analysis to the IGM region
+by excluding the disk region of NGC 4631, the frac-
+tion of PB-attenuated FAST flux missed by the WSRT
+data dramatically increases to 71.2%, the fraction of PB-
+attenuated excess Hi classified into the low-surface den-
+sity type slightly increases to 14.5%, and the fraction
+found beyond the dense Hi region (equivalent to the tail
+region) slightly increases to 56.3%. These fractions also
+indicate that, in the tail region, the amounts of dense
+Hi and diffuse Hi are roughly equal.
+4.3. Relating the diffuse HI to properties of the dense
+HI
+In the following, we take advantage of the high resolu-
+tion of the WSRT data, quantify the localized kinematic
+properties of dense Hi, and search for the preferred kine-
+matic condition traced by the dense Hi to form the dif-
+fuse Hi. The analysis of this section is limited to the tail
+region.
+We use BAYGAUD (Oh et al. 2022) to fit multi-Gaussian
+models to the line-of-sight spectra of the WSRT cube.
+BAYGAUD uses Bayesian analysis techniques to decide
+the optimal number of Gaussian components. Figure 10
+shows the map of the number of components. The max-
+imum number reaches 4, but those line-of-sights with
+4 Gaussian components are mostly within the galactic
+disks. The NGC 4631 disk region has many Gaussian
+components possibly because of the edge-on geometry,
+the tidal perturbation, and the energy input from mas-
+sive young stars. These complexities support our deci-
+sion to leave aside the disk region and focus on the tail
+region.
+The profiles which are best fit with only one Gaussian
+component are referred to as the single-Gaussian pro-
+files, otherwise the multi-Gaussian profiles.
+For each
+multi-Gaussian profile, we identify the the Gaussian
+component with the highest intensity as the primary
+component.
+Figure 11 shows the distribution of σ of
+all the single or primary Gaussian components of dense
+Hi in the tail region. We divide the Gaussian compo-
+nents into narrow (warm) and broad (hot) ones by a σ
+of 8 km s−1, thermally corresponding to a temperature
+of 3600 K though the σ here are not really thermal.
+We use not only the number of Gaussian components
+but also profile broadness to indicate the kinematic hot-
+ness of the dense Hi. The expectations are: 1) for single-
+Gaussian profiles, velocity dispersion σ is indicative of
+kinematic hotness, and high column densities of the
+
+13
+20
+10
+0
+10
+20
+30
+40
+fHI, F(mJy/bF)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+frac (excess HI)
+FAST PB attenuated
+20
+10
+0
+10
+20
+30
+40
+fHI, W(mJy/bF)
+WSRT smoothed
+Figure 8.
+The distribution of attenuated excess Hi as a function of voxel values in data cubes. The left panel is for the
+attenuated FAST cube, and the right the smoothed WSRT cube. In each panel, the solid grey curve is the cumulative distribution
+starting from the low-value side, and the dashed grey curve is for the peak-value normalized differential distribution. The cyan
+band is the ±3-σ range of the smoothed WSRT cube.
+broad (narrow) components tend to be associated with a
+high level of kinematic hotness (coolness); 2) in general,
+single-Gaussian profiles tend to be kinematically cooler
+than multi-Gaussian profiles if they are not significantly
+affected by projection effect; 3) for a multi-Gaussian pro-
+file, the narrower Gaussian component with the smaller
+value of σ is relatively cooler than the broader ones; 4)
+for multi-Gaussian profiles, profiles with narrow compo-
+nents tend to be kinematically cooler than those with-
+out, and those with a high fraction of flux in narrow
+components tend to be cooler than otherwise.
+We study how the column density of diffuse Hi is re-
+lated to these kinematical properties of the dense Hi. In
+each panel of Figure 12, we select and divide into two
+subsets the line-of-sights along dense Hi by one type of
+dense Hi kinematic property described above. We com-
+pare the distributions of column density in associated
+diffuse Hi between the two subsets. Systematic trends
+arise from the comparisons. For single-Gaussian narrow
+profiles, high levels of diffuse Hi prefer those that are
+broader in widths (panel a), but do not have a clear
+trend with the column density (panel b).
+For single-
+Gaussian broad profiles, they show a slight tendency
+toward the broad widths (panel c) and high column
+densities (panel d). For all profiles, they prefer multi-
+Gaussian profiles over single-Gaussian profiles (panel e),
+and regions where there is no narrow Hi over otherwise
+(panel f). For multi-Gaussian profiles, they slightly pre-
+fer those with low fractions of narrow components (panel
+g).
+Together, these trends indicate that the localized
+kinematic hotness of the dense Hi and the column den-
+sity of the diffuse Hi seem to be boosted simultaneously
+in the tail region. There might be a pipeline of the Hi
+shifting from the narrow, to the broad, and then to the
+diffuse status, or in the opposite direction.
+4.4. The localized kinematics of the diffuse HI
+From the spectra displayed in Figure 6, the FAST
+flux does not extend further in velocity than the WSRT
+flux. In the literature, such an excess of Hi in the same
+velocity range is typically attributed to a tidal origin
+(Verdes-Montenegro et al. 2001). Those integral spec-
+tra mix the effect of bulk motions and localized kine-
+matics. In the following, we remove the velocity shift
+due to bulk motions and derive super profiles to reflect
+localized kinematics. In order to minimize the projec-
+tion effect of multiple velocity components, we select the
+line-of-sights which have single-Gaussian profiles in the
+dense Hi, which comprise 51%, 14%, and 65% of the
+line-of-sights in the NGC 4631 region (disk region+tail
+region), the disk region, and the tail region, respectively.
+We keep in mind that in addition to thermal motions,
+beam smearing, and turbulence should significantly con-
+tribute to the broadening of line widths.
+We use the velocity centers of line-of-sight spectra in
+the WSRT cube, which have been obtained using BAY-
+GAUD (Oh et al. 2022). We stack the line-of-sight spectra
+
+14
+12h44m
+43m
+42m
+41m
+40m
+33°00'
+32°45'
+30'
+15'
+00'
+ra (deg)
+dec (deg)
+Missing HI: the diffuse HI
+18.0
+18.5
+19.0
+19.5
+20.0
+20.5
+logNHI(1020 cm
+2)
+12h44m
+43m
+42m
+41m
+40m
+33°00'
+32°45'
+30'
+15'
+00'
+ra (deg)
+dec (deg)
+HI missed due to limited sensitivity
+18.0
+18.5
+19.0
+19.5
+20.0
+20.5
+logNHI(1020 cm
+2)
+12h44m
+43m
+42m
+41m
+40m
+33°00'
+32°45'
+30'
+15'
+00'
+ra (deg)
+dec (deg)
+HI missed due to limited baseline
+18.0
+18.5
+19.0
+19.5
+20.0
+20.5
+logNHI(1020 cm
+2)
+Figure 9.
+Column density maps of the excess Hi in the NGC 4631 region. The top panel shows the PB-free excess Hi missed
+by WSRT. The bottom-left and bottom-right panels divide the PB-free excess Hi into two parts: the one missed by WSRT due
+to the limited sensitivity (the low-surface density Hi) and the one missed missed by WSRT due to the limited shortest baseline
+(the large-angular scale Hi), respectively. Some of the low-surface density Hi shown in the bottom-left panel may actually belong
+to the large-angular scale Hi in the bottom-right panel; please refer to the main text for more details.
+of the WSRT cube, after register them to the same ve-
+locity center. The stacking is performed for the WSRT-
+detected NGC 4631 region, the disk region, and the tail
+region, respectively. We do the same stacking for the
+smoothed WSRT cube and the PB-attenuated FAST
+cube, using the same velocity centroid determined from
+the WSRT cube. We display these super profiles in Fig-
+ure 13. From the top panel, the PB-attenuated excess
+Hi of FAST is found throughout the localized velocity
+range, but not preferentially in the wings of the dense
+Hi. The conclusion above holds for both disk and tail
+regions displayed in the middle and bottom panels, but
+the super profiles of the former are much broader than
+the latter, indicating influences from the galactic inter-
+nal structures, geometry, and stellar feedbacks. In the
+following of this section, we therefore limit the analysis
+to the tail region to focus on tidal effects.
+We use emcee (Foreman-Mackey et al. 2013), the
+Python implementation of Goodman & Weare’s Affine
+Invariant Markov Chain Monte Carlo (MCMC) Ensem-
+
+15
+12h44m
+43m
+42m
+41m
+40m
+33°00'
+32°45'
+30'
+15'
+00'
+ra (deg)
+dec (deg)
+Number of G components
+1
+2
+3
+4
+5
+ncomp
+Figure 10.
+Map of number of Gaussian components from
+BAYGAUD fit for the WSRT cube. The numbers 1 to 4 is
+denoted by colors from cyan to red.
+0
+5
+10
+15
+20
+25
+HI(km s
+1)
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+frac (pixel)
+Velocity dispersion of the single or primary Gaussian component
+narrow
+broad
+Figure 11.
+The distribution of the velocity dispersion of
+the single or primary Gaussian components in the WSRT
+cube.
+The vertical and dashed line at 8 km s−1 divides
+the Gaussian components into the narrow (warm) and broad
+(hot) types.
+ble sampler, to fit a double-Gaussian model to each of
+the super profiles of the tail region.
+The details and
+best-fit models are present in appendix G.
+It is interesting to point out that, the narrow-Gaussian
+component accounts for roughly half the total flux in
+the FAST super profile, which is close to the ratio of
+the dense Hi flux over the FAST detected Hi flux in
+the tail region.
+Thus, it is possible that the narrow
+component of the FAST super profile corresponds to the
+dense Hi detected by WSRT, while the broad component
+corresponds to a diffuse envelope missed by WSRT.
+We use the square root difference between the veloc-
+ity dispersions of the WSRT and the smoothed WSRT
+cubes to correct for beam smearing effects. After the
+correction, the narrow and broad Gaussian components
+of the FAST super profile have σ of 13.4 and 51.0 km s−1
+respectively. It is obvious that the width of the broad
+component is unlikely thermal, but should be possibly
+dominated by turbulence, and perhaps also some con-
+tribution from beam smearing of where no WSRT flux
+is detected.
+5. THE HYDRO-DYNAMIC AND TIDAL
+ENVIRONMENTS
+In this section, we investigate the thermal, radiative,
+and gravitational environments around NGC 4631. We
+investigate, what is the fate of the Hi and particularly
+the diffuse Hi in the IGM and tidal region, and what
+physical mechanisms drive that.
+5.1. The hydro-dynamic effects
+We come back to the column density map of FAST
+detected Hi in Figure 3. The high density part, where
+NHI ≥ 1019cm−2, extends for ∼120 kpc across. Near
+the edge, NHI drops by nearly 1 dex within a length
+comparable to the beam size of 3.24′, or 7.1 kpc.
+Similar but sharper (due to the use of images with a
+higher resolution) edges of Hi distribution were noticed
+before at a similar column density level, particularly by
+the pioneering work of Corbelli et al. (1989) and van
+Gorkom (1993), in deep Hi imaging of the nearby galax-
+ies M33 and NGC 3198.
+The truncation of Hi disks
+was attributed to the ionisation by the cosmic ultra-
+violet (UV) background (Maloney 1993).
+The preva-
+lence of the truncation and the uniformity of the thresh-
+old column density are questioned recently by deep Hi
+imaging of more galaxies (Bland-Hawthorn et al. 2017;
+Ianjamasimanana et al. 2018), as both the local UV
+background and the clumpiness of Hi affect the ionizing
+status while both factors are quite uncertain (Bland-
+Hawthorn et al. 2017). The condition for Hi to survive
+and evolve in the hot gas halo of N4631g may also dif-
+fer from those benchmark galaxies M33 and NGC 3198.
+Firstly, the tidal Hi reaches far into the IGM while re-
+taining a high column density, which may induce effi-
+cient cooling of the hot gas.
+Secondly, the relatively
+high SFR of NGC 4631 may enhance the local UV radi-
+ation.
+In the following, we discuss the fate of Hi in the IGM
+region in the context of different hydro-dynamic pro-
+cesses as a function of radius from NGC 4631. We note
+
+16
+0.50
+0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+NHI, diffuse(1020cm
+2)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+frac (pixel)
+a) single-G: velocity dispersion of narrow line
+low
+sg, narrow
+high
+sg, narrow
+0.50
+0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+NHI, diffuse(1020cm
+2)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+frac (pixel)
+b) single-G: column density of narrow line
+low
+sg, narrow
+high
+sg, narrow
+0.50
+0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+NHI, diffuse(1020cm
+2)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+frac (pixel)
+c) single-G: velocity dispersion of broad line
+low
+sg, broad
+high
+sg, broad
+0.50
+0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+NHI, diffuse(1020cm
+2)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+frac (pixel)
+d) single-G: column density of broad line
+low
+sg, broad
+high
+sg, broad
+0.50
+0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+NHI, diffuse(1020cm
+2)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+frac (pixel)
+e) all: number of components
+ncomp = 1
+ncomp > 1
+0.50
+0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+NHI, diffuse(1020cm
+2)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+frac (pixel)
+f) all: the existence of narrow components
+with narrow comp
+without narrow comp
+0.50
+0.25
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+NHI, diffuse(1020cm
+2)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+frac (pixel)
+g) mutliple-G: narrow-component fraction
+high
+fracnarrow
+low
+fracnarrow
+Figure 12.
+Comparing the cumulative distributions of diffuse Hi column densities between line-of-sights with different localized
+kinematic properties of the dense Hi. The properties considered include the velocity dispersion of narrow/broad single-Gaussian
+components (panel a/c), and the column density of narrow/broad single-Gaussian components (panel b/d), the number of
+Gaussian components (panel e), the existence of the narrow component (panel f), and the flux fraction of narrow components
+along line-of-sights with multi-Gaussian components (panel g).
+
+17
+200
+150
+100
+50
+0
+50
+100
+150
+200
+v(km/s)
+0
+50
+100
+150
+200
+f(mJy/bF)
+whole
+WSRT (sg fit)
+WSRT
+WSRT (smooth)
+FAST
+200
+150
+100
+50
+0
+50
+100
+150
+200
+v(km/s)
+0
+5
+10
+15
+20
+25
+30
+f(mJy/bF)
+disk
+WSRT (sg fit)
+WSRT
+WSRT (smooth)
+FAST
+200
+150
+100
+50
+0
+50
+100
+150
+200
+v(km/s)
+0
+20
+40
+60
+80
+100
+120
+140
+f(mJy/bF)
+tail
+WSRT (sg fit)
+WSRT
+WSRT (smooth)
+FAST
+Figure 13.
+Super profiles of Hi from stacking line-of-sights
+of data cubes. The line-of-sights are selected to have single-
+Gaussian profiles in the dense Hi.
+The top, middle, and
+bottom panels plot the super profiles of the whole WSRT Hi
+detected region, the disk region, and the tail region, respec-
+tively.
+The cubes include the WSRT cube, the smoothed
+WSRT cube, and the PB-attenuated FAST cubes, which
+are plotted in orange, green and red. The stacking centers
+and stacking regions are determined by single-Gaussian fit
+to line-of-sights from the WSRT cube; the super profile of
+the single-Gaussian fits is plotted in cyan.
+that the following discussion is based on first order ap-
+proximations of the complex interplay between the dif-
+ferent phases and dynamics in the IGM. As such they
+merely provide a first indication of what might be hap-
+pening to the Hi in the tidal region.
+We point out that, the models discussed are 3-
+dimensional but the observed Hi is projected.
+The
+galactocentric distances can be underestimated, and
+the projection and overlapping of structures can arti-
+ficially enhance the Hi column density, which may be
+major sources of uncertainty in the discussion of Hi
+survival in the IGM. On the other hand, the projected
+phase-space distribution of flux (Figure16, discussed in
+section 5.2.2) suggests that the overlapping of structures
+seems not severe in most parts of tail 1, 3 and 4, which
+may mitigate the problem. To overcome this observa-
+tional limitation in the future, hydrodynamic modeling
+specifically conducted to reproduce the Hi distribution
+in N4631g will greatly help; alternatively, a sample of
+many interacting systems like N4631g will provide a
+statistical and representative view for comparison with
+and constraint on general hydrodynamic simulation of
+interacting systems.
+Despite the uncertainties, a major advance here is
+that, the calculations are based on real measurements
+of the diffuse Hi, which were lacking in most previous
+observations.
+5.1.1. Thermal conduction
+Based on the theory of Cowie & McKee (1977), we use
+the following simplified calculation to discuss the status
+of thermal conduction of the Hi in the IGM region.
+We assume a density distribution for the hot gas in the
+IGM (nIGM) following the single-β models presented in
+Eckert et al. (2011) (See appendix E for details). The
+temperature is assumed to be uniform at the virial tem-
+perature of 8×105 K (appendix D). Based on our mea-
+sured super profiles, we fix the velocity dispersion of the
+diffuse Hi to σHI = 51.0km s−1 (section 4.4). We assume
+the Hi travels in the hot gas halo in an external pressure-
+confined way, and derive the volume density of the dif-
+fuse Hi (nHI) accordingly. The value of log(nHI/cm−3)
+drops from −2.4 at 10 kpc to −3.1 at 60 kpc, consis-
+tent with the typical values of tidal Hi discussed in the
+literature (e.g. Borthakur et al. 2010).
+For an Hi cloud with a radius rc, the dimensionless
+“global saturation parameter” σ0 =
+(TIGM/1.5×107 K)2
+nIGM rc
+separates the gas at the interface between Hi and hot gas
+into regimes of saturated evaporation, classical evapora-
+tion, and cooling flows (Cowie & McKee 1977). Using
+the critical value σ0 = 0.027 (Cowie & McKee 1977),
+we derive the critical rc as a function of distance from
+
+18
+NGC 4631. Then we calculate the critical column den-
+sity NHI,c,evap = nHI rc = 1018.5 cm−2 for classical evap-
+oration in N4631g. Because N4631g has a relatively low
+mass and thus low virial temperature, thermal evapo-
+ration is only relevant on small scales, corresponding to
+low column densities. This critical value does not vary
+significantly with distance to NGC 4631 because the Hi
+volume density scales with the ICM density in our as-
+sumed model.
+For both the FAST detected Hi and the diffuse Hi
+(Figure 3 and 9), this critical column density value is
+only reached at the very periphery of the IGM region.
+It is also clear in Figure 14, where we plot the number
+density of pixels as a function of column density of the
+diffuse Hi and radius. Between a distance of 20 and 60
+kpc, the number densities peak where log(NHI/cm−2) >
+19.5, and sharply drop where log(NHI/cm−2) < 18.8.
+The NHI,c,evap values lie right below where the sharp
+drop begins. Thus the majority of the Hi in the IGM
+region is more likely to induce cooling out of the IGM
+at its surface instead of thermally evaporating itself.
+We make a similar plot replacing the diffuse Hi by
+all the Hi detected by FAST in the bottom panel of
+Figure 14. The discussion above still applies, but the
+previous sharp pattern of number density dropping at
+log(NHI/cm−2) < 18.8 is more blurred.
+In summary, there seems to be efficient cooling instead
+of evaporation associated with the Hi in the IGM region.
+We note that the lack of direct measurements on the
+temperature and density of the IGM, and the magnetic
+fields (Cowie & Songaila 1977) in the tidal region are
+major sources of uncertainty in the derivation of the
+evaporation related parameters.
+5.1.2. Photon ionisation
+The Hi remains neutral in the UV radiation field
+through self-shelding. The quantity to derive is the crit-
+ical Hi column density (NHI,c,ion) where half of the hy-
+drogen gets ionized due to the photon ionisation by stars
+plus the cosmic background. We estimate the dimen-
+sionless ionisation parameter of stars (Ustar) from the
+SFR of NGC 4631 based on the equation in Tumlinson
+et al. (2011). We use Cloudy (Ferland et al. 1998) to sim-
+ulate the ionisation rate of hydrogen at different levels
+of Ustar plus the comic background. We derive NHI,c,ion
+as a function of distance to NGC 4631 based on prod-
+ucts of the simulation. More technical details can be
+found in section H of the appendix. We emphasize that
+in the model Ustar is only attenuated as a function of
+radius squared, but the possible absorption of tidal Hi
+(and possibly also dust) as the photons travel through
+0
+10
+20
+30
+40
+50
+60
+r (kpc)
+18
+19
+20
+21
+22
+logNHI(cm
+2)
+Diffuse HI
+NHI, c, evap
+NHI, c, ion
+FAST beam
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+1.75
+2.00
+log N
+0
+10
+20
+30
+40
+50
+60
+r (kpc)
+18
+19
+20
+21
+22
+logNHI(cm
+2)
+FAST detected HI
+NHI, c, evap
+NHI, c, ion
+FAST beam
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+1.75
+2.00
+log N
+Figure 14.
+The distribution of Hi column density as a
+function of projected distance from NGC 4631.
+The top
+panel is for the diffuse (excess) Hi, while the bottom panel
+for all Hi. Each pixel in the plot is color coded by logarithm
+of the number of pixels from the relevant column density
+map. The two dashed curves in each plot show the critical
+column densities to survive thermal evaporation (magenta),
+and UV ionisation (yellow) respectively. The brown curves
+show the shape of the FAST beam.
+it is not considered. So the NHI,c,ion derived should be
+viewed as upper limits.
+In Figure 14, the NHI,c,ion values lie roughly be-
+tween
+where
+the
+number
+densities
+of
+pixels
+con-
+centrate (log(NHI/cm−2) > 19.5) and sharply drop
+(log(NHI/cm−2) < 18.8).
+The transition in number
+densities is not sharply defined by NHI,c,ion, imply-
+ing the aforementioned over-estimation of NHI,c,ion and
+other uncertainties in the modeling, as well as possible
+counteracting effects of IGM cooling. Despite the likely
+over-estimation of NHI,c,ion, most pixels of diffuse Hi
+have NHI above them, indicating that most diffuse Hi
+are safe against photon ionisation in N4631g.
+5.2. Tidal interactions of the HI
+We investigate the distribution of Hi in N4631g in re-
+sponse to the past and on-going tidal interactions. We
+visualize the 3-dimensional distribution, and also pro-
+vide a characterization of the phase-space distribution.
+
+19
+5.2.1. The 3-dimensional visualization
+We provide snapshots of a 3-dimensional visualization
+of the Hi distribution in N4631g in Figure 15.
+The
+visualization is realized using the software SlicerAstro
+(Punzo et al. 2017). We use it to provide a first im-
+pression of the complex morphology and kinematics of
+Hi in the N4631g. Similar discussions were presented
+in Rand (1994) based on channel maps and position-
+velocity slices of an early WSRT data.
+From the snapshots of FAST data, tail 1 and 2 clearly
+connect NGC 4631 and NGC 4656. Tail 1 starts from
+the east and low-velocity side of NGC 4631, and reaches
+NGC 4656 on its east and high-velocity side (snapshot
+1, 2, 3, 5, 6, 8). Tail 2 starts from near the disk center of
+NGC 4631, and reaches NGC 4656 on its west and low-
+velocity side (snapshot 1, 2, 5, 6, 8). The connection
+between the two galaxies by tail 2 was not so clear in
+the WSRT data of HALOGAS, or the early WSRT data
+of Rand (1994); probably consequently, Combes (1978)
+tended to attribute the formation of tail 2 primarily to
+the perturbation of the much smaller but closer com-
+panion NGC 4627, and only secondarily to NGC 4656.
+From the snapshots of the FAST data, tail 3 starts
+from the high-velocity and western side of NGC 4631
+(snapshot 1, 3, 4, 5, 8), extends to the intermediate
+velocity and joins tail 1 in the south (snapshot 2, 5,
+8). This link between tail 3 and 1 was tentatively seen
+but again unclear in the WSRT data. Tail 4 is short in
+both the FAST and WSRT data. It starts from the west
+end of the NGC 4631 disk, and extends to the east and
+low-velocity direction (snapshot 1, 5, 8).
+5.2.2. Analysis of the phase-space distribution
+We study the projected phase-space distribution of Hi
+around NGC 4631. The projected phase-space diagram
+is a diagram of radial velocity offset versus projected
+distance to the center of NGC 4631. We are limited by
+observational projections, but a first-order characteri-
+zation can still be obtained about the bulk motions of
+Hi.
+We plot the distribution of Hi in the regions of the
+NGC 4631 disk and the 4 tails in the projected phase-
+space diagram in Figure 16.
+We focus our discussion
+on the distribution of PB-corrected dense Hi, as it is a
+good tracer of the kinematic skeleton of tidal tails. But
+we also outline the distribution of diffuse Hi using the
+PB-corrected, mmerge combined cube. The distribution
+of dense Hi in the NGC 4631 disk shows the pattern
+of a rotating disk with a maximum velocity around 150
+km s−1, which is by construction when defining the disk
+region. To guide the eye, the distribution of Hi in the
+disk region is repeated in all panels of the tails. To assist
+the analysis, we also plot contours of the gravitational
+potential with linear steps (see details in appendix I),
+and mark the truncation radius imposed by NGC 4656
+at 41.9 kpc which we derive using the equation of Byrd
+& Valtonen (1990).
+We find three distinct patterns of the Hi distribution
+in the projected phase-space diagram. Tail 1 and 3 both
+start from the end of the disk, and deaccelerate in rela-
+tively radial velocity while extending to large projected
+distance until reaching around the truncation radius im-
+posed by NGC 4656. Tail 4 is almost a parallel shift of
+the lower envelope of the disk in the projected phase-
+space diagram.
+This linear shape suggests an almost
+solid-body rotation, which are often found in systems of
+slow encounters (e.g. M81, Sorgho et al. 2019). Tail 2
+looks much broader in morphology and possibly higher
+in energy than the other tails. Its furthest end crosses
+the truncation radius of NGC 4656, while the relative
+radial velocity is still high. In the projected view, the
+furthest end reaches a gravitational potential level sim-
+ilar to those of tail 1 and 3, and much higher than that
+of tail 4. Its high energy and complex morphology sug-
+gests it likely to have been perturbed by more than one
+galaxy (i.e. both NGC 4656 and NGC 4627), which was
+supported by previous particle simulations to reproduce
+the dense Hi distribution in N4631g (Combes 1978).
+Limited by projection effects, it is difficult to deduce
+the motion of gas without the aid of hydrodynamic simu-
+lations designed to reproduce the morphology. But from
+the complexity of Hi distribution in the projected phase-
+space diagram, we can still infer that there are more
+than one tidal encounters in N4631g, which should ex-
+plain the widely spreading Hi, and may input turbulent
+energy through shocks to produce the diffuse Hi.
+6. SUMMARY AND CONCLUSION
+We present a deep FAST image of Hi in and around
+NGC 4631. We identify a component of excess Hi de-
+tected by FAST but missed by WSRT. Our major results
+are summarized below:
+1. The nature of the excess HI is likely large-
+scale, diffuse HI. This excess Hi has a low spatial fre-
+quency, corresponding to a characteristic angular scale
+≥ 14′ or 30 kpc, missed by WSRT due to the limited
+shortest baseline. It is also highly turbulent, with a ve-
+locity dispersion around 44 km s−1. Around 40% (70%)
+of the excess Hi in the NGC 4631 region (IGM region)
+is found beyond the regions where dense Hi is detected
+by the WSRT.
+2.
+The diffuse HI is more closely related to
+the dense HI that is kinematically hot than that
+is warm. When overlapping with the dense Hi in the
+
+20
+Figure 15.
+Snapshots of 3-dimensional visualization of Hi distribution in the FAST and WSRT cubes. An animated version
+of this figure is available as on-line material.
+The duration of the animation is 28 s, and the content is the 3-dimensional
+visualization of the FAST and WSRT cubes (WCS system registered) continuously rotating by 360◦. The viewing angles are
+denoted as direction axes, with N, E, W, z and Z pointing toward the north, east, west, low-redshift (velocity), and high-redshift
+(velocity) direction, respectively. The visualization is realized using the software SlicerAstro (Punzo et al. 2017). The figure
+here shows 8 snapshots from that animation, which are evenly distributed in a rotation of 360◦, and are ordered by number
+denoted in the top-left corner of panels. For visual clarity, the 4 tidal tails are denoted in the figure (but not in the animation),
+and each pair of FAST and WSRT snapshots are vertically arranged (while horizontally arranged in the animation). To be
+continued.
+
+1
+2
+T3
+Z
+3
+W
+W
+FAST
+FAST
+Z
+W
+W
+WSRT
+WSRT
+3
+4
+3
+W
+W
+专
+FAST
+FAST
+W
+W
+WSRT
+WSRT
+E
+ZE21
+Figure 15.
+Continued.
+
+5
+6
+T4
+T3
+T3
+W
+Wt
+Z
+.
+T2
+12
+FAST
+FAST
+W
+Wt
+Z
+WSRT
+WSRT
+2
+7
+8
+T3
+13
+E
+W
+T4
+T2
+T2
+FAST
+FAST
+E
+E
+W
+WSRT
+N
+WSRT
+Z
+E22
+0
+50
+100
+150
+200
+d
+80.0 
+0
+50
+100
+150
+200
+vrad(kms
+1)
+t1
+80.0 
+4.0 
+0
+50
+100
+150
+200
+vrad(kms
+1)
+t2
+80.0 
+4.0 
+4.0 
+0
+50
+100
+150
+200
+vrad(kms
+1)
+t3
+80.0 
+4.0 
+4.0 
+0
+10
+20
+30
+40
+50
+60
+dproj(kpc)
+0
+50
+100
+150
+200
+vrad(kms
+1)
+t4
+80.0 
+4.0 
+0
+200
+400
+600
+800
+Jyb
+1kms
+1
+10
+20
+30
+40
+Jyb
+1kms
+1
+10
+20
+30
+40
+Jyb
+1kms
+1
+10
+20
+30
+40
+Jyb
+1kms
+1
+10
+20
+30
+40
+Jyb
+1kms
+1
+Figure 16.
+The projected phase-space distribution of Hi flux around NGC 4631. From top to bottom, the distribution of Hi
+in the disk and the 4 tail regions are plotted respectively. The pixels are color coded by Hi flux from the PB-corrected WSRT
+cube, and the distributions are outlined by solid contours at the level of 4 (80) Jy b−1 km s−1 for the tail (disk) flux. The
+distribution of Hi flux from the PB-corrected, FAST+WSRT combined cube is outlined by dashed contours at the same level.
+The disk region is repeated in every panel to guide the eye. Contours of gravitational potential with linear interval steps are
+plotted as grey dotted curves. The truncation radius for NGC 4656 to strip gas from NGC 4631 is plotted as the thick, pink
+vertical line. The pink arrow mark the radial velocity deviation of NGC 4631 from NGC 4656.
+
+23
+tail region, the diffuse Hi increases in column density
+with the dense Hi, and is particularly closely associated
+with the “hotter” part of the dense Hi. It is preferen-
+tially found where the dense Hi is more dominated by
+the broad-velocity components, or has multiple velocity
+components.
+3.
+The diffuse HI is likely to induce cooling
+flows of the hot IGM.
+The diffuse Hi in the IGM
+region typically have a column density ≥ 1019.2 cm−2,
+which is far above the critical column density for ther-
+mal evaporation, and likely safe from photon ionization.
+This relatively high Hi column density is consistent with
+a condition to induce efficient cooling flows from the hot
+IGM.
+The results above involve gases of four different phases
+in the IGM region, namely the hot IGM, the diffuse
+Hi characterized in result 1, the “hot” dense Hi, and
+the “warm” dense Hi, sorted roughly in reverse order of
+energy. Result 3 indicates that, except for the periphery
+of the widely spreading IGM region, the hot IGM is
+likely cooling into the diffuse Hi. An important reason
+for cooling flows to be induced near Hi gas, is that the
+thermal temperature of the interface between Hi and the
+hot IGM produced by turbulent mixing is intermediate
+between these two gas phases, reaching close to the value
+of 105 K for the radiative cooling function to peak (Dere
+et al. 2009).
+Indeed, if we take the radiative cooling
+function of Dere et al. (2009) for the solar metallicity
+and assume no heating, the isochoric cooling time for
+hot gas at the virial temperature of N4631g is close to
+the dynamical time of N4631g (∼400 Myr at a radius
+of 30 kpc), indicative of difficult cooling.
+But if the
+temperature drops to 105 K, the cooling time drops by
+more than one order of magnitude.
+The diffuse Hi further links to the dense Hi gas. Result
+2 indicates a continuous shift in phases between the dif-
+fuse Hi, the hot dense Hi, and the warm dense Hi, while
+the shift could be in either direction. Indeed, tidal in-
+teractions can both enhance cooling through mixing of
+metals, and heating through tidally induced shocks. If
+the net effect is the diffuse Hi progressively cooling into
+the dense Hi, then there is a unidirectional accretion
+pipeline that transfers gas from the hot IGM through
+the diffuse Hi to the dense Hi. If, on the other hand,
+the dense Hi is being progressively heated into the dif-
+fuse Hi, the surface area of Hi in the IGM enlarges, and
+the cooling rate of the hot IGM increases as a result.
+In both cases, the diffuse Hi plays an important role in
+the gas accretion from the hot IGM, either more as a
+transfer station of the accreted gas, or more a catalyst
+for cooling from the hot IGM.
+Given such an important role of diffuse Hi in gas
+accretion, the tidal interaction may have significantly
+boosted the gas accreting rate (i.e., the integral cool-
+ing rate from the hot IGM) of NGC 4631. N4631g has
+M200 ∼ 1012.1 M⊙ (appendix D), putting NGC 4631 in
+a theoretical regime where heating from cosmic gas ac-
+cretion and internal feedbacks start to efficiently prevent
+gas cooling (Kereˇs et al. 2005). The gas accretion could
+be effectively slow in NGC 4631 if it was an unperturbed
+galaxy. Tidal interaction enhances the gas accreting rate
+by spreading Hi widely in the IGM. The tidal Hi, par-
+ticularly when in the diffuse phase, greatly increases the
+area of interface between the Hi and and the hot IGM,
+thus induce significantly extra cooling. The tidal effects
+also put the gas in a kinematic status prone to shocks,
+ram pressure, and tidal compression, causing localized
+gaseous condensation and thermal instabilities directly
+relevant for enhanced cooling. The tidal effects further
+help transport metals throughout the IGM which is im-
+portant for radiative cooling (Dere et al. 2009). If such
+a scenario of enhanced cooling is true, we speculate the
+existence of a large amount of warm, ionized gas as an
+intermediate phase between the hot IGM and the dif-
+fuse Hi, which was indeed tentatively detected in Hα
+throughout the group (Donahue et al. 1995). It might be
+worth mentioning that, in a recent cosmological zoom-
+in magnetohydrodynamics simulation by Sparre et al.
+(2022), one simulated galaxy pair shows a broad Hi
+bridge, which is qualitatively similar to the structure ob-
+served between NGC 4631 and NGC 4656. Sparre et al.
+(2022) found that the gas that had been in the CGM
+prior to the tidal interaction contributed to nearly half
+of the mass in the gas bridge, and more than one fourth
+of the fueling to star formation during the interaction.
+Previous observational studies based on individual or
+statistical samples of tidally interacting systems found
+evidence for Hi to be both depleted and replenished
+in galaxies (Verdes-Montenegro et al. 2001; Hess et al.
+2017; Ellison et al. 2018). Theoretically, both effects are
+physically possible (Boselli & Gavazzi 2006; Hani et al.
+2018; Stevens et al. 2019). On the whole, there seems
+to be a high level of physical complexities in mergers,
+which may smooth out in statistical analysis of integral
+Hi measurements, and cannot be fully captured by in-
+dividual systems. Our study put NGC 4631 in the cate-
+gory where the tidal interaction induces Hi fueling, but
+the main contribution is characterizing and highlighting
+the role of the diffuse Hi, instead of just adding vote to
+one side in the question of fueling or depletion.
+To put NGC 4631 in the context of general galaxy
+evolution, in Figure 17, we compare the SFR and Hi
+mass of it and NGC 4656 to other galaxies of a stellar
+
+24
+mass selected sample, and particularly to the main se-
+quences of the two properties. It is interesting to notice
+that the FAST measurements of the Hi mass put the
+two galaxies in the regime of Hi-excess galaxies, while
+the WSRT measurements put them in the Hi main se-
+quence of normal star-forming galaxies. We will need a
+dataset like the one used in this paper but for a census
+of interacting galactic systems with different mass ra-
+tios, gas richnesses, merging distances, and large-scale
+environments, as well as for a sample of control galaxies
+in relative isolations. Such a dataset will be available in
+the future by combining data from FEASTS and from
+existing and SKA related interferometry surveys.
+We conclude that, tidal interaction should be an ef-
+ficient channel to accrete the IGM gas to the galaxy
+NGC 4631. The excess Hi detected by FAST provides
+the crucial, new information to reach this conclusion.
+We thank the anonymous referee for very construc-
+tive comments!
+We thank Xu Kong, Thijs van der
+Hulst, Zhiyuan Li, Ningyu Tang, Tobias Westmeier,
+Feng Yuan, Pei Zuo for useful discussions. JW thank
+support of the research grants from Ministry of Sci-
+ence and Technology of the People’s Republic of China
+(NO. 2022YFA1602902), the National Science Foun-
+dation of China (NO. 12073002, 11721303), and the
+science research grants from the China Manned Space
+Project (NO. CMS-CSST-2021-B02). S.H.OH. acknowl-
+edges support from the National Research Foundation
+of Korea (NRF) grant funded by the Korea govern-
+ment (Ministry of Science and ICT: MSIT; No.
+RS-
+2022-00197685). LCH was supported by the National
+Science Foundation of China (11721303,
+11991052,
+12011540375) and the China Manned Space Project
+(CMS-CSST-2021-A04, CMS-CSST-2021-A06).
+KMH
+acknowledges financial support from the State Agency
+for Research of the Spanish Ministry of Science, Innova-
+tion and Universities through the ”Center of Excellence
+Severo Ochoa” awarded to the Instituto de Astrofísica
+de Andalucía (SEV-2017-0709), from the coordina-
+tion of the participation in SKA-SPAIN, funded by
+the Ministry of Science and Innovation (MCIN), and
+financial support from grant RTI2018-096228-B-C31
+(MCIU/AEI/FEDER,UE). PK acknowledges financial
+support by the German Federal Ministry of Educa-
+tion and Research (BMBF) Verbundforschung grant
+05A20PC4 (Verbundprojekt D-MeerKAT-II). Parts of
+this research were supported by High-performance Com-
+puting Platform of Peking University.
+This work made use of the data from FAST (Five-
+hundred-meter Aperture Spherical radio Telescope).
+FAST is a Chinese national mega-science facility, oper-
+ated by National Astronomical Observatories, Chinese
+Academy of Sciences.
+Facilities: FAST, GALEX, Spitzer, WSRT
+Software: Astropy(AstropyCollaborationetal.2013,
+2018, 2022), Astrosclicer (Punzo et al. 2017), BAYGAUD
+(Oh et al. 2022), 3D-Barolo (Di Teodoro & Fraternali
+2015), Cloudy (Ferland et al. 1998), galpy (Bovy 2015,
+v1.8.0), numpy (van der Walt et al. 2011, v1.21.4), photu-
+tils (Bradley et al. 2019, v1.2.0), Python (Perez & Granger
+2007, v3.9.13), scipy (Virtanen et al. 2020, 1.8.0)
+REFERENCES
+Andreon, S., Wang, J., Trinchieri, G., Moretti, A., & Serra,
+A. L. 2017, A&A, 606, A24,
+doi: 10.1051/0004-6361/201730722
+Astropy Collaboration, Robitaille, T. P., Tollerud, E. J.,
+et al. 2013, A&A, 558, A33,
+doi: 10.1051/0004-6361/201322068
+Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M.,
+et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
+Astropy Collaboration, Price-Whelan, A. M., Lim, P. L.,
+et al. 2022, ApJ, 935, 167, doi: 10.3847/1538-4357/ac7c74
+Barnes, D. G., Staveley-Smith, L., de Blok, W. J. G., et al.
+2001, MNRAS, 322, 486,
+doi: 10.1046/j.1365-8711.2001.04102.x
+Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ,
+450, 559, doi: 10.1086/176166
+Behroozi, P. S., Conroy, C., & Wechsler, R. H. 2010, ApJ,
+717, 379, doi: 10.1088/0004-637X/717/1/379
+Bland-Hawthorn, J., Maloney, P. R., Stephens, A., Zovaro,
+A., & Popping, A. 2017, ApJ, 849, 51,
+doi: 10.3847/1538-4357/aa8f45
+Blumenthal, K. A., & Barnes, J. E. 2018, MNRAS, 479,
+3952, doi: 10.1093/mnras/sty1605
+Borthakur, S., Yun, M. S., & Verdes-Montenegro, L. 2010,
+ApJ, 710, 385, doi: 10.1088/0004-637X/710/1/385
+Borthakur, S., Yun, M. S., Verdes-Montenegro, L., et al.
+2015, ApJ, 812, 78, doi: 10.1088/0004-637X/812/1/78
+Borthakur, S., Heckman, T., Tumlinson, J., et al. 2016,
+ApJ, 833, 259, doi: 10.3847/1538-4357/833/2/259
+Bose, S., Eisenstein, D. J., Hernquist, L., et al. 2019,
+MNRAS, 490, 5693, doi: 10.1093/mnras/stz2546
+Boselli, A., Fossati, M., & Sun, M. 2022, A&A Rv, 30, 3,
+doi: 10.1007/s00159-022-00140-3
+Boselli, A., & Gavazzi, G. 2006, PASP, 118, 517,
+doi: 10.1086/500691
+
+25
+9.0
+9.5
+10.0
+10.5
+11.0
+11.5
+log M * (M )
+3
+2
+1
+0
+1
+2
+log SFR (M
+yr
+1)
+N4631
+N4656
+9.0
+9.5
+10.0
+10.5
+11.0
+11.5
+log M * (M )
+7.5
+8.0
+8.5
+9.0
+9.5
+10.0
+10.5
+11.0
+log MHI(M )
+N4631
+N4656
+FAST
+WSRT (PBcor)
+Figure 17. The position of NGC 4631 and NGC 4656 in the diagram of SFR versus stellar mass and Hi mass versus stellar
+mass. The two red or orange dots represent NGC 4636 and NGC 4656, with the former having the higher stellar mass. The
+background data points are from the xGASS sample (Catinella et al. 2018). Left: the red and orange dots are for Hi masses from
+the FAST cube and the PB-corrected WSRT cube respectively; the solid and dashed curves are the position and scatter of star
+forming main sequence from (Saintonge et al. 2016). Right: the blue and cyan points in the background represent measurements
+and upper limits for Hi detected and un-detected galaxies; the solid and dashed curves are the position and scatter of Hi main
+sequence of star-forming galaxies from Janowiecki et al. (2020).
+Bovy, J. 2015, ApJS, 216, 29,
+doi: 10.1088/0067-0049/216/2/29
+Bradley, L., Sip˝ocz, B., Robitaille, T., et al. 2019,
+astropy/photutils: v0.7.2, v0.7.2, Zenodo, Zenodo,
+doi: 10.5281/zenodo.3568287
+Byrd, G., & Valtonen, M. 1990, ApJ, 350, 89,
+doi: 10.1086/168362
+Catinella, B., Saintonge, A., Janowiecki, S., et al. 2018,
+MNRAS, 476, 875, doi: 10.1093/mnras/sty089
+Chabrier, G. 2003, ApJL, 586, L133, doi: 10.1086/374879
+Chown, R., Li, C., Athanassoula, E., et al. 2019, MNRAS,
+484, 5192, doi: 10.1093/mnras/stz349
+Chung, A., van Gorkom, J. H., Kenney, J. D. P., &
+Vollmer, B. 2007, ApJL, 659, L115, doi: 10.1086/518034
+Combes, F. 1978, A&A, 65, 47
+Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998,
+AJ, 115, 1693, doi: 10.1086/300337
+Corbelli, E., Schneider, S. E., & Salpeter, E. E. 1989, AJ,
+97, 390, doi: 10.1086/114989
+Cortese, L., Catinella, B., & Smith, R. 2021, PASA, 38,
+e035, doi: 10.1017/pasa.2021.18
+Cowie, L. L., & McKee, C. F. 1977, ApJ, 211, 135,
+doi: 10.1086/154911
+Cowie, L. L., & Songaila, A. 1977, Nature, 266, 501,
+doi: 10.1038/266501a0
+Dale, D. A., Cohen, S. A., Johnson, L. C., et al. 2009, ApJ,
+703, 517, doi: 10.1088/0004-637X/703/1/517
+Das, S., Sardone, A., Leroy, A. K., et al. 2020, ApJ, 898,
+15, doi: 10.3847/1538-4357/ab97b9
+de Blok, W. J. G., Walter, F., Ferguson, A. M. N., et al.
+2018, ApJ, 865, 26, doi: 10.3847/1538-4357/aad557
+Dere, K. P., Landi, E., Young, P. R., et al. 2009, A&A, 498,
+915, doi: 10.1051/0004-6361/200911712
+Di Teodoro, E. M., & Fraternali, F. 2015, MNRAS, 451,
+3021, doi: 10.1093/mnras/stv1213
+Donahue, M., Aldering, G., & Stocke, J. T. 1995, ApJL,
+450, L45, doi: 10.1086/316771
+Dutton, A. A., & Macci`o, A. V. 2014, MNRAS, 441, 3359,
+doi: 10.1093/mnras/stu742
+Eckert, D., Molendi, S., & Paltani, S. 2011, A&A, 526, A79,
+doi: 10.1051/0004-6361/201015856
+Ekers, R. D., & Sancisi, R. 1977, A&A, 54, 973
+Ellison, S. L., Catinella, B., & Cortese, L. 2018, MNRAS,
+478, 3447, doi: 10.1093/mnras/sty1247
+Ellison, S. L., Mendel, J. T., Patton, D. R., & Scudder,
+J. M. 2013, MNRAS, 435, 3627,
+doi: 10.1093/mnras/stt1562
+Ettori, S. 2015, MNRAS, 446, 2629,
+doi: 10.1093/mnras/stu2292
+Ferland, G. J., Korista, K. T., Verner, D. A., et al. 1998,
+PASP, 110, 761, doi: 10.1086/316190
+Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman,
+J. 2013, PASP, 125, 306, doi: 10.1086/670067
+Golla, G., Dettmar, R. J., & Domgoergen, H. 1996, A&A,
+313, 439
+
+26
+Guo, H., Jones, M. G., Wang, J., & Lin, L. 2021, ApJ, 918,
+53, doi: 10.3847/1538-4357/ac062e
+Hani, M. H., Sparre, M., Ellison, S. L., Torrey, P., &
+Vogelsberger, M. 2018, MNRAS, 475, 1160,
+doi: 10.1093/mnras/stx3252
+Haynes, M. P., Giovanelli, R., Kent, B. R., et al. 2018, ApJ,
+861, 49, doi: 10.3847/1538-4357/aac956
+Heald, G., J´ozsa, G., Serra, P., et al. 2011, A&A, 526,
+A118, doi: 10.1051/0004-6361/201015938
+Heiles, C., Perillat, P., Nolan, M., et al. 2001, PASP, 113,
+1247, doi: 10.1086/323290
+Hess, K. M., Cluver, M. E., Yahya, S., et al. 2017, MNRAS,
+464, 957, doi: 10.1093/mnras/stw2338
+Ianjamasimanana, R., Walter, F., de Blok, W. J. G., Heald,
+G. H., & Brinks, E. 2018, AJ, 155, 233,
+doi: 10.3847/1538-3881/aabbaa
+Irwin, J., Beck, R., Benjamin, R. A., et al. 2012, AJ, 144,
+44, doi: 10.1088/0004-6256/144/2/44
+Janowiecki, S., Catinella, B., Cortese, L., Saintonge, A., &
+Wang, J. 2020, MNRAS, 493, 1982,
+doi: 10.1093/mnras/staa178
+Jarrett, T. H., Chester, T., Cutri, R., et al. 2000, AJ, 119,
+2498, doi: 10.1086/301330
+Jiang, P., Yue, Y., Gan, H., et al. 2019, Science China
+Physics, Mechanics, and Astronomy, 62, 959502,
+doi: 10.1007/s11433-018-9376-1
+Jiang, P., Tang, N.-Y., Hou, L.-G., et al. 2020, Research in
+Astronomy and Astrophysics, 20, 064,
+doi: 10.1088/1674-4527/20/5/64
+Jones, M. G., Verdes-Montenegro, L., Damas-Segovia, A.,
+et al. 2019, A&A, 632, A78,
+doi: 10.1051/0004-6361/201936349
+Kereˇs, D., Katz, N., Weinberg, D. H., & Dav´e, R. 2005,
+MNRAS, 363, 2, doi: 10.1111/j.1365-2966.2005.09451.x
+Koopmann, R. A., Giovanelli, R., Haynes, M. P., et al.
+2008, ApJL, 682, L85, doi: 10.1086/591124
+Kourkchi, E., & Tully, R. B. 2017, ApJ, 843, 16,
+doi: 10.3847/1538-4357/aa76db
+Lan, T.-W., & Mo, H. 2018, ApJ, 866, 36,
+doi: 10.3847/1538-4357/aadc08
+Lee, J. C., Gil de Paz, A., Kennicutt, Robert C., J., et al.
+2011, ApJS, 192, 6, doi: 10.1088/0067-0049/192/1/6
+Lee-Waddell, K., Koribalski, B. S., Westmeier, T., et al.
+2019, MNRAS, 487, 5248, doi: 10.1093/mnras/stz017
+Leitherer, C., Ortiz Ot´alvaro, P. A., Bresolin, F., et al.
+2010, ApJS, 189, 309, doi: 10.1088/0067-0049/189/2/309
+Maloney, P. 1993, ApJ, 414, 41, doi: 10.1086/173055
+Martin, C., & Kern, B. 2001, ApJ, 555, 258,
+doi: 10.1086/323161
+Mart´ınez-Delgado, D., D’Onghia, E., Chonis, T. S., et al.
+2015, AJ, 150, 116, doi: 10.1088/0004-6256/150/4/116
+Mel´endez, M., Veilleux, S., Martin, C., et al. 2015, ApJ,
+804, 46, doi: 10.1088/0004-637X/804/1/46
+Monachesi, A., Bell, E. F., Radburn-Smith, D. J., et al.
+2016, MNRAS, 457, 1419, doi: 10.1093/mnras/stv2987
+Mora-Partiarroyo, S. C., Krause, M., Basu, A., et al. 2019a,
+A&A, 632, A10, doi: 10.1051/0004-6361/201834571
+—. 2019b, A&A, 632, A11,
+doi: 10.1051/0004-6361/201935961
+Namumba, B., Koribalski, B. S., J´ozsa, G. I. G., et al. 2021,
+MNRAS, 505, 3795, doi: 10.1093/mnras/stab1524
+Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ,
+490, 493, doi: 10.1086/304888
+Oh, S.-H., Kim, S., For, B.-Q., & Staveley-Smith, L. 2022,
+ApJ, 928, 177, doi: 10.3847/1538-4357/ac5905
+Perez, F., & Granger, B. E. 2007, Computing in Science
+and Engineering, 9, 21, doi: 10.1109/MCSE.2007.53
+Punzo, D., van der Hulst, J. M., Roerdink, J. B. T. M.,
+Fillion-Robin, J. C., & Yu, L. 2017, Astronomy and
+Computing, 19, 45, doi: 10.1016/j.ascom.2017.03.004
+Putman, M. E. 2017, in Astrophysics and Space Science
+Library, Vol. 430, Gas Accretion onto Galaxies, ed.
+A. Fox & R. Dav´e, 1, doi: 10.1007/978-3-319-52512-9 1
+Putman, M. E., Peek, J. E. G., & Joung, M. R. 2012,
+ARA&A, 50, 491,
+doi: 10.1146/annurev-astro-081811-125612
+Querejeta, M., Meidt, S. E., Schinnerer, E., et al. 2015,
+ApJS, 219, 5, doi: 10.1088/0067-0049/219/1/5
+Radburn-Smith, D. J., de Jong, R. S., Seth, A. C., et al.
+2011, ApJS, 195, 18, doi: 10.1088/0067-0049/195/2/18
+Rand, R. J. 1994, A&A, 285, 833
+—. 2000, ApJ, 535, 663, doi: 10.1086/308869
+Reichert, A., B¨ohringer, H., Fassbender, R., & M¨uhlegger,
+M. 2011, A&A, 535, A4,
+doi: 10.1051/0004-6361/201116861
+Richter, P., Winkel, B., Wakker, B. P., et al. 2018, ApJ,
+868, 112, doi: 10.3847/1538-4357/aae838
+Saintonge, A., Catinella, B., Cortese, L., et al. 2016,
+MNRAS, 462, 1749, doi: 10.1093/mnras/stw1715
+Saintonge, A., Catinella, B., Tacconi, L. J., et al. 2017,
+ApJS, 233, 22, doi: 10.3847/1538-4365/aa97e0
+Schechtman-Rook, A., & Hess, K. M. 2012, ApJ, 750, 171,
+doi: 10.1088/0004-637X/750/2/171
+Serra, P., Koribalski, B., Duc, P.-A., et al. 2013, MNRAS,
+428, 370, doi: 10.1093/mnras/sts033
+Serra, P., Westmeier, T., Giese, N., et al. 2015, MNRAS,
+448, 1922, doi: 10.1093/mnras/stv079
+Seth, A. C., Dalcanton, J. J., & de Jong, R. S. 2005, AJ,
+129, 1331, doi: 10.1086/427859
+
+27
+Shangguan, J., Ho, L. C., Li, R., et al. 2019, ApJ, 870, 104,
+doi: 10.3847/1538-4357/aaf21a
+Sorgho, A., Foster, T., Carignan, C., & Chemin, L. 2019,
+MNRAS, 486, 504, doi: 10.1093/mnras/stz696
+Sparre, M., Whittingham, J., Damle, M., et al. 2022,
+MNRAS, 509, 2720, doi: 10.1093/mnras/stab3171
+Stanimirovic, S. 2002, in Astronomical Society of the
+Pacific Conference Series, Vol. 278, Single-Dish Radio
+Astronomy: Techniques and Applications, ed.
+S. Stanimirovic, D. Altschuler, P. Goldsmith, & C. Salter,
+375–396. https://arxiv.org/abs/astro-ph/0205329
+Stevens, A. R. H., & Brown, T. 2017, MNRAS, 471, 447,
+doi: 10.1093/mnras/stx1596
+Stevens, A. R. H., Diemer, B., Lagos, C. d. P., et al. 2019,
+MNRAS, 483, 5334, doi: 10.1093/mnras/sty3451
+Strickland, D. K., Heckman, T. M., Colbert, E. J. M.,
+Hoopes, C. G., & Weaver, K. A. 2004, ApJ, 606, 829,
+doi: 10.1086/383136
+Swaters, R. A., van Albada, T. S., van der Hulst, J. M., &
+Sancisi, R. 2002, A&A, 390, 829,
+doi: 10.1051/0004-6361:20011755
+T¨ullmann, R., Pietsch, W., Rossa, J., Breitschwerdt, D., &
+Dettmar, R. J. 2006, A&A, 448, 43,
+doi: 10.1051/0004-6361:20052936
+Tully, R. B. 2015, AJ, 149, 54,
+doi: 10.1088/0004-6256/149/2/54
+Tully, R. B., Courtois, H. M., Dolphin, A. E., et al. 2013,
+AJ, 146, 86, doi: 10.1088/0004-6256/146/4/86
+Tumlinson, J., Werk, J. K., Thom, C., et al. 2011, ApJ,
+733, 111, doi: 10.1088/0004-637X/733/2/111
+van der Walt, S., Colbert, S. C., & Varoquaux, G. 2011,
+Computing in Science and Engineering, 13, 22,
+doi: 10.1109/MCSE.2011.37
+van Gorkom, J. 1993, in Astrophysics and Space Science
+Library, Vol. 188, The Environment and Evolution of
+Galaxies, ed. J. M. Shull & H. A. Thronson, 345,
+doi: 10.1007/978-94-011-1882-8 20
+Verdes-Montenegro, L., Del Olmo, A., Yun, M. S., & Perea,
+J. 2005, A&A, 430, 443, doi: 10.1051/0004-6361:20047084
+Verdes-Montenegro, L., Yun, M. S., Williams, B. A., et al.
+2001, A&A, 377, 812, doi: 10.1051/0004-6361:20011127
+Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020,
+Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2
+Wang, E., Wang, J., Kauffmann, G., J´ozsa, G. I. G., & Li,
+C. 2015, MNRAS, 449, 2010, doi: 10.1093/mnras/stv390
+Wang, J., Catinella, B., Saintonge, A., et al. 2020, ApJ,
+890, 63, doi: 10.3847/1538-4357/ab68dd
+Wang, J., Kauffmann, G., J´ozsa, G. I. G., et al. 2013,
+MNRAS, 433, 270, doi: 10.1093/mnras/stt722
+Wang, Q. D., Immler, S., Walterbos, R., Lauroesch, J. T.,
+& Breitschwerdt, D. 2001, ApJL, 555, L99,
+doi: 10.1086/323179
+Wang, Q. D., Walterbos, R. A. M., Steakley, M. F.,
+Norman, C. A., & Braun, R. 1995, ApJ, 439, 176,
+doi: 10.1086/175162
+Weliachew, L., Sancisi, R., & Guelin, M. 1978, A&A, 65, 37
+Wolfe, S. A., Pisano, D. J., Lockman, F. J., McGaugh,
+S. S., & Shaya, E. J. 2013, Nature, 497, 224,
+doi: 10.1038/nature12082
+Yamasaki, N. Y., Sato, K., Mitsuishi, I., & Ohashi, T. 2009,
+PASJ, 61, S291, doi: 10.1093/pasj/61.sp1.S291
+Yu, N., Ho, L. C., & Wang, J. 2022, ApJ, 930, 85,
+doi: 10.3847/1538-4357/ac5f07
+Yun, M. S., Ho, P. T. P., & Lo, K. Y. 1994, Nature, 372,
+530, doi: 10.1038/372530a0
+Zhu, M., Yu, H., Wang, J., et al. 2021, ApJL, 922, L21,
+doi: 10.3847/2041-8213/ac350a
+Zuo, P., Xu, C. K., Yun, M. S., et al. 2018, ApJS, 237, 2,
+doi: 10.3847/1538-4365/aabd30
+
+28
+APPENDIX
+A. THE AVERAGE BEAM IMAGE OF FAST
+We derive a clean average beam image of the 19 beams, gridded in the same way as for the N4631 data. We use the
+calibrated mapping data of point sources from Jiang et al. (2020) to derive the average beam of FAST. The observation
+was specifically designed to characterize the beam properties of FAST. The data are in total 100 minutes’ mapping of
+point sources in raster scan mode along right ascension or declination directions, with a high sampling rate of per 10′′.
+We refer the readers to Jiang et al. (2020) for more details of the data and of the properties of the 19 beams of FAST.
+We use the same procedure that has produced the NGC 4631 cube in this paper to make the images of the 19 beams
+separately. We note that, a different 2-dimensional interpolation method was used in Jiang et al. (2020) for gridding,
+which is improper for the NGC 4631 data here whose sampling rate is much lower. After masking contaminating
+sources in the neighborhood, we follow the steps in Jiang et al. (2020) and fit a skew Gaussian to each of the 19 beam
+images. We stack the images of the 19 beams after register them to the same Gaussian center. The stacking procedure
+takes the 3-sigma clipped mean value for each pixel. The directly stacked beam image looks like a smoothed version of
+beam 1 displayed in Jiang et al. (2020) because of additional smoothing in gridding. It has a central core surrounded
+by a side-lobe ring, and then a axisymmetric periodical pattern with 6 broad peaks. It still has some noise patterns in
+the background and imperfectness in the periodical pattern. We clean the beam image by first using the segmentation
+function of the python package astropy.photutils to flag and mask the noise patterns in the background. We then
+perform a Fourier decomposition of the periodical pattern, and find that the pattern can be well represented by only
+retaining the m = 6 mode of the Fourier components. After these two steps, we obtain a relatively clean and average
+beam image for the NGC 4631 FAST image data. We show the directly stacked beam image, the cleaned beam image,
+and a difference map of the two images in Figure 18.
+In Figure 18, we also present an azimuthally averaged radial profile of the cleaned beam image. Within a radius of
+∼ 3.5′, the inner region of the profile is well fitted by a Gaussian function with a FWHM of 3.24′. Beyond that, the real
+beam deviate from the Gaussian approximation, with a level of around 1%. The level of the first side-lobe is around
+1/10 that of Arecibo (Heiles et al. 2001), indicating the power of FAST to map low-surface density, extended Hi.
+However, the level also suggests that the scattered light due to side-lobes cannot be fully ignored when we investigate
+extended Hi with column densities close to 1018cm−2. Therefore, in section 2.6, we convolve the WSRT cube with the
+real beam of FAST, before comparing the distribution of Hi fluxes between the WSRT and FAST data.
+We caution that, the beam shape of the NGC 4631 data may differ from the data of in Jiang et al. (2020), as
+the observing times are quite different. Moreover, the beam shapes, particularly the side-lobes, differ between the 19
+beams, as shown in Jiang et al. (2020). However, this average beam image is the best we can achieve with the resources
+in hand. And, the variation among beams is an intrinsic systematic uncertainty of the 19-beam mapping, which is a
+necessary compromise for the mapping efficiency.
+B. THE DISK AND TIDAL TAIL REGIONS OF NGC 4631
+We manually separate the FAST-detected region of the NGC 4631 and NGC 4656 system by arbitrarily drawing a
+line roughly along the disk direction of NGC 4656 (the white dashed line in Figure 5). We separate the WSRT-detected
+NGC 4631 region into regions of the main disk and 4 tidal tails. We firstly determine the region of the main disk of
+NGC 4631 in the data cube. We take the parameters of the kinematic model of the main disk of NGC 4631 from
+Rand (1994), and use 3D-Barolo (Di Teodoro & Fraternali 2015) to make a 3 dimensional data cube based on the
+parameters. We arbitrarily take a density threshold equivalent to 0.02% the peak density of the model to draw a mask
+of the NGC 4631 disk region in the cube. The region belonging to the two satellite galaxies NGC 4656 and Dwarf A
+are already labeled by SoFiA. The cube space beyond the disk region of NGC 4631, NGC 4656 and Dwarf A, but are
+within the SoFiA mask of the WSRT cube are considered the tail region.
+The separation of the tail region into different tails is performed with the 3-dimensional watershed algorithm of the
+python package skimage.segmentation. The outputs are 3-dimensional flagging masks of the separate components. A
+previous study, Combes (1978) manually separated the tidal features into four tails, denoting them by number 1 to 4,
+and used numerical simulation of interaction to reproduce the morphology and kinematics of these 4 tails. The same
+denoting system has been adopted by studies later to have a coherence context of discussion (e.g. Rand 1994). Our
+watershed results directly flag tail 3 and 4, but 1 and 2 are blended. We manually and arbitrarily draw a division line
+in the sky plane to separate tail 1 from 2 in the blended region to qualitatively match the separation in Rand (1994).
+
+29
+75
+50
+25
+0
+25
+50
+75
+x (arcmin)
+80
+60
+40
+20
+0
+20
+40
+60
+80
+y (arcmin)
+stacked beam
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+level
+75
+50
+25
+0
+25
+50
+75
+x (arcmin)
+80
+60
+40
+20
+0
+20
+40
+60
+80
+y (arcmin)
+cleaned beam
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+level
+0
+2
+4
+6
+8
+r (arcmin)
+4.0
+3.5
+3.0
+2.5
+2.0
+1.5
+1.0
+0.5
+0.0
+logf/fpeak
+beam profile
+Gaussian model
+Figure 18.
+The beam of the FAST Hi data.
+Top-left and top-right panels are the stacked beam and the cleaned beam
+respectively. The bottom panel is the azimuthally averaged radial profile of the beam, and its best-fit Gaussian model with a
+FWHM of 3.24′.
+The sky projected view of these regions are displayed in Figure 5.
+C. THE TEMPERATURE OF THE HOT GAS NEAR THE DISK
+There are abundant studies in the literature on the properties of the X-ray emitting hot gas near the disk within a
+distance of around 10 kpc. This part of the hot gas halo mostly represents hot gas outflows from the galactic disk,
+especially from its inner actively star-forming region. Therefore its temperature should be higher than, and can be
+used as upper limit of that in a hydrostatic equilibrium in the galaxy’s potential.
+Wang et al. (1995) used ROSAT data to detect the soft X-ray radiation of the hot gas of NGC 4631 out to 8 kpc
+above the disk plane. They estimated a characteristic thermal temperature of 0.25±0.03 keV. Wang et al. (2001)
+used Chandra to detect the halo out to a similar distance. They performed a 2-component thermal plasma model fit,
+obtaining a hot component of 0.61±0.12 keV close to the disk and a cooler component of 0.18±0.02 keV dominating
+the outer corona. As in this study we focus on the tidal Hi far away from the disk, we only take the temperature of
+the further component. T¨ullmann et al. (2006) used XMM-Newton to derive the temperature out of 3 stripes south
+of the disk, and 5 stripes north of the disk, reaching out to nearly 11 kpc. They used 5 bands ranging from super-soft
+to hard, so they managed to derive two characteristic temperatures for both a soft and a hard components. The
+hard component has a mean temperature of 0.24±0.03 keV, and a slightly higher but comparable number density of
+IGM throughout the analysis regions. The soft component has a temperature that is roughly 4 times lower, and we
+thus take the temperature of the more energetic hard component. Finally, Yamasaki et al. (2009) used the Imaging
+Spectrometer of Suzaku to trance X-ray halo out to about 10 kpc from the disk. They fit 2-component thermal models
+to the disk and the halo regions separately. In the halo region, the hard component of 0.3±0.016 keV is dominating
+over the soft component by 5 times more flux.
+
+.30
+Taking together these four sets of previous measurements, we calculate a mean value of 0.24±0.03 keV, equivalent
+to 2.8 × 106 K, as the temperature of the hot gas halo within 10 kpc around the NGC 4631 disk.
+D. THE DARK MATTER HALO MASS OF N4631G
+We use M500 as the fiducial measure of the dark matter halo mass, the mass within r500 the radius where the average
+density is 500 times the critical density of the universe. Characteristic masses are also defined at alternative averaged
+density levels, like M200 and M101 (the virial mass at redshift z= 0 in ΛCDM cosmology). They are convertible with
+each other assuming a NFW model (Navarro et al. 1997) of the dark matter halo with a concentration index c∆ of 8,
+as is expected for a halo of roughly 1012 M⊙ at redshift z = 0 (Dutton & Macci`o 2014).
+We use the stellar mass-halo mass relation in Behroozi et al. (2010) to derive a lower limit of log M500/M⊙ = 11.61.
+It is viewed as a lower limit because from halo occupation distribution studies, dark matter halos with a mass around
+1012 M⊙ should have the number of satellites which have stellar masses above 109.28 M⊙ far less than unity (Bose
+et al. 2019).
+We use the M500-IGM temperature relation from Reichert et al. (2011), in combination with the characteristic
+temperature of the near-disk hot gas summarized above, to derive an upper limit of log M500/M⊙ = 12.13 ± 0.06.
+The N4631g can be found in the group catalog of Kourkchi & Tully (2017) with a PGC id of 42637. From that
+group catalog, it has 10 member galaxies. These member galaxies have a radial velocity dispersion σc of 217 km s−1,
+and a projected gravitational radius Rg of 92 kpc. Based on the equation of Tully (2015), we derivelog M500/M⊙ of
+11.97. This value is between the lower and upper limits derived above, and is taken to be the final estimate.
+Accordingly, the r500, r200, and M200 of N4631g are 148 kpc, 224 kpc, and 1012.1 M⊙ respectively. The corresponding
+virial mass implies a virial temperature of 8×105 K, considerably lower than that of the X-ray emitting and outflowing
+hot gas near the disk.
+E. THE DENSITY OF THE HOT GAS HALO
+We base on the M500 estimated in appendix D to derive M500,gas, the hot gas mass within R500.
+We use the
+M500,gas-M500 relations from Andreon et al. (2017) and Ettori (2015), which derive log M500,gas/M⊙ of 10.56±0.17
+and 10.51±0.10 respectively. The two values are consistent within the error bar, and we take the one with smaller
+error.
+We consider a single-β model distribution of the IGM. Following the specifics in Eckert et al. (2011), we assume
+the β value to be 0.64, and the core radius rc = 0.19r500. Cumulating the IGM model profile from center to R500,
+we derive a central density of 5.778×10−4 cm−3. We also consider a double-β model, to match the fact that many
+previous studies found two thermal components in the hot gas halo. Following Eckert et al. (2011), we set the outer
+component to have core radius rc = 0.03r500. We arbitrarily set the central density of the outer and inner components
+to be equal, partly motivated by the fact that in T¨ullmann et al. (2006) the density of the hot and cold components are
+roughly equal in the inner corona. We plot both models in Figure 19. Although the double-β model fit the measured
+densities from Yamasaki et al. (2009) better, both models are close beyond a radius of 10 kpc in the IGM region. We
+thus adopt the single-β model for simpler assumptions.
+F. AMPLITUDE SPECTRAL ANALYSIS THROUGHOUT APPLICABLE CHANNELS
+To demonstrate the consistency of amplitudes cross the applicable channels (which have flux intensity greater than
+0.15 Jy), we plot the relation between the normalized amplitudes of all these channels in the left panel of Figure 20.
+The normalization factor of each channel is taken to be the maximum amplitude from the PB-attenuated FAST cube
+in the selected angular scale range (4 to 24.5′). The data points distribute close to the y = x line. To demonstrate the
+deviation of critical angular scales, in the right panel of Figure 20, we show the relation between amplitude ratios and
+angular scales from the selected channels. Each curve represents the median relation from a channel map, and starts
+from 4′. The curves start to exceed unity near the mean critical angular scale of 13.6′.
+G. MCMC RESULT OF DOUBLE-GAUSSIAN FIT TO THE SUPER PROFILES
+We use emcee (Foreman-Mackey et al. 2013) to conduct a double-Gaussian fit to the super profile stacked from the
+line-of-sights with single-Gaussian spectra in dense Hi in the tail region of the projected FAST cube. The amplitude a
+and σ of the narrow and broad Gaussian components are denoted by 1 and 2 respectively. We also include a fraction
+uncertainty of the model f in the fitting. The corner figure of probability distribution of parameters are displayed in
+
+31
+0
+10
+20
+30
+40
+50
+r (kpc)
+3.8
+3.6
+3.4
+3.2
+3.0
+2.8
+lognICM (cm
+3)
+single
+double
+N
+S
+Figure 19.
+IGM density profiles of N4631g. The black and pink solid lines are the single and double-β models. The black
+dashed lines are the 1-σ uncertainty range of the single-β model due to uncertainty in the estimate of M500,gas. The blue and
+cyan dots are measurements from Yamasaki et al. (2018) at distances from the north and south sides of the disk.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+AWSRT, normalized
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+AFAST, normalized
+2.6
+2.8
+3.0
+3.2
+3.4
+log Angular scale (arcsec)
+0.3
+0.2
+0.1
+0.0
+0.1
+0.2
+0.3
+log AFAST/AWSRT
+Figure 20.
+The comparison between amplitudes of amplitude spectra from the WSRT cube and PB-attenuated FAST cube.
+Left: relation of normalized amplitudes from the two types of cubes selected from the angular scale range between 4′ and 24.5′
+as in Figure 7. The dashed line mark the y = x line. Right: the median curves of the ratio of amplitudes from the two cubes
+as a function of the angular scale. Each curve corresponds to one channel. The horizontal dashed line mark the y position of
+zero. The red vertical line marks the mean critical angular scale of 13.6′ for FAST amplitudes to exceed the WSRT amplitudes
+by 1%. The black vertical line marks the angular scale corresponding to the shortest baseline of the WSRT array configuration.
+Figure 21. We do not find strong degeneracy between model parameters from the corner figures, where the probability
+distribution are projected onto 2-dimensional diagrams of the parameters. The fractional uncertainty of the model is
+low. So the double-Gaussian model seems a good description of the super profiles.
+We do the same for the smoothed WSRT cube, and the original WSRT cube. The results are displayed in Figure 22,
+and 23 respectively. The degeneracies of σ1 and σ2 with a1/(a1+a2) become stronger, but the probability distributions
+are still relatively narrow. So the double-Gaussian model seems still a reasonable description of the super profiles.
+The best-fit σ of the narrow and broad Gaussian components, and the ratio of peak intensities between
+them are 16.3+0.37
+−0.33 km s−1, 58.0+1.43
+−1.39 km s−1, and 0.76+0.011
+0.010
+for the super profile of FAST data.
+The values
+are 12.9+0.30
+−0.29 km s−1, 30.9+1.63
+−1.38 km s−1, and 0.74+0.028
+−0.028 for the super profile of the smoothed WSRT cube, and
+8.9+0.45
+−0.55 km s−1, 13.9+1.17
+−0.91 km s−1 and 0.61+0.118
+−0.136 for the super profile of the WSRT cube.
+
+32
+15.6
+16.2
+16.8
+17.4
+18.0
+1(kms
+1)
+55.0
+57.5
+60.0
+62.5
+2(kms
+1)
+0.72
+0.74
+0.76
+0.78
+0.80
+a1/(a1 + a2)
+4.0
+3.6
+3.2
+2.8
+log(f)
+15.6
+16.2
+16.8
+17.4
+18.0
+1(kms
+1)
+55.0
+57.5
+60.0
+62.5
+2(kms
+1)
+4.0
+3.6
+3.2
+2.8
+log(f)
+FAST (tail region)
+Figure 21. Corner figure of parameter probabilities of the double-Gaussian model for the Hi super profile of FAST data cube
+in the tail region.
+H. USING CLOUDY TO PREDICT THE CRITICAL COLUMN DENSITY OF HI FOR PHOTON IONISATION
+The procedure below is a modified version of the one described in Borthakur et al. (2015).
+We consider two sources contributing to the UV photons, the cosmic background UV radiation, and the photons from
+the young stars in NGC 4631. For the UV photons associated with young stars, we use the equation from Tumlinson
+et al. (2011) to estimate the dimensionless ionisation parameter Ustar which depends on the SFR of NGC 4631 and
+the distance squared. It also assumes a uniform fraction of 0.1 for the UV photons to escape from the interstellar
+medium. We have ignored the UV photons from NGC 4656, as its SFR is around one fourth, thus the distance to
+have the same level of Ustar is half that of NGC 4631. The UV photons from NGC 4656 only start to be important
+when the distance from NGC 4631 is larger than 52.5 kpc along the direction connecting these two galaxies. Diffuse
+stellar features have been found around NGC 4631, but mostly consisting of old stars (Mart´ınez-Delgado et al. 2015),
+unlikely to provide additional UV photons.
+We use starburst99 (Leitherer et al. 2010) to generate a young stellar population with a solar metallicity and an age
+of 4 Myr. We use the spectral energy distribution of this stellar population as input for Cloudy. We generate a three
+dimensional grid of hydrogen density nH, the hydrogen column density NH, and the stellar ionisation parameter Ustar.
+log nH ranges from -2.6 to -1.8 with a step of 0.2, log NH range 17.5 to 22.5 with a step of 0.25, and Ustar from -6 to
+-1.4 with a step of 0.2. We use the default “background” and “Background cosmic ray”, to add the ionizing effects
+of the cosmic UV background and the cosmic ray background. In the top panel of Figure 24, we plot the resulting
+
+33
+7.2
+8.0
+8.8
+9.6
+1(kms
+1)
+12
+14
+16
+18
+2(kms
+1)
+0.30
+0.45
+0.60
+0.75
+a1/(a1 + a2)
+8
+6
+4
+log(f)
+7.2
+8.0
+8.8
+9.6
+1(kms
+1)
+12
+14
+16
+18
+2(kms
+1)
+8
+6
+4
+log(f)
+WSRT (tail region)
+Figure 22. Corner figure of parameter probabilities of the double-Gaussian model for the Hi super profile of WSRT data cube
+in the tail region.
+neutral fraction of hydrogen (NHI/NH), as a function of log NHI in different bins of U, fixing log nHI at -2.6. We can
+see that toward the low values of Ustar (dark purple), NHI/NH converges to the highest possible value at a given NHI,
+because the comic UV background starts to dominate there. Setting NHI/NH = 0.5, we derive the critical Hi column
+density (NHI,c,ion) from each curve. We plot NHI,c,ion as a function of Ustar for different values of nH in the righ panel
+of Figure 24. We assume nH = 2nHI, and interpolate in this parameter space to derive the critical column density of
+Hi as a function of distance.
+We plot NHI,c,ion as a function of radius to NGC 4631 in the right panel of Figure 14. The values of NHI,c,ion flatten
+around 1019.2 cm−2 beyond a distance of 30 kpc. The value of 1019.2 cm−2 is close to many previously derived when
+only accounting for the cosmic background of UV radiation (Maloney 1993), but if we remove the effect of young stars
+in NGC 4631, NHI,c,ion would drop to one third of its current value at a radius of 30 kpc.
+We note that the leakage fraction of UV photons, the extent of shielding by Hi in tails at smaller distances, the
+lack of information on the filling factor and clumpiness of Hi, and the contribution of ionizing energy from shocks, are
+major sources of uncertainties in the deviation of the ionisation related parameters.
+I. THE GRAVITATIONAL POTENTIAL AROUND NGC 4631
+We use galpy (Bovy 2015) to model the mass distribution and gravitational potential around NGC 4631. We use the
+Miyamoto-Nagai model with the Milky Way specifics (scale length 3 kpc and scale height 0.28 kpc) to represent the
+
+34
+12
+13
+14
+15
+1(kms
+1)
+27
+30
+33
+36
+39
+2(kms
+1)
+0.66
+0.72
+0.78
+0.84
+a1/(a1 + a2)
+8
+6
+4
+log(f)
+12
+13
+14
+15
+1(kms
+1)
+27
+30
+33
+36
+39
+2(kms
+1)
+8
+6
+4
+log(f)
+WSRT (tail region, smoothed)
+Figure 23. Corner figure of parameter probabilities of the double-Gaussian model for the Hi super profile of smoothed WSRT
+data cube in the tail region.
+disk, the NFW model with scale radius equal to r200/c∆ to represent the dark matter, and use the rotational velocity
+of 145 km s−1 at a radius of 8 kpc (Rand 1994) to calibrate the normalization. The resulted mass model has a disk
+mass of 1010.2 M⊙ within 8 kpc, and a halo mass of 1012.02 M⊙ within r500 derived in appendix D. Thus the mass
+model is close to the observed stellar mass and M500 of NGC 4631. Then we use the evaluatePotentials task of galpy
+to evaluate the potential distribution around NGC 4631.
+
+35
+17.5
+18.0
+18.5
+19.0
+19.5
+20.0
+20.5
+logNHI(cm
+2)
+4.0
+3.5
+3.0
+2.5
+2.0
+1.5
+1.0
+0.5
+0.0
+logNHI/NH
+Ionization by UV photons from stars and background
+6
+5
+4
+3
+2
+Ustar
+18
+19
+20
+21
+logNHI, c, ion(cm
+2)
+nH = -2.6
+nH = -2.4
+nH = -2.2
+nH = -2.0
+nH = -1.8
+nH = -1.6
+nH = -1.4
+Figure 24. Photon ionisation of hydrogen in grids of stellar ionisation parameter, hydrogen density and hydrogen column
+density.
+Left: the neutral ratio of hydrogen, NHI/NH, is plotted as a function of the Hi column density in bins of stellar
+ionisation parameter Ustar. The values of Ustar range from -6 to -1.4 with a linear step of 0.2, and the curves in lighter purple
+colors correspond to higher values of Ustar. The dashed, horizontal line mark where the neutral ratio is 50%. Right: the critical
+Hi column density, where the ionisation or neutral ratio is 50%, as a function of Ustar in different bins of nH. The darker blue
+colors correspond to lower values of nH.
+
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new file mode 100644
index 0000000000000000000000000000000000000000..3f0eae5289e4d7e1eded3d35d7cfc0167991182a
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+page_content='1 Ziming Liu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='5 Shun Wang (王舜),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1 and Ming Zhu5  1 Kavli Institute for Astronomy and Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Peking University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Beijing 100871,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' China  2Department of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Sejong University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 209 Neungdong-ro,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Gwangjin-gu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Seoul,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Republic of Korea  3International Centre for Radio Astronomy Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' University of Western Australia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 35 Stirling Highway,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Crawley,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' WA 6009,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Australia  4ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Australia  5National Astronomical Observatories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 20A Datun Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Chaoyang District,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Beijing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' People’s Republic of  China  6Astronomy Department,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' University of Massachusetts,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Amherst,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' MA 01003,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' USA  7Instituto de Astrof´ısica de Andaluc´ıa (CSIC),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Glorieta de la Astronom´ıa s/n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 18008 Granada,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Spain  8ASTRON,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' the Netherlands Institute for Radio Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Postbus 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 7990 AA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Dwingeloo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The Netherlands  9Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' School of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Peking University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Beijing 100871,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' People’s Republic of China  10Ruhr University Bochum,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Faculty of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Astronomical Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 44780 Bochum,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Germany  11CAS Key Laboratory for Research in Galaxies and Cosmology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' University of Science and Technology of  China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Hefei 230026,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' People’s Republic of China  12 School of Astronomy and Space Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' University of Science and Technology of China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Hefei 230026,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' People’s Republic of China  ABSTRACT  We use the single-dish radio telescope FAST to map the Hi in the tidally interacting NGC 4631  group with a resolution of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='24′ (7 kpc), reaching a 5-σ column density limit of 1017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9 cm−2 assuming  a line width of 20 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Taking the existing interferometric Hi image from the HALOGAS project  of WSRT as reference, we are able to identify and characterize a significant excess of large-scale, low-  density, and diffuse Hi in the group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This diffuse Hi extends for more than 120 kpc across, and accounts  for more than one fourth of the total Hi detected by FAST in and around the galaxy NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the  region of the tidal tails, the diffuse Hi has a typical column density above 1019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5 cm−2, and is highly  turbulent with a velocity dispersion around 50 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It increases in column density with the dense  Hi, and tends to be associated with the kinematically “hotter” part of the dense Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Through simple  modeling, we find that the majority of the diffuse Hi in the tail region is likely to induce cooling out  of the hot IGM instead of evaporating or being radiatively ionized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Given these relations of gas in  different phases, the diffuse Hi may represent a condensing phase of the IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Active tidal interactions  on-going and in the past may have produced the wide-spreading Hi distribution, and triggered the gas  accretion to NGC 4631 through the phase of the diffuse Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Keywords: Galaxy evolution, interstellar medium  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' INTRODUCTION  The loss and gain of Hi are important drivers of galac-  tic evolution, as Hi is in the phase where the star-  forming gas starts to cool and settle down onto a galactic  Corresponding author: Jing Wang  jwang astro@pku.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='cn  Corresponding author: S-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Oh  seheonoh@kasi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='kr  disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Although Hi disks can be several times more ex-  tended from the galactic center than the optical disks  where most star formation occurs (Swaters et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013), the integral Hi richness is correlated  with the amount of Hi on optical disks (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022), and further with the specific star forma-  tion rate (SFR) (Saintonge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Guo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Such a link of SFR with Hi far away extends further into  the circum-galactic medium, indicated by the strengths  of Lyman-α absorbers (Borthakur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Lan &  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00937v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='GA]  3 Jan 2023  2  Mo 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' These correlations imply a quasi-equilibrium  state of baryonic flow through galaxies, and supports the  role of Hi as the reservoir of raw material for forming  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Tidal interactions are significant channels for galax-  ies to both gain and lose Hi (Putman 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Verdes-  Montenegro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001), but the net effects on the  whole and in each step of physical processes remain to  be studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' For example, Hi tails and clouds possibly  of tidal origin are often found, including the Magellanic  stream and at least some of the high-velocity cloud com-  plexes around the Milky Way (Putman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  They indicate a redistribution of gas between galaxies  due to tidal interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  These extra-planar Hi fea-  tures should be prone to thermal evaporation (Cowie &  McKee 1977), radiative ionisation, and dispersal due to  Kelvin-Helmholtz instability and Rayleigh-Taylor insta-  bility, but long-lasting ones have been found in massive  clusters (Chung et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2007), loose groups (Koopmann  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2021), and compact groups (Serra  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It indicates a complex interplay between  the Hi gas and the circum(inter)-galactic environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  For another example, starbursts are often found in gas-  rich interacting pairs (Ellison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Chown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2019), possibly caused by gas inflows driven by tidal  shocks, torques, and instabilities (Blumenthal & Barnes  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Despite the enhanced consumption of gas, the  integral Hi masses of mergers and post-mergers are not  found to decrease compared to control samples (Ellison  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Zuo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Shangguan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  This unexpected consistency in Hi amount may be due  to a boosted CGM cooling out of thermal instabilities,  or suppressed atomic-to-molecular conversion efficiency  out of turbulent Hi, but the exact reason is unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In  most of the puzzles of this type, a major difficulty arises  from the physical nature that various gravitational and  hydrodynamic effects are involved and interact, and that  gas exchanges between phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Sorting out the response of Hi during tidal interac-  tions is important for a refined evolutionary theory of  galaxies of different types and in different environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Semi-analytical models of galaxy evolution have been  plagued by the fact that environmental and internal ef-  fects have a strong degeneracy when reproducing the  observed Hi or SFR scaling relations of satellite galaxies  (Stevens & Brown 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Because different environmen-  tal mechanisms co-exist, it is hard to separate and assess  the role of each (Boselli & Gavazzi 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Cortese et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2021), even in groups and the outskirts of clusters where  tidal interactions should dominate other environmental  effects (Boselli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The most promising way  forward may be a more detailed analysis of existing and  newly observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Characterizing the distribution  and kinematics of Hi in prominent tidally interacting  galaxy samples will help us identify signatures to sep-  arate the tidal effects from other environmental effects;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  comparing quantified properties with physical models,  and formulating empirical relations to be implemented  into semi-analytical models, will help us break the de-  generacy between internal and external causes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Luckily, there have been long-lasting efforts in this di-  rection of characterizing detailed Hi properties in tidal  interactions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Rand 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Yun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Wolfe  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Lee-Waddell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Sorgho et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Namumba et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  A highlight among them are  the systematic research on compact groups (Verdes-  Montenegro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Borthakur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Serra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Built upon these benchmarking papers, in this paper  we study in detail one classical interacting system, the  NGC 4631 group (N4631g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We contribute the following  unique inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use the Five hundred meter Aperture  Spherical Telescope (FAST, Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019) to obtain  an Hi image with a high sensitivity, and moderate reso-  lution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A first impression of the N4631g and its Hi distri-  bution can be obtained from Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The FAST data  reveals and spatially resolves a significant excess of Hi  compared to a previous deep interferometric observation  with the Westerbork Synthesis Radio Telescope (WSRT)  by Hydrogen Accretion in LOcal GAlaxieS (HALOGAS)  survey (Heald et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This paper thus addresses  in particular the existence of such an extended Hi enve-  lope around NGC 4631, which the WSRT observations  miss because it is too faint and too extended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The com-  bined data show this well and allow an assessment of  how much there is, how it is distributed, what its kine-  matics are and how it is connected to the higher density  Hi that the HALOGAS project found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The amount tells  us about the total gas reservoir around galaxies, while  the detailed properties tells us about the tidal interac-  tion and the physics of the IGM (intra-galactic medium),  CGM (circum-galactic medium), and ISM (inter-stellar  medium) connection that are essential to gas accretion  and depletion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The combination of single dish data and synthesis  data, which is essential to obtain the new results in this  paper, is a known but difficult problem (Stanimirovic  2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This paper demonstrates the power of FAST as  compared to existing attempts to add extended emis-  sion restricted to other single-dish telescopes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' GBT  and Parkes, de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020), which  have much smaller dishes and hence have less overlap in  u,v space with the synthesis data, or relatively signif-  icant side-lobes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Arecibo, Heiles et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Hess  3  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Closely relevant to this paper, Richter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  (2018) used Hi image taken by the GBT in combination  with the WSRT image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Limited by the resolution of the  GBT image, the two types of Hi data were compared  mainly in a qualitative way, and the focus of that work  was instead on one line-of-sight with ultraviolet spectro-  scopic data taken by the Hubble Space Telescope (HST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The FAST image used in this work has three times bet-  ter resolution than the GBT image, has a much wider  uv coverage in common with the WSRT data, and there-  fore enables a relatively better quantified characteriza-  tion and comparison of the Hi properties throughout the  tidally interacting region in the group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  This paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We introduce the  sample, the Hi data , and the multi-wavelength data in  section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Particularly, we describe the observation and  reduction of the FAST Hi data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In section 3, we ver-  ify that the flux calibrations are consistent between the  FAST and WSRT data, and show globally the existence  of excess Hi detected by FAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In section 4, we con-  duct detailed analysis of the excess Hi, which is likely  large-scale and low-density diffuse Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We quantify the  distribution and localized kinematics of it, and its rela-  tion to the dense Hi detected by WSRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In section 5,  we quantify the hydrodynamic and gravitational envi-  ronment around the galaxy NGC 4631, and discuss the  fate and motion of the (diffuse) Hi in the IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Finally  we summarize in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Throughout the paper, we  assume a Chabrier (2003) initial mass function to esti-  mate the stellar mass and SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' DATA AND ANALYSIS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The NGC 4631 galaxy and group  The galaxy NGC 4631, known as the Whale galaxy,  is an edge-on spiral galaxy, and has remarkable Hi tidal  structures (Weliachew et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1978;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Rand 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  It is  centered at α2000 = 190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9905◦, δ2000 = 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1682◦, ac-  cording to the 2MASS Extended Source Catalog (Jar-  rett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It has a heliocentric systematic velocity  of 615 km s−1 (Rand 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We take the error weighted  mean of luminosity distances derived with the TRGB  method in the literature (Seth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tully et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Radburn-Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Monachesi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2016),  which is 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='53 Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The members of N4631g have a velocity dispersion σc  of 217 km s−1 (Kourkchi & Tully 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' As the brightest  galaxy of the N4631g, NGC 4631 has two major com-  panions, NGC 4656 and NGC 4627, 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6 kpc  away in projected distance respectively, the interaction  with which should have produced most of the Hi tidal  structures around NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Its interaction with NGC  4656 might start only a few hundreds of million years  ago, as suggested by the age of a tidal dwarf near NGC  4656 (Schechtman-Rook & Hess 2012), and the simula-  tion of Combes (1978) in an attempt to reproduce its  Hi tidal tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It also has many other fainter dwarf com-  panions, and stellar tidal tails which do not correspond  to the Hi tails (Mart´ınez-Delgado et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' These  properties indicate a dynamic, actively interacting envi-  ronment around NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  NGC 4631 has an active star formation possibly due  to the active tidal interaction with neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The ac-  tive star formation may have triggered powerful outflows  of mass and energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' These outflows reveal themselves  as super-shells and anomalous velocity features in the  Hi (Rand 1994) and CO images (Rand 2000), filamen-  tary structures of dust (Mel´endez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015), ionized  gas (Golla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Martin & Kern 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Strickland  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' T¨ullmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2006) extending above the  disk plane, and magnetic fields perpendicular to the disk  plane (Mora-Partiarroyo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The present  and past outflows may have built the prominent hot  gaseous halo that is bright in the radio continuum (Ek-  ers & Sancisi 1977;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Irwin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2012) and X-ray (Wang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1995, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' But we point out that, the Hi struc-  ture detected in this work which is large than 60 kpc  in radius extends much further than the X-ray emitting  hot gas halo which is roughly 10 kpc in radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The FAST HI observation  The FAST Hi observations of NGC 4631 were  carried out on 2022 March 25/26/27 (proposal ID:  PT2021 0071) as part of the FAST Extended Atlas  of Selected Targets Survey (FEASTS)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The zenith an-  gles were < 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7◦ during the observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A rectangle  of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6◦ × 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5◦ is targeted around α2000 = 190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7027◦,  δ2000 = 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4058◦, an arbitrary position (grey cross in  top panel of Figure 3) between NGC 4631 and NGC  4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The rectangle is scanned in the on-the-fly (OTF)  mode with six passes, evenly divided into vertical and  horizontal ones to achieve basket weaving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The scans are  conducted with the L-band (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='05 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='45 GHz) 19-beam  receiver rotated by 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4/53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4◦(horizontal/vertical), and  the spacing of scanning stripes set to be 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='66′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We  show in the left panel of Figure 2 how these stripes are  arranged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' They cover extra regions on the four sides, in  order to achieve relatively uniform sampling densities in  the targeted region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The full width half maximum (FWHM) of the raw  beam is ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9′ at a frequency of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='42 GHz (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The effective angular separation between scan  lines is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15′, and the effective integration time per po-  1 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='com/FEASTS/LVgal/wiki  4  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  A false color image demonstrating the NGC 4631 group and its Hi gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' On top of the optical image, the blue  colored halo shows the diffuse Hi flux imaged by FAST (beam FWHM=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='24′ or 7 kpc) in this study, while the light-blue finer  structures are the denser Hi previously detected in the WSRT HALOGAS (Heald et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011) observation (beam FWHM=40′′  or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='46 kpc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The names of 6 relatively prominent member galaxies are denoted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  sition is 235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The total integration time is 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='47 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The observation is accompanied by a 10-K noise diode  turned on for 1 s every 60 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The data is recorded by  the Spec (W+N) backend, with a sampling time of 1 s,  and channel width of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='63 kHz, or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='61 km/s for Hi 21  cm observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The FAST data reduction  We extract a low-redshift frequency slice of 1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7-  1425.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2 MHz (equivalent to 76-1609 km s−1), and focus  on this part of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The data reduction is carried  out with a pipeline developed following the standard  procedures of reducing radio single-dish image data, par-  ticularly those from Arecibo Legacy Fast ALFA Survey  (ALFALFA, Haynes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018) and HI Parkes All Sky  Survey (HIPASS, Barnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It has 4 major  modules, including RFI flagging, calibration, imaging,  and baseline flattening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Many of these steps go back-  ward and iterate till convergency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We briefly introduce  Keeler 529  NGC4627  Dwarf A  NGC4631  MCG+06-28-022  NGC4656  FAST  WSRT  10 kpc5  the steps below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' An early version of the pipeline is also  described in Zuo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' RFI flagging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We flag the radio frequency in-  terferences (RFIs) in two major steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Firstly, we  use the conventional waterfall map, which is distri-  bution of flux in the diagram of frequency versus  time, to identify outstanding stripes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Secondly,  the whole image region is scanned with 6 passes,  so that after gridding the data by sky position for  each of the 6 passes, we can use a median and 3-  σ based outlier finder to reject RFI contaminated  data for the same sky position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The whole RFI  flagging procedure is reviewed again after the steps  of bandpass removal and flux calibration in the cal-  ibration module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The RFI contamination rate is  minimal in the FAST data used in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The bandpass is derived per beam  for each stripe of the scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The Hi emission is  masked from the waterfall map with a best effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The mask starts with a subjective, rough region  with knowledge of Hi distribution from the litera-  ture (Rand 1994), and is adjusted later with rms  level based criterion after the first round of cal-  ibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tests are conducted to decide an opti-  mized smoothing width of 240 s for determining  the bandpasses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The data and bandpass are cali-  brated against the bandpass-removed sampling of  the noise diode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The mask of the Hi emission is up-  dated with the bandpass-removed and scaled data  with the criterion of at least 200 connected pixels  above 2-σ threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The procedure goes back to  the step of determining the bandpasses and is it-  erated for 3 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Finally, the bandpass-removed  and scaled data is corrected for a zenith angle  dependent effective gain value of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5-16 to ac-  count for scaling differences from the perfect gain  and aperture efficiency at almost zero zenith angle  (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' For the analysis of this paper, we pro-  duce two sets of data cubes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The first set is a con-  ventional FAST cube, with pixel size of of 30′′, and  the channel width of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='61 km/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The second set is  a projected FAST cube, gridded to match the area  and WCS system of the WSRT HALOGAS data  (see section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A Gaussian kernel with FWHM  equivalent to half the FWHM of the raw beam  is used to grid the data into channel maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  FWHM of the raw beam is taken to be 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9′, the  median value of the 19 beams typically at the se-  lected frequency (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This gridding  process effectively smoothes the data, increasing  the FWHM of the actual beam to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='24′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The right  panel of Figure 2 displays the the relative sampling  densities of the observed data when gridding them  into pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The density is roughly uniform with a  1-σ scatter of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='48% around the median value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Baseline flattening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We remove the continuum  in the full range 1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7-1425.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2 MHz of the se-  lected frequency slice by modeling it with a first-  order polynomial function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Before removing the  continuum, the Hi emissions are masked using a  mask file generated by SoFiA (Serra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We then remove the residual continuum, standing  waves, and other global irregularities in the spec-  tra, which are referred to together as the resid-  ual continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The residual continuum is mod-  eled with the S-G filter with an effective poly-  nomial order of 2, and a width of 480 km s−1  (or 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='274 MHz), which are optimized after exper-  iments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  For reference, the major standing wave  due to reflection between the dish and the receiver  bin is ∼ 200 km s−1 (∼ 1 MHz) for FAST (Jiang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This module is iterated for 3 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The FAST data cube  We use SoFiA (Serra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015) on the conven-  tional FAST cube to generate the detection mask for Hi  emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use the threshold-based smooth+clipping  source finding algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The threshold is set to be 3-  σ, and the smoothing kernels have widths of 0, 3, and 5  pixels in the sky direction, and of 0 and 3 channels in the  velocity direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The reliability module is used with a  threshold of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='99 to exclude false detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The result-  ing mask is used to project the cube into moment maps  and integral spectrum, and also to select emission-free  regions to derive the rms level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The FAST data cube  has an rms level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='965 mJy b−1  F , where bF denotes  the beam area of FAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It corresponds to a 5-σ column  density limit of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0×1017 cm−2, assuming a line width of  20 km s−1, or a 5-σ point source mass limit of 105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9 M⊙,  assuming a line width of 150 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We show the column density map derived from the  moment-0 images in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Apparent from the mo-  ment images are the main target NGC 4631, its major  satellite NGC 4656 to the south-east, and a known op-  tically faint companion Dwarf A to the north-west.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' An-  other two Hi bearing dwarfs previously detected in the  WSRT cube of Rand (1994), Keeler 529 and MCG+06-  28-022, are blended into the tidal feature on the north  and south-east.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Due to their relatively small Hi masses  (each ∼ 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15 M⊙, Rand 1994), we will not distinguish  6  192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5°  191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5°  190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5°  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5°  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5°  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5°  RA(deg)  DEC(deg)  scan track  Cut_region  191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3°  191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7°  190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3°  190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7°  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3°  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0°  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7°  RA(deg)  Dec(deg)  sampling density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Left: one set of vertical and horizontal scanning stripes of the observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Lines of different colors represent different  IDs of the 19 beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The blue square represents the imaging region of the final data cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' One can see that the scanning mode  is not the traditional basket weaving, but using evenly distributed horizontal and vertical scans to micmic a basket weaving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Right: the relative sampling density of the whole observed data set when gridding them into pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The densities are normalized  to the median value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  them from the tidal structures in the analysis later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We  also show the moment-1 and -2 images in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' De-  spite the relatively low spatial resolution, the moment-1  image shows velocity gradients in the disk regions of  NGC 4631 and NGC 4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It also shows several steep  gradients in the region of tidal tails, possibly reflect-  ing sharp turning in the direction of motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  These  steep gradients are accompanied by high values in the  moment-2 image, where the relative large beam of FAST  tends to mix velocity structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the moment-2 im-  age, the particularly high values are also caused by over-  lapping structures that are separated in velocity space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We run SoFiA similarly for the projected FAST cube,  but the smoothing kernels have widths of 0, 3, 11, and  41 pixels in the sky direction instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In unit of arcsec,  the maximum extents of smoothing are actually similar  for the conventional and projected FAST cubes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Expect-  edly, the depths and moment images from the projected  FAST cube are similar to those from the conventional  FAST cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The WSRT data cube  We use the naturally weighted data cube from the  WSRT HALOGAS project (Heald et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It was  observed with an integration time of 10×12h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The obser-  vation has the shortest and longest baselines of WSRT  around 36 m and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7 km, corresponding to a nominal  largest and smallest angular scale of 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5′ and 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6′′, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The data cube has a synthesis beam major  and minor axes of 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0′′ and 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It has a pixel size  of 4′′, and a channel width of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='12 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The WSRT  data cube covers an area of roughly 1◦×1◦ around NGC  4631, so the companion NGC 4656 is near the edge of  the image, and quite some of the tidal Hi is near or  beyond the FWHM of the WSRT primary beam (PB)  which has a size of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We run SoFiA on the WSRT cube to generate the  detection mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The parameter setting is similar to  that for the projected FAST cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  With the SoFiA  mask, we produce the moment images and integral spec-  tra, and derive the rms level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The moment images are  close to those published in Richter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  column density map derived from the moment-0 im-  age is displayed in the bottom-left panel of Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The WSRT cube has a rms level σW of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='257 mJy b−1,  where b denotes the beam area of the WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This  rms level corresponds to a 5-σ column density limit of  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='32 × 1018 cm−2 assuming a line width of 20 km s−1  and 5-σ point source mass limit of 105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='54 M⊙ assuming  a line width of 150 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content="  Through visual inspection, we find noticeable so-called  “negative bowl” artifacts throughout the cube indicative  of missing short-spacing information, particularly in the  7  12h44m  42m  40m  33°00'  32°40'  20'  00'  ra (deg)  dec (deg)  FAST  18." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content="5  logNHI(cm  2)  12h44m  43m  42m  41m  40m  33°00'  32°45'  30'  15'  00'  ra (deg)  dec (deg)  WSRT  18." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content="0  logNHI(cm  2)  12h44m  43m  42m  41m  40m  33°00'  32°45'  30'  15'  00'  ra (deg)  dec (deg)  FAST+WSRT  18." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  logNHI(cm  2)  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The Hi column density maps of NGC 4631 field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The maps are derived from the FAST cube (top), WSRT cube  (bottom-left), and the FAST+WSRT combined cube (bottom-right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the top panel, the center of the FAST observational  field is marked with a grey cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the bottom-left panel, the FWHM of the WSRT PB is shown as the grey dashed circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In the bottom-right panel, the grey dashed circle has a diameter equal to the critical angular scale for WSRT to miss extended  Hi (see section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The bottom-right image does not look like the sum of the other two because the combination is done in  the Fourier space thus the FAST flux is conserved, and because the PB attenuation effect of the WSRT cube is applied (see  section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Beam shapes are denoted as green and open ellipses at the bottom left corner of each map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  velocity range between 500 and 700 km s−1 where tidal  features are strong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' They highlight the need of single-  dish image to fill this missing part, but also add un-  certainties and complexities when we directly compare  the FAST and WSRT images to characterize the spatial  distribution of the large-scale Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Luckily, the typical  absolute level of those “negative bowl” is around 1-σ of  the WSRT data cube, and as we will show in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  and Figure 8, the associated cumulative absolute flux is  low compared to the excess Hi detected by FAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' These  facts mitigate the problem, but future investigation of  optimized strategy of combining the single-dish and in-  terferometric data in the uv space may better solve this  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Derived cubes  For convenience of comparison, we produce a few de-  rived cubes to control for the effects of the PSF (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' the  FAST beam and the WSRT synthesis beam) and the  WSRT PB attenuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use the equation from Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2015) to pro-  duce a data cube of PB attenuation levels (the PB cube  hereafter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=" The equation is a function of the distance  from the image center, and was calibrated using con-  8  12h44m  42m  40m  33°00'  32°40'  20'  00'  31°40'  ra (deg)  dec (deg)  450  500  550  600  650  700  750  v (km/s)  12h44m  42m  40m  33°00'  32°40'  20'  00'  31°40'  ra (deg)  dec (deg)  10  20  30  40  50  60  70  v (km/s)  Figure 4." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Moment 1 (top) and 2 (bottom) images of the  NGC 4631 field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The images are derived from the FAST  cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The column density contour of the WSRT data at the  level of 1019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5cm−2 is plotted on top to guide the eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  tinuum sources from NRAO VLA Sky Survey (NVSS,  Condon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1998) and Faint Images of the Radio Sky  at Twenty centimeters (FIRST, Becker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We  produce the PB-corrected WSRT cube by dividing the  original WSRT cube by the PB cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We produce the smoothed WSRT cube by convolving  the channel maps of the WSRT cube with the FAST  beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The beam image of the FAST is derived by stack-  ing point source images of the 19 beams with data from  Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' More details and discussion regard-  ing the beam image can be found in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  flux of the smoothed WSRT cube is converted to the  unit of Jy b−1  F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We produce the PB-attenuated FAST cube by mul-  tiplying the projected FAST cube with the PB cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We subtract the smoothed WSRT cube from the PB-  attenuated FAST cube, and obtain the PB-attenuated  excess Hi cube2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We apply PB correction to the PB-  attenuated excess Hi cube, and obtain the PB-free excess  Hi cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The PB-free excess Hi cube is largely positive,  and the very few negative regions (most apparent ones  are the two small white patches near the N4631 disk  in the top panel of Figure 9) are likely due to point-  ing uncertainties, deviation of real FAST beam from the  adopted averaged one, and noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The PB-attenuated excess Hi cube has the advantage  of a relatively uniform rms level, convenient for thresh-  old based analysis, while the PB-free one has the advan-  tage of reflecting the actual amount of excess Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We  will show in section 4 that, the PB-free excess Hi cube  is practically the diffuse HI cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Definition of regions  We define the NGC 4631 region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We take the SoFiA  mask of the projected FAST cube, exclude the region  of Dwarf A, and separate the region of NGC 4631 and  NGC 4656 by arbitrarily drawing a line roughly along  the disk direction of NGC 4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The line and the resul-  tant NGC 4631 region to the north-west are shown in  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This region is delineated in order to study the  distribution of any excess Hi detected by FAST (sec-  tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We exclude NGC 4656 because it is at the  corner of the WSRT field of view, where the PB atten-  uation factor reaches 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1 and where the rms level will  thus be increased by 10 times after PB correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We separate the WSRT-detected NGC 4631 region  into the disk region and the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The disk and tail  regions are defined to compare the localized kinemat-  ics and distribution of Hi fluxes detected by FAST and  WSRT (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The tail region is further  divided into the regions of four tails to study their bulk  motions (section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' These regions are defined based  on the SoFiA mask of the WSRT cube and the tilted  ring model of the NGC 4631 disk from Rand (1994),  and through the watershed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The technique  details are presented in appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The sky projected  view of these regions are displayed in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We exclude the disk region from the NGC 4631 re-  gion, and define the IGM region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This region is mainly  2  Strictly  speaking,  we  should  compare  (FAST  cube) ∗  (WSRT beam) with (WSRT cube)∗(FAST beam), where ∗ is the  sign of operation for convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We thus also tried smoothing  the projected FAST cube with the WSRT beam, before applying  the PB attenuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We find the two products do not differ much  due to the relatively small size of the WSRT beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content="  9  12h44m  43m  42m  41m  40m  33°00'  32°45'  30'  15'  00'  ra (deg)  dec (deg)  region labels  0  1  2  3  4  5  6  7  8  Region  Figure 5." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Label of regions in the WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The id from  1 to 7 (color from dark blue to brown) corresponds to tail  1, tail 2, tail 3, tail 4, NGC 4656, Dwarf A, and NGC 4631  disk region respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The light blue color (id 0) marks  the region detected in Hi by the projected FAST cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  white dashed line separates the NGC 4631 and NGC 4656  regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  for highlighting where the excess Hi dominates the Hi  detected by FAST (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2), and discussing the hy-  drodynamical effects in the IGM (section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Multi-wavelength measurements from the literature  We derive the stellar mass for NGC 4631 with Spitzer  IRAC1 and 2 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5 µm) fluxes from the Local Vol-  ume Legacy (LVL) project (Dale et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use  the equation from Querejeta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2015), to derive the  IRAC1−IRAC2 color dependent IRAC1 mass-to-light  ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The equation was calibrated using fluxes decom-  posed into stellar and non-stellar components through  independent component analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The estimated stellar  mass log M∗/M⊙ = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use the star for-  mation rates (SFR) derived in Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2011) based  on the far-ultraviolet and the total-infrared luminosi-  ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The total-infrared luminosity accounts for the  dust attenuation of the far-ultraviolet luminosity, and  was derived through spectral energy distribution fit-  ting of mid- and far-infrared bands taken by Spitzer  as part of the LVL project (Dale et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The  SFR= 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25 M⊙yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We also obtain these two  parameters for NGC 4656 from the same datasets, with  log M∗/M⊙ = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1, and SFR= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='07 M⊙yr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We summarize from the literature and estimate more  properties about the N4631g in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Partic-  ularly, in appendix D, we show that, based on the the  local grouping of satellites, the characteristic radius r200  within which the averaged density is 200 times the cos-  mic critical density is around 249 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Accordingly the  virial temperature of the IGM should be around 8× 105  K, though the near-disk outflowing hot gas reaches a  temperature of nearly 2×106 K (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A  single-β model of the density profile of the IGM hot gas  is presented and discussed in appendix E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' COMPARING THE FAST AND WSRT DATA  In this section, we provide integral spectra, fluxes and  masses of Hi for galaxies in N4631g, and analyze Hi dis-  tribution on different angular scales (inverse of spatial  frequency) in the FAST and WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The difference  of the integral measurements for galaxies between the  two datasets provides a first-order measure of the excess  Hi detected by FAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Comparing integral fluxes of com-  pact sources, and comparing amplitudes in an angular-  scale range corresponding to overlapping region in the  uv space help verify the consistency of flux calibrations  between the two datasets, which is the basis for char-  acterizing any excess Hi detected by FAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Through  comparing the amplitudes of the two datasets on large  angular scales, we can further derive the critical angular  scale for WSRT to miss extended Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The integral spectra and integrated fluxes  In Figure 6, we show the integral Hi spectra of the  N4631g from the FAST data, and compare it with those  from the WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The conventional FAST spectrum is slightly higher  than the projected FAST spectrum at the high velocity  end, consistent with the truncation of the galaxy NGC  4656 at the edge of the field of view of the WSRT ob-  servation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The projected FAST Hi flux is in excess of  the PB-corrected WSRT one throughout the velocity  range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The integral fluxes from the FAST data, the  projected FAST data, the WSRT cube, and the PB-  corrected WSRT data are 1345.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9±134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6, 1314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6±131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5,  593.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8±59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4, and 852.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1±85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2 Jy km s−1 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The error bars are dominated by an assumed flux cali-  bration uncertainty of 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  From the FAST cube, the Hi masses of NGC 4631,  its major satellite NGC 4656, and dwarf companion  Dwarf A are 1010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04, 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04, and 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04 M⊙  (all assuming the distance of NGC 4656) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In comparison, the corresponding values from the PB-  corrected WSRT cube are 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04, 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='38±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04, and  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' To show the very little influence of reso-  10  400  450  500  550  600  650  700  750  800  vel (km/s)  0  1  2  3  4  5  6  7  f (Jy)  FAST  FAST (proj)  WSRT  WSRT (PBc)  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Integral Hi spectra of N4631g from different  cubes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The spectra from the FAST cube, the projected FAST  cube, the WSRT cube, and the PB-corrected WSRT cube are  plotted in red, pink, green and purple, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  lution in this comparison, we also derive the correspond-  ing values from the PB-corrected smoothed WSRT cube,  which are are 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='90±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04, 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='39±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04, and 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04  M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  There is clear excess Hi detected by FAST for NGC  4631 and NGC 4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The excess Hi may be caused  by the existence of diffuse Hi, which has large angular  size or low surface densities 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' There is no excess Hi  detected by FAST for Dwarf A, which is relatively small  in angular size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Comparing the amplitude spectra  One concern that arises when comparing the FAST  and WSRT data is whether the flux calibrations are con-  sistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The consistent integral fluxes of Dwarf A sup-  port it, but we further justify it by comparing the am-  plitude spectra between the PB-attenuated FAST cube  and the smoothed WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The analysis exploits modified scripts from the pack-  age uvcombine 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Each channel image is Fourier trans-  formed, and becomes a complex image of amplitudes and  phases where the position of a pixel reflects the spatial  frequency (inverse of the angular scale).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The relation  between the amplitude A and the angular scale is called  the amplitude spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The right panel of Figure 7  shows the amplitude spectra for both datasets at a se-  lected channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The two spectra converge at intermedi-  ate angular scales, largely between a lower and upper  3 We note that, when the definition of low-surface density is  based on the rms level of the WSRT cube, it is influenced by the  effect of PB attenuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We will discuss more on this point in  section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  4 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='com/radio-astro-tools/uvcombine/  limit angular scales of 4′ and 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The lower limit is  just slightly (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25 times) higher than the FWHM of the  FAST beam, while the upper one corresponds to the  shortest baseline (36 m) of the WSRT array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We select  the data points of the two datasets between the limiting  angular scales, and compare their spectral amplitudes  as well as the related real and imaginary parts in the  left panel of Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The data points all lie close to  the one-to-one line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We select the channels (in total 50)  where the maximum FAST amplitudes are higher than  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15 Jy, and derive the average linear scaling factor of  FAST amplitudes over the WSRT amplitudes for each  of these channels (more details in appendix F and left  panel of Figure 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The average scaling factors have a  median value and standard deviation of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='98 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='02  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' They strongly support the consistency of  fluxes from FAST and WSRT observations on the se-  lected overlapping angular scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We do not correct for  this 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='02 scaling difference, but if we do so the amount of  excess Hi derived in this work should be systematically  enlarged by 2%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In the left panel of Figure 7, we see a hint of the FAST  amplitudes exceeding the WSRT amplitudes on the high  amplitude end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It indicates the start of the regime where  the WSRT tends to miss large-scale diffuse flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In order  to investigate whether this hint is really, we select chan-  nels (50 in total) where the PB-attenuated FAST inten-  sity is higher than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15 Jy and higher than the WSRT  intensity by more than 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' For each channel, we derive  the critical angular scale above which the FAST A are  higher than the WSRT A by more than 1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The critical  angular scales have a relative narrow range, and a mean  value of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6′ ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9′ (more details in appendix F and  right panel of Figure 20), corresponding to a baseline of  65 m and a physical scale of 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This critical an-  gular scale is roughly half the theoretical value derived  from the shortest baseline of the WSRT array, possibly  due to a combined effect of the PB attenuation, and the  limited WSRT sampling density of the shortest baseline  which can be exacerbated by RFI flagging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' THE DIFFUSE HI DETECTED BY FAST  This section characterizes the diffuse Hi detected by  FAST, including how much there is, how it is dis-  tributed, what its kinematics are, and how it is con-  nected to the higher density Hi that the HALOGAS  project detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Combining the HI data  Because the FAST beam has a relatively low side-  lobe level of around 1% beyond a radius of ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5′ (ap-  pendix A), we use the MIRIAD procedure immerge to  11  2  1  0  1  2  AWSRT  2  1  0  1  2  AFAST  channel-31  imag  real  A  103  Angular scale (arcsec)  10  4  10  3  10  2  10  1  100  A  smoothed WSRT  PB attenuated FAST  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  An example of amplitude spectral analysis of channel maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The two channel maps analyzed have the same channel  number 31 (corresponding to a velocity of 477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7 km s−1), but are from the PB-attenuated FAST cube and the smoothed WSRT  cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Left: a one-to-one comparison in amplitudes (purple), the real parts (yellow), and the imaginary parts (green) between  the two types of data, selected to have angular scales between the limiting values marked in the right panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The dashed line  is the y = x line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The solid line shows the best-fit linear relation between the two types of amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Right: the amplitude  spectra of the amplitude (A) as a function of the angular scale, for the FAST (red dots) and WSRT data (blue dots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The two  black, thick, vertical lines mark the limiting angular scales of 4′ and 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5′, between which both FAST and WSRT data should  have relatively good sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Here this channel 31 is arbitrarily chosen, and the emission of that channel map is relatively  compact in morphology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In Figure 20 of appendix F, we show a similar comparison between the FAST and WSRT datasets  with data from all channels which have significant flux (FAST amplitudes>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15 Jy) putting together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  combine the projected FAST and WSRT cubes, which  uses the Gaussian functions to approximate beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  procedure immerge combines the two types of data in  the Fourier domain, with a unit weight for the projected  FAST data and a tapering for the WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The ef-  fect of the tappering is to make a Gaussian beam equiv-  alent to the WSRT synthesis beam, after adding the  tapered WSRT synthesis beam to the FAST beam in  the Fourier domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The output is an image combining  the spatial information of both data, but with the same  PB attenuation effect as the WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The proce-  dure also derives a calibration factor of WSRT flux over  FAST flux to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='98, consistent with the result from  our amplitude spectral analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The combined data give us a visual impression where  and how significant FAST detects the diffuse Hi that  is lacking in the WSRT observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The combined  moment-0 image is displayed in the bottom-right panel  of Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' FAST detects an excess of Hi widely sur-  rounding the denser tidal structures previously detected  by WSRT, typically on a scale larger than the critical  angular scale for WSRT to miss extended fluxes (see  section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The immerge process adds not only a lot  of new, diffuse Hi near the WSRT detection limit of  1018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='86 cm−2, but also thickens the structures at a rel-  atively higher column density of 1020 cm−2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' FAST  also detects more relatively high-density gas).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Because the side-lobe level of the FAST beam cannot  be ignored (appendix A), the combined data cube and  image are mainly for visual inspection here and later  in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the following, we analyze the FAST-  detected excess, diffuse Hi combining the two datasets,  but not directly based on the immerge combined data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Relating the diffuse HI to large-angular scale gas  We classify and quantify the distribution of excess Hi  detected in the FAST data with respect to the WSRT  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Unless otherwise specified, we focus on the NGC  4631 region in this section, as NGC 4656 is heavily at-  tenuated by the PB effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the NGC 4631 region,  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3% of the flux from the PB-attenuated FAST cube  are missed by the WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The missed part may be  related to the existence of low-surface density or large-  angular scale Hi, which we refer to together as the diffuse  Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use the rms level of the WSRT data, to separate  the PB-attenuated excess Hi into the low-surface density  and the large-angular scale types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We remind that, the  noise level of the PB-attenuated FAST cube decreases  as a function of radius from the image center while that  of the WSRT cube remains roughly constant, so the rel-  ative level of low-surface density Hi that is missed by  WSRT for being below the rms-based threshold should  increase toward large radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This effect biases our anal-  ysis toward attributing excess Hi to the low-surface den-  sity type at large radius, and undermines the detection  of large-angular scale type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  12  In Figure 8, we study the cumulative distribution of  the PB-attenuated excess Hi as a function of the asso-  ciated flux in the PB-attenuated FAST cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The 3-σ  detection threshold line of the smoothed WSRT cube is  marked in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The distribution to the left of the  positive threshold line (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' the right-side edge of the  cyan band) reflects the part of PB-attenuated excess Hi  missed by WSRT due to its low-surface density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' There is  only 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3% of PB-attenuated excess Hi in this part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  remaining part (89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7%) of PB-attenuated excess Hi is  likely missed by WSRT due to its large-angular scale dis-  tribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Because the periphery of large-angular scale  Hi distribution naturally has low densities, and because  of the PB attenuation effects described above, the ac-  tual fraction of large-angular scale Hi missed by WSRT  should be higher than this value of 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Thus, the  majority of the diffuse Hi are invisible to WSRT not  because of the limited sensitivity, but because of the  limited shortest baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We display the column density maps of the diffuse  Hi (PB-free excess Hi), its low-surface density part (the  part below the WSRT detection threshold before apply-  ing the correction for PB attenuation), and the large-  angular scale part (the diffuse Hi minus the low-surface  density part) for the NGC 4631 region in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  As discussed before, the low-surface density and large-  angular scale parts displayed here are upper and lower  limits of the actual parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The displayed large-angular  scale Hi is almost always higher in level than the dis-  played low-surface density Hi, except for the periphery  of the whole region and a small region on the south-  west.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  It confirms that, a considerable fraction of the  low-surface density Hi is attached to the large-angular  scale Hi in the outskirts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The majority of the excess Hi  is by nature the large-angular scale Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  It is still questionable whether the diffuse Hi primar-  ily overlaps with or is beyond the region of dense Hi  detected in the WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In Figure 8, the right  panel is similar to the left panel, but the x-axis is re-  placed by the associated flux of the smoothed WSRT  cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The distribution to the left of the positive thresh-  old line now reflects the part of PB-attenuated excess Hi  residing in regions where the WSRT data detects no Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Only 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3% of the PB-attenuated excess Hi are found in  blank regions of the WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' More than half of the  PB-attenuated excess Hi overlaps in regions with where  the WSRT detects the dense Hi (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' disk region+tail  region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Another noticeable feature in the right panel of  Figure 8 is that, the WSRT flux distribution is peaked  at a value below zero (∼ −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5 mJy b−1  F ), likely related  to the “negative bowl” artifacts discussed in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Multiplying this absolute peak value with the number of  voxels which have smoothed WSRT flux below 3-σ but  non-zero excess Hi provides a rough estimate of the re-  lated uncertainty for the fraction 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3% derived above,  which is 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  If we further limit the analysis to the IGM region  by excluding the disk region of NGC 4631, the frac-  tion of PB-attenuated FAST flux missed by the WSRT  data dramatically increases to 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2%, the fraction of PB-  attenuated excess Hi classified into the low-surface den-  sity type slightly increases to 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5%, and the fraction  found beyond the dense Hi region (equivalent to the tail  region) slightly increases to 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' These fractions also  indicate that, in the tail region, the amounts of dense  Hi and diffuse Hi are roughly equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Relating the diffuse HI to properties of the dense  HI  In the following, we take advantage of the high resolu-  tion of the WSRT data, quantify the localized kinematic  properties of dense Hi, and search for the preferred kine-  matic condition traced by the dense Hi to form the dif-  fuse Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The analysis of this section is limited to the tail  region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use BAYGAUD (Oh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022) to fit multi-Gaussian  models to the line-of-sight spectra of the WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  BAYGAUD uses Bayesian analysis techniques to decide  the optimal number of Gaussian components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Figure 10  shows the map of the number of components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The max-  imum number reaches 4, but those line-of-sights with  4 Gaussian components are mostly within the galactic  disks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The NGC 4631 disk region has many Gaussian  components possibly because of the edge-on geometry,  the tidal perturbation, and the energy input from mas-  sive young stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' These complexities support our deci-  sion to leave aside the disk region and focus on the tail  region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The profiles which are best fit with only one Gaussian  component are referred to as the single-Gaussian pro-  files, otherwise the multi-Gaussian profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  For each  multi-Gaussian profile, we identify the the Gaussian  component with the highest intensity as the primary  component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Figure 11 shows the distribution of σ of  all the single or primary Gaussian components of dense  Hi in the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We divide the Gaussian compo-  nents into narrow (warm) and broad (hot) ones by a σ  of 8 km s−1, thermally corresponding to a temperature  of 3600 K though the σ here are not really thermal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use not only the number of Gaussian components  but also profile broadness to indicate the kinematic hot-  ness of the dense Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The expectations are: 1) for single-  Gaussian profiles, velocity dispersion σ is indicative of  kinematic hotness, and high column densities of the  13  20  10  0  10  20  30  40  fHI, F(mJy/bF)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  frac (excess HI)  FAST PB attenuated  20  10  0  10  20  30  40  fHI, W(mJy/bF)  WSRT smoothed  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The distribution of attenuated excess Hi as a function of voxel values in data cubes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The left panel is for the  attenuated FAST cube, and the right the smoothed WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In each panel, the solid grey curve is the cumulative distribution  starting from the low-value side, and the dashed grey curve is for the peak-value normalized differential distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The cyan  band is the ±3-σ range of the smoothed WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  broad (narrow) components tend to be associated with a  high level of kinematic hotness (coolness);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2) in general,  single-Gaussian profiles tend to be kinematically cooler  than multi-Gaussian profiles if they are not significantly  affected by projection effect;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 3) for a multi-Gaussian pro-  file, the narrower Gaussian component with the smaller  value of σ is relatively cooler than the broader ones;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 4)  for multi-Gaussian profiles, profiles with narrow compo-  nents tend to be kinematically cooler than those with-  out, and those with a high fraction of flux in narrow  components tend to be cooler than otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We study how the column density of diffuse Hi is re-  lated to these kinematical properties of the dense Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In  each panel of Figure 12, we select and divide into two  subsets the line-of-sights along dense Hi by one type of  dense Hi kinematic property described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We com-  pare the distributions of column density in associated  diffuse Hi between the two subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Systematic trends  arise from the comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' For single-Gaussian narrow  profiles, high levels of diffuse Hi prefer those that are  broader in widths (panel a), but do not have a clear  trend with the column density (panel b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  For single-  Gaussian broad profiles, they show a slight tendency  toward the broad widths (panel c) and high column  densities (panel d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' For all profiles, they prefer multi-  Gaussian profiles over single-Gaussian profiles (panel e),  and regions where there is no narrow Hi over otherwise  (panel f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' For multi-Gaussian profiles, they slightly pre-  fer those with low fractions of narrow components (panel  g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Together, these trends indicate that the localized  kinematic hotness of the dense Hi and the column den-  sity of the diffuse Hi seem to be boosted simultaneously  in the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' There might be a pipeline of the Hi  shifting from the narrow, to the broad, and then to the  diffuse status, or in the opposite direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The localized kinematics of the diffuse HI  From the spectra displayed in Figure 6, the FAST  flux does not extend further in velocity than the WSRT  flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the literature, such an excess of Hi in the same  velocity range is typically attributed to a tidal origin  (Verdes-Montenegro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Those integral spec-  tra mix the effect of bulk motions and localized kine-  matics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the following, we remove the velocity shift  due to bulk motions and derive super profiles to reflect  localized kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In order to minimize the projec-  tion effect of multiple velocity components, we select the  line-of-sights which have single-Gaussian profiles in the  dense Hi, which comprise 51%, 14%, and 65% of the  line-of-sights in the NGC 4631 region (disk region+tail  region), the disk region, and the tail region, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We keep in mind that in addition to thermal motions,  beam smearing, and turbulence should significantly con-  tribute to the broadening of line widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use the velocity centers of line-of-sight spectra in  the WSRT cube, which have been obtained using BAY-  GAUD (Oh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=" We stack the line-of-sight spectra  14  12h44m  43m  42m  41m  40m  33°00'  32°45'  30'  15'  00'  ra (deg)  dec (deg)  Missing HI: the diffuse HI  18." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content="5  logNHI(1020 cm  2)  12h44m  43m  42m  41m  40m  33°00'  32°45'  30'  15'  00'  ra (deg)  dec (deg)  HI missed due to limited sensitivity  18." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content="5  logNHI(1020 cm  2)  12h44m  43m  42m  41m  40m  33°00'  32°45'  30'  15'  00'  ra (deg)  dec (deg)  HI missed due to limited baseline  18." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  logNHI(1020 cm  2)  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Column density maps of the excess Hi in the NGC 4631 region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The top panel shows the PB-free excess Hi missed  by WSRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The bottom-left and bottom-right panels divide the PB-free excess Hi into two parts: the one missed by WSRT due  to the limited sensitivity (the low-surface density Hi) and the one missed missed by WSRT due to the limited shortest baseline  (the large-angular scale Hi), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Some of the low-surface density Hi shown in the bottom-left panel may actually belong  to the large-angular scale Hi in the bottom-right panel;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' please refer to the main text for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  of the WSRT cube, after register them to the same ve-  locity center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The stacking is performed for the WSRT-  detected NGC 4631 region, the disk region, and the tail  region, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We do the same stacking for the  smoothed WSRT cube and the PB-attenuated FAST  cube, using the same velocity centroid determined from  the WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We display these super profiles in Fig-  ure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' From the top panel, the PB-attenuated excess  Hi of FAST is found throughout the localized velocity  range, but not preferentially in the wings of the dense  Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The conclusion above holds for both disk and tail  regions displayed in the middle and bottom panels, but  the super profiles of the former are much broader than  the latter, indicating influences from the galactic inter-  nal structures, geometry, and stellar feedbacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the  following of this section, we therefore limit the analysis  to the tail region to focus on tidal effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use emcee (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=" 2013), the  Python implementation of Goodman & Weare’s Affine  Invariant Markov Chain Monte Carlo (MCMC) Ensem-  15  12h44m  43m  42m  41m  40m  33°00'  32°45'  30'  15'  00'  ra (deg)  dec (deg)  Number of G components  1  2  3  4  5  ncomp  Figure 10." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Map of number of Gaussian components from  BAYGAUD fit for the WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The numbers 1 to 4 is  denoted by colors from cyan to red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  0  5  10  15  20  25  HI(km s  1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25  frac (pixel)  Velocity dispersion of the single or primary Gaussian component  narrow  broad  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The distribution of the velocity dispersion of  the single or primary Gaussian components in the WSRT  cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The vertical and dashed line at 8 km s−1 divides  the Gaussian components into the narrow (warm) and broad  (hot) types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  ble sampler, to fit a double-Gaussian model to each of  the super profiles of the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The details and  best-fit models are present in appendix G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  It is interesting to point out that, the narrow-Gaussian  component accounts for roughly half the total flux in  the FAST super profile, which is close to the ratio of  the dense Hi flux over the FAST detected Hi flux in  the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Thus, it is possible that the narrow  component of the FAST super profile corresponds to the  dense Hi detected by WSRT, while the broad component  corresponds to a diffuse envelope missed by WSRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use the square root difference between the veloc-  ity dispersions of the WSRT and the smoothed WSRT  cubes to correct for beam smearing effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' After the  correction, the narrow and broad Gaussian components  of the FAST super profile have σ of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4 and 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0 km s−1  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It is obvious that the width of the broad  component is unlikely thermal, but should be possibly  dominated by turbulence, and perhaps also some con-  tribution from beam smearing of where no WSRT flux  is detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' THE HYDRO-DYNAMIC AND TIDAL  ENVIRONMENTS  In this section, we investigate the thermal, radiative,  and gravitational environments around NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We  investigate, what is the fate of the Hi and particularly  the diffuse Hi in the IGM and tidal region, and what  physical mechanisms drive that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The hydro-dynamic effects  We come back to the column density map of FAST  detected Hi in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The high density part, where  NHI ≥ 1019cm−2, extends for ∼120 kpc across.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Near  the edge, NHI drops by nearly 1 dex within a length  comparable to the beam size of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='24′, or 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Similar but sharper (due to the use of images with a  higher resolution) edges of Hi distribution were noticed  before at a similar column density level, particularly by  the pioneering work of Corbelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (1989) and van  Gorkom (1993), in deep Hi imaging of the nearby galax-  ies M33 and NGC 3198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The truncation of Hi disks  was attributed to the ionisation by the cosmic ultra-  violet (UV) background (Maloney 1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The preva-  lence of the truncation and the uniformity of the thresh-  old column density are questioned recently by deep Hi  imaging of more galaxies (Bland-Hawthorn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Ianjamasimanana et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018), as both the local UV  background and the clumpiness of Hi affect the ionizing  status while both factors are quite uncertain (Bland-  Hawthorn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The condition for Hi to survive  and evolve in the hot gas halo of N4631g may also dif-  fer from those benchmark galaxies M33 and NGC 3198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Firstly, the tidal Hi reaches far into the IGM while re-  taining a high column density, which may induce effi-  cient cooling of the hot gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Secondly, the relatively  high SFR of NGC 4631 may enhance the local UV radi-  ation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In the following, we discuss the fate of Hi in the IGM  region in the context of different hydro-dynamic pro-  cesses as a function of radius from NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We note  16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='  Comparing the cumulative distributions of diffuse Hi column densities between line-of-sights with different localized  kinematic properties of the dense Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The properties considered include the velocity dispersion of narrow/broad single-Gaussian  components (panel a/c), and the column density of narrow/broad single-Gaussian components (panel b/d), the number of  Gaussian components (panel e), the existence of the narrow component (panel f), and the flux fraction of narrow components  along line-of-sights with multi-Gaussian components (panel g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  17  200  150  100  50  0  50  100  150  200  v(km/s)  0  50  100  150  200  f(mJy/bF)  whole  WSRT (sg fit)  WSRT  WSRT (smooth)  FAST  200  150  100  50  0  50  100  150  200  v(km/s)  0  5  10  15  20  25  30  f(mJy/bF)  disk  WSRT (sg fit)  WSRT  WSRT (smooth)  FAST  200  150  100  50  0  50  100  150  200  v(km/s)  0  20  40  60  80  100  120  140  f(mJy/bF)  tail  WSRT (sg fit)  WSRT  WSRT (smooth)  FAST  Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Super profiles of Hi from stacking line-of-sights  of data cubes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The line-of-sights are selected to have single-  Gaussian profiles in the dense Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The top, middle, and  bottom panels plot the super profiles of the whole WSRT Hi  detected region, the disk region, and the tail region, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The cubes include the WSRT cube, the smoothed  WSRT cube, and the PB-attenuated FAST cubes, which  are plotted in orange, green and red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The stacking centers  and stacking regions are determined by single-Gaussian fit  to line-of-sights from the WSRT cube;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' the super profile of  the single-Gaussian fits is plotted in cyan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  that the following discussion is based on first order ap-  proximations of the complex interplay between the dif-  ferent phases and dynamics in the IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' As such they  merely provide a first indication of what might be hap-  pening to the Hi in the tidal region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We point out that, the models discussed are 3-  dimensional but the observed Hi is projected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The  galactocentric distances can be underestimated, and  the projection and overlapping of structures can arti-  ficially enhance the Hi column density, which may be  major sources of uncertainty in the discussion of Hi  survival in the IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' On the other hand, the projected  phase-space distribution of flux (Figure16, discussed in  section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2) suggests that the overlapping of structures  seems not severe in most parts of tail 1, 3 and 4, which  may mitigate the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' To overcome this observa-  tional limitation in the future, hydrodynamic modeling  specifically conducted to reproduce the Hi distribution  in N4631g will greatly help;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' alternatively, a sample of  many interacting systems like N4631g will provide a  statistical and representative view for comparison with  and constraint on general hydrodynamic simulation of  interacting systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Despite the uncertainties, a major advance here is  that, the calculations are based on real measurements  of the diffuse Hi, which were lacking in most previous  observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Thermal conduction  Based on the theory of Cowie & McKee (1977), we use  the following simplified calculation to discuss the status  of thermal conduction of the Hi in the IGM region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We assume a density distribution for the hot gas in the  IGM (nIGM) following the single-β models presented in  Eckert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2011) (See appendix E for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  temperature is assumed to be uniform at the virial tem-  perature of 8×105 K (appendix D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Based on our mea-  sured super profiles, we fix the velocity dispersion of the  diffuse Hi to σHI = 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0km s−1 (section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We assume  the Hi travels in the hot gas halo in an external pressure-  confined way, and derive the volume density of the dif-  fuse Hi (nHI) accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The value of log(nHI/cm−3)  drops from −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4 at 10 kpc to −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1 at 60 kpc, consis-  tent with the typical values of tidal Hi discussed in the  literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Borthakur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  For an Hi cloud with a radius rc, the dimensionless  “global saturation parameter” σ0 =  (TIGM/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5×107 K)2  nIGM rc  separates the gas at the interface between Hi and hot gas  into regimes of saturated evaporation, classical evapora-  tion, and cooling flows (Cowie & McKee 1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Using  the critical value σ0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='027 (Cowie & McKee 1977),  we derive the critical rc as a function of distance from  18  NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Then we calculate the critical column den-  sity NHI,c,evap = nHI rc = 1018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5 cm−2 for classical evap-  oration in N4631g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Because N4631g has a relatively low  mass and thus low virial temperature, thermal evapo-  ration is only relevant on small scales, corresponding to  low column densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This critical value does not vary  significantly with distance to NGC 4631 because the Hi  volume density scales with the ICM density in our as-  sumed model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  For both the FAST detected Hi and the diffuse Hi  (Figure 3 and 9), this critical column density value is  only reached at the very periphery of the IGM region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  It is also clear in Figure 14, where we plot the number  density of pixels as a function of column density of the  diffuse Hi and radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Between a distance of 20 and 60  kpc, the number densities peak where log(NHI/cm−2) >  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5, and sharply drop where log(NHI/cm−2) < 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The NHI,c,evap values lie right below where the sharp  drop begins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Thus the majority of the Hi in the IGM  region is more likely to induce cooling out of the IGM  at its surface instead of thermally evaporating itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We make a similar plot replacing the diffuse Hi by  all the Hi detected by FAST in the bottom panel of  Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The discussion above still applies, but the  previous sharp pattern of number density dropping at  log(NHI/cm−2) < 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8 is more blurred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In summary, there seems to be efficient cooling instead  of evaporation associated with the Hi in the IGM region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We note that the lack of direct measurements on the  temperature and density of the IGM, and the magnetic  fields (Cowie & Songaila 1977) in the tidal region are  major sources of uncertainty in the derivation of the  evaporation related parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Photon ionisation  The Hi remains neutral in the UV radiation field  through self-shelding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The quantity to derive is the crit-  ical Hi column density (NHI,c,ion) where half of the hy-  drogen gets ionized due to the photon ionisation by stars  plus the cosmic background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We estimate the dimen-  sionless ionisation parameter of stars (Ustar) from the  SFR of NGC 4631 based on the equation in Tumlinson  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use Cloudy (Ferland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1998) to sim-  ulate the ionisation rate of hydrogen at different levels  of Ustar plus the comic background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We derive NHI,c,ion  as a function of distance to NGC 4631 based on prod-  ucts of the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' More technical details can be  found in section H of the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We emphasize that  in the model Ustar is only attenuated as a function of  radius squared, but the possible absorption of tidal Hi  (and possibly also dust) as the photons travel through  0  10  20  30  40  50  60  r (kpc)  18  19  20  21  22  logNHI(cm  2)  Diffuse HI  NHI, c, evap  NHI, c, ion  FAST beam  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  log N  0  10  20  30  40  50  60  r (kpc)  18  19  20  21  22  logNHI(cm  2)  FAST detected HI  NHI, c, evap  NHI, c, ion  FAST beam  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='00  log N  Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The distribution of Hi column density as a  function of projected distance from NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The top  panel is for the diffuse (excess) Hi, while the bottom panel  for all Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Each pixel in the plot is color coded by logarithm  of the number of pixels from the relevant column density  map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The two dashed curves in each plot show the critical  column densities to survive thermal evaporation (magenta),  and UV ionisation (yellow) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The brown curves  show the shape of the FAST beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  it is not considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' So the NHI,c,ion derived should be  viewed as upper limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In Figure 14, the NHI,c,ion values lie roughly be-  tween  where  the  number  densities  of  pixels  con-  centrate (log(NHI/cm−2) > 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5) and sharply drop  (log(NHI/cm−2) < 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The transition in number  densities is not sharply defined by NHI,c,ion, imply-  ing the aforementioned over-estimation of NHI,c,ion and  other uncertainties in the modeling, as well as possible  counteracting effects of IGM cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Despite the likely  over-estimation of NHI,c,ion, most pixels of diffuse Hi  have NHI above them, indicating that most diffuse Hi  are safe against photon ionisation in N4631g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tidal interactions of the HI  We investigate the distribution of Hi in N4631g in re-  sponse to the past and on-going tidal interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We  visualize the 3-dimensional distribution, and also pro-  vide a characterization of the phase-space distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  19  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The 3-dimensional visualization  We provide snapshots of a 3-dimensional visualization  of the Hi distribution in N4631g in Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The  visualization is realized using the software SlicerAstro  (Punzo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use it to provide a first im-  pression of the complex morphology and kinematics of  Hi in the N4631g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Similar discussions were presented  in Rand (1994) based on channel maps and position-  velocity slices of an early WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  From the snapshots of FAST data, tail 1 and 2 clearly  connect NGC 4631 and NGC 4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tail 1 starts from  the east and low-velocity side of NGC 4631, and reaches  NGC 4656 on its east and high-velocity side (snapshot  1, 2, 3, 5, 6, 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tail 2 starts from near the disk center of  NGC 4631, and reaches NGC 4656 on its west and low-  velocity side (snapshot 1, 2, 5, 6, 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The connection  between the two galaxies by tail 2 was not so clear in  the WSRT data of HALOGAS, or the early WSRT data  of Rand (1994);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' probably consequently, Combes (1978)  tended to attribute the formation of tail 2 primarily to  the perturbation of the much smaller but closer com-  panion NGC 4627, and only secondarily to NGC 4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  From the snapshots of the FAST data, tail 3 starts  from the high-velocity and western side of NGC 4631  (snapshot 1, 3, 4, 5, 8), extends to the intermediate  velocity and joins tail 1 in the south (snapshot 2, 5,  8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This link between tail 3 and 1 was tentatively seen  but again unclear in the WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tail 4 is short in  both the FAST and WSRT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It starts from the west  end of the NGC 4631 disk, and extends to the east and  low-velocity direction (snapshot 1, 5, 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Analysis of the phase-space distribution  We study the projected phase-space distribution of Hi  around NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The projected phase-space diagram  is a diagram of radial velocity offset versus projected  distance to the center of NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We are limited by  observational projections, but a first-order characteri-  zation can still be obtained about the bulk motions of  Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We plot the distribution of Hi in the regions of the  NGC 4631 disk and the 4 tails in the projected phase-  space diagram in Figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We focus our discussion  on the distribution of PB-corrected dense Hi, as it is a  good tracer of the kinematic skeleton of tidal tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' But  we also outline the distribution of diffuse Hi using the  PB-corrected, mmerge combined cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The distribution  of dense Hi in the NGC 4631 disk shows the pattern  of a rotating disk with a maximum velocity around 150  km s−1, which is by construction when defining the disk  region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' To guide the eye, the distribution of Hi in the  disk region is repeated in all panels of the tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' To assist  the analysis, we also plot contours of the gravitational  potential with linear steps (see details in appendix I),  and mark the truncation radius imposed by NGC 4656  at 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9 kpc which we derive using the equation of Byrd  & Valtonen (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We find three distinct patterns of the Hi distribution  in the projected phase-space diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tail 1 and 3 both  start from the end of the disk, and deaccelerate in rela-  tively radial velocity while extending to large projected  distance until reaching around the truncation radius im-  posed by NGC 4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tail 4 is almost a parallel shift of  the lower envelope of the disk in the projected phase-  space diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  This linear shape suggests an almost  solid-body rotation, which are often found in systems of  slow encounters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M81, Sorgho et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tail 2  looks much broader in morphology and possibly higher  in energy than the other tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Its furthest end crosses  the truncation radius of NGC 4656, while the relative  radial velocity is still high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the projected view, the  furthest end reaches a gravitational potential level sim-  ilar to those of tail 1 and 3, and much higher than that  of tail 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Its high energy and complex morphology sug-  gests it likely to have been perturbed by more than one  galaxy (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' both NGC 4656 and NGC 4627), which was  supported by previous particle simulations to reproduce  the dense Hi distribution in N4631g (Combes 1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Limited by projection effects, it is difficult to deduce  the motion of gas without the aid of hydrodynamic simu-  lations designed to reproduce the morphology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' But from  the complexity of Hi distribution in the projected phase-  space diagram, we can still infer that there are more  than one tidal encounters in N4631g, which should ex-  plain the widely spreading Hi, and may input turbulent  energy through shocks to produce the diffuse Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' SUMMARY AND CONCLUSION  We present a deep FAST image of Hi in and around  NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We identify a component of excess Hi de-  tected by FAST but missed by WSRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Our major results  are summarized below:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The nature of the excess HI is likely large-  scale, diffuse HI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This excess Hi has a low spatial fre-  quency, corresponding to a characteristic angular scale  ≥ 14′ or 30 kpc, missed by WSRT due to the limited  shortest baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It is also highly turbulent, with a ve-  locity dispersion around 44 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Around 40% (70%)  of the excess Hi in the NGC 4631 region (IGM region)  is found beyond the regions where dense Hi is detected  by the WSRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The diffuse HI is more closely related to  the dense HI that is kinematically hot than that  is warm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' When overlapping with the dense Hi in the  20  Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Snapshots of 3-dimensional visualization of Hi distribution in the FAST and WSRT cubes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' An animated version  of this figure is available as on-line material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The duration of the animation is 28 s, and the content is the 3-dimensional  visualization of the FAST and WSRT cubes (WCS system registered) continuously rotating by 360◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The viewing angles are  denoted as direction axes, with N, E, W, z and Z pointing toward the north, east, west, low-redshift (velocity), and high-redshift  (velocity) direction, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The visualization is realized using the software SlicerAstro (Punzo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The figure  here shows 8 snapshots from that animation, which are evenly distributed in a rotation of 360◦, and are ordered by number  denoted in the top-left corner of panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' For visual clarity, the 4 tidal tails are denoted in the figure (but not in the animation),  and each pair of FAST and WSRT snapshots are vertically arranged (while horizontally arranged in the animation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' To be  continued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  1  2  T3  Z  3  W  W  FAST  FAST  Z  W  W  WSRT  WSRT  3  4  3  W  W  专  FAST  FAST  W  W  WSRT  WSRT  E  ZE21  Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Continued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  5  6  T4  T3  T3  W  Wt  Z  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  T2  12  FAST  FAST  W  Wt  Z  WSRT  WSRT  2  7  8  T3  13  E  W  T4  T2  T2  FAST  FAST  E  E  W  WSRT  N  WSRT  Z  E22  0  50  100  150  200  d  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  0  50  100  150  200  vrad(kms  1)  t1  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  0  50  100  150  200  vrad(kms  1)  t2  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  0  50  100  150  200  vrad(kms  1)  t3  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  0  10  20  30  40  50  60  dproj(kpc)  0  50  100  150  200  vrad(kms  1)  t4  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  0  200  400  600  800  Jyb  1kms  1  10  20  30  40  Jyb  1kms  1  10  20  30  40  Jyb  1kms  1  10  20  30  40  Jyb  1kms  1  10  20  30  40  Jyb  1kms  1  Figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The projected phase-space distribution of Hi flux around NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' From top to bottom, the distribution of Hi  in the disk and the 4 tail regions are plotted respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The pixels are color coded by Hi flux from the PB-corrected WSRT  cube, and the distributions are outlined by solid contours at the level of 4 (80) Jy b−1 km s−1 for the tail (disk) flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  distribution of Hi flux from the PB-corrected, FAST+WSRT combined cube is outlined by dashed contours at the same level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The disk region is repeated in every panel to guide the eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Contours of gravitational potential with linear interval steps are  plotted as grey dotted curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The truncation radius for NGC 4656 to strip gas from NGC 4631 is plotted as the thick, pink  vertical line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The pink arrow mark the radial velocity deviation of NGC 4631 from NGC 4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  23  tail region, the diffuse Hi increases in column density  with the dense Hi, and is particularly closely associated  with the “hotter” part of the dense Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It is preferen-  tially found where the dense Hi is more dominated by  the broad-velocity components, or has multiple velocity  components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The diffuse HI is likely to induce cooling  flows of the hot IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The diffuse Hi in the IGM  region typically have a column density ≥ 1019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2 cm−2,  which is far above the critical column density for ther-  mal evaporation, and likely safe from photon ionization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  This relatively high Hi column density is consistent with  a condition to induce efficient cooling flows from the hot  IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The results above involve gases of four different phases  in the IGM region, namely the hot IGM, the diffuse  Hi characterized in result 1, the “hot” dense Hi, and  the “warm” dense Hi, sorted roughly in reverse order of  energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Result 3 indicates that, except for the periphery  of the widely spreading IGM region, the hot IGM is  likely cooling into the diffuse Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' An important reason  for cooling flows to be induced near Hi gas, is that the  thermal temperature of the interface between Hi and the  hot IGM produced by turbulent mixing is intermediate  between these two gas phases, reaching close to the value  of 105 K for the radiative cooling function to peak (Dere  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Indeed, if we take the radiative cooling  function of Dere et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2009) for the solar metallicity  and assume no heating, the isochoric cooling time for  hot gas at the virial temperature of N4631g is close to  the dynamical time of N4631g (∼400 Myr at a radius  of 30 kpc), indicative of difficult cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  But if the  temperature drops to 105 K, the cooling time drops by  more than one order of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The diffuse Hi further links to the dense Hi gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Result  2 indicates a continuous shift in phases between the dif-  fuse Hi, the hot dense Hi, and the warm dense Hi, while  the shift could be in either direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Indeed, tidal in-  teractions can both enhance cooling through mixing of  metals, and heating through tidally induced shocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' If  the net effect is the diffuse Hi progressively cooling into  the dense Hi, then there is a unidirectional accretion  pipeline that transfers gas from the hot IGM through  the diffuse Hi to the dense Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' If, on the other hand,  the dense Hi is being progressively heated into the dif-  fuse Hi, the surface area of Hi in the IGM enlarges, and  the cooling rate of the hot IGM increases as a result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In both cases, the diffuse Hi plays an important role in  the gas accretion from the hot IGM, either more as a  transfer station of the accreted gas, or more a catalyst  for cooling from the hot IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Given such an important role of diffuse Hi in gas  accretion, the tidal interaction may have significantly  boosted the gas accreting rate (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', the integral cool-  ing rate from the hot IGM) of NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' N4631g has  M200 ∼ 1012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1 M⊙ (appendix D), putting NGC 4631 in  a theoretical regime where heating from cosmic gas ac-  cretion and internal feedbacks start to efficiently prevent  gas cooling (Kereˇs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The gas accretion could  be effectively slow in NGC 4631 if it was an unperturbed  galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Tidal interaction enhances the gas accreting rate  by spreading Hi widely in the IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The tidal Hi, par-  ticularly when in the diffuse phase, greatly increases the  area of interface between the Hi and and the hot IGM,  thus induce significantly extra cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The tidal effects  also put the gas in a kinematic status prone to shocks,  ram pressure, and tidal compression, causing localized  gaseous condensation and thermal instabilities directly  relevant for enhanced cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The tidal effects further  help transport metals throughout the IGM which is im-  portant for radiative cooling (Dere et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' If such  a scenario of enhanced cooling is true, we speculate the  existence of a large amount of warm, ionized gas as an  intermediate phase between the hot IGM and the dif-  fuse Hi, which was indeed tentatively detected in Hα  throughout the group (Donahue et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It might be  worth mentioning that, in a recent cosmological zoom-  in magnetohydrodynamics simulation by Sparre et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  (2022), one simulated galaxy pair shows a broad Hi  bridge, which is qualitatively similar to the structure ob-  served between NGC 4631 and NGC 4656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Sparre et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  (2022) found that the gas that had been in the CGM  prior to the tidal interaction contributed to nearly half  of the mass in the gas bridge, and more than one fourth  of the fueling to star formation during the interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Previous observational studies based on individual or  statistical samples of tidally interacting systems found  evidence for Hi to be both depleted and replenished  in galaxies (Verdes-Montenegro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Hess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Ellison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Theoretically, both effects are  physically possible (Boselli & Gavazzi 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Hani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Stevens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' On the whole, there seems  to be a high level of physical complexities in mergers,  which may smooth out in statistical analysis of integral  Hi measurements, and cannot be fully captured by in-  dividual systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Our study put NGC 4631 in the cate-  gory where the tidal interaction induces Hi fueling, but  the main contribution is characterizing and highlighting  the role of the diffuse Hi, instead of just adding vote to  one side in the question of fueling or depletion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  To put NGC 4631 in the context of general galaxy  evolution, in Figure 17, we compare the SFR and Hi  mass of it and NGC 4656 to other galaxies of a stellar  24  mass selected sample, and particularly to the main se-  quences of the two properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It is interesting to notice  that the FAST measurements of the Hi mass put the  two galaxies in the regime of Hi-excess galaxies, while  the WSRT measurements put them in the Hi main se-  quence of normal star-forming galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We will need a  dataset like the one used in this paper but for a census  of interacting galactic systems with different mass ra-  tios, gas richnesses, merging distances, and large-scale  environments, as well as for a sample of control galaxies  in relative isolations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Such a dataset will be available in  the future by combining data from FEASTS and from  existing and SKA related interferometry surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We conclude that, tidal interaction should be an ef-  ficient channel to accrete the IGM gas to the galaxy  NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The excess Hi detected by FAST provides  the crucial, new information to reach this conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We thank the anonymous referee for very construc-  tive comments!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We thank Xu Kong, Thijs van der  Hulst, Zhiyuan Li, Ningyu Tang, Tobias Westmeier,  Feng Yuan, Pei Zuo for useful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' JW thank  support of the research grants from Ministry of Sci-  ence and Technology of the People’s Republic of China  (NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022YFA1602902), the National Science Foun-  dation of China (NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 12073002, 11721303), and the  science research grants from the China Manned Space  Project (NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' CMS-CSST-2021-B02).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='OH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' acknowl-  edges support from the National Research Foundation  of Korea (NRF) grant funded by the Korea govern-  ment (Ministry of Science and ICT: MSIT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  RS-  2022-00197685).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' LCH was supported by the National  Science Foundation of China (11721303,  11991052,  12011540375) and the China Manned Space Project  (CMS-CSST-2021-A04, CMS-CSST-2021-A06).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  KMH  acknowledges financial support from the State Agency  for Research of the Spanish Ministry of Science, Innova-  tion and Universities through the ”Center of Excellence  Severo Ochoa” awarded to the Instituto de Astrofísica  de Andalucía (SEV-2017-0709), from the coordina-  tion of the participation in SKA-SPAIN, funded by  the Ministry of Science and Innovation (MCIN), and  financial support from grant RTI2018-096228-B-C31  (MCIU/AEI/FEDER,UE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' PK acknowledges financial  support by the German Federal Ministry of Educa-  tion and Research (BMBF) Verbundforschung grant  05A20PC4 (Verbundprojekt D-MeerKAT-II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Parts of  this research were supported by High-performance Com-  puting Platform of Peking University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  This work made use of the data from FAST (Five-  hundred-meter Aperture Spherical radio Telescope).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  FAST is a Chinese national mega-science facility, oper-  ated by National Astronomical Observatories, Chinese  Academy of Sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Facilities: FAST, GALEX, Spitzer, WSRT  Software: Astropy(AstropyCollaborationetal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2013,  2018, 2022), Astrosclicer (Punzo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017), BAYGAUD  (Oh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022), 3D-Barolo (Di Teodoro & Fraternali  2015), Cloudy (Ferland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1998), galpy (Bovy 2015,  v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0), numpy (van der Walt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011, v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4), photu-  tils (Bradley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019, v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0), Python (Perez & Granger  2007, v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='13), scipy (Virtanen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0)  REFERENCES  Andreon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Trinchieri, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Moretti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Serra,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017, A&A, 606, A24,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/201730722  Astropy Collaboration, Robitaille, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Tollerud, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013, A&A, 558, A33,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/201322068  Astropy Collaboration, Price-Whelan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Sip˝ocz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, AJ, 156, 123, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-3881/aabc4f  Astropy Collaboration, Price-Whelan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Lim, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022, ApJ, 935, 167, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/ac7c74  Barnes, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Staveley-Smith, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', de Blok, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2001, MNRAS, 322, 486,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1046/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='04102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='x  Becker, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', White, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Helfand, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1995, ApJ,  450, 559, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/176166  Behroozi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Conroy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Wechsler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2010, ApJ,  717, 379, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-637X/717/1/379  Bland-Hawthorn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Maloney, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Stephens, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Zovaro,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Popping, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017, ApJ, 849, 51,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/aa8f45  Blumenthal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Barnes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, MNRAS, 479,  3952, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/sty1605  Borthakur, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Verdes-Montenegro, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2010,  ApJ, 710, 385, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-637X/710/1/385  Borthakur, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Verdes-Montenegro, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2015, ApJ, 812, 78, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-637X/812/1/78  Borthakur, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Heckman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Tumlinson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2016,  ApJ, 833, 259, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/833/2/259  Bose, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Eisenstein, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Hernquist, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019,  MNRAS, 490, 5693, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stz2546  Boselli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Fossati, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Sun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022, A&A Rv, 30, 3,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1007/s00159-022-00140-3  Boselli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Gavazzi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='1086/500691  25  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Left: the red and orange dots are for Hi masses from  the FAST cube and the PB-corrected WSRT cube respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Right: the blue and cyan points in the background represent measurements  and upper limits for Hi detected and un-detected galaxies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content=', Sip˝ocz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Robitaille, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019,  astropy/photutils: v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='3568287  Byrd, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Valtonen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1990, ApJ, 350, 89,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/168362  Catinella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Saintonge, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Janowiecki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018,  MNRAS, 476, 875, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/sty089  Chabrier, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2003, ApJL, 586, L133, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/374879  Chown, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Athanassoula, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019, MNRAS,  484, 5192, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stz349  Chung, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', van Gorkom, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Kenney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', &  Vollmer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2007, ApJL, 659, L115, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/518034  Combes, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1978, A&A, 65, 47  Condon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Cotton, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Greisen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1998,  AJ, 115, 1693, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/300337  Corbelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Schneider, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Salpeter, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1989, AJ,  97, 390, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/114989  Cortese, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Catinella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Smith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2021, PASA, 38,  e035, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1017/pasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='18  Cowie, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & McKee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1977, ApJ, 211, 135,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/154911  Cowie, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Songaila, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1977, Nature, 266, 501,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1038/266501a0  Dale, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Cohen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Johnson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2009, ApJ,  703, 517, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-637X/703/1/517  Das, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Sardone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Leroy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020, ApJ, 898,  15, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/ab97b9  de Blok, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Walter, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Ferguson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2018, ApJ, 865, 26, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/aad557  Dere, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Landi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Young, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2009, A&A, 498,  915, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/200911712  Di Teodoro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Fraternali, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015, MNRAS, 451,  3021, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stv1213  Donahue, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Aldering, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Stocke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1995, ApJL,  450, L45, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/316771  Dutton, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Macci`o, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2014, MNRAS, 441, 3359,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stu742  Eckert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Molendi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Paltani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011, A&A, 526, A79,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/201015856  Ekers, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Sancisi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1977, A&A, 54, 973  Ellison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Catinella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Cortese, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, MNRAS,  478, 3447, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/sty1247  Ellison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Mendel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Patton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Scudder,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013, MNRAS, 435, 3627,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stt1562  Ettori, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015, MNRAS, 446, 2629,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stu2292  Ferland, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Korista, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Verner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1998,  PASP, 110, 761, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/316190  Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Hogg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Lang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Goodman,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013, PASP, 125, 306, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/670067  Golla, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Dettmar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Domgoergen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1996, A&A,  313, 439  26  Guo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Jones, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Lin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2021, ApJ, 918,  53, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/ac062e  Hani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Sparre, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Ellison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Torrey, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', &  Vogelsberger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, MNRAS, 475, 1160,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stx3252  Haynes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Giovanelli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Kent, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, ApJ,  861, 49, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/aac956  Heald, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', J´ozsa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Serra, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011, A&A, 526,  A118, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/201015938  Heiles, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Perillat, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Nolan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001, PASP, 113,  1247, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/323290  Hess, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Cluver, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Yahya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017, MNRAS,  464, 957, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stw2338  Ianjamasimanana, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Walter, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', de Blok, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Heald,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Brinks, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, AJ, 155, 233,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-3881/aabbaa  Irwin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Beck, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Benjamin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2012, AJ, 144,  44, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-6256/144/2/44  Janowiecki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Catinella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Cortese, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Saintonge, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', &  Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020, MNRAS, 493, 1982,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/staa178  Jarrett, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Chester, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Cutri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2000, AJ, 119,  2498, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/301330  Jiang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Yue, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Gan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019, Science China  Physics, Mechanics, and Astronomy, 62, 959502,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1007/s11433-018-9376-1  Jiang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Tang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Hou, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020, Research in  Astronomy and Astrophysics, 20, 064,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/1674-4527/20/5/64  Jones, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Verdes-Montenegro, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Damas-Segovia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=',  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019, A&A, 632, A78,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/201936349  Kereˇs, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Katz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Weinberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Dav´e, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2005,  MNRAS, 363, 2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='09451.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='x  Koopmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Giovanelli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Haynes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2008, ApJL, 682, L85, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/591124  Kourkchi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Tully, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017, ApJ, 843, 16,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/aa76db  Lan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Mo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, ApJ, 866, 36,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/aadc08  Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Gil de Paz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Kennicutt, Robert C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2011, ApJS, 192, 6, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0067-0049/192/1/6  Lee-Waddell, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Koribalski, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Westmeier, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2019, MNRAS, 487, 5248, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stz017  Leitherer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Ortiz Ot´alvaro, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Bresolin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2010, ApJS, 189, 309, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0067-0049/189/2/309  Maloney, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1993, ApJ, 414, 41, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/173055  Martin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Kern, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001, ApJ, 555, 258,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/323161  Mart´ınez-Delgado, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', D’Onghia, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Chonis, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2015, AJ, 150, 116, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-6256/150/4/116  Mel´endez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Veilleux, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Martin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015, ApJ,  804, 46, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-637X/804/1/46  Monachesi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Bell, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Radburn-Smith, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2016, MNRAS, 457, 1419, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stv2987  Mora-Partiarroyo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Krause, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Basu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019a,  A&A, 632, A10, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/201834571  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019b, A&A, 632, A11,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/201935961  Namumba, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Koribalski, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', J´ozsa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2021,  MNRAS, 505, 3795, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stab1524  Navarro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Frenk, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & White, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1997, ApJ,  490, 493, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/304888  Oh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', For, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Staveley-Smith, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022,  ApJ, 928, 177, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/ac5905  Perez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Granger, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2007, Computing in Science  and Engineering, 9, 21, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1109/MCSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='53  Punzo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', van der Hulst, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Roerdink, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=',  Fillion-Robin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017, Astronomy and  Computing, 19, 45, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='ascom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='004  Putman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017, in Astrophysics and Space Science  Library, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 430, Gas Accretion onto Galaxies, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Fox & R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Dav´e, 1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1007/978-3-319-52512-9 1  Putman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Peek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Joung, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2012,  ARA&A, 50, 491,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1146/annurev-astro-081811-125612  Querejeta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Meidt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Schinnerer, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015,  ApJS, 219, 5, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0067-0049/219/1/5  Radburn-Smith, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', de Jong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Seth, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2011, ApJS, 195, 18, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0067-0049/195/2/18  Rand, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1994, A&A, 285, 833  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2000, ApJ, 535, 663, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/308869  Reichert, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', B¨ohringer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Fassbender, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & M¨uhlegger,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011, A&A, 535, A4,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361/201116861  Richter, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Winkel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Wakker, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, ApJ,  868, 112, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/aae838  Saintonge, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Catinella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Cortese, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2016,  MNRAS, 462, 1749, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stw1715  Saintonge, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Catinella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Tacconi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017,  ApJS, 233, 22, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4365/aa97e0  Schechtman-Rook, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Hess, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2012, ApJ, 750, 171,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-637X/750/2/171  Serra, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Koribalski, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Duc, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013, MNRAS,  428, 370, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/sts033  Serra, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Westmeier, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Giese, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015, MNRAS,  448, 1922, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stv079  Seth, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Dalcanton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & de Jong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2005, AJ,  129, 1331, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/427859  27  Shangguan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Ho, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019, ApJ, 870, 104,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/aaf21a  Sorgho, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Foster, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Carignan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Chemin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019,  MNRAS, 486, 504, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stz696  Sparre, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Whittingham, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Damle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022,  MNRAS, 509, 2720, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stab3171  Stanimirovic, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2002, in Astronomical Society of the  Pacific Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 278, Single-Dish Radio  Astronomy: Techniques and Applications, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Stanimirovic, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Altschuler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Goldsmith, & C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Salter,  375–396.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='org/abs/astro-ph/0205329  Stevens, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Brown, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2017, MNRAS, 471, 447,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stx1596  Stevens, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Diemer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Lagos, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019,  MNRAS, 483, 5334, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/sty3451  Strickland, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Heckman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Colbert, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=',  Hoopes, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Weaver, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2004, ApJ, 606, 829,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/383136  Swaters, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', van Albada, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', van der Hulst, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', &  Sancisi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2002, A&A, 390, 829,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361:20011755  T¨ullmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Pietsch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Rossa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Breitschwerdt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', &  Dettmar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2006, A&A, 448, 43,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361:20052936  Tully, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015, AJ, 149, 54,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-6256/149/2/54  Tully, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Courtois, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Dolphin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013,  AJ, 146, 86, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-6256/146/4/86  Tumlinson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Werk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Thom, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011, ApJ,  733, 111, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1088/0004-637X/733/2/111  van der Walt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Colbert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Varoquaux, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2011,  Computing in Science and Engineering, 13, 22,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1109/MCSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='37  van Gorkom, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1993, in Astrophysics and Space Science  Library, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 188, The Environment and Evolution of  Galaxies, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Shull & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Thronson, 345,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1007/978-94-011-1882-8 20  Verdes-Montenegro, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Del Olmo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Perea,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2005, A&A, 430, 443, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361:20047084  Verdes-Montenegro, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Williams, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  2001, A&A, 377, 812, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1051/0004-6361:20011127  Virtanen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Gommers, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Oliphant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020,  Nature Methods, 17, 261, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1038/s41592-019-0686-2  Wang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Kauffmann, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', J´ozsa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Li,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015, MNRAS, 449, 2010, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stv390  Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Catinella, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Saintonge, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2020, ApJ,  890, 63, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/ab68dd  Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Kauffmann, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', J´ozsa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013,  MNRAS, 433, 270, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/mnras/stt722  Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Immler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Walterbos, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Lauroesch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=',  & Breitschwerdt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001, ApJL, 555, L99,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/323179  Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Walterbos, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Steakley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=',  Norman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Braun, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1995, ApJ, 439, 176,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1086/175162  Weliachew, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Sancisi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Guelin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1978, A&A, 65, 37  Wolfe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Pisano, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Lockman, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', McGaugh,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Shaya, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013, Nature, 497, 224,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1038/nature12082  Yamasaki, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Sato, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Mitsuishi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Ohashi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2009,  PASJ, 61, S291, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1093/pasj/61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='sp1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='S291  Yu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Ho, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2022, ApJ, 930, 85,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4357/ac5f07  Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Ho, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', & Lo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1994, Nature, 372,  530, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1038/372530a0  Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Yu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2021, ApJL, 922, L21,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/2041-8213/ac350a  Zuo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Xu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2018, ApJS, 237, 2,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3847/1538-4365/aabd30  28  APPENDIX  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' THE AVERAGE BEAM IMAGE OF FAST  We derive a clean average beam image of the 19 beams, gridded in the same way as for the N4631 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use the  calibrated mapping data of point sources from Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2020) to derive the average beam of FAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The observation  was specifically designed to characterize the beam properties of FAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The data are in total 100 minutes’ mapping of  point sources in raster scan mode along right ascension or declination directions, with a high sampling rate of per 10′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We refer the readers to Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2020) for more details of the data and of the properties of the 19 beams of FAST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use the same procedure that has produced the NGC 4631 cube in this paper to make the images of the 19 beams  separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We note that, a different 2-dimensional interpolation method was used in Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2020) for gridding,  which is improper for the NGC 4631 data here whose sampling rate is much lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' After masking contaminating  sources in the neighborhood, we follow the steps in Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2020) and fit a skew Gaussian to each of the 19 beam  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We stack the images of the 19 beams after register them to the same Gaussian center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The stacking procedure  takes the 3-sigma clipped mean value for each pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The directly stacked beam image looks like a smoothed version of  beam 1 displayed in Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2020) because of additional smoothing in gridding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It has a central core surrounded  by a side-lobe ring, and then a axisymmetric periodical pattern with 6 broad peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It still has some noise patterns in  the background and imperfectness in the periodical pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We clean the beam image by first using the segmentation  function of the python package astropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='photutils to flag and mask the noise patterns in the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We then  perform a Fourier decomposition of the periodical pattern, and find that the pattern can be well represented by only  retaining the m = 6 mode of the Fourier components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' After these two steps, we obtain a relatively clean and average  beam image for the NGC 4631 FAST image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We show the directly stacked beam image, the cleaned beam image,  and a difference map of the two images in Figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  In Figure 18, we also present an azimuthally averaged radial profile of the cleaned beam image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Within a radius of  ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5′, the inner region of the profile is well fitted by a Gaussian function with a FWHM of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='24′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Beyond that, the real  beam deviate from the Gaussian approximation, with a level of around 1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The level of the first side-lobe is around  1/10 that of Arecibo (Heiles et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2001), indicating the power of FAST to map low-surface density, extended Hi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  However, the level also suggests that the scattered light due to side-lobes cannot be fully ignored when we investigate  extended Hi with column densities close to 1018cm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Therefore, in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6, we convolve the WSRT cube with the  real beam of FAST, before comparing the distribution of Hi fluxes between the WSRT and FAST data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We caution that, the beam shape of the NGC 4631 data may differ from the data of in Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2020), as  the observing times are quite different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Moreover, the beam shapes, particularly the side-lobes, differ between the 19  beams, as shown in Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' However, this average beam image is the best we can achieve with the resources  in hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' And, the variation among beams is an intrinsic systematic uncertainty of the 19-beam mapping, which is a  necessary compromise for the mapping efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' THE DISK AND TIDAL TAIL REGIONS OF NGC 4631  We manually separate the FAST-detected region of the NGC 4631 and NGC 4656 system by arbitrarily drawing a  line roughly along the disk direction of NGC 4656 (the white dashed line in Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We separate the WSRT-detected  NGC 4631 region into regions of the main disk and 4 tidal tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We firstly determine the region of the main disk of  NGC 4631 in the data cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We take the parameters of the kinematic model of the main disk of NGC 4631 from  Rand (1994), and use 3D-Barolo (Di Teodoro & Fraternali 2015) to make a 3 dimensional data cube based on the  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We arbitrarily take a density threshold equivalent to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='02% the peak density of the model to draw a mask  of the NGC 4631 disk region in the cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The region belonging to the two satellite galaxies NGC 4656 and Dwarf A  are already labeled by SoFiA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The cube space beyond the disk region of NGC 4631, NGC 4656 and Dwarf A, but are  within the SoFiA mask of the WSRT cube are considered the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The separation of the tail region into different tails is performed with the 3-dimensional watershed algorithm of the  python package skimage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The outputs are 3-dimensional flagging masks of the separate components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' A  previous study, Combes (1978) manually separated the tidal features into four tails, denoting them by number 1 to 4,  and used numerical simulation of interaction to reproduce the morphology and kinematics of these 4 tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The same  denoting system has been adopted by studies later to have a coherence context of discussion (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Rand 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Our  watershed results directly flag tail 3 and 4, but 1 and 2 are blended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We manually and arbitrarily draw a division line  in the sky plane to separate tail 1 from 2 in the blended region to qualitatively match the separation in Rand (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  29  75  50  25  0  25  50  75  x (arcmin)  80  60  40  20  0  20  40  60  80  y (arcmin)  stacked beam  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='5  level  75  50  25  0  25  50  75  x (arcmin)  80  60  40  20  0  20  40  60  80  y (arcmin)  cleaned beam  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  logf/fpeak  beam profile  Gaussian model  Figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The beam of the FAST Hi data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Top-left and top-right panels are the stacked beam and the cleaned beam  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The bottom panel is the azimuthally averaged radial profile of the beam, and its best-fit Gaussian model with a  FWHM of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='24′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The sky projected view of these regions are displayed in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' THE TEMPERATURE OF THE HOT GAS NEAR THE DISK  There are abundant studies in the literature on the properties of the X-ray emitting hot gas near the disk within a  distance of around 10 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This part of the hot gas halo mostly represents hot gas outflows from the galactic disk,  especially from its inner actively star-forming region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Therefore its temperature should be higher than, and can be  used as upper limit of that in a hydrostatic equilibrium in the galaxy’s potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (1995) used ROSAT data to detect the soft X-ray radiation of the hot gas of NGC 4631 out to 8 kpc  above the disk plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' They estimated a characteristic thermal temperature of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='03 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2001)  used Chandra to detect the halo out to a similar distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' They performed a 2-component thermal plasma model fit,  obtaining a hot component of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='61±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='12 keV close to the disk and a cooler component of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='18±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='02 keV dominating  the outer corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' As in this study we focus on the tidal Hi far away from the disk, we only take the temperature of  the further component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' T¨ullmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2006) used XMM-Newton to derive the temperature out of 3 stripes south  of the disk, and 5 stripes north of the disk, reaching out to nearly 11 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' They used 5 bands ranging from super-soft  to hard, so they managed to derive two characteristic temperatures for both a soft and a hard components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The  hard component has a mean temperature of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='03 keV, and a slightly higher but comparable number density of  IGM throughout the analysis regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The soft component has a temperature that is roughly 4 times lower, and we  thus take the temperature of the more energetic hard component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Finally, Yamasaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2009) used the Imaging  Spectrometer of Suzaku to trance X-ray halo out to about 10 kpc from the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' They fit 2-component thermal models  to the disk and the halo regions separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the halo region, the hard component of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='016 keV is dominating  over the soft component by 5 times more flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='30  Taking together these four sets of previous measurements, we calculate a mean value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='03 keV, equivalent  to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8 × 106 K, as the temperature of the hot gas halo within 10 kpc around the NGC 4631 disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' THE DARK MATTER HALO MASS OF N4631G  We use M500 as the fiducial measure of the dark matter halo mass, the mass within r500 the radius where the average  density is 500 times the critical density of the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Characteristic masses are also defined at alternative averaged  density levels, like M200 and M101 (the virial mass at redshift z= 0 in ΛCDM cosmology).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' They are convertible with  each other assuming a NFW model (Navarro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 1997) of the dark matter halo with a concentration index c∆ of 8,  as is expected for a halo of roughly 1012 M⊙ at redshift z = 0 (Dutton & Macci`o 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use the stellar mass-halo mass relation in Behroozi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2010) to derive a lower limit of log M500/M⊙ = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  It is viewed as a lower limit because from halo occupation distribution studies, dark matter halos with a mass around  1012 M⊙ should have the number of satellites which have stellar masses above 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='28 M⊙ far less than unity (Bose  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use the M500-IGM temperature relation from Reichert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2011), in combination with the characteristic  temperature of the near-disk hot gas summarized above, to derive an upper limit of log M500/M⊙ = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='13 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The N4631g can be found in the group catalog of Kourkchi & Tully (2017) with a PGC id of 42637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' From that  group catalog, it has 10 member galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' These member galaxies have a radial velocity dispersion σc of 217 km s−1,  and a projected gravitational radius Rg of 92 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Based on the equation of Tully (2015), we derivelog M500/M⊙ of  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' This value is between the lower and upper limits derived above, and is taken to be the final estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Accordingly, the r500, r200, and M200 of N4631g are 148 kpc, 224 kpc, and 1012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1 M⊙ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The corresponding  virial mass implies a virial temperature of 8×105 K, considerably lower than that of the X-ray emitting and outflowing  hot gas near the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' THE DENSITY OF THE HOT GAS HALO  We base on the M500 estimated in appendix D to derive M500,gas, the hot gas mass within R500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use the  M500,gas-M500 relations from Andreon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2017) and Ettori (2015), which derive log M500,gas/M⊙ of 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='56±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='17  and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='10 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The two values are consistent within the error bar, and we take the one with smaller  error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We consider a single-β model distribution of the IGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Following the specifics in Eckert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2011), we assume  the β value to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='64, and the core radius rc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='19r500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Cumulating the IGM model profile from center to R500,  we derive a central density of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='778×10−4 cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We also consider a double-β model, to match the fact that many  previous studies found two thermal components in the hot gas halo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Following Eckert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2011), we set the outer  component to have core radius rc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='03r500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We arbitrarily set the central density of the outer and inner components  to be equal, partly motivated by the fact that in T¨ullmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2006) the density of the hot and cold components are  roughly equal in the inner corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We plot both models in Figure 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Although the double-β model fit the measured  densities from Yamasaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2009) better, both models are close beyond a radius of 10 kpc in the IGM region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We  thus adopt the single-β model for simpler assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' AMPLITUDE SPECTRAL ANALYSIS THROUGHOUT APPLICABLE CHANNELS  To demonstrate the consistency of amplitudes cross the applicable channels (which have flux intensity greater than  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='15 Jy), we plot the relation between the normalized amplitudes of all these channels in the left panel of Figure 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The normalization factor of each channel is taken to be the maximum amplitude from the PB-attenuated FAST cube  in the selected angular scale range (4 to 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The data points distribute close to the y = x line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' To demonstrate the  deviation of critical angular scales, in the right panel of Figure 20, we show the relation between amplitude ratios and  angular scales from the selected channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Each curve represents the median relation from a channel map, and starts  from 4′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The curves start to exceed unity near the mean critical angular scale of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' MCMC RESULT OF DOUBLE-GAUSSIAN FIT TO THE SUPER PROFILES  We use emcee (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2013) to conduct a double-Gaussian fit to the super profile stacked from the  line-of-sights with single-Gaussian spectra in dense Hi in the tail region of the projected FAST cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The amplitude a  and σ of the narrow and broad Gaussian components are denoted by 1 and 2 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We also include a fraction  uncertainty of the model f in the fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The corner figure of probability distribution of parameters are displayed in  31  0  10  20  30  40  50  r (kpc)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8  lognICM (cm  3)  single  double  N  S  Figure 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  IGM density profiles of N4631g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The black and pink solid lines are the single and double-β models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The black  dashed lines are the 1-σ uncertainty range of the single-β model due to uncertainty in the estimate of M500,gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The blue and  cyan dots are measurements from Yamasaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2018) at distances from the north and south sides of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='0  AWSRT, normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='0  AFAST, normalized  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='4  log Angular scale (arcsec)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='3  log AFAST/AWSRT  Figure 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The comparison between amplitudes of amplitude spectra from the WSRT cube and PB-attenuated FAST cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Left: relation of normalized amplitudes from the two types of cubes selected from the angular scale range between 4′ and 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5′  as in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The dashed line mark the y = x line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Right: the median curves of the ratio of amplitudes from the two cubes  as a function of the angular scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Each curve corresponds to one channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The horizontal dashed line mark the y position of  zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The red vertical line marks the mean critical angular scale of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6′ for FAST amplitudes to exceed the WSRT amplitudes  by 1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The black vertical line marks the angular scale corresponding to the shortest baseline of the WSRT array configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Figure 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We do not find strong degeneracy between model parameters from the corner figures, where the probability  distribution are projected onto 2-dimensional diagrams of the parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The fractional uncertainty of the model is  low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' So the double-Gaussian model seems a good description of the super profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We do the same for the smoothed WSRT cube, and the original WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The results are displayed in Figure 22,  and 23 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The degeneracies of σ1 and σ2 with a1/(a1+a2) become stronger, but the probability distributions  are still relatively narrow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' So the double-Gaussian model seems still a reasonable description of the super profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The best-fit σ of the narrow and broad Gaussian components, and the ratio of peak intensities between  them are 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='37  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='33 km s−1, 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='43  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='39 km s−1, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='76+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='010  for the super profile of FAST data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  The values  are 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='29 km s−1, 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='63  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='38 km s−1, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='028  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='028 for the super profile of the smoothed WSRT cube, and  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='9+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='118  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='136 for the super profile of the WSRT cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  32  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='80  a1/(a1 + a2)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='8  log(f)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+page_content='0  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  2(kms  1)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8  log(f)  FAST (tail region)  Figure 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Corner figure of parameter probabilities of the double-Gaussian model for the Hi super profile of FAST data cube  in the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' USING CLOUDY TO PREDICT THE CRITICAL COLUMN DENSITY OF HI FOR PHOTON IONISATION  The procedure below is a modified version of the one described in Borthakur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We consider two sources contributing to the UV photons, the cosmic background UV radiation, and the photons from  the young stars in NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' For the UV photons associated with young stars, we use the equation from Tumlinson  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' (2011) to estimate the dimensionless ionisation parameter Ustar which depends on the SFR of NGC 4631 and  the distance squared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' It also assumes a uniform fraction of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='1 for the UV photons to escape from the interstellar  medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We have ignored the UV photons from NGC 4656, as its SFR is around one fourth, thus the distance to  have the same level of Ustar is half that of NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The UV photons from NGC 4656 only start to be important  when the distance from NGC 4631 is larger than 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5 kpc along the direction connecting these two galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Diffuse  stellar features have been found around NGC 4631, but mostly consisting of old stars (Mart´ınez-Delgado et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2015),  unlikely to provide additional UV photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We use starburst99 (Leitherer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' 2010) to generate a young stellar population with a solar metallicity and an age  of 4 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use the spectral energy distribution of this stellar population as input for Cloudy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We generate a three  dimensional grid of hydrogen density nH, the hydrogen column density NH, and the stellar ionisation parameter Ustar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  log nH ranges from -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6 to -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8 with a step of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2, log NH range 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5 to 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5 with a step of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='25, and Ustar from -6 to  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4 with a step of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use the default “background” and “Background cosmic ray”, to add the ionizing effects  of the cosmic UV background and the cosmic ray background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' In the top panel of Figure 24, we plot the resulting  33  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  1(kms  1)  12  14  16  18  2(kms  1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='75  a1/(a1 + a2)  8  6  4  log(f)  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  1(kms  1)  12  14  16  18  2(kms  1)  8  6  4  log(f)  WSRT (tail region)  Figure 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Corner figure of parameter probabilities of the double-Gaussian model for the Hi super profile of WSRT data cube  in the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  neutral fraction of hydrogen (NHI/NH), as a function of log NHI in different bins of U, fixing log nHI at -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We can  see that toward the low values of Ustar (dark purple), NHI/NH converges to the highest possible value at a given NHI,  because the comic UV background starts to dominate there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Setting NHI/NH = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5, we derive the critical Hi column  density (NHI,c,ion) from each curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We plot NHI,c,ion as a function of Ustar for different values of nH in the righ panel  of Figure 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We assume nH = 2nHI, and interpolate in this parameter space to derive the critical column density of  Hi as a function of distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We plot NHI,c,ion as a function of radius to NGC 4631 in the right panel of Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The values of NHI,c,ion flatten  around 1019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2 cm−2 beyond a distance of 30 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The value of 1019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2 cm−2 is close to many previously derived when  only accounting for the cosmic background of UV radiation (Maloney 1993), but if we remove the effect of young stars  in NGC 4631, NHI,c,ion would drop to one third of its current value at a radius of 30 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  We note that the leakage fraction of UV photons, the extent of shielding by Hi in tails at smaller distances, the  lack of information on the filling factor and clumpiness of Hi, and the contribution of ionizing energy from shocks, are  major sources of uncertainties in the deviation of the ionisation related parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' THE GRAVITATIONAL POTENTIAL AROUND NGC 4631  We use galpy (Bovy 2015) to model the mass distribution and gravitational potential around NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' We use the  Miyamoto-Nagai model with the Milky Way specifics (scale length 3 kpc and scale height 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='28 kpc) to represent the  34  12  13  14  15  1(kms  1)  27  30  33  36  39  2(kms  1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='66  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='84  a1/(a1 + a2)  8  6  4  log(f)  12  13  14  15  1(kms  1)  27  30  33  36  39  2(kms  1)  8  6  4  log(f)  WSRT (tail region, smoothed)  Figure 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Corner figure of parameter probabilities of the double-Gaussian model for the Hi super profile of smoothed WSRT  data cube in the tail region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  disk, the NFW model with scale radius equal to r200/c∆ to represent the dark matter, and use the rotational velocity  of 145 km s−1 at a radius of 8 kpc (Rand 1994) to calibrate the normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The resulted mass model has a disk  mass of 1010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2 M⊙ within 8 kpc, and a halo mass of 1012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='02 M⊙ within r500 derived in appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Thus the mass  model is close to the observed stellar mass and M500 of NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Then we use the evaluatePotentials task of galpy  to evaluate the potential distribution around NGC 4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  35  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  logNHI(cm  2)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  logNHI/NH  Ionization by UV photons from stars and background  6  5  4  3  2  Ustar  18  19  20  21  logNHI, c, ion(cm  2)  nH = -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  nH = -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4  nH = -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2  nH = -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='0  nH = -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='8  nH = -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='6  nH = -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4  Figure 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Photon ionisation of hydrogen in grids of stellar ionisation parameter, hydrogen density and hydrogen column  density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='  Left: the neutral ratio of hydrogen, NHI/NH, is plotted as a function of the Hi column density in bins of stellar  ionisation parameter Ustar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The values of Ustar range from -6 to -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='4 with a linear step of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content='2, and the curves in lighter purple  colors correspond to higher values of Ustar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The dashed, horizontal line mark where the neutral ratio is 50%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' Right: the critical  Hi column density, where the ionisation or neutral ratio is 50%, as a function of Ustar in different bins of nH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
+page_content=' The darker blue  colors correspond to lower values of nH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAzT4oBgHgl3EQfA_rZ/content/2301.00937v1.pdf'}
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+arXiv:2301.05470v1  [math.AG]  13 Jan 2023
+LOOP GROUP SCHEMES AND ABHYANKAR’S LEMMA
+P. GILLE
+Abstract. We define the notion of reductive group schemes defined over the lo-
+calization of a regular henselian ring A at a strict normal crossing divisor D. We
+provide a criterion for the existence for parabolic subgroups of a given type.
+Keywords: Reductive group schemes, normal crossing divisor, parabolic subgroups.
+MSC 2000: 14L15, 20G15, 20G35.
+1. Introduction
+In the reference [7], we investigated a theory of loop reductive group schemes over
+the ring of Laurent polynomials k[t±1
+1 , . . . , t±1
+n ]. Using Bruhat-Tits’ theory, this per-
+mitted to relate the study of those group schemes to that of reductive algebraic groups
+over the field of iterated Laurent series k((t1)) . . . ((tn)). The main issue of this note is
+to start a similar approach for reductive group schemes defined over the localization
+AD of a regular henselian ring A at a strict normal crossing divisor D and to relate
+with algebraic groups defined over a natural field associated to A and D, namely
+the completion Kv of the fraction field K with respect to the valuation arising from
+the blow-up of Spec(A) at its maximal ideal. The example which connects the two
+viewpoints is k[[t1, . . . , tn]][ 1
+t1, . . . 1
+tn] where Kv ∼= k
+� t1
+tn, . . . ,
+t1
+tn−1 )((tn))
+After defining the notion of loop reductive group schemes in this setting, we show
+that for this class of group schemes, the existence of parabolic subgroups over the
+localization AD is controlled by the parabolic subgroups over Kv (Theorem 4.1).
+Acknowledgements. We thank R. Parimala for her insight about the presented
+results.
+2. Tame fundamental group
+2.1. Abhyankar’s lemma. Let X = Spec(A) be a regular local scheme. Let k be
+the residue field of A and p ≥ 0 be its characteristic. We put �Z′ = �
+l̸=p Zl. Let K
+be the fraction field of A, and let Ks be a separable closure of K. It determines a
+base point ξ : Spec(K) → X so that we can deal with the Grothendieck fundamental
+group Π1(X, ξ) [10].
+Date: January 16, 2023.
+1
+
+2
+P. GILLE
+Let (f1, . . . , fr) be a regular sequence of A and consider the divisor D = � Di =
+� div(fi), it has strict normal crossing. We put U = X \ D = Spec(AD).
+We recall that a finite étale cover V → U is tamely ramified with respect to D if the
+associated étale K–algebra L = L1 × · · · × La is tamely ramified at the D′
+is, that is,
+for each i, there exists ji such that for the Galois closure �Lji/K of Lji/K, the inertia
+group associated to vDi has order prime to p [10, XIII.2.0].
+Grothendieck and Murre defined the tame (modéré in French) fundamental group
+ΠD
+1 (U, ξ) with respect to U ⊂ X as defined in [10, XIII.2.1.3] and [8, §2]. This is
+a profinite quotient of Π1(U, ξ) whose quotients by open subgroups provides finite
+Galois tame cover of U.
+We are given a finite étale tame cover V → U. In this case Abhyankar’s lemma
+states that there exists a flat Kummer cover X′ = Spec(A′) → X where
+A′ = A[T1, . . . , Tr]/(T n1
+1
+− f1, . . . , T nr
+r
+− fr)
+and the ni’s are coprime to p such that V ′ = V ×X X′ → X′ extends uniquely to a
+finite étale cover Y ′ → X′ [10, XIII.5.2].
+Lemma 2.1. Let V → U be a finite étale cover which is tame. Then Pic(V ) = 0.
+Proof. We use the some notation as above. We know that X′ is regular [10, XIII.5.1] so
+a fortiori locally factorial. It follows that the restriction maps Pic(X′) → Pic(V ′) →
+Pic(V ) are surjective [5, 21.6.11]. Since A′ is finite over the local ring A, it is semilocal
+so that Pic(A′) = Pic(X′) = 0. Thus Pic(V ) = 0 as desired.
+□
+From now on we assume that A is henselian. According to [5, 18.5.10], the finite
+A–ring A′ is a finite product of henselian local rings. We observe that A′ ⊗A k =
+k[T1, . . . , Tr]/(T n1
+1 , . . . , T nr
+r ) is a local Artinian algebra so that A′ is connected. It
+follows that A′ is a henselian local ring. Its maximal ideal is m′ = m⊗AA′+⟨T1, . . . , Tr⟩
+so that A′/m′ = k. Since there is an equivalence of categories between finite étale
+covers of A (resp. A′) and étale k–algebras [5, 18.5.15], the base change from A to
+A′ provides an equivalence of categories between the category of finite étale covers of
+A and that of A′.
+It follows that Y ′ → X′ descends uniquely to a finite étale cover �f : �Y → X. From
+now on, we assume that V is furthermore connected, it implies that
+H0(V, OV ) = B[T1, . . . , Tr]/(T n
+1 − f1, . . . , T n
+r − fr)
+where B is finite connected étale cover of A. If follows that V → U is a quotient of
+a Galois cover of the shape
+Bn = B[T ±1
+1 , . . . , T ±1
+r ]/(T n
+1 − f1, . . . , T n
+r − fr)
+where B is Galois cover of A containing a primitive n–root of unity. We record that
+Bn is the localization at T1 . . . Tr of B′
+n = B[T1, . . . , Tr]/(T n
+1 − f1, . . . , T n
+r − fr). We
+
+LOOP GROUP SCHEMES AND ABHYANKAR’S LEMMA
+3
+have
+Gal(Bn/AD) =
+� r�
+i=1
+µn(B)
+�
+⋊ Gal(B/A).
+Passing to the limit we obtain an isomorphism
+πt
+1(U, ξ) ∼=
+� r�
+i=1
+�Z′(1)
+�
+⋊ π1(X, ξ).
+We denote by f : Usc,t → U the profinite étale cover associated to the quotient
+πt
+1(U, ξ) of π1(U, ξ). According to [8, thm. 2.4.2], it is the universal tamely ramified
+cover of U. It is a localization of the inductive limit �B′ of the B′
+n. On the other hand
+we consider the inductive limit �B of the B’s and se that �B′ is a �B-ring.
+2.2. Blow-up. We follow a blowing-up construction arising from [5, lemma 15.1.1.6].
+We denote by X the blow-up of Spec(A) at his closed point, this is a regular scheme
+[9, §8.1, th. 1.19] and the exceptional divisor E ⊂ X is a Cartier divisor isomomorphic
+to Pr−1
+k
+. We denote by R = OX,η the local ring at the generic point η of E. The ring
+R is a DVR of fraction field K and of residue field F = k(E) = k(t1, . . . , tr−1) where
+ti is the image of fi
+fr ∈ R by the specialization map. We denote by v : K× → Z the
+discrete valuation associated to R.
+We deal now with a Galois extension Bn of AD as above. Since B is a connected
+finite étale cover of A, B is regular and local; it is furthermore henselian [5, 18.5.10].
+We denote by L the field of fraction of B and by Ln that of Bn. We have [Ln : L] = nr.
+We want to extend the valuation v to L and to Ln.
+We denote by l = B/mB the residue field of B, this is a finite Galois field extension
+of k. Also (t1, . . . , tr) is a system of parameters for B. We denote by w : L× → Z the
+discrete valuation associated to the exceptional divisor of the blow-up of Spec(B) at
+its closed point. Then w extends v and Lw/Kv is an unramified extension of degree
+[L : K] and of residual extension Fl = l(t1, . . . , tr−1)/k(t1, . . . , tr−1).
+On the other hand we denote by wn : L×
+n → Z the discrete valuation associated to
+the exceptional divisor of the blow-up of Spec(Bn) at its closed point. We put ln =
+Bn/mBn, we have l = ln. The valuation wn
+n on Ln extends w and its residual extension
+is Fl,n = l
+�
+t1/n
+1
+, . . . , t1/n
+r−1
+�
+/k
+�
+t1, . . . , tr−1
+�
+so that [Fl,n : Fl] = nr−1. Furthermore the
+ramification index en of Ln/L is ≥ n. Since nr ≤ en [Fl,n : Fl] ≤ [Ln : K] = nr(where
+the last inequality is [2, §VI.3, prop. 2]) it follows that en = n. The same statement
+shows that the map Lw ⊗L Ln → Lwn is an isomorphism. To summarize Lwn/Lw
+is tamely ramified of ramification index n and of degree nr. All together we have
+Lwn = Lw ⊗K Ln so that Lwn is Galois over Kv of group �
+i µn(B) ⋊ Gal(B/A) =
+�
+i µn(l) ⋊ Gal(l/k).
+
+4
+P. GILLE
+We denote by ∆ : µn(l) ⊂ �
+i µn(l) the diagonal subgroup. We put L∆
+wn = L∆(µn(B))
+n
+.
+Since tr is an uniformizing parameter of Kv and since ∆(ζ) . tr = ζ.tr for each ζ ∈
+µn(B), it follows that (Lwn)∆ is the maximal unramified extension of Lwn/Kv.
+2.3. Loop cocycles and loop torsors. Let G be an affine X–group scheme locally
+of finite presentation. A loop cocycle is an element of Z1�
+πt
+1(U), G( �B)
+�
+and it defines a
+Galois cocycle in Z1(πt
+1(U), G(Usc,t)). We denote by Z1
+loop(πt
+1(U), G(Usc,t)) the image
+of the map Z1�
+πt
+1(U), G( �B)
+�
+→ Z1(πt
+1(U), G(Usc,t)) and by H1
+loop(U, G) the image of
+the map
+Z1�
+πt
+1(U), G( �B)
+�
+→ H1(πt
+1(U), G(Usc,t)) → H1(U, G).
+We say that a G-torsor E over U (resp. a fppf sheaf G-torsor) is a loop torsor if its
+class belongs to H1
+loop(U, G) ⊂ H1(U, G).
+A given class γ ∈ H1
+loop(U, G) is represented by a 1–cocycle φ : Gal(Bn/AD) →
+G(B) for some cover Bn/A as above.
+Its restriction φar : Gal(B/A) → G(B) to
+the subgroup Gal(B/A) of Gal(Bn/A) is called the “arithmetic part” and the other
+restriction φgeo : �
+i µn(B) → G(B) is called the geometric part. We observe that
+φgeo is a B-group homomorphism.
+Furthermore for σ ∈ Gal(B/A) and τ ∈ �
+i µn(B) the computation of [7, page 16]
+shows that φgeo(στσ−1) = φar(σ) σφ(τ) φar(σ)−1 so that φgeo descends to a homomor-
+phism of A-group schemes φgeo : µr
+n → φarG. This provides a parameterization of loop
+cocycles.
+Lemma 2.2. (1) For Bn/A as above, the map φ �→ (φar, φgeo) provides a bijection be-
+tween Z1
+loop
+�
+Gal(Bn/AD), G(B)
+�
+and the couples (z, η) where z ∈ Z1�
+Gal(B/A), G(B))
+and η : �
+i µn → zG is an A–group homomorphism.
+(2) The map φ �→ (φar, φgeo) provides a bijection between Z1
+loop
+�
+π1(U, ξ)t, G( �B)
+�
+and
+the couples (z, η) where z ∈ Z1�
+π1(X, ξ), G( �B)) and η : �r
+i=1 �Z′ → zG is an A–group
+homomorphism.
+Proof. This is similar with [7, lemma 3.7].
+□
+We examine more closely the case of a finite étale X–group scheme F of constant
+degree d.
+Lemma 2.3. (1) F( �B) = F(Xsc) = F(Usc,t).
+(2) We assume that d is prime to p. We have H1
+loop(U, F) = H1(U, F).
+(3) We assume that d is prime to p. Let f : F → H be a homomorphism of A–group
+schemes (locally of finite type). Then f∗
+�
+H1(U, F)
+�
+⊂ H1
+loop(U, H).
+Proof. (1) We are given a cover Bn/A as above such that FBn ∼= ΓBn is finite constant.
+as above.
+Since B and Bn are connected, the map F(B) → F(Bn) reads as the
+
+LOOP GROUP SCHEMES AND ABHYANKAR’S LEMMA
+5
+identity Γ ∼= F(B) → F(Bn) ∼= Γ so is bijective. By passing to the limit we get
+F( �B) = F(Usc,t).
+(2) Let E be a F–torsor over U. This is a finite étale U–scheme. Since U is noetherian
+and connected, we have a decomposition E = V1 ×U · · · ×U Vl where each Vi is a
+connected finite étale U–scheme of constant degree di. We have d1 + · · · + dl = d so
+that we can assume that d1 is prime to p. We have then E(V1) ̸= ∅.
+It follows that f1 : V1 → U is a finite étale cover so that there exists a fac-
+torization Usc,t → V1
+h−→ U of f so that E(Usc,t) ̸= ∅.
+Therefore [E] arises from
+H1(πt
+1(U, ξ), F(Usc,t)) ⊂ H1(U, F). It follows that H1(πt
+1(U, ξ), F(Usc,t))
+∼
+−→ H1(U, F).
+We use now (1) and obtain the desired bijection H1(πt
+1(U, ξ), F(B))
+∼
+−→ H1(U, F).
+(3) This follows readily from (2).
+□
+2.4. Twisting by loop torsors. We assume that the A–group scheme G acts on an
+A–scheme Z. Let φ : (�r
+i µn)(B) ⋊ Gal(B/A) → G(B) be a loop cocycle. It gives
+rise to an A–action of µr
+n on φarZ. We denote by (φarZ)φgeo the fixed point locus for
+this action, it is representable by a closed A–subscheme of φarZ [4, A.8.10.(1)]. We
+have a closed embedding (φarZ)φgeo ×X U ⊂ φZ of U-schemes.
+3. Fixed points method
+Theorem 3.1. Let X = Spec(A) be a henselian regular local scheme and U = X\D as
+above. We denote by v : K× → Z the discrete valuation associated to the exceptional
+divisor E of the blow-up of X at its closed point.
+Let G be an affine A-group scheme of finite presentation acting on a proper smooth
+A–scheme Z. Let φ be a loop cocycle for G. Then Y =
+�
+φarZ
+�φgeo
+is a smooth proper
+A–scheme and the following are equivalent:
+(i) (φZ)(Kv) ̸= ∅;
+(ii) Y (k) ̸= ∅;
+(iii) Y (U) ̸= ∅;
+(iv) (φZ)(U) ̸= ∅.
+This is quite similar with the fixed point theorem [7, §, thm. 7.1]. The following
+example makes the connection.
+Example
+3.2. We
+assume
+that
+A
+=
+k[[t1, . . . , tr]]
+for
+a
+field
+k
+and
+k[U] = k[[t1, . . . , tn]]
+� 1
+t1, . . . , 1
+tr
+�
+. We are given an affine algebraic k–group G act-
+ing on a smooth proper k–scheme Z. In this case K = k((t1, . . . , tr)) and A embeds
+in k
+� t1
+tr , . . . , tr−1
+tr
+�
+[[tr]] so that K embeds in k
+� t1
+tn, . . . , tr−1
+tr
+�
+((tr)) which is nothing but
+the complete field Kv. If Q is a loop G-torsor over U, the statement is then that
+QZ(U) ̸= ∅ if and only if QZ(Kv) ̸= ∅. Taking a cocycle φ ∈ Z1(π1(U)t, G(ks)) for E,
+this rephrases by the equivalence between (φZ)(U) ̸= ∅ and (φZ)(Kv) ̸= ∅.
+
+6
+P. GILLE
+What we have from [7, thm. 7.1] (in characteristic zero but this extends to this tame
+setting) is the equivalence between (φZ)(k[t±1
+1 , . . . , t±1
+r ]) ̸= ∅ and (φZ)
+�
+k((t1)) . . . ((tr))
+�
+̸=
+∅. Since (φZ)(k[t±1
+1 , . . . , t±1
+r ]) ⊂ (φZ)(U) and (φZ)
+�
+Kv
+�
+⊂ (φZ)
+�
+k((t1)) . . . ((tr))
+�
+, it
+follows that this special case of Theorem 3.1 is a consequence of the fixed point result
+of [7].
+We proceed to the proof of Theorem 3.1.
+Proof. According to [4, A.8.10.(1)], Y =
+�
+φar(Zφgeo)
+�
+is a closed A–scheme of φarZ so
+is proper. It is smooth over X according to point (2) of the same reference.
+Let φ : Gal(Bn/AD) → G(B) be the loop 1-cocycle for some Galois cover Bn/AD as
+above for some n prime to p. Up to replace G by φarG and G by φarZ, we can assume
+that φar = 1 without lost of generality.
+(ii) =⇒ (iii). Since Yk is the special fiber of the smooth X–scheme Y , Hensel’s lemma
+shows that Y (A) → Y (k) is onto. Since Y (k) is not empty, it follows that Y (A) is
+not empty and so is Y (U).
+(iii) =⇒ (iv). Since Y (U) ⊂ φZ(U), Y (U) ̸= ∅ implies that φZ(U) ̸= ∅.
+(iv) =⇒ (i). This is obvious.
+(i) =⇒ (ii). We assume that (φZ)(Kv) ̸= ∅. By definition we have
+(φZ)(Kv) =
+�
+z ∈ Z(Lwn) | φ(σ).σ(z) = z ∀σ ∈ Gal(Ln/K)
+�
+and our assumption is that this set is non-empty. Let Own be the valuation ring of
+Z(Lwn). Since Z is proper over X, we have a specialization map Z(Lwn) = Z(Own) →
+Zk(Fl,n). We get that the set
+�
+z ∈ Zk(Fl,n), | φ(σ).σ(z) = z ∀σ ∈ Gal(Lwn/Kv)
+�
+is not empty. Since we have an embedding
+Fl,n = l
+�
+t1/n
+1
+, . . . , tr−1) ֒→ l
+��
+t1/n
+1
+��
+. . .
+��
+t1/n
+r−1
+��
+in a higher field of Laurent series successive specializations, along the coordinates
+t1/n
+1
+, ..., t1/n
+r−1 show similarly that the set
+(3.1)
+�
+z ∈ (Zk)
+�
+l
+�
+| φ(σ).σ(z) = z ∀σ ∈ Gal(Lwn/Kv)
+�
+is not empty. Since ηar = 1, this set is (Zk)ηgeo(k). Thus Y (k) = (Zk)ηgeo(k) is non
+empty.
+□
+4. Parabolic subgroups of loop reductive group schemes
+4.1. Chevalley groups. Let G0 be Chevalley group defined over Z. Let T0 be a
+maximal split Z-subtorus of G0 together with a Borel subgroup B0 containing it. We
+denote by ∆0 the Dynkin diagram of (G0, B0, T0). We denote by G0,ad the adjoint
+
+LOOP GROUP SCHEMES AND ABHYANKAR’S LEMMA
+7
+quotient of G0 and by Gsc
+0 the simply connected covering of DG0. We have a map
+Aut(G0) → Aut(Gsc
+0 )
+∼
+−→ Aut(G0,ad) and a fundamental exact sequence
+1 → G0,ad → Aut(G0,ad) → Out(G0,ad) → 1
+where Out(G0,ad)
+∼
+−→ Aut(∆0) We recall that there is a bijection I → P0,I be-
+tween the finite subsets of ∆0 and the parabolic subgroups of G0 containing B0
+[11, XXVI.3.8]; it is increasing for the inclusion order, in particular B0 = P0,∅ and
+G0 = P0,∆0. We consider the total scheme ParG0 of parabolic subgroups of G0, it is
+a projective smooth Z–scheme equipped with a type map t : ParG0 → Of(∆0) where
+Of(∆0) stands for the finite constant scheme attached to the set of subsets of ∆0 [11,
+XXVI.3]. The fiber at I is denoted by ParG0,I, it has connected fibers and is the
+scheme of parabolic subgroups of G0 of type I. We have a natural action of Aut(G0)
+on ParG0. As in [6, §5.1], we denote by AutI(G0) the stabilizer of I for this action.
+By construction AutI(G0) acts on ParG0,I.
+4.2. Definition. Let G be a reductive U-group scheme in the sense of Demazure-
+Grothendieck [11, XIX]. Since U is connected and G is locally splittable [11, XXII.2.2]
+for the étale topology, G is an étale form of a Chevalley group G0 as above defined
+over Z.
+We say that G is a loop group scheme if the Aut(G0)-torsor Q = Isom(G0, G)
+(defined in [11, XXIV.1.9]) is a loop Aut(G0)-torsor. We denote by G0,ad the adjoint
+quotient of G0 and ny Gsc
+0 the simply connected covering of DG0. We have a map
+Aut(G0) → Aut(Gsc
+0 )
+∼
+−→ Aut(G0,ad) which permits to see Gad (resp. Gsc) as twisted
+forms of G0,ad (resp. Gsc
+0 ) so that Gad and Gsc are also loop reductive group schemes.
+We consider the map Aut(G0) → Aut(G0,ad) → Out(G0,ad)
+∼
+−→ Aut(∆0).
+If φ : Gal(Bn/A) → Aut(G0)(B) is a loop cocycle, we get an action of Gal(Bn/A)
+on ∆0 called the star action. If I is stable under the star action, we can twist ParG0,I
+by φ and deal with the scheme φParG0,I which is the scheme of parabolic subgroup
+schemes of G of type I.
+4.3. Parabolics.
+Theorem 4.1. Assume that G is a loop U-group scheme and let φ : Gal(Bn/AD) →
+Aut(G0)(B) be a loop cocycle such that G ∼= φG0. Let I ⊂ ∆0 be a subset stable under
+the star action defined by φ. Then the following are equivalent:
+(i) G admits a U–parabolic subgroup of type I;
+(ii) the k–morphism ηgeo
+k
+: µr
+n → Aut(ηarG0)k =
+�
+ηarAut(G0)
+�
+k normalizes a para-
+bolic k–subgroup of ηarG0,k of type I;
+(iii) GKv admits a parabolic subgroup of type I.
+Proof. Without loss of generality we can assume that G is adjoint. Our assumption
+on the star action rephrases by saying that φ takes values in AutI(G0).
+
+8
+P. GILLE
+We apply Theorem 3.1 to the action of AutI(G0) on the proper A-scheme ParG0,I.
+We consider the A-scheme Y = (φarParG0,I)φgeo. Theorem 3.1 shows that the following
+statements are equivalent.
+(i’) (φParG0,I)(U) ̸= ∅;
+(ii’) Y (k) ̸= ∅.
+(iii’) (φParG0,I)(Kv) ̸= ∅.
+Clearly (i’) is equivalent to condition (i) of the Theorem and similarly we have
+(iii′) ⇐⇒ (iii). It remains to establish the equivalence between (ii) and (ii’).
+Assume that (φarParG0,I)φgeo(k) is not empty and pick a k–point z. Then the sta-
+bilizer (φarG0)z is a k–parabolic subgroup of φarG0 of type I which is stabilized by the
+action φgeo
+k . In other words, φgeo
+k
+normalizes (φarG)z. Conversely we assume that φarG
+admits a k–parabolic subgroup of type I normalized by φgeo.
+Conversely assume that φarG admits a k–parabolic parabolic k–subgroup of type I
+normalized by φgeo. It defines then a point z ∈ (φarParG0,I)(k) which is fixed by φgeo.
+□
+4.4. An example. Assume that the residue field k is not of characteristic two and
+consider the diagonal quadratic form of dimension 2r
+q =
+�
+I⊂{1,...,r}
+uI tI(xI)2
+where tI = �
+i∈I ti and uI ∈ A×. Then SO(q) is a loop reductive group scheme over
+U. Since the projective quadric {q = 0} is a scheme of parabolic subgroups of SO(q),
+Theorem 4.1 shows that q is isotropic over AD if and only if q is isotropic over Kv.
+The two dimensional case is related with [3, proof of Theorem 3.1].
+References
+[1] A. Borel, Linear algebraic groups, 2nd edn, Graduate Texts in Mathematics 126 (Springer, New
+York, 1991).
+[2] N. Bourbaki, Algèbre commutative, Ch. 1 à 10, Springer.
+[3] J.-L. Colliot-Thélène, R. Parimala, V. Suresh, Patching and local-global principles for homoge-
+neous spaces over function fields of p-adic curves, Comment. Math. Helv. 87 (2012), 1011-1033.
+[4] B. Conrad, O. Gabber, G. Prasad, Pseudo-reductive groups, Cambridge University Press, second
+edition (2016).
+[5] A. Grothendieck (avec la collaboration de J. Dieudonné), Eléments de Géométrie Algébrique
+IV, Publications mathématiques de l’I.H.É.S. no 20, 24, 28 and 32 (1964 - 1967).
+[6] P. Gille, Sur la classification des schémas en groupes semi-simples, “Autour des schémas en
+groupes, III”, Panoramas et Synthèses 47 (2015), 39-110.
+[7] P. Gille and A. Pianzola, Torsors, reductive group schemes and extended affine Lie algebras,
+Memoirs of AMS 1063 (2013).
+[8] A. Grothendieck, J. P. Murre, The tame fundamental group of a formal neighbourhood of a
+divisor with normal crossings on a scheme, Lecture Notes in Mathematics 208 (1971), Springer-
+Verlag, Berlin-New York.
+
+LOOP GROUP SCHEMES AND ABHYANKAR’S LEMMA
+9
+[9] Q. Liu, Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics 6
+(2002), Oxford University Press, Oxford.
+[10] Séminaire de Géométrie algébrique de l’I.H.E.S., Revêtements étales et groupe fondamental,
+dirigé par A. Grothendieck, Documents mathématiques vol. 3 (2003), Société mathématique de
+France.
+[11] Séminaire de Géométrie algébrique de l’I. H. E. S., 1963-1964, schémas en groupes, dirigé par
+M. Demazure et A. Grothendieck, Lecture Notes in Math. 151-153. Springer (1970).
+UMR 5208 Institut Camille Jordan - Université Claude Bernard Lyon 1 43 boule-
+vard du 11 novembre 1918 69622 Villeurbanne cedex - France
+Email address: gille@math.univ-lyon1.fr
+
diff --git a/ttFKT4oBgHgl3EQf2y5g/content/tmp_files/2301.11925v1.pdf.txt b/ttFKT4oBgHgl3EQf2y5g/content/tmp_files/2301.11925v1.pdf.txt
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--- /dev/null
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@@ -0,0 +1,659 @@
+OCTUPOLES FOR OCTAHEDRAL SYMMETRY
+YU. NESTERENKO
+Abstract. Spherical harmonics of degree 4 are widely used in volumetric
+frame fields design due to their ability to reproduce octahedral symmetry.
+In this paper we show how to use harmonics of degree 3 (octupoles) for the
+same purpose, thereby reducing number of parameters and computational
+complexity. The key ingredients of the presented approach are
+• implicit equations for the manifold of octupoles possessing octahedral
+symmetry up to multiplication by −1,
+• corresponding rotationally invariant measure of octupole’s deviation
+from the specified symmetry,
+• smoothing penalty term compensating the lack of octupoles’ symme-
+tries during a field optimization.
+1. Introduction
+The most common state-of-the-art approaches for volumetric frame fields de-
+sign involve the use of 4th-degree spherical harmonics as a representation of
+field values (see [7, 11]). This choice is quite natural due to the fact that such
+harmonics form the linear space closed under 3D rotations and containing har-
+monics possessing octahedral symmetry. Moreover, algebraic conditions for this
+symmetry expressed both in terms of implicit equations and penalty function
+are also known ([10]).
+The major practical disadvantage of this representation is the dimension of
+the space — 9, which is three times the minimum required to parameterise
+frame rotations. In this paper we show how to reduce the dimension by passing
+from the 4th-degree spherical harmonics to the 3rd-degree ones also known as
+octupoles (see Landau and Lifshitz [9] clarifying the connection with the tensor
+formalism).
+In a nutshell, our suggestion is to sacrifice the half of symmetries of frame repre-
+sentation, but compensating for this by additional symmetries in the smoothing
+penalty term.
+Figure 1.
+Spherical plots of basis functions Y3,−3, . . . , Y3,3.
+arXiv:2301.11925v1  [math.NA]  23 Jan 2023
+
+2
+YU. NESTERENKO
+2. Semisymmetric octupoles
+As stated, we consider real-valued spherical harmonics of degree 3 on the unit
+sphere — octupoles. These polynomials form the 7D linear space with standard
+orthonormal basis Y3,−3, . . . , Y3,3 (see [6]).
+With them being odd functions, none of the octupoles (except zero) are oc-
+tahedrally symmetric by itself, but some of their modules are. Two of such
+semisymmetric octupoles — Y3,−2 and Y3,2 — possessing the half of octahedral
+symmetries (while the remaining are satisfied up to multiplication by −1) can
+be seen in Figure 1.
+Since the space we are working in is an eigenspace of the Laplace operator, all
+possible rotations of its functions lie in the same space and may be represented
+as a linear combinations of its basis functions.
+Figure 2.
+The reference harmonic and its rotation.
+This applies in particular to semisymmetric harmonics. Moreover, in coordinate
+form all harmonics of this kind may be obtained from a reference one (let it be
+Y3,−2) by the formula
+a = Rx(α) × Ry(β) × Rz(γ) × ˜a.
+Here ˜a = (0, 1, 0, 0, 0, 0, 0)T and a are coordinates of the reference and the
+rotated harmonics respectively, and α, β and γ are Euler angles of the corre-
+sponding rotation.
+Appendix A.1 describes the construction of the rotation matrices Rx, Ry and
+Rz.
+From the geometrical point of view, all a(α, β, γ) form the manifold of dimension
+3 embedded in R7. The next lemma claims that this manifold is simply an
+intersection of quadrics (hypersurfaces of the second order).
+Lemma 1. The manifold of all semisymmetric octupoles is given by the system
+of equations
+(2.1)
+�
+aT a = 1,
+aT Mk a = 0,
+k = 1, . . . , 3,
+
+R
+~h
+hOCTUPOLES FOR OCTAHEDRAL SYMMETRY
+3
+where M1, M2, M3 are the symmetric matrices defined as follows.
+(2.2)
+M1 =
+�
+���������
+−5
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+3
+0
+0
+0
+0
+0
+0
+0
+4
+0
+0
+0
+0
+0
+0
+0
+3
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+0
+−5
+�
+���������
+(2.3)
+M2 =
+�
+���������
+0
+5
+0
+0
+0
+0
+0
+5
+0
+√
+15
+0
+0
+0
+0
+0
+√
+15
+0
+0
+0
+0
+0
+0
+0
+0
+0
+2
+0
+0
+0
+0
+0
+2
+0
+√
+15
+0
+0
+0
+0
+0
+√
+15
+0
+5
+0
+0
+0
+0
+0
+5
+0
+�
+���������
+(2.4)
+M3 =
+�
+���������
+0
+0
+0
+0
+0
+5
+0
+0
+0
+0
+0
+√
+15
+0
+−5
+0
+0
+0
+2
+0
+−
+√
+15
+0
+0
+0
+2
+0
+0
+0
+0
+0
+√
+15
+0
+0
+0
+0
+0
+5
+0
+−
+√
+15
+0
+0
+0
+0
+0
+−5
+0
+0
+0
+0
+0
+�
+���������
+Idea of proof. The given implicit equations may be obtained by the standard
+technique based on rational parametrization of the unit circle (to eliminate
+trigonometric expressions) and Gr¨obner basis construction (see [5]). The state-
+ment can be verified by direct calculations.
+Topology of the manifold of semisymmetric octupoles is described in Appendix
+A.2.
+Figure 3.
+Iterative semisymmetrization
+
+2
+3
+204
+YU. NESTERENKO
+3. Semisymmetry enforcement
+Now we are ready to construct the polynomial penalty function enforcing its
+argument — octupole — to be semisymmetric.
+Lemma 2. Homogeneous 4th-degree polynomial
+d(a) = 25a4
+−3 + 50a2
+−3a2
+−2 + 20
+√
+15a−3a2
+−2a−1 − 10a2
+−3a2
+−1+
+30a2
+−2a2
+−1 + 8
+√
+15a−3a3
+−1 + 21a4
+−1 − 40a2
+−3a2
+0 + 80a2
+−2a2
+0+
+32a2
+−1a2
+0 + 16a4
+0 + 120a−3a−2a0a1 − 16
+√
+15a−2a−1a0a1−
+10a2
+−3a2
+1 + 30a2
+−2a2
+1 − 24
+√
+15a−3a−1a2
+1 + 42a2
+−1a2
+1 + 32a2
+0a2
+1+
+21a4
+1 + 120a−3a−1a0a2 + 8
+√
+15a2
+−1a0a2 + 40
+√
+15a−3a−2a1a2−
+8
+√
+15a0a2
+1a2 + 50a2
+−3a2
+2 − 20
+√
+15a−3a−1a2
+2 + 30a2
+−1a2
+2+
+80a2
+0a2
+2 + 30a2
+1a2
+2 − 120a−2a−1a0a3 − 20
+√
+15a2
+−2a1a3+
+24
+√
+15a2
+−1a1a3 − 8
+√
+15a3
+1a3 + 40
+√
+15a−2a−1a2a3+
+120a0a1a2a3 + 20
+√
+15a1a2
+2a3 + 50a2
+−3a2
+3 + 50a2
+−2a2
+3−
+10a2
+−1a2
+3 − 40a2
+0a2
+3 − 10a2
+1a2
+3 + 50a2
+2a2
+3 + 25a4
+3,
+(3.1)
+where a = (a−3, a−2, a−1, a0, a1, a2, a3) ∈ R7 consists of octupole coordinates in
+basis Y3,−3, . . . , Y3,3, defines the rotationally invariant measure of octupole devi-
+ation from semisymmetry.
+Idea of proof. The statement follows from the method of obtaining this poly-
+nomial. It consists of averaging the trial non-invariant deviation measure
+(3.2)
+�d(a) =
+3
+�
+k=1
+(aT Mk a)2
+over SO3 action’s orbits. The next formula can be verified by direct calculations.
+d(a) =
+1
+vol SO3
+�
+R∈SO3
+�d(R · a) dµ =
+1
+8π2
+2π
+�
+0
+π
+�
+0
+2π
+�
+0
+�d(Rz(α) × Rx(β) × Rz(γ) × a) sin β dγ dβ dα.
+(3.3)
+4. Numerical example
+In this section we show how deviation measure (3.1) works. We use the next
+combination of the scale and semisymmetry controlling terms with positive
+weights w1 = 5 and w2 = 2.5
+(4.1)
+p(a; w1, w2) = w1(aT a − 1)2 + w2 d(a),
+
+OCTUPOLES FOR OCTAHEDRAL SYMMETRY
+5
+as the penalty function together with a simple gradient descent method. Figure
+3 shows the convergence process of the sample initial octupole to the semisym-
+metrical one.
+The plots below describe the distance to the nearest semisymmetrical octupole
+and square root of the penalty value. One can see distance-like behavior of the
+square root of p(a; w1, w2).
+0
+2
+4
+6
+8
+10 12 14 16 18 20
+10−4
+10−3
+10−2
+10−1
+100
+Iterations
+Distance measures
+distance
+sqrt penalty
+Note that due to the invariance of (4.1) under 3D rotations, its symmetrization
+effect is orientation agnostic. Therefore, applying it to a field values during
+the optimization process does not affect octupoles’ orientations but helps to
+maintain their symmetries. This topic is discussed in the next section.
+5. Fields smoothing
+Since octupoles possess octahedral symmetries only up to multiplication by −1,
+we need to compensate for this by defining field smoothness in a special way. For
+this purpose we propose quite an intuitive expression of the form |x−y|2|x+y|2
+as the smoothing penalty term.
+Thus, in discrete cases the final field energy (consideration of boundary condi-
+tions is outside the scope of our discussion) becomes
+(5.1)
+E =
+�
+a∼b
+|a − b|2|a + b|2 +
+�
+a
+p(a, w1, w2).
+Here, the first terms enforce smoothness and the second are responsible for
+maintenance of the field values semisymmetry during the optimization.
+The described energy function in combination with coarse-to-fine optimiza-
+tion strategy shows results comparable to the ”classic” frame fields design ap-
+proaches ([7, 11]) while using 7 instead of 9 unknowns per frame.
+Two simple examples of this approach are provided in Appendix A.3.
+
+6
+YU. NESTERENKO
+6. Conclusion
+The implicit equations for the manifold of octupoles possessing octahedral sym-
+metry up to multiplication by −1, and the corresponding rotationally invariant
+deviation measure have been found. The smoothing penalty for octupole fields
+compensating for the lack of their symmetries has been constructed.
+In comparison to existing approaches, the obtained results allow to reduce num-
+ber of unknowns and computational costs of volumetric frame fields design
+problems.
+7. Appendix A.1
+The rotational matrices Rx, Ry and Rz for spherical harmonics of degree 3 are
+defined as follows.
+(7.1)
+Rz(γ) =
+�
+���������
+cos 3γ
+0
+0
+0
+0
+0
+sin 3γ
+0
+cos 2γ
+0
+0
+0
+sin 2γ
+0
+0
+0
+cos γ
+0
+sin γ
+0
+0
+0
+0
+0
+1
+0
+0
+0
+0
+0
+− sin γ
+0
+cos γ
+0
+0
+0
+− sin 2γ
+0
+0
+0
+cos 2γ
+0
+− sin 3γ
+0
+0
+0
+0
+0
+cos 3γ
+�
+���������
+(7.2)
+Rx(π
+2 ) = 1
+4
+�
+���������
+0
+0
+0
+√
+10
+0
+−
+√
+6
+0
+0
+−4
+0
+0
+0
+0
+0
+0
+0
+0
+√
+6
+0
+√
+10
+0
+−
+√
+10
+0
+−
+√
+6
+0
+0
+0
+0
+0
+0
+0
+0
+−1
+0
+−
+√
+15
+√
+6
+0
+−
+√
+10
+0
+0
+0
+0
+0
+0
+0
+0
+−
+√
+15
+0
+1
+�
+���������
+(7.3)
+Ry(β) = Rx(π
+2 ) × Rz(β) × Rx(π
+2 )T
+(7.4)
+Rx(α) = Ry(π
+2 )T × Rz(α) × Ry(π
+2 )
+See [2, 3, 4, 8] for more details.
+
+OCTUPOLES FOR OCTAHEDRAL SYMMETRY
+7
+8. Appendix A.2
+The manifold of frame rotations has the topology of the quotient space SO3 / S4,
+where S4 denotes the group of order 24 of all octahedral symmetries. Semisym-
+metric octupoles are invariant only under even S4 transformations. Hence the
+corresponding topology is SO3 / A4, where A4 denotes the corresponding sub-
+group.
+x
+y
+z
+Figure 4.
+Fundamental zones for S4 and A4 symmetries.
+It’s possible to describe these topologies using the Rodriguez representation
+of 3D rotations (see [1]).
+The fundamental zone for S4 symmetries in this
+representation has the form of a truncated cube with 6 regular octagonal faces
+and 8 regular triangular faces.
+For A4 symmetries the fundamental zone is
+the regular octahedron. The inclusion A4 ⊂ S4 implicates the reverse one for
+the fundamental zones (see figure 4, note that the triangular faces are pairwise
+coplanar).
+The topologies we consider are obtained by gluing the opposite octagons and
+the corresponding opposite triangles with 45◦ and 60◦ turn respectively. The
+colors in the picture indicate how the vertices map to each other. Note that all
+octahedron’s vertices are coincident and correspond to the octupole opposite to
+the reference one (i.e. −Y3,−2).
+
+8
+YU. NESTERENKO
+9. Appendix A.3
+The pictures below show usual singular structures (see [7, 11]) of frame fields
+optimized using energy function (5.1).
+Figure 5.
+Frame fields singularities of valence 3.
+References
+[1] R. Becker and S. Panchanadeeswaran. Crystal rotations represented as Rodrigues vectors.
+Texture, Stress, and Microstructure, 10:167–194, 1989.
+[2] M.A. Blanco, M. Florez, and M. Bermejo. Evaluation of the rotation matrices in the basis
+of real spherical harmonics. Journal of Molecular Structure: THEOCHEM, 419(1-3):19–
+27, 1997.
+[3] C.H. Choi, J. Ivanic, M.S. Gordon, and K. Ruedenberg. Rapid and stable determination
+of rotation matrices between spherical harmonics by direct recursion. The Journal of
+Chemical Physics, 111(19):8825–8831, 1999.
+[4] J.R.A. Collado, J.F. Rico, R. Lopez, M. Paniagua, and G. Ramirez. Rotation of real
+spherical harmonics. Computer Physics Communications, 52(3):323–331, 1989.
+[5] D. O’Shea D. A. Cox, J. Little. Ideals, Varieties, and Algorithms. Undergraduate Texts
+in Mathematics. Springer, forth edition, 2015.
+[6] C. G¨orller-Walrand and K. Binnemans. Rationalization of crystal-field parametrization.
+Handbook on the Physics and Chemistry of Rare Earths, 23:121–283, 1996.
+[7] J. Huang, Y. Tong, H. Wei, and H. Bao. Boundary aligned smooth 3D cross-frame field.
+ACM Transactions on Graphics, 30(6):143:1–143:8, 2011.
+[8] J. Ivanic and K. Ruedenberg. Rotation matrices for real spherical harmonics. Direct
+determination by recursion. The Journal of Chemical Physics, 100(15):6342–6347, 1996.
+[9] L. Landau and E. Lifshitz. The Classical Theory of Fields, pages 96–99. Course of Theo-
+retical Physics, Volume 2. Pergamon Press, 3rd revised english edition, 1971.
+[10] Yu. Nesterenko. On spherical harmonics possessing octahedral symmetry. ArXiv,
+2012.12614, 2020.
+[11] N. Ray and D. Sokolov. On smooth 3D frame field design. ArXiv, 1507.03351, 2015.
+Siemens Digital Industries Software
+Email address: Yuri.Nesterenko@siemens.com
+
diff --git a/ttFKT4oBgHgl3EQf2y5g/content/tmp_files/load_file.txt b/ttFKT4oBgHgl3EQf2y5g/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a02a988517e7d4b566365d424093a03e3da1bfef
--- /dev/null
+++ b/ttFKT4oBgHgl3EQf2y5g/content/tmp_files/load_file.txt
@@ -0,0 +1,300 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf,len=299
+page_content='OCTUPOLES FOR OCTAHEDRAL SYMMETRY  YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' NESTERENKO  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Spherical harmonics of degree 4 are widely used in volumetric  frame fields design due to their ability to reproduce octahedral symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  In this paper we show how to use harmonics of degree 3 (octupoles) for the  same purpose, thereby reducing number of parameters and computational  complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The key ingredients of the presented approach are  implicit equations for the manifold of octupoles possessing octahedral  symmetry up to multiplication by −1,  corresponding rotationally invariant measure of octupole’s deviation  from the specified symmetry,  smoothing penalty term compensating the lack of octupoles’ symme-  tries during a field optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Introduction  The most common state-of-the-art approaches for volumetric frame fields de-  sign involve the use of 4th-degree spherical harmonics as a representation of  field values (see [7, 11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' This choice is quite natural due to the fact that such  harmonics form the linear space closed under 3D rotations and containing har-  monics possessing octahedral symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Moreover, algebraic conditions for this  symmetry expressed both in terms of implicit equations and penalty function  are also known ([10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  The major practical disadvantage of this representation is the dimension of  the space — 9, which is three times the minimum required to parameterise  frame rotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' In this paper we show how to reduce the dimension by passing  from the 4th-degree spherical harmonics to the 3rd-degree ones also known as  octupoles (see Landau and Lifshitz [9] clarifying the connection with the tensor  formalism).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  In a nutshell, our suggestion is to sacrifice the half of symmetries of frame repre-  sentation, but compensating for this by additional symmetries in the smoothing  penalty term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Spherical plots of basis functions Y3,−3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' , Y3,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='11925v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='NA]  23 Jan 2023  2  YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' NESTERENKO  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Semisymmetric octupoles  As stated, we consider real-valued spherical harmonics of degree 3 on the unit  sphere — octupoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' These polynomials form the 7D linear space with standard  orthonormal basis Y3,−3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' , Y3,3 (see [6]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  With them being odd functions, none of the octupoles (except zero) are oc-  tahedrally symmetric by itself, but some of their modules are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Two of such  semisymmetric octupoles — Y3,−2 and Y3,2 — possessing the half of octahedral  symmetries (while the remaining are satisfied up to multiplication by −1) can  be seen in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Since the space we are working in is an eigenspace of the Laplace operator, all  possible rotations of its functions lie in the same space and may be represented  as a linear combinations of its basis functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  The reference harmonic and its rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  This applies in particular to semisymmetric harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Moreover, in coordinate  form all harmonics of this kind may be obtained from a reference one (let it be  Y3,−2) by the formula  a = Rx(α) × Ry(β) × Rz(γ) × ˜a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Here ˜a = (0, 1, 0, 0, 0, 0, 0)T and a are coordinates of the reference and the  rotated harmonics respectively, and α, β and γ are Euler angles of the corre-  sponding rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1 describes the construction of the rotation matrices Rx, Ry and  Rz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  From the geometrical point of view, all a(α, β, γ) form the manifold of dimension  3 embedded in R7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The next lemma claims that this manifold is simply an  intersection of quadrics (hypersurfaces of the second order).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The manifold of all semisymmetric octupoles is given by the system  of equations  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1)  �  aT a = 1,  aT Mk a = 0,  k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' , 3,  R  ~h  hOCTUPOLES FOR OCTAHEDRAL SYMMETRY  3  where M1, M2, M3 are the symmetric matrices defined as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='2)  M1 =  �  ���������  −5  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  3  0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  −5  �  ���������  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3)  M2 =  �  ���������  0  5  0  0  0  0  0  5  0  √  15  0  0  0  0  0  √  15  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  √  15  0  0  0  0  0  √  15  0  5  0  0  0  0  0  5  0  �  ���������  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='4)  M3 =  �  ���������  0  0  0  0  0  5  0  0  0  0  0  √  15  0  −5  0  0  0  2  0  −  √  15  0  0  0  2  0  0  0  0  0  √  15  0  0  0  0  0  5  0  −  √  15  0  0  0  0  0  −5  0  0  0  0  0  �  ���������  Idea of proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The given implicit equations may be obtained by the standard  technique based on rational parametrization of the unit circle (to eliminate  trigonometric expressions) and Gr¨obner basis construction (see [5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The state-  ment can be verified by direct calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Topology of the manifold of semisymmetric octupoles is described in Appendix  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Iterative semisymmetrization  2  3  204  YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' NESTERENKO  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Semisymmetry enforcement  Now we are ready to construct the polynomial penalty function enforcing its  argument — octupole — to be semisymmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Homogeneous 4th-degree polynomial  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='d(a) = 25a4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='−3 + 50a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
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+page_content='−2 + 20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
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+page_content='−2a−1 − 10a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
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+page_content='2 − 120a−2a−1a0a3 − 20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='√  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='15a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
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+page_content='24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='√  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='15a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='−1a1a3 − 8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='√  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='15a3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1a3 + 40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='√  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='15a−2a−1a2a3+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='120a0a1a2a3 + 20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='√  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='15a1a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='2a3 + 50a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='−3a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3 + 50a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='−2a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='10a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='−1a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3 − 40a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='0a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3 − 10a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3 + 50a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='2a2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3 + 25a4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1)  where a = (a−3, a−2, a−1, a0, a1, a2, a3) ∈ R7 consists of octupole coordinates in  basis Y3,−3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' , Y3,3, defines the rotationally invariant measure of octupole devi-  ation from semisymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Idea of proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The statement follows from the method of obtaining this poly-  nomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' It consists of averaging the trial non-invariant deviation measure  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='2)  �d(a) =  3  �  k=1  (aT Mk a)2  over SO3 action’s orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The next formula can be verified by direct calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  d(a) =  1  vol SO3  �  R∈SO3  �d(R · a) dµ =  1  8π2  2π  �  0  π  �  0  2π  �  0  �d(Rz(α) × Rx(β) × Rz(γ) × a) sin β dγ dβ dα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Numerical example  In this section we show how deviation measure (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1) works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' We use the next  combination of the scale and semisymmetry controlling terms with positive  weights w1 = 5 and w2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='5  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1)  p(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' w1, w2) = w1(aT a − 1)2 + w2 d(a),  OCTUPOLES FOR OCTAHEDRAL SYMMETRY  5  as the penalty function together with a simple gradient descent method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Figure  3 shows the convergence process of the sample initial octupole to the semisym-  metrical one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  The plots below describe the distance to the nearest semisymmetrical octupole  and square root of the penalty value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' One can see distance-like behavior of the  square root of p(a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' w1, w2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  0  2  4  6  8  10 12 14 16 18 20  10−4  10−3  10−2  10−1  100  Iterations  Distance measures  distance  sqrt penalty  Note that due to the invariance of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1) under 3D rotations, its symmetrization  effect is orientation agnostic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Therefore, applying it to a field values during  the optimization process does not affect octupoles’ orientations but helps to  maintain their symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' This topic is discussed in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Fields smoothing  Since octupoles possess octahedral symmetries only up to multiplication by −1,  we need to compensate for this by defining field smoothness in a special way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' For  this purpose we propose quite an intuitive expression of the form |x−y|2|x+y|2  as the smoothing penalty term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Thus, in discrete cases the final field energy (consideration of boundary condi-  tions is outside the scope of our discussion) becomes  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1)  E =  �  a∼b  |a − b|2|a + b|2 +  �  a  p(a, w1, w2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Here, the first terms enforce smoothness and the second are responsible for  maintenance of the field values semisymmetry during the optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  The described energy function in combination with coarse-to-fine optimiza-  tion strategy shows results comparable to the ”classic” frame fields design ap-  proaches ([7, 11]) while using 7 instead of 9 unknowns per frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Two simple examples of this approach are provided in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  6  YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' NESTERENKO  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Conclusion  The implicit equations for the manifold of octupoles possessing octahedral sym-  metry up to multiplication by −1, and the corresponding rotationally invariant  deviation measure have been found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The smoothing penalty for octupole fields  compensating for the lack of their symmetries has been constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  In comparison to existing approaches, the obtained results allow to reduce num-  ber of unknowns and computational costs of volumetric frame fields design  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1  The rotational matrices Rx, Ry and Rz for spherical harmonics of degree 3 are  defined as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1)  Rz(γ) =  �  ���������  cos 3γ  0  0  0  0  0  sin 3γ  0  cos 2γ  0  0  0  sin 2γ  0  0  0  cos γ  0  sin γ  0  0  0  0  0  1  0  0  0  0  0  − sin γ  0  cos γ  0  0  0  − sin 2γ  0  0  0  cos 2γ  0  − sin 3γ  0  0  0  0  0  cos 3γ  �  ���������  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='2)  Rx(π  2 ) = 1  4  �  ���������  0  0  0  √  10  0  −  √  6  0  0  −4  0  0  0  0  0  0  0  0  √  6  0  √  10  0  −  √  10  0  −  √  6  0  0  0  0  0  0  0  0  −1  0  −  √  15  √  6  0  −  √  10  0  0  0  0  0  0  0  0  −  √  15  0  1  �  ���������  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3)  Ry(β) = Rx(π  2 ) × Rz(β) × Rx(π  2 )T  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='4)  Rx(α) = Ry(π  2 )T × Rz(α) × Ry(π  2 )  See [2, 3, 4, 8] for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  OCTUPOLES FOR OCTAHEDRAL SYMMETRY  7  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='2  The manifold of frame rotations has the topology of the quotient space SO3 / S4,  where S4 denotes the group of order 24 of all octahedral symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Semisym-  metric octupoles are invariant only under even S4 transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Hence the  corresponding topology is SO3 / A4, where A4 denotes the corresponding sub-  group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  x  y  z  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Fundamental zones for S4 and A4 symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  It’s possible to describe these topologies using the Rodriguez representation  of 3D rotations (see [1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  The fundamental zone for S4 symmetries in this  representation has the form of a truncated cube with 6 regular octagonal faces  and 8 regular triangular faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  For A4 symmetries the fundamental zone is  the regular octahedron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The inclusion A4 ⊂ S4 implicates the reverse one for  the fundamental zones (see figure 4, note that the triangular faces are pairwise  coplanar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  The topologies we consider are obtained by gluing the opposite octagons and  the corresponding opposite triangles with 45◦ and 60◦ turn respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The  colors in the picture indicate how the vertices map to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Note that all  octahedron’s vertices are coincident and correspond to the octupole opposite to  the reference one (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' −Y3,−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  8  YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' NESTERENKO  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='3  The pictures below show usual singular structures (see [7, 11]) of frame fields  optimized using energy function (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Frame fields singularities of valence 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  References  [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Becker and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Panchanadeeswaran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Crystal rotations represented as Rodrigues vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Texture, Stress, and Microstructure, 10:167–194, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Blanco, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Florez, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Bermejo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Evaluation of the rotation matrices in the basis  of real spherical harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Journal of Molecular Structure: THEOCHEM, 419(1-3):19–  27, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Choi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Ivanic, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Gordon, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Ruedenberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Rapid and stable determination  of rotation matrices between spherical harmonics by direct recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The Journal of  Chemical Physics, 111(19):8825–8831, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Collado, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Rico, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Lopez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Paniagua, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Ramirez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Rotation of real  spherical harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Computer Physics Communications, 52(3):323–331, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [5] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' O’Shea D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Cox, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Little.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Ideals, Varieties, and Algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Undergraduate Texts  in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Springer, forth edition, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [6] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' G¨orller-Walrand and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Binnemans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Rationalization of crystal-field parametrization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Handbook on the Physics and Chemistry of Rare Earths, 23:121–283, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Tong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Wei, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Bao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Boundary aligned smooth 3D cross-frame field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  ACM Transactions on Graphics, 30(6):143:1–143:8, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Ivanic and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Ruedenberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Rotation matrices for real spherical harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Direct  determination by recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The Journal of Chemical Physics, 100(15):6342–6347, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Landau and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Lifshitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' The Classical Theory of Fields, pages 96–99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Course of Theo-  retical Physics, Volume 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Pergamon Press, 3rd revised english edition, 1971.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [10] Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Nesterenko.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' On spherical harmonics possessing octahedral symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' ArXiv,  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='12614, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  [11] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Ray and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' Sokolov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' On smooth 3D frame field design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content=' ArXiv, 1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='03351, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='  Siemens Digital Industries Software  Email address: Yuri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='Nesterenko@siemens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
+page_content='com' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttFKT4oBgHgl3EQf2y5g/content/2301.11925v1.pdf'}
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